Galois group: 34T39

• Label: 34T39
• Degree: $34$
• Order: $9248$
• Cyclic: no
• Abelian: no
• Solvable: yes
• Primitive: no
• $p$-group: no
• Group: $D_{17}^2.Q_8$

Group invariants

Abstract group:		$D_{17}^2.Q_8$
Order:		$9248=2^{5} \cdot 17^{2}$
Cyclic:		no
Abelian:		no
Solvable:		yes
Nilpotency class:		not nilpotent

Group action invariants

Degree $n$:		$34$
Transitive number $t$:		$39$
Parity:		$-1$
Primitive:		no
$\card{\Aut(F/K)}$:		$1$
Generators:		$(1,25,3,28,12,33,10,30)(2,18,16,22,11,23,14,19)(4,21,8,27,9,20,5,31)(6,24,17,32,7,34,13,26)(15,29)$, $(1,33,10,22,12,29,3,23)(2,28,14,19,11,34,16,26)(4,18,5,30,9,27,8,32)(6,25,13,24,7,20,17,21)(15,31)$

Low degree resolvents

$\card{(G/N)}$	Galois groups for stem field(s)
$2$:	$C_2$ x 3
$4$:	$C_4$ x 2, $C_2^2$
$8$:	$D_{4}$, $C_4\times C_2$, $Q_8$
$16$:	$C_4:C_4$
$32$:	16T49

Resolvents shown for degrees $\leq 47$

Subfields

Degree 2: $C_2$

Degree 17: None

Low degree siblings

There are no siblings with degree $\leq 47$

A number field with this Galois group has no arithmetically equivalent fields.

Conjugacy classes

Label	Cycle Type	Size	Order	Index	Representative
1A	$1^{34}$	$1$	$1$	$0$	$()$
2A	$2^{8},1^{18}$	$34$	$2$	$8$	$( 1, 4)( 2, 3)( 5,17)( 6,16)( 7,15)( 8,14)( 9,13)(10,12)$
2B	$2^{16},1^{2}$	$289$	$2$	$16$	$( 1,10)( 2, 9)( 3, 8)( 4, 7)( 5, 6)(11,17)(12,16)(13,15)(18,20)(21,34)(22,33)(23,32)(24,31)(25,30)(26,29)(27,28)$
4A1	$4^{8},1^{2}$	$289$	$4$	$24$	$( 1,13,10,15)( 2,17, 9,11)( 3, 4, 8, 7)( 5,12, 6,16)(18,32,20,23)(21,27,34,28)(22,31,33,24)(25,26,30,29)$
4A-1	$4^{8},1^{2}$	$289$	$4$	$24$	$( 1,15,10,13)( 2,11, 9,17)( 3, 7, 8, 4)( 5,16, 6,12)(18,23,20,32)(21,28,34,27)(22,24,33,31)(25,29,30,26)$
4B	$4^{8},1^{2}$	$578$	$4$	$24$	$( 1, 6, 9, 4)( 2,10, 8,17)( 3,14, 7,13)(11,12,16,15)(18,32,27,30)(19,28,26,34)(20,24,25,21)(22,33,23,29)$
8A1	$8^{4},1^{2}$	$578$	$8$	$28$	$( 1,14, 6, 7, 9,13, 4, 3)( 2,16,10,15, 8,11,17,12)(18,29,32,22,27,33,30,23)(19,20,28,24,26,25,34,21)$
8A-1	$8^{4},1^{2}$	$578$	$8$	$28$	$( 1, 3, 4,13, 9, 7, 6,14)( 2,12,17,11, 8,15,10,16)(18,23,30,33,27,22,32,29)(19,21,34,25,26,24,28,20)$
8B1	$8^{4},1^{2}$	$578$	$8$	$28$	$( 1, 4,15,10, 3,17, 6,11)( 5,13,14,12,16, 8, 7, 9)(18,30,24,27,34,22,28,25)(19,21,20,29,33,31,32,23)$
8B3	$8^{4},1^{2}$	$578$	$8$	$28$	$( 1,10, 6, 4, 3,11,15,17)( 5,12, 7,13,16, 9,14, 8)(18,27,28,30,34,25,24,22)(19,29,32,21,33,23,20,31)$
8C1	$8^{4},2$	$1156$	$8$	$29$	$( 1,25,13,26,10,30,15,29)( 2,18,17,32, 9,20,11,23)( 3,28, 4,21, 8,27, 7,34)( 5,31,12,33, 6,24,16,22)(14,19)$
8C-1	$8^{4},2$	$1156$	$8$	$29$	$( 1,29,15,30,10,26,13,25)( 2,23,11,20, 9,32,17,18)( 3,34, 7,27, 8,21, 4,28)( 5,22,16,24, 6,33,12,31)(14,19)$
8D1	$8^{4},2$	$1156$	$8$	$29$	$( 1,31, 3,21,11,32, 9,25)( 2,26, 7,18,10,20, 5,28)( 4,33,15,29, 8,30,14,34)( 6,23)(12,27,13,22,17,19,16,24)$
8D-1	$8^{4},2$	$1156$	$8$	$29$	$( 1,25, 9,32,11,21, 3,31)( 2,28, 5,20,10,18, 7,26)( 4,34,14,30, 8,29,15,33)( 6,23)(12,24,16,19,17,22,13,27)$
17A1	$17,1^{17}$	$16$	$17$	$16$	$(18,31,27,23,19,32,28,24,20,33,29,25,21,34,30,26,22)$
17A3	$17,1^{17}$	$16$	$17$	$16$	$(18,23,28,33,21,26,31,19,24,29,34,22,27,32,20,25,30)$
17B1	$17^{2}$	$32$	$17$	$32$	$( 1,11, 4,14, 7,17,10, 3,13, 6,16, 9, 2,12, 5,15, 8)(18,34,33,32,31,30,29,28,27,26,25,24,23,22,21,20,19)$
17B3	$17^{2}$	$32$	$17$	$32$	$( 1,14,10, 6, 2,15,11, 7, 3,16,12, 8, 4,17,13, 9, 5)(18,32,29,26,23,20,34,31,28,25,22,19,33,30,27,24,21)$
17C1	$17^{2}$	$32$	$17$	$32$	$( 1,13, 8, 3,15,10, 5,17,12, 7, 2,14, 9, 4,16,11, 6)(18,34,33,32,31,30,29,28,27,26,25,24,23,22,21,20,19)$
17C3	$17^{2}$	$32$	$17$	$32$	$( 1,10, 2,11, 3,12, 4,13, 5,14, 6,15, 7,16, 8,17, 9)(18,32,29,26,23,20,34,31,28,25,22,19,33,30,27,24,21)$
17D1	$17^{2}$	$32$	$17$	$32$	$( 1, 9,17, 8,16, 7,15, 6,14, 5,13, 4,12, 3,11, 2,10)(18,34,33,32,31,30,29,28,27,26,25,24,23,22,21,20,19)$
17D2	$17^{2}$	$32$	$17$	$32$	$( 1,17,16,15,14,13,12,11,10, 9, 8, 7, 6, 5, 4, 3, 2)(18,33,31,29,27,25,23,21,19,34,32,30,28,26,24,22,20)$
17D3	$17^{2}$	$32$	$17$	$32$	$( 1, 8,15, 5,12, 2, 9,16, 6,13, 3,10,17, 7,14, 4,11)(18,32,29,26,23,20,34,31,28,25,22,19,33,30,27,24,21)$
17D6	$17^{2}$	$32$	$17$	$32$	$( 1,15,12, 9, 6, 3,17,14,11, 8, 5, 2,16,13,10, 7, 4)(18,29,23,34,28,22,33,27,21,32,26,20,31,25,19,30,24)$
34A1	$17,2^{8},1$	$272$	$34$	$24$	$( 1, 4)( 2, 3)( 5,17)( 6,16)( 7,15)( 8,14)( 9,13)(10,12)(18,33,31,29,27,25,23,21,19,34,32,30,28,26,24,22,20)$
34A3	$17,2^{8},1$	$272$	$34$	$24$	$( 1, 4)( 2, 3)( 5,17)( 6,16)( 7,15)( 8,14)( 9,13)(10,12)(18,29,23,34,28,22,33,27,21,32,26,20,31,25,19,30,24)$

Malle's constant $a(G)$:     $1/8$

Character table

		1A	2A	2B	4A1	4A-1	4B	8A1	8A-1	8B1	8B3	8C1	8C-1	8D1	8D-1	17A1	17A3	17B1	17B3	17C1	17C3	17D1	17D2	17D3	17D6	34A1	34A3
	Size	1	34	289	289	289	578	578	578	578	578	1156	1156	1156	1156	16	16	32	32	32	32	32	32	32	32	272	272
	2 P	1A	1A	1A	2B	2B	2B	4B	4B	4B	4B	4A1	4A-1	4A1	4A-1	17A1	17A3	17B1	17B3	17C1	17C3	17D2	17D1	17D6	17D3	17A1	17A3
	17 P	1A	2A	2B	4A1	4A-1	4B	8A1	8A-1	8B1	8B3	8C1	8C-1	8D1	8D-1	1A	1A	1A	1A	1A	1A	1A	1A	1A	1A	2A	2A
	Type
9248.y.1a	R	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$
9248.y.1b	R	$1$	$1$	$1$	$1$	$1$	$1$	$-1$	$-1$	$-1$	$-1$	$-1$	$-1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$
9248.y.1c	R	$1$	$1$	$1$	$1$	$1$	$1$	$-1$	$-1$	$-1$	$-1$	$1$	$1$	$-1$	$-1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$
9248.y.1d	R	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$-1$	$-1$	$-1$	$-1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$
9248.y.1e1	C	$1$	$-1$	$1$	$-1$	$-1$	$1$	$-1$	$-1$	$1$	$1$	$-i$	$i$	$-i$	$i$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$-1$	$-1$
9248.y.1e2	C	$1$	$-1$	$1$	$-1$	$-1$	$1$	$-1$	$-1$	$1$	$1$	$i$	$-i$	$i$	$-i$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$-1$	$-1$
9248.y.1f1	C	$1$	$-1$	$1$	$-1$	$-1$	$1$	$1$	$1$	$-1$	$-1$	$-i$	$i$	$i$	$-i$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$-1$	$-1$
9248.y.1f2	C	$1$	$-1$	$1$	$-1$	$-1$	$1$	$1$	$1$	$-1$	$-1$	$i$	$-i$	$-i$	$i$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$-1$	$-1$
9248.y.2a	R	$2$	$-2$	$2$	$2$	$2$	$-2$	$0$	$0$	$0$	$0$	$0$	$0$	$0$	$0$	$2$	$2$	$2$	$2$	$2$	$2$	$2$	$2$	$2$	$2$	$-2$	$-2$
9248.y.2b	S	$2$	$2$	$2$	$-2$	$-2$	$-2$	$0$	$0$	$0$	$0$	$0$	$0$	$0$	$0$	$2$	$2$	$2$	$2$	$2$	$2$	$2$	$2$	$2$	$2$	$2$	$2$
9248.y.2c1	C	$2$	$0$	$-2$	$-2{\zeta }_8^2$	$2{\zeta }_8^2$	$0$	$-{\zeta }_8-{\zeta }_8^3$	${\zeta }_8+{\zeta }_8^3$	$-{\zeta }_8^{-1}-{\zeta }_8$	${\zeta }_8^{-1}+{\zeta }_8$	$0$	$0$	$0$	$0$	$2$	$2$	$2$	$2$	$2$	$2$	$2$	$2$	$2$	$2$	$0$	$0$
9248.y.2c2	C	$2$	$0$	$-2$	$2{\zeta }_8^2$	$-2{\zeta }_8^2$	$0$	${\zeta }_8+{\zeta }_8^3$	$-{\zeta }_8-{\zeta }_8^3$	$-{\zeta }_8^{-1}-{\zeta }_8$	${\zeta }_8^{-1}+{\zeta }_8$	$0$	$0$	$0$	$0$	$2$	$2$	$2$	$2$	$2$	$2$	$2$	$2$	$2$	$2$	$0$	$0$
9248.y.2c3	C	$2$	$0$	$-2$	$-2{\zeta }_8^2$	$2{\zeta }_8^2$	$0$	${\zeta }_8+{\zeta }_8^3$	$-{\zeta }_8-{\zeta }_8^3$	${\zeta }_8^{-1}+{\zeta }_8$	$-{\zeta }_8^{-1}-{\zeta }_8$	$0$	$0$	$0$	$0$	$2$	$2$	$2$	$2$	$2$	$2$	$2$	$2$	$2$	$2$	$0$	$0$
9248.y.2c4	C	$2$	$0$	$-2$	$2{\zeta }_8^2$	$-2{\zeta }_8^2$	$0$	$-{\zeta }_8-{\zeta }_8^3$	${\zeta }_8+{\zeta }_8^3$	${\zeta }_8^{-1}+{\zeta }_8$	$-{\zeta }_8^{-1}-{\zeta }_8$	$0$	$0$	$0$	$0$	$2$	$2$	$2$	$2$	$2$	$2$	$2$	$2$	$2$	$2$	$0$	$0$
9248.y.16a1	R	$16$	$8$	$0$	$0$	$0$	$0$	$0$	$0$	$0$	$0$	$0$	$0$	$0$	$0$	${\zeta }_{17}^{-7}+{\zeta }_{17}^{-6}+{\zeta }_{17}^{-5}+{\zeta }_{17}^{-3}+8+{\zeta }_{17}^3+{\zeta }_{17}^5+{\zeta }_{17}^6+{\zeta }_{17}^7$	$-{\zeta }_{17}^{-7}-{\zeta }_{17}^{-6}-{\zeta }_{17}^{-5}-{\zeta }_{17}^{-3}+7-{\zeta }_{17}^3-{\zeta }_{17}^5-{\zeta }_{17}^6-{\zeta }_{17}^7$	$-2{\zeta }_{17}^{-7}-2{\zeta }_{17}^{-6}-2{\zeta }_{17}^{-5}-2{\zeta }_{17}^{-3}-2-2{\zeta }_{17}^3-2{\zeta }_{17}^5-2{\zeta }_{17}^6-2{\zeta }_{17}^7$	$2{\zeta }_{17}^{-7}+2{\zeta }_{17}^{-6}+2{\zeta }_{17}^{-5}+2{\zeta }_{17}^{-3}+2{\zeta }_{17}^3+2{\zeta }_{17}^5+2{\zeta }_{17}^6+2{\zeta }_{17}^7$	$-1$	$-1$	$-1$	$2{\zeta }_{17}^{-7}+2{\zeta }_{17}^{-6}+2{\zeta }_{17}^{-5}+2{\zeta }_{17}^{-3}+2{\zeta }_{17}^3+2{\zeta }_{17}^5+2{\zeta }_{17}^6+2{\zeta }_{17}^7$	$-1$	$-2{\zeta }_{17}^{-7}-2{\zeta }_{17}^{-6}-2{\zeta }_{17}^{-5}-2{\zeta }_{17}^{-3}-2-2{\zeta }_{17}^3-2{\zeta }_{17}^5-2{\zeta }_{17}^6-2{\zeta }_{17}^7$	${\zeta }_{17}^{-7}+{\zeta }_{17}^{-6}+{\zeta }_{17}^{-5}+{\zeta }_{17}^{-3}+{\zeta }_{17}^3+{\zeta }_{17}^5+{\zeta }_{17}^6+{\zeta }_{17}^7$	$-{\zeta }_{17}^{-7}-{\zeta }_{17}^{-6}-{\zeta }_{17}^{-5}-{\zeta }_{17}^{-3}-1-{\zeta }_{17}^3-{\zeta }_{17}^5-{\zeta }_{17}^6-{\zeta }_{17}^7$
9248.y.16a2	R	$16$	$8$	$0$	$0$	$0$	$0$	$0$	$0$	$0$	$0$	$0$	$0$	$0$	$0$	$-{\zeta }_{17}^{-7}-{\zeta }_{17}^{-6}-{\zeta }_{17}^{-5}-{\zeta }_{17}^{-3}+7-{\zeta }_{17}^3-{\zeta }_{17}^5-{\zeta }_{17}^6-{\zeta }_{17}^7$	${\zeta }_{17}^{-7}+{\zeta }_{17}^{-6}+{\zeta }_{17}^{-5}+{\zeta }_{17}^{-3}+8+{\zeta }_{17}^3+{\zeta }_{17}^5+{\zeta }_{17}^6+{\zeta }_{17}^7$	$2{\zeta }_{17}^{-7}+2{\zeta }_{17}^{-6}+2{\zeta }_{17}^{-5}+2{\zeta }_{17}^{-3}+2{\zeta }_{17}^3+2{\zeta }_{17}^5+2{\zeta }_{17}^6+2{\zeta }_{17}^7$	$-2{\zeta }_{17}^{-7}-2{\zeta }_{17}^{-6}-2{\zeta }_{17}^{-5}-2{\zeta }_{17}^{-3}-2-2{\zeta }_{17}^3-2{\zeta }_{17}^5-2{\zeta }_{17}^6-2{\zeta }_{17}^7$	$-1$	$-1$	$-1$	$-2{\zeta }_{17}^{-7}-2{\zeta }_{17}^{-6}-2{\zeta }_{17}^{-5}-2{\zeta }_{17}^{-3}-2-2{\zeta }_{17}^3-2{\zeta }_{17}^5-2{\zeta }_{17}^6-2{\zeta }_{17}^7$	$-1$	$2{\zeta }_{17}^{-7}+2{\zeta }_{17}^{-6}+2{\zeta }_{17}^{-5}+2{\zeta }_{17}^{-3}+2{\zeta }_{17}^3+2{\zeta }_{17}^5+2{\zeta }_{17}^6+2{\zeta }_{17}^7$	$-{\zeta }_{17}^{-7}-{\zeta }_{17}^{-6}-{\zeta }_{17}^{-5}-{\zeta }_{17}^{-3}-1-{\zeta }_{17}^3-{\zeta }_{17}^5-{\zeta }_{17}^6-{\zeta }_{17}^7$	${\zeta }_{17}^{-7}+{\zeta }_{17}^{-6}+{\zeta }_{17}^{-5}+{\zeta }_{17}^{-3}+{\zeta }_{17}^3+{\zeta }_{17}^5+{\zeta }_{17}^6+{\zeta }_{17}^7$
9248.y.16b1	R	$16$	$-8$	$0$	$0$	$0$	$0$	$0$	$0$	$0$	$0$	$0$	$0$	$0$	$0$	${\zeta }_{17}^{-7}+{\zeta }_{17}^{-6}+{\zeta }_{17}^{-5}+{\zeta }_{17}^{-3}+8+{\zeta }_{17}^3+{\zeta }_{17}^5+{\zeta }_{17}^6+{\zeta }_{17}^7$	$-{\zeta }_{17}^{-7}-{\zeta }_{17}^{-6}-{\zeta }_{17}^{-5}-{\zeta }_{17}^{-3}+7-{\zeta }_{17}^3-{\zeta }_{17}^5-{\zeta }_{17}^6-{\zeta }_{17}^7$	$-2{\zeta }_{17}^{-7}-2{\zeta }_{17}^{-6}-2{\zeta }_{17}^{-5}-2{\zeta }_{17}^{-3}-2-2{\zeta }_{17}^3-2{\zeta }_{17}^5-2{\zeta }_{17}^6-2{\zeta }_{17}^7$	$2{\zeta }_{17}^{-7}+2{\zeta }_{17}^{-6}+2{\zeta }_{17}^{-5}+2{\zeta }_{17}^{-3}+2{\zeta }_{17}^3+2{\zeta }_{17}^5+2{\zeta }_{17}^6+2{\zeta }_{17}^7$	$-1$	$-1$	$-1$	$2{\zeta }_{17}^{-7}+2{\zeta }_{17}^{-6}+2{\zeta }_{17}^{-5}+2{\zeta }_{17}^{-3}+2{\zeta }_{17}^3+2{\zeta }_{17}^5+2{\zeta }_{17}^6+2{\zeta }_{17}^7$	$-1$	$-2{\zeta }_{17}^{-7}-2{\zeta }_{17}^{-6}-2{\zeta }_{17}^{-5}-2{\zeta }_{17}^{-3}-2-2{\zeta }_{17}^3-2{\zeta }_{17}^5-2{\zeta }_{17}^6-2{\zeta }_{17}^7$	$-{\zeta }_{17}^{-7}-{\zeta }_{17}^{-6}-{\zeta }_{17}^{-5}-{\zeta }_{17}^{-3}-{\zeta }_{17}^3-{\zeta }_{17}^5-{\zeta }_{17}^6-{\zeta }_{17}^7$	${\zeta }_{17}^{-7}+{\zeta }_{17}^{-6}+{\zeta }_{17}^{-5}+{\zeta }_{17}^{-3}+1+{\zeta }_{17}^3+{\zeta }_{17}^5+{\zeta }_{17}^6+{\zeta }_{17}^7$
9248.y.16b2	R	$16$	$-8$	$0$	$0$	$0$	$0$	$0$	$0$	$0$	$0$	$0$	$0$	$0$	$0$	$-{\zeta }_{17}^{-7}-{\zeta }_{17}^{-6}-{\zeta }_{17}^{-5}-{\zeta }_{17}^{-3}+7-{\zeta }_{17}^3-{\zeta }_{17}^5-{\zeta }_{17}^6-{\zeta }_{17}^7$	${\zeta }_{17}^{-7}+{\zeta }_{17}^{-6}+{\zeta }_{17}^{-5}+{\zeta }_{17}^{-3}+8+{\zeta }_{17}^3+{\zeta }_{17}^5+{\zeta }_{17}^6+{\zeta }_{17}^7$	$2{\zeta }_{17}^{-7}+2{\zeta }_{17}^{-6}+2{\zeta }_{17}^{-5}+2{\zeta }_{17}^{-3}+2{\zeta }_{17}^3+2{\zeta }_{17}^5+2{\zeta }_{17}^6+2{\zeta }_{17}^7$	$-2{\zeta }_{17}^{-7}-2{\zeta }_{17}^{-6}-2{\zeta }_{17}^{-5}-2{\zeta }_{17}^{-3}-2-2{\zeta }_{17}^3-2{\zeta }_{17}^5-2{\zeta }_{17}^6-2{\zeta }_{17}^7$	$-1$	$-1$	$-1$	$-2{\zeta }_{17}^{-7}-2{\zeta }_{17}^{-6}-2{\zeta }_{17}^{-5}-2{\zeta }_{17}^{-3}-2-2{\zeta }_{17}^3-2{\zeta }_{17}^5-2{\zeta }_{17}^6-2{\zeta }_{17}^7$	$-1$	$2{\zeta }_{17}^{-7}+2{\zeta }_{17}^{-6}+2{\zeta }_{17}^{-5}+2{\zeta }_{17}^{-3}+2{\zeta }_{17}^3+2{\zeta }_{17}^5+2{\zeta }_{17}^6+2{\zeta }_{17}^7$	${\zeta }_{17}^{-7}+{\zeta }_{17}^{-6}+{\zeta }_{17}^{-5}+{\zeta }_{17}^{-3}+1+{\zeta }_{17}^3+{\zeta }_{17}^5+{\zeta }_{17}^6+{\zeta }_{17}^7$	$-{\zeta }_{17}^{-7}-{\zeta }_{17}^{-6}-{\zeta }_{17}^{-5}-{\zeta }_{17}^{-3}-{\zeta }_{17}^3-{\zeta }_{17}^5-{\zeta }_{17}^6-{\zeta }_{17}^7$
9248.y.32a1	R	$32$	$0$	$0$	$0$	$0$	$0$	$0$	$0$	$0$	$0$	$0$	$0$	$0$	$0$	$4{\zeta }_{17}^{-7}+4{\zeta }_{17}^{-6}+4{\zeta }_{17}^{-5}+4{\zeta }_{17}^{-3}+4{\zeta }_{17}^3+4{\zeta }_{17}^5+4{\zeta }_{17}^6+4{\zeta }_{17}^7$	$-4{\zeta }_{17}^{-7}-4{\zeta }_{17}^{-6}-4{\zeta }_{17}^{-5}-4{\zeta }_{17}^{-3}-4-4{\zeta }_{17}^3-4{\zeta }_{17}^5-4{\zeta }_{17}^6-4{\zeta }_{17}^7$	$-2$	$-2$	$2{\zeta }_{17}^{-7}+2{\zeta }_{17}^{-6}+2{\zeta }_{17}^{-5}+2{\zeta }_{17}^{-3}-1+2{\zeta }_{17}^3+2{\zeta }_{17}^5+2{\zeta }_{17}^6+2{\zeta }_{17}^7$	$-2{\zeta }_{17}^{-7}-2{\zeta }_{17}^{-6}-2{\zeta }_{17}^{-5}-2{\zeta }_{17}^{-3}-3-2{\zeta }_{17}^3-2{\zeta }_{17}^5-2{\zeta }_{17}^6-2{\zeta }_{17}^7$	$-2{\zeta }_{17}^{-7}-2{\zeta }_{17}^{-6}-2{\zeta }_{17}^{-5}-2{\zeta }_{17}^{-3}-3-2{\zeta }_{17}^3-2{\zeta }_{17}^5-2{\zeta }_{17}^6-2{\zeta }_{17}^7$	$-{\zeta }_{17}^{-7}-{\zeta }_{17}^{-6}-{\zeta }_{17}^{-5}-{\zeta }_{17}^{-3}+6-{\zeta }_{17}^3-{\zeta }_{17}^5-{\zeta }_{17}^6-{\zeta }_{17}^7$	$2{\zeta }_{17}^{-7}+2{\zeta }_{17}^{-6}+2{\zeta }_{17}^{-5}+2{\zeta }_{17}^{-3}-1+2{\zeta }_{17}^3+2{\zeta }_{17}^5+2{\zeta }_{17}^6+2{\zeta }_{17}^7$	${\zeta }_{17}^{-7}+{\zeta }_{17}^{-6}+{\zeta }_{17}^{-5}+{\zeta }_{17}^{-3}+7+{\zeta }_{17}^3+{\zeta }_{17}^5+{\zeta }_{17}^6+{\zeta }_{17}^7$	$0$	$0$
9248.y.32a2	R	$32$	$0$	$0$	$0$	$0$	$0$	$0$	$0$	$0$	$0$	$0$	$0$	$0$	$0$	$-4{\zeta }_{17}^{-7}-4{\zeta }_{17}^{-6}-4{\zeta }_{17}^{-5}-4{\zeta }_{17}^{-3}-4-4{\zeta }_{17}^3-4{\zeta }_{17}^5-4{\zeta }_{17}^6-4{\zeta }_{17}^7$	$4{\zeta }_{17}^{-7}+4{\zeta }_{17}^{-6}+4{\zeta }_{17}^{-5}+4{\zeta }_{17}^{-3}+4{\zeta }_{17}^3+4{\zeta }_{17}^5+4{\zeta }_{17}^6+4{\zeta }_{17}^7$	$-2$	$-2$	$-2{\zeta }_{17}^{-7}-2{\zeta }_{17}^{-6}-2{\zeta }_{17}^{-5}-2{\zeta }_{17}^{-3}-3-2{\zeta }_{17}^3-2{\zeta }_{17}^5-2{\zeta }_{17}^6-2{\zeta }_{17}^7$	$2{\zeta }_{17}^{-7}+2{\zeta }_{17}^{-6}+2{\zeta }_{17}^{-5}+2{\zeta }_{17}^{-3}-1+2{\zeta }_{17}^3+2{\zeta }_{17}^5+2{\zeta }_{17}^6+2{\zeta }_{17}^7$	$2{\zeta }_{17}^{-7}+2{\zeta }_{17}^{-6}+2{\zeta }_{17}^{-5}+2{\zeta }_{17}^{-3}-1+2{\zeta }_{17}^3+2{\zeta }_{17}^5+2{\zeta }_{17}^6+2{\zeta }_{17}^7$	${\zeta }_{17}^{-7}+{\zeta }_{17}^{-6}+{\zeta }_{17}^{-5}+{\zeta }_{17}^{-3}+7+{\zeta }_{17}^3+{\zeta }_{17}^5+{\zeta }_{17}^6+{\zeta }_{17}^7$	$-2{\zeta }_{17}^{-7}-2{\zeta }_{17}^{-6}-2{\zeta }_{17}^{-5}-2{\zeta }_{17}^{-3}-3-2{\zeta }_{17}^3-2{\zeta }_{17}^5-2{\zeta }_{17}^6-2{\zeta }_{17}^7$	$-{\zeta }_{17}^{-7}-{\zeta }_{17}^{-6}-{\zeta }_{17}^{-5}-{\zeta }_{17}^{-3}+6-{\zeta }_{17}^3-{\zeta }_{17}^5-{\zeta }_{17}^6-{\zeta }_{17}^7$	$0$	$0$
9248.y.32b1	R	$32$	$0$	$0$	$0$	$0$	$0$	$0$	$0$	$0$	$0$	$0$	$0$	$0$	$0$	$4{\zeta }_{17}^{-7}+4{\zeta }_{17}^{-6}+4{\zeta }_{17}^{-5}+4{\zeta }_{17}^{-3}+4{\zeta }_{17}^3+4{\zeta }_{17}^5+4{\zeta }_{17}^6+4{\zeta }_{17}^7$	$-4{\zeta }_{17}^{-7}-4{\zeta }_{17}^{-6}-4{\zeta }_{17}^{-5}-4{\zeta }_{17}^{-3}-4-4{\zeta }_{17}^3-4{\zeta }_{17}^5-4{\zeta }_{17}^6-4{\zeta }_{17}^7$	${\zeta }_{17}^{-7}+{\zeta }_{17}^{-6}+{\zeta }_{17}^{-5}+{\zeta }_{17}^{-3}+7+{\zeta }_{17}^3+{\zeta }_{17}^5+{\zeta }_{17}^6+{\zeta }_{17}^7$	$-{\zeta }_{17}^{-7}-{\zeta }_{17}^{-6}-{\zeta }_{17}^{-5}-{\zeta }_{17}^{-3}+6-{\zeta }_{17}^3-{\zeta }_{17}^5-{\zeta }_{17}^6-{\zeta }_{17}^7$	$-2{\zeta }_{17}^{-7}-2{\zeta }_{17}^{-6}-2{\zeta }_{17}^{-5}-2{\zeta }_{17}^{-3}-3-2{\zeta }_{17}^3-2{\zeta }_{17}^5-2{\zeta }_{17}^6-2{\zeta }_{17}^7$	$2{\zeta }_{17}^{-7}+2{\zeta }_{17}^{-6}+2{\zeta }_{17}^{-5}+2{\zeta }_{17}^{-3}-1+2{\zeta }_{17}^3+2{\zeta }_{17}^5+2{\zeta }_{17}^6+2{\zeta }_{17}^7$	$2{\zeta }_{17}^{-7}+2{\zeta }_{17}^{-6}+2{\zeta }_{17}^{-5}+2{\zeta }_{17}^{-3}-1+2{\zeta }_{17}^3+2{\zeta }_{17}^5+2{\zeta }_{17}^6+2{\zeta }_{17}^7$	$-2$	$-2{\zeta }_{17}^{-7}-2{\zeta }_{17}^{-6}-2{\zeta }_{17}^{-5}-2{\zeta }_{17}^{-3}-3-2{\zeta }_{17}^3-2{\zeta }_{17}^5-2{\zeta }_{17}^6-2{\zeta }_{17}^7$	$-2$	$0$	$0$
9248.y.32b2	R	$32$	$0$	$0$	$0$	$0$	$0$	$0$	$0$	$0$	$0$	$0$	$0$	$0$	$0$	$-4{\zeta }_{17}^{-7}-4{\zeta }_{17}^{-6}-4{\zeta }_{17}^{-5}-4{\zeta }_{17}^{-3}-4-4{\zeta }_{17}^3-4{\zeta }_{17}^5-4{\zeta }_{17}^6-4{\zeta }_{17}^7$	$4{\zeta }_{17}^{-7}+4{\zeta }_{17}^{-6}+4{\zeta }_{17}^{-5}+4{\zeta }_{17}^{-3}+4{\zeta }_{17}^3+4{\zeta }_{17}^5+4{\zeta }_{17}^6+4{\zeta }_{17}^7$	$-{\zeta }_{17}^{-7}-{\zeta }_{17}^{-6}-{\zeta }_{17}^{-5}-{\zeta }_{17}^{-3}+6-{\zeta }_{17}^3-{\zeta }_{17}^5-{\zeta }_{17}^6-{\zeta }_{17}^7$	${\zeta }_{17}^{-7}+{\zeta }_{17}^{-6}+{\zeta }_{17}^{-5}+{\zeta }_{17}^{-3}+7+{\zeta }_{17}^3+{\zeta }_{17}^5+{\zeta }_{17}^6+{\zeta }_{17}^7$	$2{\zeta }_{17}^{-7}+2{\zeta }_{17}^{-6}+2{\zeta }_{17}^{-5}+2{\zeta }_{17}^{-3}-1+2{\zeta }_{17}^3+2{\zeta }_{17}^5+2{\zeta }_{17}^6+2{\zeta }_{17}^7$	$-2{\zeta }_{17}^{-7}-2{\zeta }_{17}^{-6}-2{\zeta }_{17}^{-5}-2{\zeta }_{17}^{-3}-3-2{\zeta }_{17}^3-2{\zeta }_{17}^5-2{\zeta }_{17}^6-2{\zeta }_{17}^7$	$-2{\zeta }_{17}^{-7}-2{\zeta }_{17}^{-6}-2{\zeta }_{17}^{-5}-2{\zeta }_{17}^{-3}-3-2{\zeta }_{17}^3-2{\zeta }_{17}^5-2{\zeta }_{17}^6-2{\zeta }_{17}^7$	$-2$	$2{\zeta }_{17}^{-7}+2{\zeta }_{17}^{-6}+2{\zeta }_{17}^{-5}+2{\zeta }_{17}^{-3}-1+2{\zeta }_{17}^3+2{\zeta }_{17}^5+2{\zeta }_{17}^6+2{\zeta }_{17}^7$	$-2$	$0$	$0$
9248.y.32c1	R	$32$	$0$	$0$	$0$	$0$	$0$	$0$	$0$	$0$	$0$	$0$	$0$	$0$	$0$	$-2$	$-2$	$2{\zeta }_{17}^{-7}+2{\zeta }_{17}^{-6}+2{\zeta }_{17}^{-5}+2{\zeta }_{17}^{-3}-1+2{\zeta }_{17}^3+2{\zeta }_{17}^5+2{\zeta }_{17}^6+2{\zeta }_{17}^7$	$-2{\zeta }_{17}^{-7}-2{\zeta }_{17}^{-6}-2{\zeta }_{17}^{-5}-2{\zeta }_{17}^{-3}-3-2{\zeta }_{17}^3-2{\zeta }_{17}^5-2{\zeta }_{17}^6-2{\zeta }_{17}^7$	$-{\zeta }_{17}^{-8}+2{\zeta }_{17}^{-7}+2{\zeta }_{17}^{-6}-2{\zeta }_{17}^{-5}-2{\zeta }_{17}^{-3}-{\zeta }_{17}^{-2}+2-{\zeta }_{17}^2-2{\zeta }_{17}^3-2{\zeta }_{17}^5+2{\zeta }_{17}^6+2{\zeta }_{17}^7-{\zeta }_{17}^8$	$4{\zeta }_{17}^{-8}+2{\zeta }_{17}^{-7}+2{\zeta }_{17}^{-6}+{\zeta }_{17}^{-5}+{\zeta }_{17}^{-3}+4{\zeta }_{17}^{-2}+4+4{\zeta }_{17}^2+{\zeta }_{17}^3+{\zeta }_{17}^5+2{\zeta }_{17}^6+2{\zeta }_{17}^7+4{\zeta }_{17}^8$	$-4{\zeta }_{17}^{-8}-3{\zeta }_{17}^{-7}-3{\zeta }_{17}^{-6}-2{\zeta }_{17}^{-5}-2{\zeta }_{17}^{-3}-4{\zeta }_{17}^{-2}-4{\zeta }_{17}^2-2{\zeta }_{17}^3-2{\zeta }_{17}^5-3{\zeta }_{17}^6-3{\zeta }_{17}^7-4{\zeta }_{17}^8$	$2{\zeta }_{17}^{-7}+2{\zeta }_{17}^{-6}+2{\zeta }_{17}^{-5}+2{\zeta }_{17}^{-3}-1+2{\zeta }_{17}^3+2{\zeta }_{17}^5+2{\zeta }_{17}^6+2{\zeta }_{17}^7$	${\zeta }_{17}^{-8}-{\zeta }_{17}^{-7}-{\zeta }_{17}^{-6}+3{\zeta }_{17}^{-5}+3{\zeta }_{17}^{-3}+{\zeta }_{17}^{-2}+3+{\zeta }_{17}^2+3{\zeta }_{17}^3+3{\zeta }_{17}^5-{\zeta }_{17}^6-{\zeta }_{17}^7+{\zeta }_{17}^8$	$-2{\zeta }_{17}^{-7}-2{\zeta }_{17}^{-6}-2{\zeta }_{17}^{-5}-2{\zeta }_{17}^{-3}-3-2{\zeta }_{17}^3-2{\zeta }_{17}^5-2{\zeta }_{17}^6-2{\zeta }_{17}^7$	$0$	$0$
9248.y.32c2	R	$32$	$0$	$0$	$0$	$0$	$0$	$0$	$0$	$0$	$0$	$0$	$0$	$0$	$0$	$-2$	$-2$	$2{\zeta }_{17}^{-7}+2{\zeta }_{17}^{-6}+2{\zeta }_{17}^{-5}+2{\zeta }_{17}^{-3}-1+2{\zeta }_{17}^3+2{\zeta }_{17}^5+2{\zeta }_{17}^6+2{\zeta }_{17}^7$	$-2{\zeta }_{17}^{-7}-2{\zeta }_{17}^{-6}-2{\zeta }_{17}^{-5}-2{\zeta }_{17}^{-3}-3-2{\zeta }_{17}^3-2{\zeta }_{17}^5-2{\zeta }_{17}^6-2{\zeta }_{17}^7$	${\zeta }_{17}^{-8}-{\zeta }_{17}^{-7}-{\zeta }_{17}^{-6}+3{\zeta }_{17}^{-5}+3{\zeta }_{17}^{-3}+{\zeta }_{17}^{-2}+3+{\zeta }_{17}^2+3{\zeta }_{17}^3+3{\zeta }_{17}^5-{\zeta }_{17}^6-{\zeta }_{17}^7+{\zeta }_{17}^8$	$-4{\zeta }_{17}^{-8}-3{\zeta }_{17}^{-7}-3{\zeta }_{17}^{-6}-2{\zeta }_{17}^{-5}-2{\zeta }_{17}^{-3}-4{\zeta }_{17}^{-2}-4{\zeta }_{17}^2-2{\zeta }_{17}^3-2{\zeta }_{17}^5-3{\zeta }_{17}^6-3{\zeta }_{17}^7-4{\zeta }_{17}^8$	$4{\zeta }_{17}^{-8}+2{\zeta }_{17}^{-7}+2{\zeta }_{17}^{-6}+{\zeta }_{17}^{-5}+{\zeta }_{17}^{-3}+4{\zeta }_{17}^{-2}+4+4{\zeta }_{17}^2+{\zeta }_{17}^3+{\zeta }_{17}^5+2{\zeta }_{17}^6+2{\zeta }_{17}^7+4{\zeta }_{17}^8$	$2{\zeta }_{17}^{-7}+2{\zeta }_{17}^{-6}+2{\zeta }_{17}^{-5}+2{\zeta }_{17}^{-3}-1+2{\zeta }_{17}^3+2{\zeta }_{17}^5+2{\zeta }_{17}^6+2{\zeta }_{17}^7$	$-{\zeta }_{17}^{-8}+2{\zeta }_{17}^{-7}+2{\zeta }_{17}^{-6}-2{\zeta }_{17}^{-5}-2{\zeta }_{17}^{-3}-{\zeta }_{17}^{-2}+2-{\zeta }_{17}^2-2{\zeta }_{17}^3-2{\zeta }_{17}^5+2{\zeta }_{17}^6+2{\zeta }_{17}^7-{\zeta }_{17}^8$	$-2{\zeta }_{17}^{-7}-2{\zeta }_{17}^{-6}-2{\zeta }_{17}^{-5}-2{\zeta }_{17}^{-3}-3-2{\zeta }_{17}^3-2{\zeta }_{17}^5-2{\zeta }_{17}^6-2{\zeta }_{17}^7$	$0$	$0$
9248.y.32c3	R	$32$	$0$	$0$	$0$	$0$	$0$	$0$	$0$	$0$	$0$	$0$	$0$	$0$	$0$	$-2$	$-2$	$-2{\zeta }_{17}^{-7}-2{\zeta }_{17}^{-6}-2{\zeta }_{17}^{-5}-2{\zeta }_{17}^{-3}-3-2{\zeta }_{17}^3-2{\zeta }_{17}^5-2{\zeta }_{17}^6-2{\zeta }_{17}^7$	$2{\zeta }_{17}^{-7}+2{\zeta }_{17}^{-6}+2{\zeta }_{17}^{-5}+2{\zeta }_{17}^{-3}-1+2{\zeta }_{17}^3+2{\zeta }_{17}^5+2{\zeta }_{17}^6+2{\zeta }_{17}^7$	$4{\zeta }_{17}^{-8}+2{\zeta }_{17}^{-7}+2{\zeta }_{17}^{-6}+{\zeta }_{17}^{-5}+{\zeta }_{17}^{-3}+4{\zeta }_{17}^{-2}+4+4{\zeta }_{17}^2+{\zeta }_{17}^3+{\zeta }_{17}^5+2{\zeta }_{17}^6+2{\zeta }_{17}^7+4{\zeta }_{17}^8$	${\zeta }_{17}^{-8}-{\zeta }_{17}^{-7}-{\zeta }_{17}^{-6}+3{\zeta }_{17}^{-5}+3{\zeta }_{17}^{-3}+{\zeta }_{17}^{-2}+3+{\zeta }_{17}^2+3{\zeta }_{17}^3+3{\zeta }_{17}^5-{\zeta }_{17}^6-{\zeta }_{17}^7+{\zeta }_{17}^8$	$-{\zeta }_{17}^{-8}+2{\zeta }_{17}^{-7}+2{\zeta }_{17}^{-6}-2{\zeta }_{17}^{-5}-2{\zeta }_{17}^{-3}-{\zeta }_{17}^{-2}+2-{\zeta }_{17}^2-2{\zeta }_{17}^3-2{\zeta }_{17}^5+2{\zeta }_{17}^6+2{\zeta }_{17}^7-{\zeta }_{17}^8$	$-2{\zeta }_{17}^{-7}-2{\zeta }_{17}^{-6}-2{\zeta }_{17}^{-5}-2{\zeta }_{17}^{-3}-3-2{\zeta }_{17}^3-2{\zeta }_{17}^5-2{\zeta }_{17}^6-2{\zeta }_{17}^7$	$-4{\zeta }_{17}^{-8}-3{\zeta }_{17}^{-7}-3{\zeta }_{17}^{-6}-2{\zeta }_{17}^{-5}-2{\zeta }_{17}^{-3}-4{\zeta }_{17}^{-2}-4{\zeta }_{17}^2-2{\zeta }_{17}^3-2{\zeta }_{17}^5-3{\zeta }_{17}^6-3{\zeta }_{17}^7-4{\zeta }_{17}^8$	$2{\zeta }_{17}^{-7}+2{\zeta }_{17}^{-6}+2{\zeta }_{17}^{-5}+2{\zeta }_{17}^{-3}-1+2{\zeta }_{17}^3+2{\zeta }_{17}^5+2{\zeta }_{17}^6+2{\zeta }_{17}^7$	$0$	$0$
9248.y.32c4	R	$32$	$0$	$0$	$0$	$0$	$0$	$0$	$0$	$0$	$0$	$0$	$0$	$0$	$0$	$-2$	$-2$	$-2{\zeta }_{17}^{-7}-2{\zeta }_{17}^{-6}-2{\zeta }_{17}^{-5}-2{\zeta }_{17}^{-3}-3-2{\zeta }_{17}^3-2{\zeta }_{17}^5-2{\zeta }_{17}^6-2{\zeta }_{17}^7$	$2{\zeta }_{17}^{-7}+2{\zeta }_{17}^{-6}+2{\zeta }_{17}^{-5}+2{\zeta }_{17}^{-3}-1+2{\zeta }_{17}^3+2{\zeta }_{17}^5+2{\zeta }_{17}^6+2{\zeta }_{17}^7$	$-4{\zeta }_{17}^{-8}-3{\zeta }_{17}^{-7}-3{\zeta }_{17}^{-6}-2{\zeta }_{17}^{-5}-2{\zeta }_{17}^{-3}-4{\zeta }_{17}^{-2}-4{\zeta }_{17}^2-2{\zeta }_{17}^3-2{\zeta }_{17}^5-3{\zeta }_{17}^6-3{\zeta }_{17}^7-4{\zeta }_{17}^8$	$-{\zeta }_{17}^{-8}+2{\zeta }_{17}^{-7}+2{\zeta }_{17}^{-6}-2{\zeta }_{17}^{-5}-2{\zeta }_{17}^{-3}-{\zeta }_{17}^{-2}+2-{\zeta }_{17}^2-2{\zeta }_{17}^3-2{\zeta }_{17}^5+2{\zeta }_{17}^6+2{\zeta }_{17}^7-{\zeta }_{17}^8$	${\zeta }_{17}^{-8}-{\zeta }_{17}^{-7}-{\zeta }_{17}^{-6}+3{\zeta }_{17}^{-5}+3{\zeta }_{17}^{-3}+{\zeta }_{17}^{-2}+3+{\zeta }_{17}^2+3{\zeta }_{17}^3+3{\zeta }_{17}^5-{\zeta }_{17}^6-{\zeta }_{17}^7+{\zeta }_{17}^8$	$-2{\zeta }_{17}^{-7}-2{\zeta }_{17}^{-6}-2{\zeta }_{17}^{-5}-2{\zeta }_{17}^{-3}-3-2{\zeta }_{17}^3-2{\zeta }_{17}^5-2{\zeta }_{17}^6-2{\zeta }_{17}^7$	$4{\zeta }_{17}^{-8}+2{\zeta }_{17}^{-7}+2{\zeta }_{17}^{-6}+{\zeta }_{17}^{-5}+{\zeta }_{17}^{-3}+4{\zeta }_{17}^{-2}+4+4{\zeta }_{17}^2+{\zeta }_{17}^3+{\zeta }_{17}^5+2{\zeta }_{17}^6+2{\zeta }_{17}^7+4{\zeta }_{17}^8$	$2{\zeta }_{17}^{-7}+2{\zeta }_{17}^{-6}+2{\zeta }_{17}^{-5}+2{\zeta }_{17}^{-3}-1+2{\zeta }_{17}^3+2{\zeta }_{17}^5+2{\zeta }_{17}^6+2{\zeta }_{17}^7$	$0$	$0$

Regular extensions

Data not computed