Finite Group DatabasebetaFinite Group Databasebeta| order | 8768 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4 · Schur multiplier (H2) = C25 |
| direct product | C22×#14555520 |
| Sylow | C137 ⋊ C22×M16 |
298 conjugacy classes of subgroups.
584 conjugacy classes — view the full character table.
| maximal subgroup of | #31796453, #31796456, C2×#22578273, … |
| maximal normal subgroup of | #31796453, #31796456, C2×#22578273, … |
| maximal quotient of | C22×#17984143, C2×C4×#14555520, C22×#17984145, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(8768, 1623);