Finite Group DatabasebetaFinite Group Databasebeta| order | 8768 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C42 · Schur multiplier (H2) = C22×C4 |
| direct product | C4×C4⋊#10587739 |
| Fitting | C42×C137 ⋊ C4 |
| Sylow | C137 ⋊ C4×C4⋊C4 |
194 conjugacy classes of subgroups.
584 conjugacy classes — view the full character table.
| maximal subgroup of | #31795623, #31795624, #31795639, … |
| maximal normal subgroup of | #31795623, #31795624, #31795639, … |
| maximal quotient of | C4×(C2×#10587739)⋊C4, #31795965, #31795967, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(8768, 1488);