Finite Group DatabasebetaFinite Group Databasebeta| order | 900 |
| isoclinism | isoclinic class of (C5⋊D5)⋊C3 |
| automorphism | ? |
| homology | Abelianization (H1) = C32×C4 · Schur multiplier (H2) = C3×C5 |
| direct product | C3×#1039⋊C3 |
| unambiguous semidirect product | #1039⋊C32 |
| unambiguous semidirect product | (C3×#1039)⋊C3 |
| derived, Sylow | C52 ⋊ C32×C4 |
| Hall | C3×C52⋊C3 ⋊ C4 |
| Hall | #1039 ⋊ C32 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2×C3 | (C5⋊D5)⋊C3 |
| commutator, hypocenter | C52 | C32×C4 |
| Frattini | C2 | C3×(C5⋊D5)⋊C3 |
| Fitting, socle | C2×C3×C52 | C2×C3 |
| prime radical | C2×C3×C52⋊C3 | C2 |
| cosocle | C2×C52 | C2×C32 |
| LCS | G ▷ C52 | |
| UCS | C1 ◁ C2×C3 | |
48 conjugacy classes of subgroups.
| transitive degree | μt(G) = 180 |
60 conjugacy classes — view the full character table.
| maximal subgroup of | C3×#10597074, C3⋊#10597074, C3×#6033⋊C3, … |
| maximal normal subgroup of | C3×#10597074, C3⋊#10597074, C3×#6033⋊C3, … |
| maximal quotient of | C3×#6029⋊C3, C2×C3×#1039⋊C3, #16839052⋊C3, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(900, 75);