Finite Group DatabasebetaFinite Group Databasebeta| order | 6824 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C4 · Schur multiplier (H2) = C2 |
| direct product | C2×#16811794 |
| unambiguous semidirect product | D853⋊C4 |
| Fitting, socle | C2×C853 ⋊ C4 |
| derived, Sylow | C853 ⋊ C2×C4 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2 | #16811794 |
| commutator, hypocenter | C853 | C2×C4 |
| Frattini | C1 | G |
| Fitting, socle | C2×C853 | C4 |
| LCS | G ▷ C853 | |
| UCS | C1 ◁ C2 | |
16 conjugacy classes of subgroups.
434 conjugacy classes — view the full character table.
| maximal subgroup of | C4×#16811794, C22⋊#16811794, C4⋊#16811794, … |
| maximal normal subgroup of | C4×#16811794, C22⋊#16811794, C4⋊#16811794, … |
| maximal quotient of | C4×#16811794, C22⋊#16811794, C4⋊#16811794, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(6824, 14);