Finite Group DatabasebetaFinite Group Databasebeta| order | 26532 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C32×C11 · Schur multiplier (H2) = C2×C3 |
| direct product | C2×C3×C11×D67⋊C3 |
| unambiguous semidirect product | (C2×C11×D67)⋊C32 |
| unambiguous semidirect product | (C2×C3×C11×D67)⋊C3 |
| Fitting, socle | C2×C3×C11×C67 ⋊ C2×C3 |
| derived, Sylow | C67 ⋊ C22×C32×C11 |
| Hall | C3×C11×C67⋊C3 ⋊ C22 |
| Hall | C2×C11×D67 ⋊ C32 |
| Hall | C11×C67 ⋊ C22×C32 |
| Hall | C3×C67⋊C3 ⋊ C22×C11 |
| Hall | C2×D67 ⋊ C32×C11 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2×C3×C11 | D67⋊C3 |
| commutator, cosocle, hypocenter | C67 | C22×C32×C11 |
| Frattini | C1 | G |
| Fitting, socle | C2×C3×C11×C67 | C2×C3 |
| LCS | G ▷ C67 | |
| UCS | C1 ◁ C2×C3×C11 | |
120 conjugacy classes of subgroups.
| transitive degree | μt(G) = 4422 |
1122 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(26532, 110);