Finite Group DatabasebetaFinite Group Databasebeta| order | 900 |
| isoclinism | isoclinic class of #3874 |
| automorphism | ? |
| homology | Abelianization (H1) = C3×C4 · Schur multiplier (H2) = C1 |
| direct product | C3×#64470 |
| derived | C52⋊C3 ⋊ C3×C4 |
| Hall | C3×C52⋊C3 ⋊ C4 |
| Sylow | C52 ⋊ C3×Dic3 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2×C3 | #3874 |
| commutator, hypocenter | C52⋊C3 | C3×C4 |
| Frattini | C2 | C3×#3874 |
| Fitting, socle | C2×C3×C52 | D3 |
| prime radical | C2×C3×C52⋊C3 | C2 |
| cosocle | C2×C52⋊C3 | C2×C3 |
| LCS | G ▷ C52⋊C3 | |
| UCS | C1 ◁ C2×C3 | |
40 conjugacy classes of subgroups.
| transitive degree | μt(G) = 180 |
78 conjugacy classes — view the full character table.
| maximal subgroup of | C3×#10597076, C3×#10597077, C3×#10597079, … |
| maximal normal subgroup of | C3×#10597076, C3×#10597077, C3×#10597079, … |
| maximal quotient of | C3×#10597064, C2×C3×#64470, #16839047⋊C3, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(900, 73);