Finite Group DatabasebetaFinite Group Databasebeta| order | 900 |
| isoclinism | isoclinic class of C52⋊C3 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C32 · Schur multiplier (H2) = C2×C3×C5 |
| direct product | C22×C3×C52⋊C3 |
| Fitting, socle | C22×C3×C52 ⋊ C3 |
| derived, Sylow | C52 ⋊ C22×C32 |
| Hall | C22×C52 ⋊ C32 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C22×C3 | C52⋊C3 |
| commutator, cosocle, hypocenter | C52 | C22×C32 |
| Frattini | C1 | G |
| Fitting, socle | C22×C3×C52 | C3 |
| LCS | G ▷ C52 | |
| UCS | C1 ◁ C22×C3 | |
80 conjugacy classes of subgroups.
| transitive degree | μt(G) = 180 |
132 conjugacy classes — view the full character table.
| maximal subgroup of | C2×C3×#64470, C3×#10597085, C2×C3⋊#64470, … |
| maximal normal subgroup of | C2×C3×#64470, C3×#10597085, C2×C3⋊#64470, … |
| maximal quotient of | C2×C3×C4×C52⋊C3, C3×D4×C52⋊C3, C3×Q8×C52⋊C3, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(900, 139);