Finite Group DatabasebetaFinite Group Databasebeta| order | 6784 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4 · Schur multiplier (H2) = C23×C4 |
| direct product | C2×#16810683 |
| Fitting | C2×C4⋊C8×C53 ⋊ C2 |
| Sylow | C53 ⋊ C2×#433 |
| subgroup | G/H | |
|---|---|---|
| center | C22×C4 | C22×D53 |
| commutator | C22×C53 | C23×C4 |
| Frattini | C2×C4 | C23×D53 |
| Fitting | C2×C4⋊C8×C53 | C2 |
| socle | C23×C53 | C22×C4 |
| hypercenter | C2×C4⋊C8 | D53 |
| hypocenter | C53 | C2×#433 |
| LCS | G ▷ C22×C53 ▷ C53 | |
| UCS | C1 ◁ C22×C4 ◁ C2×C4⋊C8 | |
412 conjugacy classes of subgroups.
1096 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #27293297, #27382235, C4×#16810683, … |
| maximal normal subgroup of | #27293297, #27382235, C4×#16810683, … |
| maximal quotient of | C2×#20274465, C2×#20274480, C2×#20274574, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(6784, 13135);