Finite Group DatabasebetaFinite Group Databasebeta| order | 8768 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C24 |
| direct product | C2×#17984010 |
| Fitting | C22×C8×C137 ⋊ C2 |
| Sylow | C137 ⋊ C2×#102 |
202 conjugacy classes of subgroups.
2204 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #31780603, C4×#17984010, #31780613, … |
| maximal normal subgroup of | #31780603, C4×#17984010, #31780613, … |
| maximal quotient of | C2×#22577132, #31779189, #31779215, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(8768, 537);