Finite Group DatabasebetaFinite Group Databasebeta| order | 22700 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C5 · Schur multiplier (H2) = C2 |
| direct product | C2×C5×D1135 |
| unambiguous semidirect product | (C2×C5)⋊(C5×D227) |
| unambiguous semidirect product | (C2×C227)⋊(C5×D5) |
| Fitting, socle | C2×C52×C227 ⋊ C2 |
| derived | C5×C227 ⋊ C22×C5 |
| Hall | C52×C227 ⋊ C22 |
| Sylow | C227 ⋊ C2×C5×D5 |
| Sylow | C52 ⋊ C2×D227 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2×C5 | D1135 |
| commutator, cosocle, hypocenter | C5×C227 | C22×C5 |
| Frattini | C1 | G |
| Fitting, socle | C2×C52×C227 | C2 |
| LCS | G ▷ C5×C227 | |
| UCS | C1 ◁ C2×C5 | |
48 conjugacy classes of subgroups.
| transitive degree | μt(G) = 4540 |
5690 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(22700, 34);