Finite Group DatabasebetaFinite Group Databasebeta| order | 6784 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4 · Schur multiplier (H2) = C25 |
| direct product | D4×#11719912 |
| Fitting | C8×D4×C53 ⋊ C2 |
| Sylow | C53 ⋊ D4×M16 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C2×C4 | C23×D53 |
| commutator, socle | C22×C53 | C23×C4 |
| Fitting | C8×D4×C53 | C2 |
| hypercenter | C8×D4 | D53 |
| hypocenter | C53 | D4×M16 |
| LCS | G ▷ C22×C53 ▷ C53 | |
| UCS | C1 ◁ C2×C4 ◁ C8×D4 | |
544 conjugacy classes of subgroups.
1090 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #27354973, #27354979, #27354984, … |
| maximal normal subgroup of | #27354973, #27354979, #27354984, … |
| maximal quotient of | D8×#11719912, #27355517, SD16×#11719912, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(6784, 13241);