Finite Group DatabasebetaFinite Group Databasebeta| order | 19220 |
| automorphism | ? |
| homology | Abelianization (H1) = C22 · Schur multiplier (H2) = C2 |
| direct product | D5×D961 |
| unambiguous semidirect product | (D5×C961)⋊C2 |
| unambiguous semidirect product | (C5×D961)⋊C2 |
| unambiguous semidirect product | D4805⋊C2 |
| Fitting, derived, Hall | C5×C961 ⋊ C22 |
| Sylow | C961 ⋊ C2×D5 |
| Sylow | C5 ⋊ C2×D961 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C1 | G |
| commutator, Fitting, cosocle, hypocenter | C5×C961 | C22 |
| Frattini | C31 | D5×D31 |
| socle | C5×C31 | C2×D31 |
| LCS | G ▷ C5×C961 | |
| UCS | C1 | |
30 conjugacy classes of subgroups.
| transitive degree | μt(G) = 4805 |
1928 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(19220, 12);