Finite Group DatabasebetaFinite Group Databasebeta| order | 22370 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C5 · Schur multiplier (H2) = C1 |
| direct product | C5×D2237 |
| unambiguous semidirect product | C2237⋊(C2×C5) |
| Fitting, socle, Hall | C5×C2237 ⋊ C2 |
| derived, Sylow | C2237 ⋊ C2×C5 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C5 | D2237 |
| commutator, cosocle, hypocenter | C2237 | C2×C5 |
| Frattini | C1 | G |
| Fitting, socle | C5×C2237 | C2 |
| LCS | G ▷ C2237 | |
| UCS | C1 ◁ C5 | |
8 conjugacy classes of subgroups.
| transitive degree | μt(G) = 11185 |
5600 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(22370, 2);