Finite Group DatabasebetaFinite Group Databasebeta| order | 22700 |
| automorphism | ? |
| homology | Abelianization (H1) = C4×C5 · Schur multiplier (H2) = C1 |
| direct product | C5×C227⋊AGL(1,𝔽5) |
| unambiguous semidirect product | C227⋊(C5×AGL(1,𝔽5)) |
| Fitting, socle, Hall | C52×C227 ⋊ C4 |
| derived | C5×C227 ⋊ C4×C5 |
| Sylow | C227 ⋊ C5×AGL(1,𝔽5) |
| Sylow | C52 ⋊ Dic227 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C5 | C227⋊AGL(1,𝔽5) |
| commutator, hypocenter | C5×C227 | C4×C5 |
| Frattini | C1 | G |
| Fitting, socle | C52×C227 | C4 |
| prime radical | C5×D5×C227 | C2 |
| cosocle | D5×C227 | C2×C5 |
| LCS | G ▷ C5×C227 | |
| UCS | C1 ◁ C5 | |
26 conjugacy classes of subgroups.
| transitive degree | μt(G) = 4540 |
2285 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(22700, 21);