Finite Group DatabasebetaFinite Group Databasebeta| order | 6784 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C42 · Schur multiplier (H2) = C2×C4 |
| direct product | C4×#13133153 |
| Sylow | C53 ⋊ C4×#108 |
228 conjugacy classes of subgroups.
1720 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #27271009, #27271010, #27271012, … |
| maximal normal subgroup of | #27271009, #27271010, #27271012, … |
| maximal quotient of | C4×#16810374, C4×#16810376, #27275281, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(6784, 4412);