Finite Group DatabasebetaFinite Group Databasebeta| order | 10688 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C42 · Schur multiplier (H2) = C2×C4 |
| direct product | M16×Dic167 |
| Sylow | C167 ⋊ C4×M16 |
142 conjugacy classes of subgroups.
1700 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #36323929, #100×Dic167, #36323933, … |
| maximal normal subgroup of | #36323929, #100×Dic167, #36323933, … |
| maximal quotient of | M16×C167⋊C8, #36322419, #36322425, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(10688, 500);