Finite Group DatabasebetaFinite Group Databasebeta| order | 26862 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C3 · Schur multiplier (H2) = C11 |
| unambiguous semidirect product | (C11⋊D11)⋊(C37⋊C3) |
| Fitting, socle, derived, Hall | C112×C37 ⋊ C2×C3 |
| Hall | C37⋊(C112⋊C3) ⋊ C2 |
| Hall | C37×C11⋊D11 ⋊ C3 |
| Hall | C11⋊D11 ⋊ C37⋊C3 |
| Sylow | C112 ⋊ C2×C37⋊C3 |
| Sylow | C37 ⋊ (C11⋊D11)⋊C3 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, cosocle, hypocenter | C112×C37 | C2×C3 |
| LCS | G ▷ C112×C37 | |
| UCS | C1 | |
32 conjugacy classes of subgroups.
| transitive degree | μt(G) = 1221 |
Polycyclic presentation:
2,3,11^2,37|c^a=c^10,d^a=d^10,c^b=c^3d^9,d^b=cd^7,e^b=e^26770 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(26862, 20);