Finite Group DatabasebetaFinite Group Databasebeta| order | 10890 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C32×C5 · Schur multiplier (H2) = C3×C11 |
| direct product | C2×C32×#10597245 |
| Fitting, socle, Hall | C2×C32×C112 ⋊ C5 |
| derived, Sylow | C112 ⋊ C2×C32×C5 |
| Hall | C32×C112 ⋊ C2×C5 |
| Hall | C2×C112 ⋊ C32×C5 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2×C32 | #10597245 |
| commutator, cosocle, hypocenter | C112 | C2×C32×C5 |
| Frattini | C1 | G |
| Fitting, socle | C2×C32×C112 | C5 |
| LCS | G ▷ C112 | |
| UCS | C1 ◁ C2×C32 | |
120 conjugacy classes of subgroups.
522 conjugacy classes — view the full character table.
| maximal subgroup of | C32×#14559052, C32×#14559055, C32×#14559049, … |
| maximal normal subgroup of | C32×#14559052, C32×#14559055, C32×#14559049, … |
| maximal quotient of | C32×C4×#10597245, C22×C32×#10597245 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(10890, 144);