Finite Group DatabasebetaFinite Group Databasebeta| order | 8768 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C23 |
| direct product | C2×#17984156 |
| unambiguous semidirect product | D137⋊#106 |
| Fitting | C2×C8×C137 ⋊ C4 |
| Sylow | C137 ⋊ C2×#106 |
130 conjugacy classes of subgroups.
572 conjugacy classes — view the full character table.
| maximal subgroup of | #31795854, #31795855, #31795860, … |
| maximal normal subgroup of | #31795854, #31795855, #31795860, … |
| maximal quotient of | C2×#22578264, #31796331, C2×#22578265, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(8768, 1557);