Finite Group DatabasebetaFinite Group Databasebeta| order | 8768 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C22 |
| direct product | C2×#17984159 |
| Sylow | C137 ⋊ C2×#108 |
106 conjugacy classes of subgroups.
572 conjugacy classes — view the full character table.
| maximal subgroup of | #31795849, #31795850, #31795868, … |
| maximal normal subgroup of | #31795849, #31795850, #31795868, … |
| maximal quotient of | C2×#22578265, C2×#22578266, #31796339, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(8768, 1563);