Finite Group DatabasebetaFinite Group Databasebeta| order | 900 |
| isoclinism | isoclinic class of D3×(C5⋊D5)⋊C3 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C3 · Schur multiplier (H2) = C2×C5 |
| direct product | D3×(C5⋊D5)⋊C3 |
| unambiguous semidirect product | (D3×C5⋊D5)⋊C3 |
| Fitting, socle, derived | C3×C52 ⋊ C22×C3 |
| Hall | C3×C52⋊C3 ⋊ C22 |
| Sylow | C52 ⋊ C2×C3×D3 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, cosocle, hypocenter | C3×C52 | C22×C3 |
| LCS | G ▷ C3×C52 | |
| UCS | C1 | |
64 conjugacy classes of subgroups.
| transitive degree | μt(G) = 45 |
30 conjugacy classes — view the full character table.
| maximal subgroup of | D3×#64480, D3×#1043⋊C3, D3×#3874⋊C2, … |
| maximal normal subgroup of | D3×#64480, D3×#1043⋊C3, D3×#3874⋊C2, … |
| maximal quotient of | Dic3×(C5⋊D5)⋊C3, D3×#1039⋊C3, #10597113⋊C3, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(900, 97);