Finite Group DatabasebetaFinite Group Databasebeta| order | 6784 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4 · Schur multiplier (H2) = C27 |
| direct product | C2×#102×D53 |
| Fitting | C2×#102×C53 ⋊ C2 |
| Sylow | C53 ⋊ C22×#102 |
1072 conjugacy classes of subgroups.
784 conjugacy classes — view the full character table.
| maximal subgroup of | C4×#102×D53, D53×#1762, #27381900, … |
| maximal normal subgroup of | C4×#102×D53, D53×#1762, #27381900, … |
| maximal quotient of | C2×D4⋊C8×D53, D53×#1486, C2×#20273138, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(6784, 12994);