Finite Group DatabasebetaFinite Group Databasebeta| order | 22300 |
| automorphism | ? |
| homology | Abelianization (H1) = C4×C223 · Schur multiplier (H2) = C1 |
| direct product | #1035×C223 |
| Fitting, Hall | C25×C223 ⋊ C4 |
| derived, Sylow | C25 ⋊ C4×C223 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C223 | #1035 |
| commutator, hypocenter | C25 | C4×C223 |
| Frattini | C5 | AGL(1,𝔽5)×C223 |
| Fitting | C25×C223 | C4 |
| socle | C5×C223 | AGL(1,𝔽5) |
| prime radical | D25×C223 | C2 |
| cosocle | D25 | C2×C223 |
| LCS | G ▷ C25 | |
| UCS | C1 ◁ C223 | |
18 conjugacy classes of subgroups.
| transitive degree | μt(G) = 5575 |
2230 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(22300, 6);