Finite Group DatabasebetaFinite Group Databasebeta| order | 900 |
| isoclinism | isoclinic class of C52⋊C3 |
| automorphism | ? |
| homology | Abelianization (H1) = C4×C9 · Schur multiplier (H2) = C5 |
| direct product | C4×C52⋊C9 |
| unambiguous semidirect product | (C4×C52)⋊C9 |
| derived, Sylow | C52 ⋊ C4×C9 |
| Hall | C4×C52 ⋊ C9 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C3×C4 | C52⋊C3 |
| commutator, hypocenter | C52 | C4×C9 |
| Frattini | C2×C3 | C2×C52⋊C3 |
| Fitting | C3×C4×C52 | C3 |
| socle, prime radical, cosocle | C2×C3×C52 | C2×C3 |
| LCS | G ▷ C52 | |
| UCS | C1 ◁ C3×C4 | |
30 conjugacy classes of subgroups.
| transitive degree | μt(G) = 180 |
132 conjugacy classes — view the full character table.
| maximal subgroup of | #14267857, #6029⋊C9, C8×C52⋊C9, … |
| maximal normal subgroup of | #14267857, #6029⋊C9, C8×C52⋊C9, … |
| maximal quotient of | C8×C52⋊C9, C2×C4×C52⋊C9, Dic13×C52⋊C9, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(900, 21);