Finite Group DatabasebetaFinite Group Databasebeta| order | 31218 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C3 · Schur multiplier (H2) = C11 |
| unambiguous semidirect product | C11⋊(C11⋊(D43⋊C3)) |
| unambiguous semidirect product | (C43⋊C3)⋊(C11⋊D11) |
| Fitting, socle, derived, Hall | C112×C43 ⋊ C2×C3 |
| Hall | C112×C43⋊C3 ⋊ C2 |
| Hall | C11⋊D473 ⋊ C3 |
| Hall | C43⋊C3 ⋊ C11⋊D11 |
| Sylow | C112 ⋊ D43⋊C3 |
| Sylow | C43 ⋊ C3×C11⋊D11 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, cosocle, hypocenter | C112×C43 | C2×C3 |
| LCS | G ▷ C112×C43 | |
| UCS | C1 | |
112 conjugacy classes of subgroups.
| minimal degree | μ(G) = 65 |
| transitive degree | μt(G) = 5203 |
A minimal faithful permutation representation — 3 generators on 65 points:
(2,3)(4,5)(6,7)(8,9)(10,11)(13,14)(15,16)(17,18)(19,20)(21,22)(24,28,29,25,26,30)(27,36,37,31,32,46)(33,49,50,39,40,58)(34,48,44,42,38,35)(41,54,56,45,47,59)(43,60,61,52,51,55)(53,63,64,62,57,65);(12,13,15,17,19,21,22,20,18,16,14)(23,24,27,33,41,44,29,28,34,43,53,61,37,48,36,47,57,64,50,59,60,49,40,51,56,58,65,63,54,32,38,46,55,62,52,42,26,30,35,45,39,31,25);(1,2,4,6,8,10,11,9,7,5,3)Polycyclic presentation:
2,3,11^2,43|c^a=c^10,d^a=d^10,e^a=e^42,e^b=e^361033 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(31218, 25);