Finite Group DatabasebetaFinite Group Databasebeta| order | 10890 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C5×C9 · Schur multiplier (H2) = C11 |
| direct product | C2×C5×C112⋊C9 |
| unambiguous semidirect product | (C2×C5×C112)⋊C9 |
| derived, Sylow | C112 ⋊ C2×C5×C9 |
| Hall | C2×C5×C112 ⋊ C9 |
| Hall | C5×C112 ⋊ C2×C9 |
| Hall | C2×C112 ⋊ C5×C9 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2×C3×C5 | C112⋊C3 |
| commutator, hypocenter | C112 | C2×C5×C9 |
| Frattini | C3 | C2×C5×C112⋊C3 |
| Fitting, socle, prime radical | C2×C3×C5×C112 | C3 |
| cosocle | C3×C112 | C2×C3×C5 |
| LCS | G ▷ C112 | |
| UCS | C1 ◁ C2×C3×C5 | |
56 conjugacy classes of subgroups.
1290 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C5×#17983705, C5×(C11⋊Dic11)⋊C9, #36344802, … |
| maximal normal subgroup of | C5×#17983705, C5×(C11⋊Dic11)⋊C9, #36344802, … |
| maximal quotient of | C4×C5×C112⋊C9, C22×C5×C112⋊C9 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(10890, 70);