Finite Group DatabasebetaFinite Group Databasebeta| order | 8768 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C25 |
| direct product | C22×#14555497 |
| Fitting | C22×Q8×C137 ⋊ C2 |
| Sylow | C137 ⋊ C22×SD16 |
298 conjugacy classes of subgroups.
1388 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #31781120, #31781126, #31781142, … |
| maximal normal subgroup of | #31781120, #31781126, #31781142, … |
| maximal quotient of | C22×#17984008, C22×#17984012, C22×#17984019, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(8768, 1321);