Finite Group DatabasebetaFinite Group Databasebeta| order | 900 |
| isoclinism | isoclinic class of C3⋊D3 |
| automorphism | ? |
| homology | Abelianization (H1) = C4×C25 · Schur multiplier (H2) = C3 |
| direct product | C25×C3⋊Dic3 |
| unambiguous semidirect product | C3⋊(Dic3×C25) |
| derived, Sylow | C32 ⋊ C4×C25 |
| Hall | C32×C25 ⋊ C4 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2×C25 | C3⋊D3 |
| commutator, hypocenter | C32 | C4×C25 |
| Frattini | C2×C5 | C5×C3⋊D3 |
| Fitting | C2×C32×C25 | C2 |
| socle, prime radical, cosocle | C2×C32×C5 | C2×C5 |
| LCS | G ▷ C32 | |
| UCS | C1 ◁ C2×C25 | |
54 conjugacy classes of subgroups.
| transitive degree | μt(G) = 900 |
300 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C25×#622, #14267870, #14267879, … |
| maximal normal subgroup of | C25×#622, #14267870, #14267879, … |
| maximal quotient of | C25×C3⋊(C3⋊C8), C2×C25×C3⋊Dic3, C13×C25×C3⋊Dic3, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(900, 16);