Finite Group DatabasebetaFinite Group Databasebeta| order | 22300 |
| automorphism | ? |
| homology | Abelianization (H1) = C4×C223 · Schur multiplier (H2) = C5 |
| direct product | #1044×C223 |
| Fitting, socle, Hall | C52×C223 ⋊ C4 |
| derived, Sylow | C52 ⋊ C4×C223 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C223 | #1044 |
| commutator, hypocenter | C52 | C4×C223 |
| Frattini | C1 | G |
| Fitting, socle | C52×C223 | C4 |
| prime radical | C5⋊D5×C223 | C2 |
| cosocle | C5⋊D5 | C2×C223 |
| LCS | G ▷ C52 | |
| UCS | C1 ◁ C223 | |
32 conjugacy classes of subgroups.
| transitive degree | μt(G) = 2230 |
2230 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(22300, 30);