Finite Group DatabasebetaFinite Group Databasebeta| order | 22300 |
| automorphism | ? |
| homology | Abelianization (H1) = C4×C25 · Schur multiplier (H2) = C1 |
| direct product | C25×Dic223 |
| unambiguous semidirect product | C223⋊(C4×C25) |
| derived, Sylow | C223 ⋊ C4×C25 |
| Hall | C25×C223 ⋊ C4 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2×C25 | D223 |
| commutator, hypocenter | C223 | C4×C25 |
| Frattini | C2×C5 | C5×D223 |
| Fitting | C2×C25×C223 | C2 |
| socle, prime radical, cosocle | C2×C5×C223 | C2×C5 |
| LCS | G ▷ C223 | |
| UCS | C1 ◁ C2×C25 | |
18 conjugacy classes of subgroups.
| transitive degree | μt(G) = 22300 |
5650 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(22300, 3);