Finite Group DatabasebetaFinite Group Databasebeta| order | 26532 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C11 · Schur multiplier (H2) = C2 |
| direct product | D3×C3⋊(D67⋊C11) |
| unambiguous semidirect product | (C3×D3)⋊(D67⋊C11) |
| unambiguous semidirect product | (D3×D201)⋊C11 |
| unambiguous semidirect product | (D3×C67⋊C11)⋊D3 |
| Fitting, socle, derived, Hall | C32×C67 ⋊ C22×C11 |
| Hall | C32×C67⋊C11 ⋊ C22 |
| Hall | D3×D201 ⋊ C11 |
| Hall | C67⋊C11 ⋊ D32 |
| Sylow | C67 ⋊ D32×C11 |
| Sylow | C32 ⋊ C2×D67⋊C11 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, cosocle, hypocenter | C32×C67 | C22×C11 |
| LCS | G ▷ C32×C67 | |
| UCS | C1 | |
88 conjugacy classes of subgroups.
| transitive degree | μt(G) = 402 |
126 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(26532, 89);