Finite Group DatabasebetaFinite Group Databasebeta| order | 22700 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C227 · Schur multiplier (H2) = C2 |
| direct product | C2×D25×C227 |
| unambiguous semidirect product | C25⋊(C22×C227) |
| unambiguous semidirect product | (C2×C25)⋊(C2×C227) |
| Fitting | C2×C25×C227 ⋊ C2 |
| derived, Sylow | C25 ⋊ C22×C227 |
| Hall | C25×C227 ⋊ C22 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2×C227 | D25 |
| commutator, cosocle, hypocenter | C25 | C22×C227 |
| Frattini | C5 | C2×D5×C227 |
| Fitting | C2×C25×C227 | C2 |
| socle | C2×C5×C227 | D5 |
| LCS | G ▷ C25 | |
| UCS | C1 ◁ C2×C227 | |
30 conjugacy classes of subgroups.
| transitive degree | μt(G) = 11350 |
6356 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(22700, 10);