Finite Group DatabasebetaFinite Group Databasebeta| order | 18150 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C3×C11 · Schur multiplier (H2) = C5 |
| direct product | C11×C11⋊((C5⋊D5)⋊C3) |
| unambiguous semidirect product | C11⋊(C11×(C5⋊D5)⋊C3) |
| unambiguous semidirect product | (C5⋊D55)⋊(C3×C11) |
| unambiguous semidirect product | (C11×C5⋊D55)⋊C3 |
| Fitting, socle, Hall | C52×C112 ⋊ C2×C3 |
| derived | C52×C11 ⋊ C2×C3×C11 |
| Hall | C112×C52⋊C3 ⋊ C2 |
| Hall | C11×C5⋊D55 ⋊ C3 |
| Sylow | C112 ⋊ (C5⋊D5)⋊C3 |
| Hall | C52⋊C3 ⋊ C11×D11 |
| Sylow | C52 ⋊ C3×C11×D11 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C11 | C11⋊((C5⋊D5)⋊C3) |
| commutator, cosocle, hypocenter | C52×C11 | C2×C3×C11 |
| Frattini | C1 | G |
| Fitting, socle | C52×C112 | C2×C3 |
| LCS | G ▷ C52×C11 | |
| UCS | C1 ◁ C11 | |
78 conjugacy classes of subgroups.
| transitive degree | μt(G) = 330 |
715 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(18150, 174);