Finite Group DatabasebetaFinite Group Databasebeta| order | 6784 |
| automorphism | ? |
| homology | Abelianization (H1) = C25 · Schur multiplier (H2) = C28 |
| direct product | Q8×#11719947 |
| Fitting | D4×Q8×C53 ⋊ C2 |
| Sylow | C53 ⋊ Q8×#41 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C22 | C24×D53 |
| commutator, socle | C22×C53 | C25 |
| Fitting | D4×Q8×C53 | C2 |
| hypercenter | D4×Q8 | D53 |
| hypocenter | C53 | Q8×#41 |
| LCS | G ▷ C22×C53 ▷ C53 | |
| UCS | C1 ◁ C22 ◁ D4×Q8 | |
1068 conjugacy classes of subgroups.
700 conjugacy classes — view the full character table.
| maximal subgroup of | #27360069, #27360077, #27360084, … |
| maximal normal subgroup of | #27360069, #27360077, #27360084, … |
| maximal quotient of | C4⋊C4×#11719947, Q8×#13133173, Q8×#13133175, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(6784, 18087);