Finite Group DatabasebetaFinite Group Databasebeta| order | 10688 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C24 |
| direct product | C2×#19128754 |
| Fitting | C22×C8×C167 ⋊ C2 |
| Sylow | C167 ⋊ C2×#102 |
202 conjugacy classes of subgroups.
2684 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #36323952, C4×#19128754, #36323962, … |
| maximal normal subgroup of | #36323952, C4×#19128754, #36323962, … |
| maximal quotient of | C2×#24922998, #36322538, #36322564, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(10688, 537);