Finite Group DatabasebetaFinite Group Databasebeta| order | 18150 |
| isoclinism | isoclinic class of #3874 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C112 · Schur multiplier (H2) = C11 |
| direct product | C112×#3874 |
| Fitting, socle, Hall | C52×C112 ⋊ D3 |
| derived, Hall | C52⋊C3 ⋊ C2×C112 |
| Hall | C112×C52⋊C3 ⋊ C2 |
| Sylow | C52 ⋊ D3×C112 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C112 | #3874 |
| commutator, cosocle, hypocenter | C52⋊C3 | C2×C112 |
| Frattini | C1 | G |
| Fitting, socle | C52×C112 | D3 |
| LCS | G ▷ C52⋊C3 | |
| UCS | C1 ◁ C112 | |
168 conjugacy classes of subgroups.
| transitive degree | μt(G) = 1815 |
1573 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C11×D11×#3874, #3874×C11⋊D11, C112×#3874⋊C2, … |
| maximal normal subgroup of | C11×D11×#3874, #3874×C11⋊D11, C112×#3874⋊C2, … |
| maximal quotient of | C112×#64470, C2×C112×#3874 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(18150, 169);