Finite Group DatabasebetaFinite Group Databasebeta| order | 10688 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4 · Schur multiplier (H2) = C26 |
| direct product | C22×C4⋊Dic167 |
| Sylow | C167 ⋊ C22×C4⋊C4 |
418 conjugacy classes of subgroups.
2696 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #36322367, #36322368, #36322372, … |
| maximal normal subgroup of | #36322367, #36322368, #36322372, … |
| maximal quotient of | C22×C167⋊#95, C2×C4×C4⋊Dic167, C2×#24923129, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(10688, 1000);