Finite Group DatabasebetaFinite Group Databasebeta| order | 20772 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C9 · Schur multiplier (H2) = C2 |
| direct product | C2×#19104462⋊C2 |
| unambiguous semidirect product | #19104462⋊C22 |
| unambiguous semidirect product | (C2×#19104462)⋊C2 |
| Fitting, socle | C2×C577 ⋊ C2×C9 |
| derived, Sylow | C577 ⋊ C22×C9 |
| Hall | #19104462 ⋊ C22 |
| Hall | C2×D577 ⋊ C9 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2 | #19104462⋊C2 |
| commutator, hypocenter | C577 | C22×C9 |
| Frattini | C1 | G |
| Fitting, socle | C2×C577 | C2×C9 |
| prime radical | C2×D577⋊C3 | C3 |
| cosocle | C577⋊C3 | C22×C3 |
| LCS | G ▷ C577 | |
| UCS | C1 ◁ C2 | |
30 conjugacy classes of subgroups.
| transitive degree | μt(G) = 1154 |
100 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(20772, 33);