Finite Group DatabasebetaFinite Group Databasebeta| order | 18150 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C3 · Schur multiplier (H2) = C5×C11 |
| direct product | C2×C52⋊(C112⋊C3) |
| unambiguous semidirect product | (C2×C52)⋊(C112⋊C3) |
| unambiguous semidirect product | (C2×C112)⋊(C52⋊C3) |
| Fitting, socle, Hall | C2×C52×C112 ⋊ C3 |
| derived, Hall | C52×C112 ⋊ C2×C3 |
| Hall | C2×C112 ⋊ C52⋊C3 |
| Sylow | C112 ⋊ C2×C52⋊C3 |
| Hall | C2×C52 ⋊ C112⋊C3 |
| Sylow | C52 ⋊ C2×C112⋊C3 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2 | C52⋊(C112⋊C3) |
| commutator, cosocle, hypocenter | C52×C112 | C2×C3 |
| Frattini | C1 | G |
| Fitting, socle | C2×C52×C112 | C3 |
| LCS | G ▷ C52×C112 | |
| UCS | C1 ◁ C2 | |
88 conjugacy classes of subgroups.
| transitive degree | μt(G) = 330 |
2022 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #49137292, #49137296, #1039⋊(C112⋊C3), … |
| maximal normal subgroup of | #49137292, #49137296, #1039⋊(C112⋊C3), … |
| maximal quotient of | C4×C52⋊(C112⋊C3), C22×C52⋊(C112⋊C3) |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(18150, 185);