Finite Group DatabasebetaFinite Group Databasebeta| order | 26862 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C3×C11 · Schur multiplier (H2) = C1 |
| Fitting, socle, Hall | C112×C37 ⋊ C2×C3 |
| derived | C11×C37 ⋊ C2×C3×C11 |
| 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, hypercenter | C11 | C11⋊(D37⋊C3) |
| commutator, cosocle, hypocenter | C11×C37 | C2×C3×C11 |
| Frattini | C1 | G |
| Fitting, socle | C112×C37 | C2×C3 |
| LCS | G ▷ C11×C37 | |
| UCS | C1 ◁ C11 | |
52 conjugacy classes of subgroups.
| transitive degree | μt(G) = 814 |
957 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(26862, 23);