Finite Group DatabasebetaFinite Group Databasebeta| order | 900 |
| isoclinism | isoclinic class of D3×C52⋊C3 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C3 · Schur multiplier (H2) = C2×C5 |
| direct product | C2×D3×C52⋊C3 |
| unambiguous semidirect product | C3⋊(C22×C52⋊C3) |
| unambiguous semidirect product | (C2×C3)⋊(C2×C52⋊C3) |
| unambiguous semidirect product | (C2×C52×D3)⋊C3 |
| Fitting, socle | C2×C3×C52 ⋊ C2×C3 |
| derived | C3×C52 ⋊ C22×C3 |
| Hall | C3×C52⋊C3 ⋊ C22 |
| Sylow | C52 ⋊ C2×C3×D3 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2 | D3×C52⋊C3 |
| commutator, cosocle, hypocenter | C3×C52 | C22×C3 |
| Frattini | C1 | G |
| Fitting, socle | C2×C3×C52 | C2×C3 |
| LCS | G ▷ C3×C52 | |
| UCS | C1 ◁ C2 | |
64 conjugacy classes of subgroups.
| transitive degree | μt(G) = 90 |
66 conjugacy classes — view the full character table.
| maximal subgroup of | D3×#64470, #14268149, #14268150, … |
| maximal normal subgroup of | D3×#64470, #14268149, #14268150, … |
| maximal quotient of | Dic6×C52⋊C3, C4×D3×C52⋊C3, D12×C52⋊C3, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(900, 102);