Finite Group DatabasebetaFinite Group Databasebeta| order | 18150 |
| isoclinism | isoclinic class of C112⋊C3 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C3×C52 · Schur multiplier (H2) = C5×C11 |
| direct product | C2×C52×C112⋊C3 |
| Fitting, socle, Hall | C2×C52×C112 ⋊ C3 |
| derived, Sylow | C112 ⋊ C2×C3×C52 |
| Hall | C52×C112 ⋊ C2×C3 |
| Hall | C2×C112 ⋊ C3×C52 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2×C52 | C112⋊C3 |
| commutator, cosocle, hypocenter | C112 | C2×C3×C52 |
| Frattini | C1 | G |
| Fitting, socle | C2×C52×C112 | C3 |
| LCS | G ▷ C112 | |
| UCS | C1 ◁ C2×C52 | |
128 conjugacy classes of subgroups.
| transitive degree | μt(G) = 1650 |
2150 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C52×#13089712, C52×(C11⋊Dic11)⋊C3, C5×#20299971, … |
| maximal normal subgroup of | C52×#13089712, C52×(C11⋊Dic11)⋊C3, C5×#20299971, … |
| maximal quotient of | C4×C52×C112⋊C3, C22×C52×C112⋊C3 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(18150, 187);