Finite Group DatabasebetaFinite Group Databasebeta| order | 31758 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C3 · Schur multiplier (H2) = C1 |
No aliases for this group.
| Fitting, socle, derived, Hall | C67×C79 ⋊ C2×C3 |
| Hall | #30629541 ⋊ C2 |
| Hall | D5293 ⋊ C3 |
| Sylow | C79 ⋊ D67⋊C3 |
| Sylow | C67 ⋊ D79⋊C3 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, cosocle, hypocenter | C67×C79 | C2×C3 |
| LCS | G ▷ C67×C79 | |
| UCS | C1 | |
16 conjugacy classes of subgroups.
| minimal degree | μ(G) = 146 |
| transitive degree | μt(G) = 5293 |
A minimal faithful permutation representation — 2 generators on 146 points:
(2,6,7,3,4,8)(5,14,15,9,10,24)(11,27,28,17,18,41)(12,26,22,20,16,13)(19,46,47,30,31,59)(21,44,45,33,29,38)(23,25,43,35,36,39)(32,55,54,40,49,65)(34,62,63,50,48,56)(37,42,61,51,52,57)(53,60,66,58,64,67)(69,73,74,70,71,75)(72,81,82,76,77,91)(78,94,95,84,85,108)(79,93,89,87,83,80)(86,113,114,97,98,129)(88,111,112,100,96,105)(90,92,110,102,103,106)(99,134,135,116,117,145)(101,132,133,119,115,127)(104,109,131,121,118,128)(107,140,139,124,125,123)(120,141,142,126,136,143)(122,130,146,137,138,144);(1,2,5,11,19,32,36,10,16,24,38,54,66,64,31,48,55,57,59,63,28,43,44,27,42,58,51,35,22,7,6,12,21,34,50,33,20,4,8,13,23,37,53,52,18,29,39,41,56,47,61,49,62,46,60,67,65,45,15,26,14,25,40,30,17,9,3)(68,69,72,78,86,99,118,85,96,106,108,127,142,114,131,140,132,113,130,137,121,102,89,74,73,79,88,101,120,124,103,77,83,91,105,123,135,146,117,136,141,134,144,145,139,112,82,93,81,92,107,126,119,100,87,71,75,80,90,104,122,138,98,115,125,128,129,143,133,95,110,111,94,109,116,97,84,76,70)Polycyclic presentation:
2,3,67,79|c^a=c^66,d^a=d^78,c^b=c^37,d^b=d^55888 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(31758, 24);