Finite Group DatabasebetaFinite Group Databasebeta| order | 900 |
| isoclinism | isoclinic class of D32 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C52 · Schur multiplier (H2) = C2×C5 |
| direct product | C52×D32 |
| unambiguous semidirect product | (C3×D3)⋊(C2×C52) |
| unambiguous semidirect product | (C3⋊D3)⋊(C2×C52) |
| Fitting, socle, Hall | C32×C52 ⋊ C22 |
| derived, Sylow | C32 ⋊ C22×C52 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C52 | D32 |
| commutator, cosocle, hypocenter | C32 | C22×C52 |
| Frattini | C1 | G |
| Fitting, socle | C32×C52 | C22 |
| LCS | G ▷ C32 | |
| UCS | C1 ◁ C52 | |
176 conjugacy classes of subgroups.
| transitive degree | μt(G) = 150 |
225 conjugacy classes — view the full character table.
| maximal subgroup of | C52×GO+(4,𝔽2), C5×D32⋊D5, D32⋊(C5⋊D5), … |
| maximal normal subgroup of | C52×GO+(4,𝔽2), C5×D32⋊D5, D32⋊(C5⋊D5), … |
| maximal quotient of | C52×D3×Dic3, C52×#624, C52×#625, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(900, 132);