Finite Group DatabasebetaFinite Group Databasebeta| order | 900 |
| isoclinism | isoclinic class of (C3⋊D3)⋊D5 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C5 · Schur multiplier (H2) = C2 |
| direct product | C5×(C3⋊D3)⋊D5 |
| unambiguous semidirect product | (C3⋊D3)⋊(C5×D5) |
| unambiguous semidirect product | D15⋊(C5×D3) |
| Fitting, socle, Hall | C32×C52 ⋊ C22 |
| derived | C32×C5 ⋊ C22×C5 |
| Sylow | C52 ⋊ D32 |
| Sylow | C32 ⋊ C2×C5×D5 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C5 | (C3⋊D3)⋊D5 |
| commutator, cosocle, hypocenter | C32×C5 | C22×C5 |
| Frattini | C1 | G |
| Fitting, socle | C32×C52 | C22 |
| LCS | G ▷ C32×C5 | |
| UCS | C1 ◁ C5 | |
112 conjugacy classes of subgroups.
| transitive degree | μt(G) = 30 |
105 conjugacy classes — view the full character table.
| maximal subgroup of | C5×D32⋊D5, C5×#157⋊D5, #14268468, … |
| maximal normal subgroup of | C5×D32⋊D5, C5×#157⋊D5, #14268468, … |
| maximal quotient of | C5×#67154, C5×#67155, C5×#67156, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(900, 134);