Finite Group DatabasebetaFinite Group Databasebeta| order | 900 |
| isoclinism | isoclinic class of D3×C5⋊D5 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C3 · Schur multiplier (H2) = C2×C5 |
| direct product | C3×D3×C5⋊D5 |
| unambiguous semidirect product | (C5×D3)⋊(C3×D5) |
| Fitting, socle, Hall | C32×C52 ⋊ C22 |
| derived | C3×C52 ⋊ C22×C3 |
| Sylow | C52 ⋊ C2×C3×D3 |
| Sylow | C32 ⋊ C2×C5⋊D5 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C3 | D3×C5⋊D5 |
| commutator, cosocle, hypocenter | C3×C52 | C22×C3 |
| Frattini | C1 | G |
| Fitting, socle | C32×C52 | C22 |
| LCS | G ▷ C3×C52 | |
| UCS | C1 ◁ C3 | |
176 conjugacy classes of subgroups.
| transitive degree | μt(G) = 150 |
126 conjugacy classes — view the full character table.
| maximal subgroup of | C3×D3×#1043, C3×D3×#1044, D3×C3⋊#1043, … |
| maximal normal subgroup of | C3×D3×#1043, C3×D3×#1044, D3×C3⋊#1043, … |
| maximal quotient of | C3×Dic3×C5⋊D5, C3×D3×#1039, C3×#10597113, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(900, 125);