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Parity Cyclic Solvable Primitive Equivalent siblings
Degree $T$-number Order Group Nilpotency class
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Results (1-50 of 2392 matches)

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Label Name Order Parity Solvable Subfields Low Degree Siblings
27T1 $C_{27}$ $27$ $1$ ✓ $C_3$, $C_9$
27T2 $C_3\times C_9$ $27$ $1$ ✓ $C_3$ x 4, $C_9$ x 3, $C_3^2$
27T3 $\He_3$ $27$ $1$ ✓ $C_3$ x 4, $C_3^2$, $C_3^2:C_3$ x 4 9T7 x 4
27T4 $C_3^3$ $27$ $1$ ✓ $C_3$ x 13, $C_3^2$ x 13
27T5 $C_9:C_3$ $27$ $1$ ✓ $C_3$ x 4, $C_3^2$, $C_9:C_3$ 9T6
27T6 $C_3^2:S_3$ $54$ $1$ ✓ $S_3$ x 4, $C_3^2:C_2$, $(C_3^2:C_3):C_2$ x 4 9T12 x 4, 18T24 x 4
27T7 $C_3^2:S_3$ $54$ $-1$ ✓ $S_3$ x 13, $C_3^2:C_2$ x 13
27T8 $D_{27}$ $54$ $-1$ ✓ $S_3$, $D_{9}$
27T9 $C_3\times D_9$ $54$ $1$ ✓ $C_3$, $S_3$, $D_{9}$, $S_3\times C_3$ 18T19
27T10 $C_3:D_9$ $54$ $-1$ ✓ $S_3$ x 4, $D_{9}$ x 3, $C_3^2:C_2$
27T11 $C_3^2:C_6$ $54$ $1$ ✓ $C_3$, $S_3$, $S_3\times C_3$, $C_3^2 : C_6$, $C_3^2 : S_3 $ 9T11, 9T13, 18T20, 18T21, 18T22
27T12 $S_3\times C_9$ $54$ $-1$ ✓ $C_3$, $S_3$, $C_9$, $S_3\times C_3$ 18T16
27T13 $C_3^2:C_6$ $54$ $1$ ✓ $C_3$, $S_3$ x 4, $S_3\times C_3$ x 4, $C_3^2:C_2$ 18T23 x 4
27T14 $C_9:C_6$ $54$ $1$ ✓ $C_3$, $S_3$, $S_3\times C_3$, $(C_9:C_3):C_2$ 9T10, 18T18
27T15 $S_3\times C_3^2$ $54$ $-1$ ✓ $C_3$ x 4, $S_3$, $C_3^2$, $S_3\times C_3$ x 4 18T17 x 4
27T16 $C_9:C_3^2$ $81$ $1$ ✓ $C_3$ x 4, $C_3^2$, $C_9:C_3$ x 3 27T16 x 2
27T17 $C_3^2:C_9$ $81$ $1$ ✓ $C_3$, $C_9$, $C_9:C_3$ x 2, $C_3^2:C_3$ 27T17 x 2
27T18 $C_3\times \He_3$ $81$ $1$ ✓ $C_3$ x 4, $C_3^2$, $C_3^2:C_3$ x 3 27T18 x 11
27T19 $C_3\wr C_3$ $81$ $1$ ✓ $C_3$ x 4, $C_3^2$, $C_3 \wr C_3 $ x 3 9T17 x 3, 27T21, 27T27 x 3
27T20 $C_3.\He_3$ $81$ $1$ ✓ $C_3$, $C_3^2:C_3$ 27T26
27T21 $C_3\wr C_3$ $81$ $1$ ✓ $C_3$, $C_3^2:C_3$ 9T17 x 3, 27T19, 27T27 x 3
27T22 $C_{27}:C_3$ $81$ $1$ ✓ $C_3$, $C_9$
27T23 $\He_3:C_3$ $81$ $1$ ✓ $C_3$, $C_3^2:C_3$ 27T23 x 2, 27T24
27T24 $\He_3:C_3$ $81$ $1$ ✓ $C_3$ x 4, $C_3^2$ 27T23 x 3
27T25 $C_3.\He_3$ $81$ $1$ ✓ $C_3$ x 4, $C_3^2$
27T26 $C_3.\He_3$ $81$ $1$ ✓ $C_3$ x 4, $C_3^2$ 27T20
27T27 $C_3\wr C_3$ $81$ $1$ ✓ $C_3$, $C_3^2:C_3$, $C_3 \wr C_3 $ x 2 9T17 x 3, 27T19, 27T21, 27T27 x 2
27T28 $C_9.C_3^2$ $81$ $1$ ✓ $C_3$ x 4, $C_3^2$ 27T28 x 3
27T29 $C_3^2:D_6$ $108$ $1$ ✓ $S_3$ x 2, $S_3^2$, $C_3^2 : D_{6} $ x 2 9T18 x 2, 18T51 x 2, 18T55 x 2, 18T56, 18T57 x 2, 36T87 x 2, 36T90
27T30 $S_3\times D_9$ $108$ $-1$ ✓ $S_3$ x 2, $D_{9}$, $S_3^2$ 18T50, 36T86
27T31 $C_3^3:C_4$ $108$ $-1$ ✓ $S_3$, $C_3^2:C_4$ 12T72 x 2, 18T54 x 2, 36T89 x 2, 36T94 x 2
27T32 $\He_3:C_4$ $108$ $1$ ✓ $C_3^2:C_4$ 18T49 x 2, 36T85 x 2
27T33 $C_3^2:C_{12}$ $108$ $1$ ✓ $C_3$, $C_3^2:C_4$ 12T73 x 2, 18T44 x 2, 36T81 x 2, 36T95 x 2
27T34 $C_3:S_3^2$ $108$ $-1$ ✓ $S_3$ x 5, $C_3^2:C_2$, $S_3^2$ x 4 18T58 x 4, 36T91 x 4
27T35 $C_3:S_3^2$ $108$ $1$ ✓ $S_3$ x 3, $S_3^2$ x 3 12T71, 18T53 x 3, 36T88 x 3, 36T93
27T36 $C_3\times S_3^2$ $108$ $-1$ ✓ $C_3$, $S_3$ x 2, $S_3\times C_3$ x 2, $S_3^2$ 12T70, 18T43, 18T46 x 2, 36T80, 36T82 x 2, 36T92
27T37 $C_3\wr S_3$ $162$ $-1$ ✓ $C_3$, $S_3$, $S_3\times C_3$, $C_3 \wr S_3 $ x 3 9T20 x 3, 18T86 x 3, 27T50 x 3, 27T70
27T38 $\He_3.S_3$ $162$ $1$ ✓ $C_3$, $S_3$, $S_3\times C_3$ 27T64
27T39 $\He_3.C_6$ $162$ $-1$ ✓ $C_3$, $S_3$, $S_3\times C_3$ 27T39 x 3
27T40 $\He_3.C_6$ $162$ $-1$ ✓ $C_3$, $S_3$, $S_3\times C_3$ 27T49
27T41 $\He_3.S_3$ $162$ $1$ ✓ $C_3$, $S_3$, $S_3\times C_3$ 27T72
27T42 $\He_3.S_3$ $162$ $-1$ ✓ $S_3$ x 4, $C_3^2:C_2$ 27T68
27T43 $(C_3\times C_9).S_3$ $162$ $-1$ ✓ $S_3$ x 4, $C_3^2:C_2$
27T44 $\He_3:S_3$ $162$ $-1$ ✓ $S_3$ x 4, $C_3^2:C_2$ 27T66 x 3
27T45 $\He_3.C_6$ $162$ $-1$ ✓ $C_3$, $S_3$, $S_3\times C_3$ 27T69
27T46 $C_3^3:S_3$ $162$ $-1$ ✓ $C_3$, $S_3$, $S_3\times C_3$, $(C_3^2:C_3):C_2$ x 3 27T46 x 3
27T47 $C_3^2:C_{18}$ $162$ $-1$ ✓ $C_3$, $C_9$, $C_3^2 : S_3 $ 18T82
27T48 $C_3^3:C_6$ $162$ $-1$ ✓ $C_3$ x 4, $C_3^2$, $C_3^2 : S_3 $ 18T76, 18T78, 18T81 x 2, 27T60 x 3
27T49 $\He_3.C_6$ $162$ $-1$ ✓ $C_3$, $C_3^2 : S_3 $ 27T40
27T50 $C_3\wr S_3$ $162$ $1$ ✓ $S_3$, $C_3^2 : C_6$, $C_3 \wr S_3 $ 9T20 x 3, 18T86 x 3, 27T37, 27T50 x 2, 27T70
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Results are complete for degrees $\leq 23$.