Finite Group DatabasebetaFinite Group Databasebeta| order | 26268 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C3 · Schur multiplier (H2) = C2 |
| direct product | C3×D11×D199 |
| Fitting, socle, Hall | C3×C11×C199 ⋊ C22 |
| derived, Hall | C11×C199 ⋊ C22×C3 |
| Hall | C3×C199 ⋊ C2×D11 |
| Sylow | C199 ⋊ C2×C3×D11 |
| Hall | C3×C11 ⋊ C2×D199 |
| Sylow | C11 ⋊ C2×C3×D199 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C3 | D11×D199 |
| commutator, cosocle, hypocenter | C11×C199 | C22×C3 |
| Frattini | C1 | G |
| Fitting, socle | C3×C11×C199 | C22 |
| LCS | G ▷ C11×C199 | |
| UCS | C1 ◁ C3 | |
40 conjugacy classes of subgroups.
| transitive degree | μt(G) = 6567 |
2121 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(26268, 33);