Finite Group DatabasebetaFinite Group Databasebeta| order | 8768 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C22 |
| direct product | C4×#14555499 |
| Fitting | C4×C8×C137 ⋊ C2 |
| Sylow | C137 ⋊ C4×SD16 |
122 conjugacy classes of subgroups; only the 55 normal subgroups are shown.
This group has 122 conjugacy classes of subgroups — too many to draw. Only its 55 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
2204 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #31779588, C8×#14555499, #31779600, … |
| maximal normal subgroup of | #31779588, C8×#14555499, #31779600, … |
| maximal quotient of | C8×#14555499, #31779627, #31779634, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(8768, 639);