$p$-adic family 2.2.8.56a

• Label: 2.2.8.56a
• Base: 2.1.1.0a1.1
• Degree: \(16\)
• e: \(8\)
• f: \(2\)
• c: \(56\)

Defining polynomial over unramified subextension

$x^{8} + 8 b_{23} x^{7} + 4 a_{14} x^{6} + 8 a_{21} x^{5} + \left(4 b_{12} + 8 c_{20} + 16 c_{28}\right) x^{4} + 16 b_{27} x^{3} + 8 b_{18} x^{2} + 16 b_{25} x + 8 c_{16} + 2$

Invariants

Residue field characteristic:	$2$
Degree:	$16$
Base field:	$\Q_{2}$
Ramification index $e$:	$8$
Residue field degree $f$:	$2$
Discriminant exponent $c$:	$56$
Artin slopes:	$[3,\frac{7}{2},\frac{9}{2}]$
Swan slopes:	$[2,\frac{5}{2},\frac{7}{2}]$
Means:	$\langle1,\frac{7}{4},\frac{21}{8}\rangle$
Rams:	$(2,3,7)$
Field count:	$9504$ (complete)
Ambiguity:	$16$
Mass:	$9216$
Absolute Mass:	$4608$

Diagrams

Varying

Indices of inseparability:	$[21,14,8,0]$
Associated inertia:	$[1,1,1]$
Jump Set:	$[1,3,7,15]$

Galois groups and Hidden Artin slopes

Select desired size of Galois group. Note that the following data has not all been computed for fields in this family, so the tables below are incomplete.

		Galois groups of order 32
		$C_2\times D_8$ (as 16T29)	$Q_{16}:C_2$ (as 16T32)	$D_8:C_2$ (as 16T38)	$D_8:C_2$ (as 16T44)	$D_8:C_2$ (as 16T45)	$C_2\times \SD_{16}$ (as 16T48)	Total
hidden slopes	$[2]$	4	4	8	8	4	4	32

		Galois groups of order 64
		$C_8.D_4$ (as 16T132)	$C_8.D_4$ (as 16T133)	$D_4:D_4$ (as 16T142)	$D_4.D_4$ (as 16T162)	Total
hidden slopes	$[2,2]$	8	8	16	16	48

		Galois groups of order 128
		$\OD_{16}.D_4$ (as 16T215)	$\OD_{16}:D_4$ (as 16T251)	$\OD_{16}.D_4$ (as 16T267)	$(C_2\times C_4^2):C_4$ (as 16T291)	$(C_4\times C_8):C_4$ (as 16T294)	$C_4^2.D_4$ (as 16T311)	$C_4^2.D_4$ (as 16T321)	$C_4^2.Q_8$ (as 16T334)	$C_4^2.D_4$ (as 16T353)	$C_4^2.(C_2\times C_4)$ (as 16T362)	$(C_4\times C_8).C_4$ (as 16T378)	$(C_4\times C_8):C_4$ (as 16T413)	Total
hidden slopes	$[2,2,\frac{7}{2}]$										16	8	8	32
		$[2,2]^{2}$			16										16
	$[2,3,4]$		16	16		16	16	16	16	16	16				128
		Total	16	16	16	16	16	16	16	16	16	16	8	8	176

		Galois groups of order 256
		$(C_4\times \OD_{16}):C_4$ (as 16T483)	$(C_4\times \OD_{16}):C_4$ (as 16T518)	$C_4^2.(C_2^2\times C_4)$ (as 16T520)	$(C_4\times C_8).D_4$ (as 16T658)	$D_4^2:C_2^2$ (as 16T659)	$D_4^2.C_2^2$ (as 16T660)	$D_4^2.C_2^2$ (as 16T661)	$D_4^2:C_4$ (as 16T663)	$C_8^2:C_4$ (as 16T664)	$D_4^2:C_2^2$ (as 16T665)	$C_8:C_8:C_4$ (as 16T668)	$D_4^2.C_4$ (as 16T671)	$D_8:D_8$ (as 16T679)	$C_2^2.C_2\wr C_4$ (as 16T680)	$C_2^2.C_2\wr C_4$ (as 16T681)	$(C_4\times C_8).D_4$ (as 16T683)	$D_4^2:C_4$ (as 16T685)	$C_8^2:C_2^2$ (as 16T687)	$D_4^2:C_4$ (as 16T688)	$C_8:C_8:C_4$ (as 16T690)	$D_4^2.C_4$ (as 16T692)	$D_8:D_8$ (as 16T693)	$C_8^2:C_4$ (as 16T694)	$Q_8^2:C_4$ (as 16T704)	$D_8:\SD_{16}$ (as 16T706)	Total
hidden slopes	$[2,2,\frac{7}{2},\frac{15}{4}]$					32	32	32			32																128
		$[2,2,\frac{7}{2},\frac{9}{2}]$					16	16	16	16	16	16	16	16	16				16	16		16	16	16	16		16	256
	$[2,2,\frac{7}{2}]^{2}$		8	16	8																							32
		$[2,3,\frac{15}{4}]^{2}$														32	32											64
	$[2,3,4]^{2}$					16												16			16					16		64
		Total	8	16	8	16	48	48	48	16	16	48	16	16	16	32	32	16	16	16	16	16	16	16	16	16	16	544

		Galois groups of order 512
		$C_8^2:(C_2\times C_4)$ (as 16T814)	$C_8^2:(C_2\times C_4)$ (as 16T816)	$C_4^2.(C_4\times D_4)$ (as 16T852)	$(C_2\times D_4^2):C_4$ (as 16T858)	$(C_2\times D_4^2).C_4$ (as 16T859)	$C_4^3:(C_2\times C_4)$ (as 16T864)	$C_2^4.(C_4\times D_4)$ (as 16T869)	$C_2^4.(C_4\times D_4)$ (as 16T884)	$C_8^2:(C_2\times C_4)$ (as 16T892)	$(C_2\times C_4^3):C_4$ (as 16T898)	$D_4^2.(C_2\times C_4)$ (as 16T922)	$(C_4\times \OD_{16}).D_4$ (as 16T937)	$Q_8^2:(C_2\times C_4)$ (as 16T942)	$D_4^2:(C_2\times C_4)$ (as 16T943)	$C_2^5:\SD_{16}$ (as 16T970)	$C_4^3.C_2^3$ (as 16T976)	$C_2^5:\SD_{16}$ (as 16T978)	$C_2^5.(C_2\times D_4)$ (as 16T981)	$C_2^5:D_8$ (as 16T988)	$C_2^5.(C_2\times D_4)$ (as 16T1000)	$C_2^5:D_8$ (as 16T1002)	$C_4^3.D_4$ (as 16T1011)	$D_4^2.D_4$ (as 16T1020)	Total
hidden slopes	$[2,2,2,3]^{2}$			32			32																		64
		$[2,2,2,\frac{7}{2}]^{2}$							32	32																64
	$[2,2,3,\frac{15}{4}]^{2}$													64												64
		$[2,2,3,4]^{2}$			32			32	32	32		128			32	32										320
	$[2,2,3,\frac{7}{2},\frac{9}{2}]$																	128						128		256
		$[2,2,\frac{7}{2},\frac{15}{4},4]$											64												64	128
	$[2,2,\frac{7}{2},\frac{15}{4},\frac{9}{2}]$																64		64	128	64	128	64			512
		$[2,2,\frac{7}{2},\frac{9}{2}]^{2}$	32	32		32	32				64		64													256
	Total		32	32	64	32	32	64	64	64	64	128	128	64	32	32	64	128	64	128	64	128	64	128	64	1664

		Galois groups of order 1024
		$(C_2\times C_4^3).D_4$ (as 16T1108)	$(C_2\times C_4^3).D_4$ (as 16T1112)	$D_4^2:\OD_{16}$ (as 16T1120)	$C_4^3.(C_2^2\times C_4)$ (as 16T1186)	$C_2^4.C_2\wr C_4$ (as 16T1263)	$C_2^4.C_2\wr C_4$ (as 16T1269)	$C_2^4.C_2\wr C_4$ (as 16T1281)	Total
hidden slopes	$[\frac{15}{4},\frac{15}{4},2,2,\frac{5}{2},\frac{7}{2}]$						128		128
		$[\frac{15}{4},2,2,2,3]_{2}$			160					160
	$[\frac{15}{4},2,2,4,\frac{5}{2},\frac{7}{2}]$							128		128
		$[\frac{15}{4},2,2,\frac{5}{2},\frac{7}{2},\frac{9}{2}]$					256		256	512
	$[2,2,2,3,\frac{15}{4}]^{2}$				96					96
		$[2,2,2,3,4]^{2}$	96							96
	$[2,2,2,3,4]_{2}$		32							32
		$[2,2,3,\frac{7}{2},\frac{9}{2}]^{2}$		80		72				152
	$[2,2,3,\frac{7}{2},\frac{9}{2}]_{2}$			48		56				104
		Total	128	128	256	128	256	256	256	1408

		Galois groups of order 2048
		$C_2^5.C_2\wr C_4$ (as 16T1345)	$C_2^5.C_2\wr C_4$ (as 16T1354)	$C_2^5.C_2\wr C_2^2$ (as 16T1360)	$C_2^5.C_2\wr C_2^2$ (as 16T1362)	$C_2^6.(C_4\times D_4)$ (as 16T1375)	$C_2^5.C_2\wr C_4$ (as 16T1376)	$C_4^4:(C_2\times C_4)$ (as 16T1388)	$\OD_{16}^2:(C_2\times C_4)$ (as 16T1397)	$C_4^4:(C_2\times C_4)$ (as 16T1398)	$C_2^5.C_2\wr C_4$ (as 16T1401)	Total
hidden slopes	$[2,2,2,2,\frac{7}{2},\frac{9}{2}]^{2}$		8	32					16			56
		$[2,2,2,3,\frac{7}{2},\frac{9}{2}]^{2}$							8		16		24
	$[2,2,2,\frac{7}{2},\frac{15}{4},4]^{2}$					32							32
		$[2,2,2,\frac{7}{2},\frac{15}{4},\frac{9}{2}]^{2}$					48						48
	$[2,2,2,\frac{7}{2},\frac{7}{2},\frac{15}{4}]^{2}$					16							16
		$[2,2,\frac{5}{2},\frac{7}{2},\frac{15}{4},\frac{15}{4}]^{2}$						40					40
	$[2,2,\frac{5}{2},\frac{7}{2},\frac{15}{4},4]^{2}$							40					40
		$[2,2,\frac{5}{2},\frac{7}{2},\frac{15}{4},\frac{9}{2}]^{2}$	64									96	160
	Total		64	8	32	48	48	80	8	16	16	96	416

		Galois groups of order 8192
		$C_2^7.C_2\wr C_4$ (as 16T1698)	$C_2^7.D_4:D_4$ (as 16T1713)	Total
hidden slopes	$[2,2,3,3,\frac{7}{2},\frac{7}{2},\frac{15}{4},\frac{31}{8}]^{2}$		64	64
		$[2,2,3,3,\frac{7}{2},\frac{7}{2},\frac{15}{4},4]^{2}$		64	64
	$[2,2,3,3,\frac{7}{2},\frac{7}{2},\frac{15}{4},\frac{9}{2}]^{2}$		160		160
		Total	160	128	288

Fields

Showing 1-50 of 9504

  Download displayed columns for results to

Label	Packet size	Polynomial	Galois group	Galois degree	$\#\Aut(K/\Q_p)$	Artin slope content	Swan slope content	Hidden Artin slopes	Hidden Swan slopes	Ind. of Insep.	Assoc. Inertia	Resid. Poly	Jump Set
2.2.8.56a1.1	16	$( x^{2} + x + 1 )^{8} + 4 ( x^{2} + x + 1 )^{6} + 8 ( x^{2} + x + 1 )^{5} + 2$	$D_4:D_4$ (as 16T142)	$64$	$4$	$[2, 2, 3, \frac{7}{2}, \frac{9}{2}]^{2}$	$[1,1,2,\frac{5}{2},\frac{7}{2}]^{2}$	$[2,2]$	$[1,1]$	$[21, 14, 8, 0]$	$[1, 1, 1]$	$z^4 + 1,z^2 + 1,z + 1$	$[1, 3, 7, 15]$
2.2.8.56a1.2	16	$( x^{2} + x + 1 )^{8} + 4 ( x^{2} + x + 1 )^{6} + 8 ( x^{2} + x + 1 )^{5} + 16 x ( x^{2} + x + 1 )^{4} + 2$	$D_4.D_4$ (as 16T162)	$64$	$4$	$[2, 2, 3, \frac{7}{2}, \frac{9}{2}]^{2}$	$[1,1,2,\frac{5}{2},\frac{7}{2}]^{2}$	$[2,2]$	$[1,1]$	$[21, 14, 8, 0]$	$[1, 1, 1]$	$z^4 + 1,z^2 + 1,z + 1$	$[1, 3, 7, 15]$
2.2.8.56a1.3	16	$( x^{2} + x + 1 )^{8} + 4 ( x^{2} + x + 1 )^{6} + 8 ( x^{2} + x + 1 )^{5} + 16 x ( x^{2} + x + 1 )^{3} + 2$	$D_4:D_4$ (as 16T142)	$64$	$4$	$[2, 2, 3, \frac{7}{2}, \frac{9}{2}]^{2}$	$[1,1,2,\frac{5}{2},\frac{7}{2}]^{2}$	$[2,2]$	$[1,1]$	$[21, 14, 8, 0]$	$[1, 1, 1]$	$z^4 + 1,z^2 + 1,z + 1$	$[1, 3, 7, 15]$
2.2.8.56a1.4	16	$( x^{2} + x + 1 )^{8} + 4 ( x^{2} + x + 1 )^{6} + 8 ( x^{2} + x + 1 )^{5} + 16 x ( x^{2} + x + 1 )^{4} + 16 x ( x^{2} + x + 1 )^{3} + 2$	$D_4.D_4$ (as 16T162)	$64$	$4$	$[2, 2, 3, \frac{7}{2}, \frac{9}{2}]^{2}$	$[1,1,2,\frac{5}{2},\frac{7}{2}]^{2}$	$[2,2]$	$[1,1]$	$[21, 14, 8, 0]$	$[1, 1, 1]$	$z^4 + 1,z^2 + 1,z + 1$	$[1, 3, 7, 15]$
2.2.8.56a1.5	32	$( x^{2} + x + 1 )^{8} + 4 ( x^{2} + x + 1 )^{6} + 8 ( x^{2} + x + 1 )^{5} + 16 x ( x^{2} + x + 1 ) + 2$	$C_2^4.(C_4\times D_4)$ (as 16T869)	$512$	$2$	$[2, 2, 2, 3, \frac{7}{2}, \frac{7}{2}, \frac{9}{2}]^{4}$	$[1,1,1,2,\frac{5}{2},\frac{5}{2},\frac{7}{2}]^{4}$	$[2,2,2,\frac{7}{2}]^{2}$	$[1,1,1,\frac{5}{2}]^{2}$	$[21, 14, 8, 0]$	$[1, 1, 1]$	$z^4 + 1,z^2 + 1,z + 1$	$[1, 3, 7, 15]$
2.2.8.56a1.6	32	$( x^{2} + x + 1 )^{8} + 4 ( x^{2} + x + 1 )^{6} + 8 ( x^{2} + x + 1 )^{5} + 16 x ( x^{2} + x + 1 )^{4} + 16 x ( x^{2} + x + 1 ) + 2$	$C_2^4.(C_4\times D_4)$ (as 16T869)	$512$	$2$	$[2, 2, 2, 3, \frac{7}{2}, \frac{7}{2}, \frac{9}{2}]^{4}$	$[1,1,1,2,\frac{5}{2},\frac{5}{2},\frac{7}{2}]^{4}$	$[2,2,2,\frac{7}{2}]^{2}$	$[1,1,1,\frac{5}{2}]^{2}$	$[21, 14, 8, 0]$	$[1, 1, 1]$	$z^4 + 1,z^2 + 1,z + 1$	$[1, 3, 7, 15]$
2.2.8.56a1.7	32	$( x^{2} + x + 1 )^{8} + 4 ( x^{2} + x + 1 )^{6} + 8 ( x^{2} + x + 1 )^{5} + 16 x ( x^{2} + x + 1 )^{3} + 16 x ( x^{2} + x + 1 ) + 2$	$C_2^4.(C_4\times D_4)$ (as 16T869)	$512$	$2$	$[2, 2, 2, 3, \frac{7}{2}, \frac{7}{2}, \frac{9}{2}]^{4}$	$[1,1,1,2,\frac{5}{2},\frac{5}{2},\frac{7}{2}]^{4}$	$[2,2,2,\frac{7}{2}]^{2}$	$[1,1,1,\frac{5}{2}]^{2}$	$[21, 14, 8, 0]$	$[1, 1, 1]$	$z^4 + 1,z^2 + 1,z + 1$	$[1, 3, 7, 15]$
2.2.8.56a1.8	32	$( x^{2} + x + 1 )^{8} + 4 ( x^{2} + x + 1 )^{6} + 8 ( x^{2} + x + 1 )^{5} + 16 x ( x^{2} + x + 1 )^{4} + 16 x ( x^{2} + x + 1 )^{3} + 16 x ( x^{2} + x + 1 ) + 2$	$C_2^4.(C_4\times D_4)$ (as 16T869)	$512$	$2$	$[2, 2, 2, 3, \frac{7}{2}, \frac{7}{2}, \frac{9}{2}]^{4}$	$[1,1,1,2,\frac{5}{2},\frac{5}{2},\frac{7}{2}]^{4}$	$[2,2,2,\frac{7}{2}]^{2}$	$[1,1,1,\frac{5}{2}]^{2}$	$[21, 14, 8, 0]$	$[1, 1, 1]$	$z^4 + 1,z^2 + 1,z + 1$	$[1, 3, 7, 15]$
2.2.8.56a1.9	16	$( x^{2} + x + 1 )^{8} + 8 x ( x^{2} + x + 1 )^{7} + 4 ( x^{2} + x + 1 )^{6} + 8 ( x^{2} + x + 1 )^{5} + 2$	$(C_2\times C_4^2):C_4$ (as 16T291)	$128$	$4$	$[2, 3, 3, \frac{7}{2}, 4, \frac{9}{2}]^{2}$	$[1,2,2,\frac{5}{2},3,\frac{7}{2}]^{2}$	$[2,3,4]$	$[1,2,3]$	$[21, 14, 8, 0]$	$[1, 1, 1]$	$z^4 + 1,z^2 + 1,z + 1$	$[1, 3, 7, 15]$
2.2.8.56a1.10	16	$( x^{2} + x + 1 )^{8} + 8 x ( x^{2} + x + 1 )^{7} + 4 ( x^{2} + x + 1 )^{6} + 8 ( x^{2} + x + 1 )^{5} + 16 x ( x^{2} + x + 1 )^{4} + 2$	$(C_2\times C_4^2):C_4$ (as 16T291)	$128$	$4$	$[2, 3, 3, \frac{7}{2}, 4, \frac{9}{2}]^{2}$	$[1,2,2,\frac{5}{2},3,\frac{7}{2}]^{2}$	$[2,3,4]$	$[1,2,3]$	$[21, 14, 8, 0]$	$[1, 1, 1]$	$z^4 + 1,z^2 + 1,z + 1$	$[1, 3, 7, 15]$
2.2.8.56a1.11	16	$( x^{2} + x + 1 )^{8} + 8 x ( x^{2} + x + 1 )^{7} + 4 ( x^{2} + x + 1 )^{6} + 8 ( x^{2} + x + 1 )^{5} + 16 x ( x^{2} + x + 1 )^{3} + 2$	$(C_2\times C_4^2):C_4$ (as 16T291)	$128$	$4$	$[2, 3, 3, \frac{7}{2}, 4, \frac{9}{2}]^{2}$	$[1,2,2,\frac{5}{2},3,\frac{7}{2}]^{2}$	$[2,3,4]$	$[1,2,3]$	$[21, 14, 8, 0]$	$[1, 1, 1]$	$z^4 + 1,z^2 + 1,z + 1$	$[1, 3, 7, 15]$
2.2.8.56a1.12	16	$( x^{2} + x + 1 )^{8} + 8 x ( x^{2} + x + 1 )^{7} + 4 ( x^{2} + x + 1 )^{6} + 8 ( x^{2} + x + 1 )^{5} + 16 x ( x^{2} + x + 1 )^{4} + 16 x ( x^{2} + x + 1 )^{3} + 2$	$(C_2\times C_4^2):C_4$ (as 16T291)	$128$	$4$	$[2, 3, 3, \frac{7}{2}, 4, \frac{9}{2}]^{2}$	$[1,2,2,\frac{5}{2},3,\frac{7}{2}]^{2}$	$[2,3,4]$	$[1,2,3]$	$[21, 14, 8, 0]$	$[1, 1, 1]$	$z^4 + 1,z^2 + 1,z + 1$	$[1, 3, 7, 15]$
2.2.8.56a1.13	16	$( x^{2} + x + 1 )^{8} + 8 x ( x^{2} + x + 1 )^{7} + 4 ( x^{2} + x + 1 )^{6} + 8 ( x^{2} + x + 1 )^{5} + 16 ( x^{2} + x + 1 )^{3} + 2$	$(C_2\times C_4^2):C_4$ (as 16T291)	$128$	$4$	$[2, 3, 3, \frac{7}{2}, 4, \frac{9}{2}]^{2}$	$[1,2,2,\frac{5}{2},3,\frac{7}{2}]^{2}$	$[2,3,4]$	$[1,2,3]$	$[21, 14, 8, 0]$	$[1, 1, 1]$	$z^4 + 1,z^2 + 1,z + 1$	$[1, 3, 7, 15]$
2.2.8.56a1.14	16	$( x^{2} + x + 1 )^{8} + 8 x ( x^{2} + x + 1 )^{7} + 4 ( x^{2} + x + 1 )^{6} + 8 ( x^{2} + x + 1 )^{5} + 16 x ( x^{2} + x + 1 )^{4} + 16 ( x^{2} + x + 1 )^{3} + 2$	$(C_2\times C_4^2):C_4$ (as 16T291)	$128$	$4$	$[2, 3, 3, \frac{7}{2}, 4, \frac{9}{2}]^{2}$	$[1,2,2,\frac{5}{2},3,\frac{7}{2}]^{2}$	$[2,3,4]$	$[1,2,3]$	$[21, 14, 8, 0]$	$[1, 1, 1]$	$z^4 + 1,z^2 + 1,z + 1$	$[1, 3, 7, 15]$
2.2.8.56a1.15	16	$( x^{2} + x + 1 )^{8} + 8 x ( x^{2} + x + 1 )^{7} + 4 ( x^{2} + x + 1 )^{6} + 8 ( x^{2} + x + 1 )^{5} + 16 ( x^{2} + x + 1 ) + 2$	$\OD_{16}:D_4$ (as 16T251)	$128$	$4$	$[2, 3, 3, \frac{7}{2}, 4, \frac{9}{2}]^{2}$	$[1,2,2,\frac{5}{2},3,\frac{7}{2}]^{2}$	$[2,3,4]$	$[1,2,3]$	$[21, 14, 8, 0]$	$[1, 1, 1]$	$z^4 + 1,z^2 + 1,z + 1$	$[1, 3, 7, 15]$
2.2.8.56a1.16	16	$( x^{2} + x + 1 )^{8} + 8 x ( x^{2} + x + 1 )^{7} + 4 ( x^{2} + x + 1 )^{6} + 8 ( x^{2} + x + 1 )^{5} + 16 x ( x^{2} + x + 1 )^{4} + 16 ( x^{2} + x + 1 ) + 2$	$\OD_{16}:D_4$ (as 16T251)	$128$	$4$	$[2, 3, 3, \frac{7}{2}, 4, \frac{9}{2}]^{2}$	$[1,2,2,\frac{5}{2},3,\frac{7}{2}]^{2}$	$[2,3,4]$	$[1,2,3]$	$[21, 14, 8, 0]$	$[1, 1, 1]$	$z^4 + 1,z^2 + 1,z + 1$	$[1, 3, 7, 15]$
2.2.8.56a1.17	16	$( x^{2} + x + 1 )^{8} + 8 x ( x^{2} + x + 1 )^{7} + 4 ( x^{2} + x + 1 )^{6} + 8 ( x^{2} + x + 1 )^{5} + 16 x ( x^{2} + x + 1 )^{3} + 16 ( x^{2} + x + 1 ) + 2$	$\OD_{16}:D_4$ (as 16T251)	$128$	$4$	$[2, 3, 3, \frac{7}{2}, 4, \frac{9}{2}]^{2}$	$[1,2,2,\frac{5}{2},3,\frac{7}{2}]^{2}$	$[2,3,4]$	$[1,2,3]$	$[21, 14, 8, 0]$	$[1, 1, 1]$	$z^4 + 1,z^2 + 1,z + 1$	$[1, 3, 7, 15]$
2.2.8.56a1.18	16	$( x^{2} + x + 1 )^{8} + 8 x ( x^{2} + x + 1 )^{7} + 4 ( x^{2} + x + 1 )^{6} + 8 ( x^{2} + x + 1 )^{5} + 16 x ( x^{2} + x + 1 )^{4} + 16 x ( x^{2} + x + 1 )^{3} + 16 ( x^{2} + x + 1 ) + 2$	$\OD_{16}:D_4$ (as 16T251)	$128$	$4$	$[2, 3, 3, \frac{7}{2}, 4, \frac{9}{2}]^{2}$	$[1,2,2,\frac{5}{2},3,\frac{7}{2}]^{2}$	$[2,3,4]$	$[1,2,3]$	$[21, 14, 8, 0]$	$[1, 1, 1]$	$z^4 + 1,z^2 + 1,z + 1$	$[1, 3, 7, 15]$
2.2.8.56a1.19	16	$( x^{2} + x + 1 )^{8} + 8 x ( x^{2} + x + 1 )^{7} + 4 ( x^{2} + x + 1 )^{6} + 8 ( x^{2} + x + 1 )^{5} + 16 ( x^{2} + x + 1 )^{3} + 16 ( x^{2} + x + 1 ) + 2$	$\OD_{16}:D_4$ (as 16T251)	$128$	$4$	$[2, 3, 3, \frac{7}{2}, 4, \frac{9}{2}]^{2}$	$[1,2,2,\frac{5}{2},3,\frac{7}{2}]^{2}$	$[2,3,4]$	$[1,2,3]$	$[21, 14, 8, 0]$	$[1, 1, 1]$	$z^4 + 1,z^2 + 1,z + 1$	$[1, 3, 7, 15]$
2.2.8.56a1.20	16	$( x^{2} + x + 1 )^{8} + 8 x ( x^{2} + x + 1 )^{7} + 4 ( x^{2} + x + 1 )^{6} + 8 ( x^{2} + x + 1 )^{5} + 16 x ( x^{2} + x + 1 )^{4} + 16 ( x^{2} + x + 1 )^{3} + 16 ( x^{2} + x + 1 ) + 2$	$\OD_{16}:D_4$ (as 16T251)	$128$	$4$	$[2, 3, 3, \frac{7}{2}, 4, \frac{9}{2}]^{2}$	$[1,2,2,\frac{5}{2},3,\frac{7}{2}]^{2}$	$[2,3,4]$	$[1,2,3]$	$[21, 14, 8, 0]$	$[1, 1, 1]$	$z^4 + 1,z^2 + 1,z + 1$	$[1, 3, 7, 15]$
2.2.8.56a1.21	16	$( x^{2} + x + 1 )^{8} + 8 ( x^{2} + x + 1 )^{7} + 4 ( x^{2} + x + 1 )^{6} + 8 ( x^{2} + x + 1 )^{5} + 2$	$D_4:D_4$ (as 16T142)	$64$	$4$	$[2, 2, 3, \frac{7}{2}, \frac{9}{2}]^{2}$	$[1,1,2,\frac{5}{2},\frac{7}{2}]^{2}$	$[2,2]$	$[1,1]$	$[21, 14, 8, 0]$	$[1, 1, 1]$	$z^4 + 1,z^2 + 1,z + 1$	$[1, 3, 7, 15]$
2.2.8.56a1.22	16	$( x^{2} + x + 1 )^{8} + 8 ( x^{2} + x + 1 )^{7} + 4 ( x^{2} + x + 1 )^{6} + 8 ( x^{2} + x + 1 )^{5} + 16 x ( x^{2} + x + 1 )^{4} + 2$	$D_4.D_4$ (as 16T162)	$64$	$4$	$[2, 2, 3, \frac{7}{2}, \frac{9}{2}]^{2}$	$[1,1,2,\frac{5}{2},\frac{7}{2}]^{2}$	$[2,2]$	$[1,1]$	$[21, 14, 8, 0]$	$[1, 1, 1]$	$z^4 + 1,z^2 + 1,z + 1$	$[1, 3, 7, 15]$
2.2.8.56a1.23	16	$( x^{2} + x + 1 )^{8} + 8 ( x^{2} + x + 1 )^{7} + 4 ( x^{2} + x + 1 )^{6} + 8 ( x^{2} + x + 1 )^{5} + 16 x ( x^{2} + x + 1 )^{3} + 2$	$D_4:D_4$ (as 16T142)	$64$	$4$	$[2, 2, 3, \frac{7}{2}, \frac{9}{2}]^{2}$	$[1,1,2,\frac{5}{2},\frac{7}{2}]^{2}$	$[2,2]$	$[1,1]$	$[21, 14, 8, 0]$	$[1, 1, 1]$	$z^4 + 1,z^2 + 1,z + 1$	$[1, 3, 7, 15]$
2.2.8.56a1.24	16	$( x^{2} + x + 1 )^{8} + 8 ( x^{2} + x + 1 )^{7} + 4 ( x^{2} + x + 1 )^{6} + 8 ( x^{2} + x + 1 )^{5} + 16 x ( x^{2} + x + 1 )^{4} + 16 x ( x^{2} + x + 1 )^{3} + 2$	$D_4.D_4$ (as 16T162)	$64$	$4$	$[2, 2, 3, \frac{7}{2}, \frac{9}{2}]^{2}$	$[1,1,2,\frac{5}{2},\frac{7}{2}]^{2}$	$[2,2]$	$[1,1]$	$[21, 14, 8, 0]$	$[1, 1, 1]$	$z^4 + 1,z^2 + 1,z + 1$	$[1, 3, 7, 15]$
2.2.8.56a1.25	32	$( x^{2} + x + 1 )^{8} + 8 ( x^{2} + x + 1 )^{7} + 4 ( x^{2} + x + 1 )^{6} + 8 ( x^{2} + x + 1 )^{5} + 16 x ( x^{2} + x + 1 ) + 2$	$C_2^4.(C_4\times D_4)$ (as 16T869)	$512$	$2$	$[2, 2, 2, 3, \frac{7}{2}, \frac{7}{2}, \frac{9}{2}]^{4}$	$[1,1,1,2,\frac{5}{2},\frac{5}{2},\frac{7}{2}]^{4}$	$[2,2,2,\frac{7}{2}]^{2}$	$[1,1,1,\frac{5}{2}]^{2}$	$[21, 14, 8, 0]$	$[1, 1, 1]$	$z^4 + 1,z^2 + 1,z + 1$	$[1, 3, 7, 15]$
2.2.8.56a1.26	32	$( x^{2} + x + 1 )^{8} + 8 ( x^{2} + x + 1 )^{7} + 4 ( x^{2} + x + 1 )^{6} + 8 ( x^{2} + x + 1 )^{5} + 16 x ( x^{2} + x + 1 )^{4} + 16 x ( x^{2} + x + 1 ) + 2$	$C_2^4.(C_4\times D_4)$ (as 16T869)	$512$	$2$	$[2, 2, 2, 3, \frac{7}{2}, \frac{7}{2}, \frac{9}{2}]^{4}$	$[1,1,1,2,\frac{5}{2},\frac{5}{2},\frac{7}{2}]^{4}$	$[2,2,2,\frac{7}{2}]^{2}$	$[1,1,1,\frac{5}{2}]^{2}$	$[21, 14, 8, 0]$	$[1, 1, 1]$	$z^4 + 1,z^2 + 1,z + 1$	$[1, 3, 7, 15]$
2.2.8.56a1.27	32	$( x^{2} + x + 1 )^{8} + 8 ( x^{2} + x + 1 )^{7} + 4 ( x^{2} + x + 1 )^{6} + 8 ( x^{2} + x + 1 )^{5} + 16 x ( x^{2} + x + 1 )^{3} + 16 x ( x^{2} + x + 1 ) + 2$	$C_2^4.(C_4\times D_4)$ (as 16T869)	$512$	$2$	$[2, 2, 2, 3, \frac{7}{2}, \frac{7}{2}, \frac{9}{2}]^{4}$	$[1,1,1,2,\frac{5}{2},\frac{5}{2},\frac{7}{2}]^{4}$	$[2,2,2,\frac{7}{2}]^{2}$	$[1,1,1,\frac{5}{2}]^{2}$	$[21, 14, 8, 0]$	$[1, 1, 1]$	$z^4 + 1,z^2 + 1,z + 1$	$[1, 3, 7, 15]$
2.2.8.56a1.28	32	$( x^{2} + x + 1 )^{8} + 8 ( x^{2} + x + 1 )^{7} + 4 ( x^{2} + x + 1 )^{6} + 8 ( x^{2} + x + 1 )^{5} + 16 x ( x^{2} + x + 1 )^{4} + 16 x ( x^{2} + x + 1 )^{3} + 16 x ( x^{2} + x + 1 ) + 2$	$C_2^4.(C_4\times D_4)$ (as 16T869)	$512$	$2$	$[2, 2, 2, 3, \frac{7}{2}, \frac{7}{2}, \frac{9}{2}]^{4}$	$[1,1,1,2,\frac{5}{2},\frac{5}{2},\frac{7}{2}]^{4}$	$[2,2,2,\frac{7}{2}]^{2}$	$[1,1,1,\frac{5}{2}]^{2}$	$[21, 14, 8, 0]$	$[1, 1, 1]$	$z^4 + 1,z^2 + 1,z + 1$	$[1, 3, 7, 15]$
2.2.8.56a1.29	4	$( x^{2} + x + 1 )^{8} + 8 ( x^{2} + x + 1 )^{7} + 4 ( x^{2} + x + 1 )^{6} + 8 ( x^{2} + x + 1 )^{5} + 16 ( x^{2} + x + 1 ) + 2$	$C_2\times D_8$ (as 16T29)	$32$	$4$	$[2, 3, \frac{7}{2}, \frac{9}{2}]^{2}$	$[1,2,\frac{5}{2},\frac{7}{2}]^{2}$	$[2]$	$[1]$	$[21, 14, 8, 0]$	$[1, 1, 1]$	$z^4 + 1,z^2 + 1,z + 1$	$[1, 3, 7, 15]$
2.2.8.56a1.30	8	$( x^{2} + x + 1 )^{8} + 8 ( x^{2} + x + 1 )^{7} + 4 ( x^{2} + x + 1 )^{6} + 8 ( x^{2} + x + 1 )^{5} + 16 x ( x^{2} + x + 1 )^{4} + 16 ( x^{2} + x + 1 ) + 2$	$D_8:C_2$ (as 16T44)	$32$	$4$	$[2, 3, \frac{7}{2}, \frac{9}{2}]^{2}$	$[1,2,\frac{5}{2},\frac{7}{2}]^{2}$	$[2]$	$[1]$	$[21, 14, 8, 0]$	$[1, 1, 1]$	$z^4 + 1,z^2 + 1,z + 1$	$[1, 3, 7, 15]$
2.2.8.56a1.31	4	$( x^{2} + x + 1 )^{8} + 8 ( x^{2} + x + 1 )^{7} + 4 ( x^{2} + x + 1 )^{6} + 8 ( x^{2} + x + 1 )^{5} + 16 x ( x^{2} + x + 1 )^{3} + 16 ( x^{2} + x + 1 ) + 2$	$D_8:C_2$ (as 16T45)	$32$	$4$	$[2, 3, \frac{7}{2}, \frac{9}{2}]^{2}$	$[1,2,\frac{5}{2},\frac{7}{2}]^{2}$	$[2]$	$[1]$	$[21, 14, 8, 0]$	$[1, 1, 1]$	$z^4 + 1,z^2 + 1,z + 1$	$[1, 3, 7, 15]$
2.2.8.56a1.32	8	$( x^{2} + x + 1 )^{8} + 8 ( x^{2} + x + 1 )^{7} + 4 ( x^{2} + x + 1 )^{6} + 8 ( x^{2} + x + 1 )^{5} + 16 x ( x^{2} + x + 1 )^{4} + 16 x ( x^{2} + x + 1 )^{3} + 16 ( x^{2} + x + 1 ) + 2$	$D_8:C_2$ (as 16T38)	$32$	$4$	$[2, 3, \frac{7}{2}, \frac{9}{2}]^{2}$	$[1,2,\frac{5}{2},\frac{7}{2}]^{2}$	$[2]$	$[1]$	$[21, 14, 8, 0]$	$[1, 1, 1]$	$z^4 + 1,z^2 + 1,z + 1$	$[1, 3, 7, 15]$
2.2.8.56a1.33	16	$( x^{2} + x + 1 )^{8} + \left(8 x + 8\right) ( x^{2} + x + 1 )^{7} + 4 ( x^{2} + x + 1 )^{6} + 8 ( x^{2} + x + 1 )^{5} + 16 x ( x^{2} + x + 1 )^{3} + 2$	$(C_2\times C_4^2):C_4$ (as 16T291)	$128$	$4$	$[2, 3, 3, \frac{7}{2}, 4, \frac{9}{2}]^{2}$	$[1,2,2,\frac{5}{2},3,\frac{7}{2}]^{2}$	$[2,3,4]$	$[1,2,3]$	$[21, 14, 8, 0]$	$[1, 1, 1]$	$z^4 + 1,z^2 + 1,z + 1$	$[1, 3, 7, 15]$
2.2.8.56a1.34	16	$( x^{2} + x + 1 )^{8} + \left(8 x + 8\right) ( x^{2} + x + 1 )^{7} + 4 ( x^{2} + x + 1 )^{6} + 8 ( x^{2} + x + 1 )^{5} + 16 x ( x^{2} + x + 1 )^{4} + 16 x ( x^{2} + x + 1 )^{3} + 2$	$(C_2\times C_4^2):C_4$ (as 16T291)	$128$	$4$	$[2, 3, 3, \frac{7}{2}, 4, \frac{9}{2}]^{2}$	$[1,2,2,\frac{5}{2},3,\frac{7}{2}]^{2}$	$[2,3,4]$	$[1,2,3]$	$[21, 14, 8, 0]$	$[1, 1, 1]$	$z^4 + 1,z^2 + 1,z + 1$	$[1, 3, 7, 15]$
2.2.8.56a1.35	16	$( x^{2} + x + 1 )^{8} + \left(8 x + 8\right) ( x^{2} + x + 1 )^{7} + 4 ( x^{2} + x + 1 )^{6} + 8 ( x^{2} + x + 1 )^{5} + 16 x ( x^{2} + x + 1 )^{3} + 16 ( x^{2} + x + 1 ) + 2$	$\OD_{16}:D_4$ (as 16T251)	$128$	$4$	$[2, 3, 3, \frac{7}{2}, 4, \frac{9}{2}]^{2}$	$[1,2,2,\frac{5}{2},3,\frac{7}{2}]^{2}$	$[2,3,4]$	$[1,2,3]$	$[21, 14, 8, 0]$	$[1, 1, 1]$	$z^4 + 1,z^2 + 1,z + 1$	$[1, 3, 7, 15]$
2.2.8.56a1.36	16	$( x^{2} + x + 1 )^{8} + \left(8 x + 8\right) ( x^{2} + x + 1 )^{7} + 4 ( x^{2} + x + 1 )^{6} + 8 ( x^{2} + x + 1 )^{5} + 16 x ( x^{2} + x + 1 )^{4} + 16 x ( x^{2} + x + 1 )^{3} + 16 ( x^{2} + x + 1 ) + 2$	$\OD_{16}:D_4$ (as 16T251)	$128$	$4$	$[2, 3, 3, \frac{7}{2}, 4, \frac{9}{2}]^{2}$	$[1,2,2,\frac{5}{2},3,\frac{7}{2}]^{2}$	$[2,3,4]$	$[1,2,3]$	$[21, 14, 8, 0]$	$[1, 1, 1]$	$z^4 + 1,z^2 + 1,z + 1$	$[1, 3, 7, 15]$
2.2.8.56a1.37	16	$( x^{2} + x + 1 )^{8} + 4 ( x^{2} + x + 1 )^{6} + 8 x ( x^{2} + x + 1 )^{4} + 2$	$\OD_{16}.D_4$ (as 16T267)	$128$	$2$	$[2, 2, 3, \frac{7}{2}, \frac{9}{2}]^{4}$	$[1,1,2,\frac{5}{2},\frac{7}{2}]^{4}$	$[2,2]^{2}$	$[1,1]^{2}$	$[21, 14, 8, 0]$	$[1, 1, 1]$	$z^4 + 1,z^2 + 1,z + 1$	$[1, 3, 7, 15]$
2.2.8.56a1.38	16	$( x^{2} + x + 1 )^{8} + 4 ( x^{2} + x + 1 )^{6} + 24 x ( x^{2} + x + 1 )^{4} + 2$	$\OD_{16}.D_4$ (as 16T267)	$128$	$2$	$[2, 2, 3, \frac{7}{2}, \frac{9}{2}]^{4}$	$[1,1,2,\frac{5}{2},\frac{7}{2}]^{4}$	$[2,2]^{2}$	$[1,1]^{2}$	$[21, 14, 8, 0]$	$[1, 1, 1]$	$z^4 + 1,z^2 + 1,z + 1$	$[1, 3, 7, 15]$
2.2.8.56a1.39	32	$( x^{2} + x + 1 )^{8} + 4 ( x^{2} + x + 1 )^{6} + 8 x ( x^{2} + x + 1 )^{4} + 16 x ( x^{2} + x + 1 ) + 2$	$C_2^4.(C_4\times D_4)$ (as 16T884)	$512$	$2$	$[2, 2, 2, 3, \frac{7}{2}, \frac{7}{2}, \frac{9}{2}]^{4}$	$[1,1,1,2,\frac{5}{2},\frac{5}{2},\frac{7}{2}]^{4}$	$[2,2,2,\frac{7}{2}]^{2}$	$[1,1,1,\frac{5}{2}]^{2}$	$[21, 14, 8, 0]$	$[1, 1, 1]$	$z^4 + 1,z^2 + 1,z + 1$	$[1, 3, 7, 15]$
2.2.8.56a1.40	32	$( x^{2} + x + 1 )^{8} + 4 ( x^{2} + x + 1 )^{6} + 24 x ( x^{2} + x + 1 )^{4} + 16 x ( x^{2} + x + 1 ) + 2$	$C_2^4.(C_4\times D_4)$ (as 16T884)	$512$	$2$	$[2, 2, 2, 3, \frac{7}{2}, \frac{7}{2}, \frac{9}{2}]^{4}$	$[1,1,1,2,\frac{5}{2},\frac{5}{2},\frac{7}{2}]^{4}$	$[2,2,2,\frac{7}{2}]^{2}$	$[1,1,1,\frac{5}{2}]^{2}$	$[21, 14, 8, 0]$	$[1, 1, 1]$	$z^4 + 1,z^2 + 1,z + 1$	$[1, 3, 7, 15]$
2.2.8.56a1.41	32	$( x^{2} + x + 1 )^{8} + 4 ( x^{2} + x + 1 )^{6} + 8 x ( x^{2} + x + 1 )^{4} + 16 x ( x^{2} + x + 1 )^{3} + 16 x ( x^{2} + x + 1 ) + 2$	$C_2^4.(C_4\times D_4)$ (as 16T884)	$512$	$2$	$[2, 2, 2, 3, \frac{7}{2}, \frac{7}{2}, \frac{9}{2}]^{4}$	$[1,1,1,2,\frac{5}{2},\frac{5}{2},\frac{7}{2}]^{4}$	$[2,2,2,\frac{7}{2}]^{2}$	$[1,1,1,\frac{5}{2}]^{2}$	$[21, 14, 8, 0]$	$[1, 1, 1]$	$z^4 + 1,z^2 + 1,z + 1$	$[1, 3, 7, 15]$
2.2.8.56a1.42	32	$( x^{2} + x + 1 )^{8} + 4 ( x^{2} + x + 1 )^{6} + 24 x ( x^{2} + x + 1 )^{4} + 16 x ( x^{2} + x + 1 )^{3} + 16 x ( x^{2} + x + 1 ) + 2$	$C_2^4.(C_4\times D_4)$ (as 16T884)	$512$	$2$	$[2, 2, 2, 3, \frac{7}{2}, \frac{7}{2}, \frac{9}{2}]^{4}$	$[1,1,1,2,\frac{5}{2},\frac{5}{2},\frac{7}{2}]^{4}$	$[2,2,2,\frac{7}{2}]^{2}$	$[1,1,1,\frac{5}{2}]^{2}$	$[21, 14, 8, 0]$	$[1, 1, 1]$	$z^4 + 1,z^2 + 1,z + 1$	$[1, 3, 7, 15]$
2.2.8.56a1.43	16	$( x^{2} + x + 1 )^{8} + 8 x ( x^{2} + x + 1 )^{7} + 4 ( x^{2} + x + 1 )^{6} + 8 x ( x^{2} + x + 1 )^{4} + 2$	$\OD_{16}.D_4$ (as 16T215)	$128$	$4$	$[2, 3, 3, \frac{7}{2}, 4, \frac{9}{2}]^{2}$	$[1,2,2,\frac{5}{2},3,\frac{7}{2}]^{2}$	$[2,3,4]$	$[1,2,3]$	$[21, 14, 8, 0]$	$[1, 1, 1]$	$z^4 + 1,z^2 + 1,z + 1$	$[1, 3, 7, 15]$
2.2.8.56a1.44	16	$( x^{2} + x + 1 )^{8} + 8 x ( x^{2} + x + 1 )^{7} + 4 ( x^{2} + x + 1 )^{6} + 24 x ( x^{2} + x + 1 )^{4} + 2$	$\OD_{16}.D_4$ (as 16T215)	$128$	$4$	$[2, 3, 3, \frac{7}{2}, 4, \frac{9}{2}]^{2}$	$[1,2,2,\frac{5}{2},3,\frac{7}{2}]^{2}$	$[2,3,4]$	$[1,2,3]$	$[21, 14, 8, 0]$	$[1, 1, 1]$	$z^4 + 1,z^2 + 1,z + 1$	$[1, 3, 7, 15]$
2.2.8.56a1.45	16	$( x^{2} + x + 1 )^{8} + 8 x ( x^{2} + x + 1 )^{7} + 4 ( x^{2} + x + 1 )^{6} + 8 x ( x^{2} + x + 1 )^{4} + 16 ( x^{2} + x + 1 )^{3} + 2$	$\OD_{16}.D_4$ (as 16T215)	$128$	$4$	$[2, 3, 3, \frac{7}{2}, 4, \frac{9}{2}]^{2}$	$[1,2,2,\frac{5}{2},3,\frac{7}{2}]^{2}$	$[2,3,4]$	$[1,2,3]$	$[21, 14, 8, 0]$	$[1, 1, 1]$	$z^4 + 1,z^2 + 1,z + 1$	$[1, 3, 7, 15]$
2.2.8.56a1.46	16	$( x^{2} + x + 1 )^{8} + 8 x ( x^{2} + x + 1 )^{7} + 4 ( x^{2} + x + 1 )^{6} + 24 x ( x^{2} + x + 1 )^{4} + 16 ( x^{2} + x + 1 )^{3} + 2$	$\OD_{16}.D_4$ (as 16T215)	$128$	$4$	$[2, 3, 3, \frac{7}{2}, 4, \frac{9}{2}]^{2}$	$[1,2,2,\frac{5}{2},3,\frac{7}{2}]^{2}$	$[2,3,4]$	$[1,2,3]$	$[21, 14, 8, 0]$	$[1, 1, 1]$	$z^4 + 1,z^2 + 1,z + 1$	$[1, 3, 7, 15]$
2.2.8.56a1.47	16	$( x^{2} + x + 1 )^{8} + 8 x ( x^{2} + x + 1 )^{7} + 4 ( x^{2} + x + 1 )^{6} + 8 x ( x^{2} + x + 1 )^{4} + 16 ( x^{2} + x + 1 ) + 2$	$(C_4\times C_8):C_4$ (as 16T294)	$128$	$4$	$[2, 3, 3, \frac{7}{2}, 4, \frac{9}{2}]^{2}$	$[1,2,2,\frac{5}{2},3,\frac{7}{2}]^{2}$	$[2,3,4]$	$[1,2,3]$	$[21, 14, 8, 0]$	$[1, 1, 1]$	$z^4 + 1,z^2 + 1,z + 1$	$[1, 3, 7, 15]$
2.2.8.56a1.48	16	$( x^{2} + x + 1 )^{8} + 8 x ( x^{2} + x + 1 )^{7} + 4 ( x^{2} + x + 1 )^{6} + 24 x ( x^{2} + x + 1 )^{4} + 16 ( x^{2} + x + 1 ) + 2$	$(C_4\times C_8):C_4$ (as 16T294)	$128$	$4$	$[2, 3, 3, \frac{7}{2}, 4, \frac{9}{2}]^{2}$	$[1,2,2,\frac{5}{2},3,\frac{7}{2}]^{2}$	$[2,3,4]$	$[1,2,3]$	$[21, 14, 8, 0]$	$[1, 1, 1]$	$z^4 + 1,z^2 + 1,z + 1$	$[1, 3, 7, 15]$
2.2.8.56a1.49	16	$( x^{2} + x + 1 )^{8} + 8 x ( x^{2} + x + 1 )^{7} + 4 ( x^{2} + x + 1 )^{6} + 8 x ( x^{2} + x + 1 )^{4} + 16 ( x^{2} + x + 1 )^{3} + 16 ( x^{2} + x + 1 ) + 2$	$(C_4\times C_8):C_4$ (as 16T294)	$128$	$4$	$[2, 3, 3, \frac{7}{2}, 4, \frac{9}{2}]^{2}$	$[1,2,2,\frac{5}{2},3,\frac{7}{2}]^{2}$	$[2,3,4]$	$[1,2,3]$	$[21, 14, 8, 0]$	$[1, 1, 1]$	$z^4 + 1,z^2 + 1,z + 1$	$[1, 3, 7, 15]$
2.2.8.56a1.50	16	$( x^{2} + x + 1 )^{8} + 8 x ( x^{2} + x + 1 )^{7} + 4 ( x^{2} + x + 1 )^{6} + 24 x ( x^{2} + x + 1 )^{4} + 16 ( x^{2} + x + 1 )^{3} + 16 ( x^{2} + x + 1 ) + 2$	$(C_4\times C_8):C_4$ (as 16T294)	$128$	$4$	$[2, 3, 3, \frac{7}{2}, 4, \frac{9}{2}]^{2}$	$[1,2,2,\frac{5}{2},3,\frac{7}{2}]^{2}$	$[2,3,4]$	$[1,2,3]$	$[21, 14, 8, 0]$	$[1, 1, 1]$	$z^4 + 1,z^2 + 1,z + 1$	$[1, 3, 7, 15]$

  Download displayed columns for results to