Finite Group DatabasebetaFinite Group Databasebeta| order | 10688 |
| automorphism | ? |
| homology | Abelianization (H1) = C25 · Schur multiplier (H2) = C29 |
| direct product | C23×Dic334 |
| Sylow | C167 ⋊ C23×Q8 |
850 conjugacy classes of subgroups.
2696 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #36322408, #36324061, #36324072, … |
| maximal normal subgroup of | #36322408, #36324061, #36324072, … |
| maximal quotient of | C23×Dic167⋊C4, C23×C4⋊Dic167, C22×C4×Dic334, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(10688, 1373);