Finite Group DatabasebetaFinite Group Databasebeta| order | 10688 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C42 · Schur multiplier (H2) = C2×C4 |
| direct product | C4×#14581933 |
| Fitting | C4×C8×C167 ⋊ C2 |
| Sylow | C167 ⋊ C4×M16 |
142 conjugacy classes of subgroups.
2696 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C8×#14581933, #36322417, #36322424, … |
| maximal normal subgroup of | C8×#14581933, #36322417, #36322424, … |
| maximal quotient of | C8×#14581933, #36322424, #36322432, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(10688, 499);