Finite Group DatabasebetaFinite Group Databasebeta| order | 6784 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4 · Schur multiplier (H2) = C25 |
| direct product | C4×#13133237 |
| Fitting | C4×#41×C53 ⋊ C2 |
| Sylow | C53 ⋊ C4×#135 |
500 conjugacy classes of subgroups.
1096 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #27353466, C8×#13133237, #27353494, … |
| maximal normal subgroup of | #27353466, C8×#13133237, #27353494, … |
| maximal quotient of | C8×#13133237, #27353619, #27353623, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(6784, 13280);