Finite Group DatabasebetaFinite Group Databasebeta| order | 900 |
| isoclinism | isoclinic class of C52⋊C3 |
| automorphism | ? |
| homology | Abelianization (H1) = C32×C4 · Schur multiplier (H2) = C3×C5 |
| direct product | C3×C4×C52⋊C3 |
| unambiguous semidirect product | (C4×C52)⋊C32 |
| unambiguous semidirect product | (C3×C4×C52)⋊C3 |
| Fitting | C3×C4×C52 ⋊ C3 |
| derived, Sylow | C52 ⋊ C32×C4 |
| Hall | C4×C52 ⋊ C32 |
48 conjugacy classes of subgroups.
| transitive degree | μt(G) = 180 |
132 conjugacy classes — view the full character table.
| maximal subgroup of | C3×#10597064, C3⋊#10597064, C3×#6029⋊C3, … |
| maximal normal subgroup of | C3×#10597064, C3⋊#10597064, C3×#6029⋊C3, … |
| maximal quotient of | C3×C8×C52⋊C3, C2×C3×C4×C52⋊C3, C52⋊C3×Dic13⋊C3, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(900, 78);