Finite Group DatabasebetaFinite Group Databasebeta| order | 26268 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C3 · Schur multiplier (H2) = C2 |
| direct product | C2×C11⋊(D199⋊C3) |
| unambiguous semidirect product | (C2×C11)⋊(D199⋊C3) |
| unambiguous semidirect product | (C2×C199⋊C3)⋊D11 |
| unambiguous semidirect product | (C2×D2189)⋊C3 |
| Fitting, socle | C2×C11×C199 ⋊ C2×C3 |
| derived, Hall | C11×C199 ⋊ C22×C3 |
| Hall | C2×D2189 ⋊ C3 |
| Hall | C11×C199⋊C3 ⋊ C22 |
| Hall | C199⋊C3 ⋊ C2×D11 |
| Sylow | C199 ⋊ C2×C3×D11 |
| Sylow | C11 ⋊ C2×D199⋊C3 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2 | C11⋊(D199⋊C3) |
| commutator, cosocle, hypocenter | C11×C199 | C22×C3 |
| Frattini | C1 | G |
| Fitting, socle | C2×C11×C199 | C2×C3 |
| LCS | G ▷ C11×C199 | |
| UCS | C1 ◁ C2 | |
40 conjugacy classes of subgroups.
| transitive degree | μt(G) = 4378 |
768 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(26268, 31);