Finite Group DatabasebetaFinite Group Databasebeta| order | 10890 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C32×C5 · Schur multiplier (H2) = C3 |
| direct product | C32×#11925895 |
| Fitting, socle, Hall | C32×C112 ⋊ C2×C5 |
| derived, Sylow | C112 ⋊ C2×C32×C5 |
| Hall | C32×#10597243 ⋊ C2 |
| Hall | C32×C11×D11 ⋊ C5 |
| Hall | #10597243 ⋊ C2×C32 |
| Hall | C11×D11 ⋊ C32×C5 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C32 | #11925895 |
| commutator, cosocle, hypocenter | C112 | C2×C32×C5 |
| Frattini | C1 | G |
| Fitting, socle | C32×C112 | C2×C5 |
| LCS | G ▷ C112 | |
| UCS | C1 ◁ C32 | |
156 conjugacy classes of subgroups.
225 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(10890, 93);