Finite Group DatabasebetaFinite Group Databasebeta| order | 10890 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C5 · Schur multiplier (H2) = C1 |
| direct product | C5×#14546095 |
| derived, Hall | C112⋊C9 ⋊ C2×C5 |
| Hall | C5×C112⋊C9 ⋊ C2 |
| Hall | C5×C112 ⋊ D9 |
| Sylow | C112 ⋊ C5×D9 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C5 | #14546095 |
| commutator, cosocle, hypocenter | C112⋊C9 | C2×C5 |
| Frattini | C3 | C5×#10624391 |
| Fitting, socle | C3×C5×C112 | D3 |
| LCS | G ▷ C112⋊C9 | |
| UCS | C1 ◁ C5 | |
44 conjugacy classes of subgroups.
405 conjugacy classes — view the full character table.
| maximal subgroup of | C5×#14546095⋊C2, #14546095⋊D5, D5×#14546095, … |
| maximal normal subgroup of | C5×#14546095⋊C2, #14546095⋊D5, D5×#14546095, … |
| maximal quotient of | C5×#17983705, C2×C5×#14546095 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(10890, 61);