Finite Group DatabasebetaFinite Group Databasebeta| order | 900 |
| isoclinism | isoclinic class of D52 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C32 · Schur multiplier (H2) = C2×C3 |
| direct product | C32×D52 |
| unambiguous semidirect product | (C5×D5)⋊(C2×C32) |
| Fitting, socle, Hall | C32×C52 ⋊ C22 |
| derived, Sylow | C52 ⋊ C22×C32 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C32 | D52 |
| commutator, cosocle, hypocenter | C52 | C22×C32 |
| Frattini | C1 | G |
| Fitting, socle | C32×C52 | C22 |
| LCS | G ▷ C52 | |
| UCS | C1 ◁ C32 | |
144 conjugacy classes of subgroups.
| transitive degree | μt(G) = 90 |
144 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(900, 123);