Finite Group DatabasebetaFinite Group Databasebeta| order | 900 |
| isoclinism | isoclinic class of D9×C5⋊D5 |
| automorphism | ? |
| homology | Abelianization (H1) = C22 · Schur multiplier (H2) = C2×C5 |
| direct product | D9×C5⋊D5 |
| unambiguous semidirect product | (C5×D9)⋊D5 |
| Fitting, derived, Hall | C52×C9 ⋊ C22 |
| Sylow | C52 ⋊ C2×D9 |
| Sylow | C9 ⋊ C2×C5⋊D5 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C1 | G |
| commutator, Fitting, cosocle, hypocenter | C52×C9 | C22 |
| Frattini | C3 | D3×C5⋊D5 |
| socle | C3×C52 | C2×D3 |
| LCS | G ▷ C52×C9 | |
| UCS | C1 | |
120 conjugacy classes of subgroups.
| transitive degree | μt(G) = 225 |
84 conjugacy classes — view the full character table.
| maximal subgroup of | D9×#1043, D9×#1044, D52×D9, … |
| maximal normal subgroup of | D9×#1043, D9×#1044, D52×D9, … |
| maximal quotient of | #14267969, D9×#1039, #14267971, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(900, 61);