Finite Group DatabasebetaFinite Group Databasebeta| order | 4540 |
| isoclinism | isoclinic class of D227 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C5 · Schur multiplier (H2) = C2 |
| direct product | C2×C5×D227 |
| unambiguous semidirect product | C227⋊(C22×C5) |
| unambiguous semidirect product | (C2×C227)⋊(C2×C5) |
| Fitting, socle | C2×C5×C227 ⋊ C2 |
| derived, Sylow | C227 ⋊ C22×C5 |
| Hall | C5×C227 ⋊ C22 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2×C5 | D227 |
| commutator, cosocle, hypocenter | C227 | C22×C5 |
| Frattini | C1 | G |
| Fitting, socle | C2×C5×C227 | C2 |
| LCS | G ▷ C227 | |
| UCS | C1 ◁ C2×C5 | |
20 conjugacy classes of subgroups.
| transitive degree | μt(G) = 2270 |
1150 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C5×D3×D227, C2×C5×D681, C2×C3×C5×D227, … |
| maximal normal subgroup of | C2×C3×C5×D227, C2×C25×D227, C2×C52×D227, … |
| maximal quotient of | C5×D3×D227, C2×C5×D681, C2×C3×C5×D227, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4540, 11);