Finite Group DatabasebetaFinite Group Databasebeta| order | 10688 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4 · Schur multiplier (H2) = C25 |
| direct product | C2×C4×Dic334 |
| Sylow | C167 ⋊ C2×C4×Q8 |
298 conjugacy classes of subgroups.
2696 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #36322461, #36322481, C2×#24922999, … |
| maximal normal subgroup of | #36322461, #36322481, C2×#24922999, … |
| maximal quotient of | C2×C4×C4⋊Dic167, C2×C4×Dic167⋊C4, C42×Dic334, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(10688, 1014);