Finite Group DatabasebetaFinite Group Databasebeta| order | 22700 |
| automorphism | ? |
| homology | Abelianization (H1) = C4×C227 · Schur multiplier (H2) = C1 |
| direct product | #1035×C227 |
| Fitting, Hall | C25×C227 ⋊ C4 |
| derived, Sylow | C25 ⋊ C4×C227 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C227 | #1035 |
| commutator, hypocenter | C25 | C4×C227 |
| Frattini | C5 | AGL(1,𝔽5)×C227 |
| Fitting | C25×C227 | C4 |
| socle | C5×C227 | AGL(1,𝔽5) |
| prime radical | D25×C227 | C2 |
| cosocle | D25 | C2×C227 |
| LCS | G ▷ C25 | |
| UCS | C1 ◁ C227 | |
18 conjugacy classes of subgroups.
| transitive degree | μt(G) = 5675 |
2270 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(22700, 6);