Finite Group DatabasebetaFinite Group Databasebeta| order | 18150 |
| isoclinism | isoclinic class of D11 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C3×C52×C11 · Schur multiplier (H2) = C5 |
| direct product | C3×C52×C11×D11 |
| Fitting, socle, Hall | C3×C52×C112 ⋊ C2 |
| derived | C11 ⋊ C2×C3×C52×C11 |
| Hall | C52×C112 ⋊ C2×C3 |
| Hall | C3×C112 ⋊ C2×C52 |
| Sylow | C112 ⋊ C2×C3×C52 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C3×C52×C11 | D11 |
| commutator, cosocle, hypocenter | C11 | C2×C3×C52×C11 |
| Frattini | C1 | G |
| Fitting, socle | C3×C52×C112 | C2 |
| LCS | G ▷ C11 | |
| UCS | C1 ◁ C3×C52×C11 | |
208 conjugacy classes of subgroups.
| transitive degree | μt(G) = 1650 |
5775 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C3×C52×D112, C3×C5×D5×C11×D11, C3×C5×D11×D55, … |
| maximal normal subgroup of | C3×C52×D112, C3×C5×D5×C11×D11, C3×C5×D11×D55, … |
| maximal quotient of | C3×C52×C11×Dic11, C2×C3×C52×C11×D11 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(18150, 204);