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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 |
Results are complete for degrees $\leq 23$.