Finite Group DatabasebetaFinite Group Databasebeta| order | 26532 |
| automorphism | ? |
| homology | Abelianization (H1) = C32×C11 · Schur multiplier (H2) = C2×C3 |
| direct product | C11×A4×C67⋊C3 |
| unambiguous semidirect product | (C11×C22⋊(C67⋊C3))⋊C3 |
| unambiguous semidirect product | (C11×A4×C67)⋊C3 |
| unambiguous semidirect product | (C22×C11×C67⋊C3)⋊C3 |
| Fitting, socle, Hall | C22×C11×C67 ⋊ C32 |
| derived, Hall | C22×C67 ⋊ C32×C11 |
| Hall | C11×C67 ⋊ C3×A4 |
| Sylow | C67 ⋊ C3×C11×A4 |
| Hall | C22×C11 ⋊ C3×C67⋊C3 |
| Sylow | C22 ⋊ C3×C11×C67⋊C3 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C11 | A4×C67⋊C3 |
| commutator, cosocle, hypocenter | C22×C67 | C32×C11 |
| Frattini | C1 | G |
| Fitting, socle | C22×C11×C67 | C32 |
| LCS | G ▷ C22×C67 | |
| UCS | C1 ◁ C11 | |
56 conjugacy classes of subgroups.
| transitive degree | μt(G) = 2948 |
1100 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(26532, 109);