Finite Group DatabasebetaFinite Group Databasebeta| order | 6784 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C42 · Schur multiplier (H2) = C25×C4 |
| direct product | C2×C4×C4⋊#6157 |
| Fitting | C2×C42×C53 ⋊ C4 |
| Sylow | C53 ⋊ C2×C4×C4⋊C4 |
| subgroup | G/H | |
|---|---|---|
| center | C22×C4 | C2×#6157 |
| commutator | C2×C53 | C22×C42 |
| Frattini | C22 | C23×#6157 |
| Fitting | C2×C42×C53 | C4 |
| socle | C23×C53 | C22×C4 |
| hypercenter | C2×C42 | #6157 |
| hypocenter | C53 | C2×C4×C4⋊C4 |
| LCS | G ▷ C2×C53 ▷ C53 | |
| UCS | C1 ◁ C22×C4 ◁ C2×C42 | |
928 conjugacy classes of subgroups.
496 conjugacy classes — view the full character table.
| maximal subgroup of | C2×#20289549, C2×#20289550, #28300261, … |
| maximal normal subgroup of | C2×#20289549, C2×#20289550, #28300261, … |
| maximal quotient of | C2×C4×(C2×#6157)⋊C4, C42×C4⋊#6157, C2×#20289891, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(6784, 20940);