Finite Group DatabasebetaFinite Group Databasebeta| order | 31218 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C3 · Schur multiplier (H2) = C11 |
No aliases for this group.
| Fitting, socle, derived, Hall | C112×C43 ⋊ C2×C3 |
| Hall | C43⋊(C112⋊C3) ⋊ C2 |
| Hall | C11⋊D473 ⋊ C3 |
| Sylow | C112 ⋊ D43⋊C3 |
| Sylow | C43 ⋊ (C11⋊D11)⋊C3 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, cosocle, hypocenter | C112×C43 | C2×C3 |
| LCS | G ▷ C112×C43 | |
| UCS | C1 | |
32 conjugacy classes of subgroups.
| minimal degree | μ(G) = 76 |
| transitive degree | μt(G) = 1419 |
A minimal faithful permutation representation — 2 generators on 76 points:
(1,2,4)(3,6,11,7,8,16)(5,24,26,12,13,30)(9,17,25,19,20,28)(10,29,14,22,21,18)(15,31,32,27,23,33)(35,39,40,36,37,41)(38,47,48,42,43,57)(44,60,61,50,51,69)(45,59,55,53,49,46)(52,65,67,56,58,70)(54,71,72,63,62,66)(64,74,75,73,68,76);(1,3,9,21,30,33,32,26,29,19,7)(2,5,14,6,15,20,17,27,8,18,12)(4,10,23,28,11,24,13,16,25,31,22)(34,35,38,44,52,55,40,39,45,54,64,72,48,59,47,58,68,75,61,70,71,60,51,62,67,69,76,74,65,43,49,57,66,73,63,53,37,41,46,56,50,42,36)Polycyclic presentation:
2,3,11^2,43|c^a=c^10,d^a=d^10,e^a=e^42,c^b=c^3d^9,d^b=cd^7,e^b=e^36873 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(31218, 19);