Finite Group DatabasebetaFinite Group Databasebeta| order | 26862 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C3 · Schur multiplier (H2) = C11 |
| unambiguous semidirect product | C11⋊(C11⋊(D37⋊C3)) |
| unambiguous semidirect product | (C37⋊C3)⋊(C11⋊D11) |
| Fitting, socle, derived, Hall | C112×C37 ⋊ C2×C3 |
| Hall | C112×C37⋊C3 ⋊ C2 |
| Hall | C11⋊D407 ⋊ C3 |
| Sylow | C112 ⋊ D37⋊C3 |
| Hall | C37⋊C3 ⋊ C11⋊D11 |
| Sylow | C37 ⋊ C3×C11⋊D11 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, cosocle, hypocenter | C112×C37 | C2×C3 |
| LCS | G ▷ C112×C37 | |
| UCS | C1 | |
112 conjugacy classes of subgroups.
| minimal degree | μ(G) = 59 |
| transitive degree | μt(G) = 4477 |
A minimal faithful permutation representation — 3 generators on 59 points:
(2,6,7,3,4,8)(5,14,15,9,10,23)(11,26,27,17,18,34)(12,25,21,19,16,13)(20,36,37,29,28,32)(22,24,35,31,30,33)(39,40)(41,42)(43,44)(45,46)(47,48)(50,51)(52,53)(54,55)(56,57)(58,59);(1,2,5,11,18,28,33,34,31,21,7,6,12,20,30,10,16,23,32,37,15,25,14,24,29,19,4,8,13,22,27,35,36,26,17,9,3)(49,50,52,54,56,58,59,57,55,53,51);(38,39,41,43,45,47,48,46,44,42,40)Polycyclic presentation:
2,3,11^2,37|c^a=c^10,d^a=d^10,e^a=e^36,e^b=e^26912 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(26862, 25);