Finite Group DatabasebetaFinite Group Databasebeta| order | 10890 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C32×C5 · Schur multiplier (H2) = C3×C11 |
| direct product | C32×#11925893 |
| Fitting, socle, Hall | C32×C112 ⋊ C2×C5 |
| derived, Sylow | C112 ⋊ C2×C32×C5 |
| Hall | C32×#10597245 ⋊ C2 |
| Hall | C32×C11⋊D11 ⋊ C5 |
| Hall | #10597245 ⋊ C2×C32 |
| Hall | C11⋊D11 ⋊ C32×C5 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C32 | #11925893 |
| commutator, cosocle, hypocenter | C112 | C2×C32×C5 |
| Frattini | C1 | G |
| Fitting, socle | C32×C112 | C2×C5 |
| LCS | G ▷ C112 | |
| UCS | C1 ◁ C32 | |
120 conjugacy classes of subgroups.
198 conjugacy classes — view the full character table.
| maximal subgroup of | C32×#11925890⋊C2, C32×#14559075, C32×#11925896⋊C2, … |
| maximal normal subgroup of | C32×#11925890⋊C2, C32×#14559075, C32×#11925896⋊C2, … |
| maximal quotient of | C32×#14559052, C2×C32×#11925893 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(10890, 91);