Finite Group DatabasebetaFinite Group Databasebeta| order | 1800 |
| isoclinism | isoclinic class of D45⋊D5 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C23 |
| direct product | C2×D45⋊D5 |
| Fitting | C2×C52×C9 ⋊ C22 |
| derived, Hall | C52×C9 ⋊ C23 |
| Sylow | C52 ⋊ C22×D9 |
| Sylow | C9 ⋊ C2×D52 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2 | D45⋊D5 |
| commutator, cosocle, hypocenter | C52×C9 | C23 |
| Frattini | C3 | C2×D15⋊D5 |
| Fitting | C2×C52×C9 | C22 |
| socle | C2×C3×C52 | C2×D3 |
| LCS | G ▷ C52×C9 | |
| UCS | C1 ◁ C2 | |
222 conjugacy classes of subgroups.
| transitive degree | μt(G) = 180 |
144 conjugacy classes — view the full character table.
| maximal subgroup of | C2×#14268091, C2×D52×D9, C2×#14268092, … |
| maximal normal subgroup of | C2×#14268091, C2×D52×D9, C2×#14268092, … |
| maximal quotient of | #72247530 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1800, 318);