Finite Group DatabasebetaFinite Group Databasebeta| order | 900 |
| isoclinism | isoclinic class of C3⋊D3 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C52 · Schur multiplier (H2) = C2×C3×C5 |
| direct product | C2×C52×C3⋊D3 |
| unambiguous semidirect product | (C2×C3)⋊(C52×D3) |
| Fitting, socle | C2×C32×C52 ⋊ C2 |
| derived, Sylow | C32 ⋊ C22×C52 |
| Hall | C32×C52 ⋊ C22 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2×C52 | C3⋊D3 |
| commutator, cosocle, hypocenter | C32 | C22×C52 |
| Frattini | C1 | G |
| Fitting, socle | C2×C32×C52 | C2 |
| LCS | G ▷ C32 | |
| UCS | C1 ◁ C2×C52 | |
240 conjugacy classes of subgroups.
| transitive degree | μt(G) = 450 |
300 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C5×C3⋊D3×Dic5, C5×#67138, C5×#67140, … |
| maximal normal subgroup of | C5×C3⋊D3×Dic5, C5×#67138, C5×#67140, … |
| maximal quotient of | C52×#634, C4×C52×C3⋊D3, C52×C4⋊(C3⋊D3), … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(900, 147);