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Parity Cyclic Solvable Primitive Equivalent siblings
Degree $T$-number Order Group Nilpotency class
$\#\Aut(F/K)$ Transitivity
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Results (1-50 of 349 matches)

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Label Name Order Parity Solvable $\#\Aut(F/K)$ Subfields Low Degree Siblings
1T1 Trivial $1$ $1$ ✓ $1$
2T1 $C_2$ $2$ $-1$ ✓ $2$
3T1 $C_3$ $3$ $1$ ✓ $3$
3T2 $S_3$ $6$ $-1$ ✓ $1$ 6T2
4T4 $A_4$ $12$ $1$ ✓ $1$ 6T4, 12T4
4T5 $S_4$ $24$ $-1$ ✓ $1$ 6T7, 6T8, 8T14, 12T8, 12T9, 24T10
5T1 $C_5$ $5$ $1$ ✓ $5$
5T2 $D_{5}$ $10$ $1$ ✓ $1$ 10T2
5T3 $F_5$ $20$ $-1$ ✓ $1$ 10T4, 20T5
5T4 $A_5$ $60$ $1$ $1$ 6T12, 10T7, 12T33, 15T5, 20T15, 30T9
5T5 $S_5$ $120$ $-1$ $1$ 6T14, 10T12, 10T13, 12T74, 15T10, 20T30, 20T32, 20T35, 24T202, 30T22, 30T25, 30T27, 40T62
6T12 $\PSL(2,5)$ $60$ $1$ $1$ 5T4, 10T7, 12T33, 15T5, 20T15, 30T9
6T14 $\PGL(2,5)$ $120$ $-1$ $1$ 5T5, 10T12, 10T13, 12T74, 15T10, 20T30, 20T32, 20T35, 24T202, 30T22, 30T25, 30T27, 40T62
6T15 $A_6$ $360$ $1$ $1$ 6T15, 10T26, 15T20 x 2, 20T89, 30T88 x 2, 36T555, 40T304, 45T49
6T16 $S_6$ $720$ $-1$ $1$ 6T16, 10T32, 12T183 x 2, 15T28 x 2, 20T145, 20T149 x 2, 30T164 x 2, 30T166 x 2, 30T176 x 2, 36T1252, 40T589, 40T592 x 2, 45T96
7T1 $C_7$ $7$ $1$ ✓ $7$
7T2 $D_{7}$ $14$ $-1$ ✓ $1$ 14T2
7T3 $C_7:C_3$ $21$ $1$ ✓ $1$ 21T2
7T4 $F_7$ $42$ $-1$ ✓ $1$ 14T4, 21T4, 42T4
7T5 $\GL(3,2)$ $168$ $1$ $1$ 7T5, 8T37, 14T10 x 2, 21T14, 24T284, 28T32, 42T37, 42T38 x 2
7T6 $A_7$ $2520$ $1$ $1$ 15T47 x 2, 21T33, 35T28, 42T294, 42T299
7T7 $S_7$ $5040$ $-1$ $1$ 14T46, 21T38, 30T565, 35T31, 42T411, 42T412, 42T413, 42T418
8T25 $C_2^3:C_7$ $56$ $1$ ✓ $1$ 14T6, 28T11
8T36 $C_2^3:(C_7: C_3)$ $168$ $1$ ✓ $1$ 14T11, 24T283, 28T27, 42T26
8T37 $\PSL(2,7)$ $168$ $1$ $1$ 7T5 x 2, 14T10 x 2, 21T14, 24T284, 28T32, 42T37, 42T38 x 2
8T43 $\PGL(2,7)$ $336$ $-1$ $1$ 14T16, 16T713, 21T20, 24T707, 28T42, 28T46, 42T81, 42T82, 42T83
8T48 $C_2^3:\GL(3,2)$ $1344$ $1$ $1$ 8T48, 14T34 x 2, 28T153, 28T159 x 2, 42T210 x 2, 42T211 x 2
8T49 $A_8$ $20160$ $1$ $1$ 15T72 x 2, 28T433, 35T36
8T50 $S_8$ $40320$ $-1$ $1$ 16T1838, 28T502, 30T1153, 35T44
9T9 $C_3^2:C_4$ $36$ $1$ ✓ $1$ 6T10 x 2, 12T17 x 2, 18T10, 36T14
9T14 $C_3^2:Q_8$ $72$ $1$ ✓ $1$ 12T47, 18T35 x 3, 24T82, 36T55
9T15 $C_3^2:C_8$ $72$ $-1$ ✓ $1$ 12T46, 18T28, 24T81, 36T49
9T16 $S_3^2:C_2$ $72$ $-1$ ✓ $1$ 6T13 x 2, 12T34 x 2, 12T35 x 2, 12T36 x 2, 18T34 x 2, 18T36, 24T72 x 2, 36T53, 36T54 x 2
9T19 $(C_3^2:C_8):C_2$ $144$ $-1$ ✓ $1$ 12T84, 18T68, 18T71, 18T73, 24T278, 24T279, 24T280, 36T171, 36T172, 36T175
9T23 $(C_3^2:Q_8):C_3$ $216$ $1$ ✓ $1$ 12T122, 24T562, 24T569, 27T82, 36T287, 36T309
9T26 $((C_3^2:Q_8):C_3):C_2$ $432$ $-1$ ✓ $1$ 12T157, 18T157, 24T1325, 24T1326, 24T1327, 24T1334, 27T139, 36T689, 36T709
9T27 $\PSL(2,8)$ $504$ $1$ $1$ 28T70, 36T712
9T32 $\mathrm{P}\Gamma\mathrm{L}(2,8)$ $1512$ $1$ $1$ 27T391, 28T165, 36T2342
9T33 $A_9$ $181440$ $1$ $1$ 36T23796
9T34 $S_9$ $362880$ $-1$ $1$ 18T887, 36T28590
10T7 $A_{5}$ $60$ $1$ $1$ 5T4, 6T12, 12T33, 15T5, 20T15, 30T9
10T13 $S_5$ $120$ $-1$ $1$ 5T5, 6T14, 10T12, 12T74, 15T10, 20T30, 20T32, 20T35, 24T202, 30T22, 30T25, 30T27, 40T62
10T26 $\PSL(2,9)$ $360$ $1$ $1$ 6T15 x 2, 15T20 x 2, 20T89, 30T88 x 2, 36T555, 40T304, 45T49
10T30 $\PGL(2,9)$ $720$ $-1$ $1$ 12T182, 20T146, 30T171, 36T1254, 40T590, 45T110
10T31 $M_{10}$ $720$ $1$ $1$ 12T181, 20T148, 20T150 x 2, 30T162, 36T1253, 40T591, 45T109
10T32 $S_{6}$ $720$ $-1$ $1$ 6T16 x 2, 12T183 x 2, 15T28 x 2, 20T145, 20T149 x 2, 30T164 x 2, 30T166 x 2, 30T176 x 2, 36T1252, 40T589, 40T592 x 2, 45T96
10T35 $(A_6 : C_2) : C_2$ $1440$ $-1$ $1$ 12T220, 20T201, 20T204, 20T208, 24T2960, 30T264, 36T2341, 40T1198, 40T1199, 40T1201, 45T187
10T44 $A_{10}$ $1814400$ $1$ $1$ 45T1982
10T45 $S_{10}$ $3628800$ $-1$ $1$ 20T1007, 45T2246
11T1 $C_{11}$ $11$ $1$ ✓ $11$
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