Finite Group DatabasebetaFinite Group Databasebeta| order | 35244 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C3×C11 · Schur multiplier (H2) = C2 |
| Fitting, socle, Hall | C32×C89 ⋊ C22×C11 |
| derived | C3×C89 ⋊ C22×C3×C11 |
| Hall | C32×C89⋊C11 ⋊ C22 |
| Hall | C3×D3×D89 ⋊ C11 |
| Hall | C89⋊C11 ⋊ C2×C3×D3 |
| Sylow | C89 ⋊ C2×C3×D3×C11 |
| Sylow | C32 ⋊ C2×D89⋊C11 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C3 | D3×D89⋊C11 |
| commutator, cosocle, hypocenter | C3×C89 | C22×C3×C11 |
| Frattini | C1 | G |
| Fitting, socle | C32×C89 | C22×C11 |
| LCS | G ▷ C3×C89 | |
| UCS | C1 ◁ C3 | |
88 conjugacy classes of subgroups.
| transitive degree | μt(G) = 534 |
234 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(35244, 65);