Finite Group DatabasebetaFinite Group Databasebeta| order | 26862 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C3×C37 · Schur multiplier (H2) = C11 |
| direct product | C37×(C11⋊D11)⋊C3 |
| unambiguous semidirect product | (C11⋊D11)⋊(C3×C37) |
| Fitting, socle, Hall | C112×C37 ⋊ C2×C3 |
| derived, Sylow | C112 ⋊ C2×C3×C37 |
| Hall | C37×C112⋊C3 ⋊ C2 |
| Hall | C37×C11⋊D11 ⋊ C3 |
| Hall | C112⋊C3 ⋊ C2×C37 |
| Hall | C11⋊D11 ⋊ C3×C37 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C37 | (C11⋊D11)⋊C3 |
| commutator, cosocle, hypocenter | C112 | C2×C3×C37 |
| Frattini | C1 | G |
| Fitting, socle | C112×C37 | C2×C3 |
| LCS | G ▷ C112 | |
| UCS | C1 ◁ C37 | |
32 conjugacy classes of subgroups.
| transitive degree | μt(G) = 1221 |
962 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(26862, 18);