Finite Group DatabasebetaFinite Group Databasebeta| order | 900 |
| isoclinism | isoclinic class of C3⋊D15 |
| automorphism | ? |
| homology | Abelianization (H1) = C4×C5 · Schur multiplier (H2) = C3 |
| direct product | C5×C3⋊Dic15 |
| unambiguous semidirect product | C3⋊(C5×Dic15) |
| derived | C32×C5 ⋊ C4×C5 |
| Hall | C32×C52 ⋊ C4 |
| Sylow | C52 ⋊ C3⋊Dic3 |
| Sylow | C32 ⋊ C5×Dic5 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2×C5 | C3⋊D15 |
| commutator, hypocenter | C32×C5 | C4×C5 |
| Frattini | C2 | C5×C3⋊D15 |
| Fitting, socle, prime radical | C2×C32×C52 | C2 |
| cosocle | C2×C32×C5 | C2×C5 |
| LCS | G ▷ C32×C5 | |
| UCS | C1 ◁ C2×C5 | |
96 conjugacy classes of subgroups.
| transitive degree | μt(G) = 180 |
240 conjugacy classes — view the full character table.
| maximal subgroup of | C5×#67127, #14268213, C5×D5×C3⋊Dic3, … |
| maximal normal subgroup of | C5×#67127, #14268213, C5×D5×C3⋊Dic3, … |
| maximal quotient of | C5×C3⋊(C3⋊#168), C2×C5×C3⋊Dic15, C5×C13×C3⋊Dic15, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(900, 85);