Finite Group DatabasebetaFinite Group Databasebeta| order | 22764 |
| automorphism | ? |
| homology | Abelianization (H1) = C22 · Schur multiplier (H2) = C2 |
| unambiguous semidirect product | D21⋊D271 |
| unambiguous semidirect product | D813⋊D7 |
| unambiguous semidirect product | D1897⋊D3 |
| Fitting, socle, derived, Hall | C3×C7×C271 ⋊ C22 |
| Hall | C7×C271 ⋊ C2×D3 |
| Hall | C3×C271 ⋊ C2×D7 |
| Sylow | C271 ⋊ D3×D7 |
| Hall | C3×C7 ⋊ C2×D271 |
| Sylow | C7 ⋊ D3×D271 |
| Sylow | C3 ⋊ D7×D271 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, cosocle, hypocenter | C3×C7×C271 | C22 |
| LCS | G ▷ C3×C7×C271 | |
| UCS | C1 | |
40 conjugacy classes of subgroups.
| transitive degree | μt(G) = 5691 |
Polycyclic presentation:
2^2,3,7,271|d^a=d^6,e^a=e^270,c^b=c^2,d^b=d^61635 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(22764, 48);