Finite Group DatabasebetaFinite Group Databasebeta| order | 26532 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C3×C11 · Schur multiplier (H2) = C2 |
| Fitting, socle | C2×C3×C67 ⋊ C2×C3×C11 |
| derived | C3×C67 ⋊ C22×C3×C11 |
| Hall | C3×(C67⋊C3)⋊C11 ⋊ C22 |
| Hall | C2×C3⋊(D67⋊C3) ⋊ C11 |
| Hall | C67⋊C11 ⋊ C2×C3×D3 |
| Hall | C3×C67⋊C3 ⋊ C22×C11 |
| Sylow | C67 ⋊ C2×C3×D3×C11 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2 | C3⋊AGL(1,𝔽67) |
| commutator, cosocle, hypocenter | C3×C67 | C22×C3×C11 |
| Frattini | C1 | G |
| Fitting, socle | C2×C3×C67 | C2×C3×C11 |
| LCS | G ▷ C3×C67 | |
| UCS | C1 ◁ C2 | |
88 conjugacy classes of subgroups.
| transitive degree | μt(G) = 402 |
204 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(26532, 84);