Finite Group DatabasebetaFinite Group Databasebeta| order | 6784 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4 · Schur multiplier (H2) = C25 |
| direct product | C4×Q16×D53 |
| Fitting | C4×Q16×C53 ⋊ C2 |
| Sylow | C53 ⋊ C2×C4×Q16 |
488 conjugacy classes of subgroups.
784 conjugacy classes — view the full character table.
| maximal subgroup of | D53×#1332, #27293843, D53×#1334, … |
| maximal normal subgroup of | D53×#1332, #27293843, D53×#1334, … |
| maximal quotient of | C8×Q16×D53, D53×#1584, D53×#1591, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(6784, 13271);