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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 164 matches)

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Label Name Order Parity Solvable Subfields Low Degree Siblings
21T1 $C_{21}$ $21$ $1$ ✓ $C_3$, $C_7$
21T2 $C_7:C_3$ $21$ $1$ ✓ $C_3$, $C_7:C_3$ 7T3
21T3 $C_3\times D_7$ $42$ $-1$ ✓ $C_3$, $D_{7}$ 42T3
21T4 $F_7$ $42$ $-1$ ✓ $C_3$, $F_7$ 7T4, 14T4, 42T4
21T5 $D_{21}$ $42$ $1$ ✓ $S_3$, $D_{7}$ 42T5
21T6 $S_3\times C_7$ $42$ $-1$ ✓ $S_3$, $C_7$ 42T6
21T7 $C_{21}:C_3$ $63$ $1$ ✓ $C_3$, $C_7:C_3$ 21T7 x 2
21T8 $S_3\times D_7$ $84$ $-1$ ✓ $S_3$, $D_{7}$ 42T13, 42T14, 42T15
21T9 $C_3\times F_7$ $126$ $-1$ ✓ $C_3$, $F_7$ 21T9 x 2, 42T17 x 3
21T10 $C_{21}:C_6$ $126$ $1$ ✓ $S_3$, $F_7$ 42T18, 42T22
21T11 $C_{21}:C_6$ $126$ $-1$ ✓ $S_3$, $C_7:C_3$ 42T19, 42T23
21T12 $C_7^2:C_3$ $147$ $1$ ✓ $C_3$ 21T12
21T13 $C_7:C_{21}$ $147$ $1$ ✓ $C_3$ 21T13
21T14 $\PSL(2,7)$ $168$ $1$ $\GL(3,2)$ x 2 7T5 x 2, 8T37, 14T10 x 2, 24T284, 28T32, 42T37, 42T38 x 2
21T15 $S_3\times F_7$ $252$ $-1$ ✓ $S_3$, $F_7$ 42T43, 42T44, 42T45, 42T52
21T16 $C_7:F_7$ $294$ $-1$ ✓ $C_3$ 21T16, 42T55 x 2
21T17 $C_7^2:S_3$ $294$ $1$ ✓ $S_3$ 14T15, 21T18, 42T56, 42T57, 42T62
21T18 $C_7^2:S_3$ $294$ $-1$ ✓ $S_3$ 14T15, 21T17, 42T56, 42T57, 42T62
21T19 $C_7:F_7$ $294$ $-1$ ✓ $C_3$ 21T19, 42T58 x 2
21T20 $\PGL(2,7)$ $336$ $-1$ 8T43, 14T16, 16T713, 24T707, 28T42, 28T46, 42T81, 42T82, 42T83
21T21 $C_7^2:C_3^2$ $441$ $1$ ✓ $C_3$ 21T21
21T22 $C_3\times \GL(3,2)$ $504$ $1$ $C_3$, $\GL(3,2)$ 21T22, 24T1355 x 2, 24T1356, 42T96 x 2, 42T103 x 2
21T23 $C_7^2:D_6$ $588$ $-1$ ✓ $S_3$ 14T25, 21T23, 28T78, 42T110 x 2, 42T111 x 2, 42T112 x 2, 42T122
21T24 $C_7:(C_3\times F_7)$ $882$ $-1$ ✓ $C_3$ 21T24, 42T142 x 2
21T25 $C_7^2:(C_3\times S_3)$ $882$ $1$ ✓ $S_3$ 14T26, 21T26, 42T143, 42T144, 42T152, 42T153, 42T154, 42T155
21T26 $C_7^2:(C_3\times S_3)$ $882$ $-1$ ✓ $S_3$ 14T26, 21T25, 42T143, 42T144, 42T152, 42T153, 42T154, 42T155
21T27 $S_3\times \GL(3,2)$ $1008$ $-1$ $S_3$, $\GL(3,2)$ 21T27, 24T2671, 42T169 x 2, 42T170 x 2, 42T171 x 2, 42T175 x 2
21T28 $C_7\wr C_3$ $1029$ $1$ ✓ $C_3$ 21T28 x 11
21T29 $C_7^2:(C_6\times S_3)$ $1764$ $-1$ ✓ $S_3$ 14T37, 21T29, 28T170, 42T223 x 2, 42T224 x 2, 42T225 x 2, 42T252, 42T253, 42T254, 42T255
21T30 $C_7^2:D_{21}$ $2058$ $1$ ✓ $S_3$ 21T30 x 5, 42T267 x 6, 42T280 x 3, 42T283 x 2
21T31 $C_7^3:C_6$ $2058$ $-1$ ✓ $C_3$ 21T31 x 11, 42T268 x 12
21T32 $C_7\wr S_3$ $2058$ $-1$ ✓ $S_3$ 21T32 x 5, 42T269 x 6, 42T281 x 3, 42T282 x 2
21T33 $A_7$ $2520$ $1$ 7T6, 15T47 x 2, 35T28, 42T294, 42T299
21T34 $C_7^3:C_3^2$ $3087$ $1$ ✓ $C_3$ 21T34 x 11
21T35 $C_7^3:C_9$ $3087$ $1$ ✓ $C_3$ 21T35 x 18
21T36 $C_7^3:A_4$ $4116$ $1$ ✓ $C_3$ 28T275, 28T276 x 2, 42T390 x 2, 42T391, 42T406 x 2, 42T407
21T37 $C_7^3:D_6$ $4116$ $-1$ ✓ $S_3$ 21T37 x 5, 42T392 x 6, 42T393 x 6, 42T394 x 6, 42T400 x 3, 42T401 x 2
21T38 $S_7$ $5040$ $-1$ 7T7, 14T46, 30T565, 35T31, 42T411, 42T412, 42T413, 42T418
21T39 $C_3^6:C_7$ $5103$ $1$ ✓ $C_7$ 21T39 x 51
21T40 $C_7^3:(C_3\times S_3)$ $6174$ $-1$ ✓ $S_3$ 21T40 x 5, 42T464 x 6, 42T473 x 3, 42T474 x 2
21T41 $C_3^4.S_3^2$ $6174$ $1$ ✓ $S_3$ 21T41 x 5, 42T465 x 6, 42T472 x 3, 42T475 x 2
21T42 $C_7^3:C_{18}$ $6174$ $-1$ ✓ $C_3$ 21T42 x 18, 42T466 x 19
21T43 $C_5^4:D_4$ $6174$ $-1$ ✓ $C_3$ 21T43 x 11, 42T467 x 12
21T44 $C_3\times A_7$ $7560$ $1$ $C_3$, $A_7$ 45T442 x 2
21T45 $D_7\wr C_3$ $8232$ $-1$ ✓ $C_3$ 28T349, 28T350 x 2, 42T533, 42T534, 42T535 x 2, 42T536 x 2, 42T537, 42T545 x 2, 42T546
21T46 $C_7^3:S_4$ $8232$ $-1$ ✓ $S_3$ 28T347, 42T538, 42T539, 42T540, 42T548
21T47 $C_7^3:S_4$ $8232$ $1$ ✓ $S_3$ 28T348, 42T541, 42T542, 42T543, 42T547
21T48 $C_7^3:\He_3$ $9261$ $1$ ✓ $C_3$ 21T48 x 3
21T49 $C_7^3:C_9:C_3$ $9261$ $1$ ✓ $C_3$
21T50 $C_3^6.C_{14}$ $10206$ $-1$ ✓ $C_7$ 21T50 x 51, 42T554 x 52
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Results are complete for degrees $\leq 23$.