Finite Group DatabasebetaFinite Group Databasebeta| order | 6820 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C5 · Schur multiplier (H2) = C2 |
| direct product | C2×#16811780 |
| Fitting, socle | C2×C11×C31 ⋊ C2×C5 |
| derived, Hall | C11×C31 ⋊ C22×C5 |
| Hall | #13133724 ⋊ C22 |
| Hall | C2×D11×C31 ⋊ C5 |
| Hall | C2×D11 ⋊ ΓL(1,𝔽32) |
| Sylow | C31 ⋊ C2×AGL(1,𝔽11) |
| Sylow | C11 ⋊ C22×ΓL(1,𝔽32) |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2 | #16811780 |
| commutator, hypocenter | C11×C31 | C22×C5 |
| Frattini | C1 | G |
| Fitting, socle | C2×C11×C31 | C2×C5 |
| LCS | G ▷ C11×C31 | |
| UCS | C1 ◁ C2 | |
40 conjugacy classes of subgroups.
106 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(6820, 47);