Finite Group DatabasebetaFinite Group Databasebeta| order | 20772 |
| automorphism | ? |
| homology | Abelianization (H1) = C32×C4 · Schur multiplier (H2) = C3 |
| direct product | C32×#14556313 |
| Fitting, socle, Hall | C32×C577 ⋊ C4 |
| derived, Sylow | C577 ⋊ C32×C4 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C32 | #14556313 |
| commutator, hypocenter | C577 | C32×C4 |
| Frattini | C1 | G |
| Fitting, socle | C32×C577 | C4 |
| prime radical | C32×D577 | C2 |
| cosocle | D577 | C2×C32 |
| LCS | G ▷ C577 | |
| UCS | C1 ◁ C32 | |
36 conjugacy classes of subgroups.
| transitive degree | μt(G) = 5193 |
1332 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(20772, 46);