Finite Group DatabasebetaFinite Group Databasebeta| order | 900 |
| isoclinism | isoclinic class of #64480 |
| automorphism | ? |
| homology | Abelianization (H1) = C3×C4 · Schur multiplier (H2) = C5 |
| direct product | C3×#64480 |
| Fitting, socle | C3×C52 ⋊ Dic3 |
| derived | C52⋊C3 ⋊ C3×C4 |
| Hall | C3×C52⋊C3 ⋊ C4 |
| Sylow | C52 ⋊ C3×Dic3 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C3 | #64480 |
| commutator, hypocenter | C52⋊C3 | C3×C4 |
| Frattini | C1 | G |
| Fitting, socle | C3×C52 | Dic3 |
| prime radical | C3×(C5⋊D5)⋊C3 | C2 |
| cosocle | (C5⋊D5)⋊C3 | C2×C3 |
| LCS | G ▷ C52⋊C3 | |
| UCS | C1 ◁ C3 | |
40 conjugacy classes of subgroups.
| transitive degree | μt(G) = 45 |
24 conjugacy classes — view the full character table.
| maximal subgroup of | C3×#64480⋊C2, #64480⋊D3, D3×#64480, … |
| maximal normal subgroup of | C3×#64480⋊C2, #64480⋊D3, D3×#64480, … |
| maximal quotient of | C3×#10597074, C2×C3×#64480, #16839111⋊C3, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(900, 89);