Finite Group DatabasebetaFinite Group Databasebeta| order | 10688 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C25 |
| direct product | C2×#19128854 |
| Fitting | C22×C8×C167 ⋊ C2 |
| Sylow | C167 ⋊ C2×#135 |
266 conjugacy classes of subgroups.
2684 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #36324464, #36324466, #36325024, … |
| maximal normal subgroup of | #36324464, #36324466, #36325024, … |
| maximal quotient of | C2×#24923266, C2×#24923307, C2×C4×D1336, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(10688, 1331);