Finite Group DatabasebetaFinite Group Databasebeta| order | 18990 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C32×C5 · Schur multiplier (H2) = C3 |
| direct product | C2×C32×C211⋊C5 |
| unambiguous semidirect product | (C2×C32×C211)⋊C5 |
| Fitting, socle, Hall | C2×C32×C211 ⋊ C5 |
| derived, Sylow | C211 ⋊ C2×C32×C5 |
| Hall | C32×C211 ⋊ C2×C5 |
| Hall | C2×C211 ⋊ C32×C5 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2×C32 | C211⋊C5 |
| commutator, cosocle, hypocenter | C211 | C2×C32×C5 |
| Frattini | C1 | G |
| Fitting, socle | C2×C32×C211 | C5 |
| LCS | G ▷ C211 | |
| UCS | C1 ◁ C2×C32 | |
48 conjugacy classes of subgroups.
| transitive degree | μt(G) = 3798 |
846 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C32×Dic211⋊C5, C3×C3⋊(Dic211⋊C5), C3×Dic3×C211⋊C5, … |
| maximal normal subgroup of | C32×Dic211⋊C5, C3×C3⋊(Dic211⋊C5), C3×Dic3×C211⋊C5, … |
| maximal quotient of | C32×C4×C211⋊C5, C22×C32×C211⋊C5 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(18990, 36);