Finite Group DatabasebetaFinite Group Databasebeta| order | 6784 |
| automorphism | ? |
| homology | Abelianization (H1) = C25 · Schur multiplier (H2) = C29 |
| direct product | D4×Q8×D53 |
| Fitting | D4×Q8×C53 ⋊ C2 |
| Sylow | C53 ⋊ C2×D4×Q8 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C22 | C24×D53 |
| commutator, socle | C22×C53 | C25 |
| Fitting | D4×Q8×C53 | C2 |
| hypercenter | D4×Q8 | D53 |
| hypocenter | C53 | C2×D4×Q8 |
| LCS | G ▷ C22×C53 ▷ C53 | |
| UCS | C1 ◁ C22 ◁ D4×Q8 | |
1568 conjugacy classes of subgroups.
700 conjugacy classes — view the full character table.
| maximal subgroup of | D53×#1627, D53×#1637, D53×#1651, … |
| maximal normal subgroup of | D53×#1627, D53×#1637, D53×#1651, … |
| maximal quotient of | Q8×C22⋊C4×D53, D4×C4⋊C4×D53, Q8×C4⋊C4×D53, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(6784, 17980);