Finite Group DatabasebetaFinite Group Databasebeta| order | 18150 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C3 · Schur multiplier (H2) = C5×C11 |
| direct product | C52⋊C3×C11⋊D11 |
| unambiguous semidirect product | C11⋊(D11×C52⋊C3) |
| Fitting, socle, derived, Hall | C52×C112 ⋊ C2×C3 |
| Hall | C112×C52⋊C3 ⋊ C2 |
| Hall | C52×C11⋊D11 ⋊ C3 |
| Sylow | C112 ⋊ C2×C52⋊C3 |
| Sylow | C52 ⋊ C3×C11⋊D11 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, cosocle, hypocenter | C52×C112 | C2×C3 |
| LCS | G ▷ C52×C112 | |
| UCS | C1 | |
168 conjugacy classes of subgroups.
| transitive degree | μt(G) = 1815 |
682 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C52⋊C3×#92150, D112×C52⋊C3, #49137548, … |
| maximal normal subgroup of | C52⋊C3×#92150, D112×C52⋊C3, #49137548, … |
| maximal quotient of | C52⋊C3×C11⋊Dic11, C2×C52⋊C3×C11⋊D11 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(18150, 179);