Finite Group DatabasebetaFinite Group Databasebeta| order | 10890 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C32×C5 · Schur multiplier (H2) = C3 |
| Fitting, socle | C3×C112 ⋊ C2×C3×C5 |
| derived, Sylow | C112 ⋊ C2×C32×C5 |
| Hall | C3×(C112⋊C3)⋊C5 ⋊ C2 |
| Hall | C3×(C11⋊D11)⋊C3 ⋊ C5 |
| Hall | #11925892 ⋊ C32 |
| Hall | C3×C112⋊C3 ⋊ C2×C5 |
| Hall | #10597243 ⋊ C2×C32 |
| Hall | C11⋊D11 ⋊ C32×C5 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C3 | ((C11⋊D11)⋊C3)⋊C5 |
| commutator, cosocle, hypocenter | C112 | C2×C32×C5 |
| Frattini | C1 | G |
| Fitting, socle | C3×C112 | C2×C3×C5 |
| LCS | G ▷ C112 | |
| UCS | C1 ◁ C3 | |
80 conjugacy classes of subgroups.
102 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(10890, 84);