Finite Group DatabasebetaFinite Group Databasebeta| order | 900 |
| isoclinism | isoclinic class of #3874⋊C2 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C3 · Schur multiplier (H2) = C2 |
| direct product | C3×#3874⋊C2 |
| unambiguous semidirect product | #3874⋊(C2×C3) |
| unambiguous semidirect product | ((C5⋊D5)⋊C3)⋊(C2×C3) |
| Fitting, socle | C3×C52 ⋊ C2×D3 |
| derived | C52⋊C3 ⋊ C22×C3 |
| Hall | C3×C52⋊C3 ⋊ C22 |
| Sylow | C52 ⋊ C2×C3×D3 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C3 | #3874⋊C2 |
| commutator, cosocle, hypocenter | C52⋊C3 | C22×C3 |
| Frattini | C1 | G |
| Fitting, socle | C3×C52 | C2×D3 |
| LCS | G ▷ C52⋊C3 | |
| UCS | C1 ◁ C3 | |
64 conjugacy classes of subgroups.
| transitive degree | μt(G) = 45 |
42 conjugacy classes — view the full character table.
| maximal subgroup of | C3×#64480⋊C2, #14268376, D3×#3874⋊C2, … |
| maximal normal subgroup of | C3×#64480⋊C2, #14268376, D3×#3874⋊C2, … |
| maximal quotient of | C3×#10597076, C3×#10597077, C3×#10597078, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(900, 93);