Finite Group DatabasebetaFinite Group Databasebeta| order | 27150 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C3 · Schur multiplier (H2) = C5 |
| direct product | C2×C52⋊(C181⋊C3) |
| unambiguous semidirect product | (C2×C52)⋊(C181⋊C3) |
| unambiguous semidirect product | (C2×C181)⋊(C52⋊C3) |
| Fitting, socle, Hall | C2×C52×C181 ⋊ C3 |
| derived, Hall | C52×C181 ⋊ C2×C3 |
| Hall | C2×C181 ⋊ C52⋊C3 |
| Sylow | C181 ⋊ C2×C52⋊C3 |
| Hall | C2×C52 ⋊ C181⋊C3 |
| Sylow | C52 ⋊ C2×C181⋊C3 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2 | C52⋊(C181⋊C3) |
| commutator, cosocle, hypocenter | C52×C181 | C2×C3 |
| Frattini | C1 | G |
| Fitting, socle | C2×C52×C181 | C3 |
| LCS | G ▷ C52×C181 | |
| UCS | C1 ◁ C2 | |
24 conjugacy classes of subgroups.
| transitive degree | μt(G) = 5430 |
3022 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(27150, 46);