Finite Group DatabasebetaFinite Group Databasebeta| order | 6784 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C16 · Schur multiplier (H2) = C22 |
| direct product | Q8×#11719908 |
| Sylow | C53 ⋊ Q8×C16 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C2×C8 | C22×D53 |
| commutator | C2×C53 | C22×C16 |
| Fitting | C8×Q8×C53 | C2 |
| socle | C22×C53 | C22×C8 |
| hypercenter | C8×Q8 | D53 |
| hypocenter | C53 | Q8×C16 |
| LCS | G ▷ C2×C53 ▷ C53 | |
| UCS | C1 ◁ C2×C8 ◁ C8×Q8 | |
134 conjugacy classes of subgroups.
1120 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #27295855, SD16×#11719908, #27295869, … |
| maximal normal subgroup of | #27295855, SD16×#11719908, #27295869, … |
| maximal quotient of | C4⋊C4×#11719908, #27301709, #27302093, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(6784, 6414);