Finite Group DatabasebetaFinite Group Databasebeta| order | 900 |
| isoclinism | isoclinic class of D3×C52⋊C3 |
| automorphism | ? |
| homology | Abelianization (H1) = C3×C4 · Schur multiplier (H2) = C5 |
| direct product | Dic3×C52⋊C3 |
| unambiguous semidirect product | C3⋊(C4×C52⋊C3) |
| unambiguous semidirect product | (C52×Dic3)⋊C3 |
| derived | C3×C52 ⋊ C3×C4 |
| Hall | C3×C52⋊C3 ⋊ C4 |
| Sylow | C52 ⋊ C3×Dic3 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C2 | D3×C52⋊C3 |
| commutator, hypocenter | C3×C52 | C3×C4 |
| Fitting, socle, cosocle | C2×C3×C52 | C2×C3 |
| prime radical | C2×C3×C52⋊C3 | C2 |
| LCS | G ▷ C3×C52 | |
| UCS | C1 ◁ C2 | |
40 conjugacy classes of subgroups.
| transitive degree | μt(G) = 180 |
66 conjugacy classes — view the full character table.
| maximal subgroup of | #14268144, Dic3×#3874, #14268146, … |
| maximal normal subgroup of | #14268144, Dic3×#3874, #14268146, … |
| maximal quotient of | C3⋊C8×C52⋊C3, C2×Dic3×C52⋊C3, Dic3×C13×C52⋊C3, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(900, 76);