Finite Group DatabasebetaFinite Group Databasebeta| order | 900 |
| isoclinism | isoclinic class of (C5⋊D5)⋊C3 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C32 · Schur multiplier (H2) = C2×C3×C5 |
| direct product | C2×C3×(C5⋊D5)⋊C3 |
| unambiguous semidirect product | (C2×C5⋊D5)⋊C32 |
| unambiguous semidirect product | (C2×C3×C5⋊D5)⋊C3 |
| Fitting, socle | C2×C3×C52 ⋊ C2×C3 |
| derived, Sylow | C52 ⋊ C22×C32 |
| Hall | C3×C52⋊C3 ⋊ C22 |
| Hall | C2×C5⋊D5 ⋊ C32 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2×C3 | (C5⋊D5)⋊C3 |
| commutator, cosocle, hypocenter | C52 | C22×C32 |
| Frattini | C1 | G |
| Fitting, socle | C2×C3×C52 | C2×C3 |
| LCS | G ▷ C52 | |
| UCS | C1 ◁ C2×C3 | |
80 conjugacy classes of subgroups.
| transitive degree | μt(G) = 90 |
60 conjugacy classes — view the full character table.
| maximal subgroup of | C3×#10597079, C3×#10597080, #14268161, … |
| maximal normal subgroup of | C3×#10597079, C3×#10597080, #14268161, … |
| maximal quotient of | C3×#6045⋊C3, C3×C4×(C5⋊D5)⋊C3, C3×C4⋊((C5⋊D5)⋊C3), … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(900, 101);