Finite Group DatabasebetaFinite Group Databasebeta| order | 10688 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C42 · Schur multiplier (H2) = C23×C4 |
| direct product | C4×C22⋊Dic167 |
| Sylow | C167 ⋊ C4×C22⋊C4 |
258 conjugacy classes of subgroups.
2696 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #36321984, #36321985, #36321990, … |
| maximal normal subgroup of | #36321984, #36321985, #36321990, … |
| maximal quotient of | C4×C167⋊#95, #36322361, #36322365, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(10688, 397);