Finite Group DatabasebetaFinite Group Databasebeta| order | 10688 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4 · Schur multiplier (H2) = C25 |
| direct product | C22×#14581934 |
| Sylow | C167 ⋊ C22×M16 |
298 conjugacy classes of subgroups.
2696 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #36323831, #36323832, #36323834, … |
| maximal normal subgroup of | #36323831, #36323832, #36323834, … |
| maximal quotient of | C22×#19128743, C2×C4×#14581934, C22×C22⋊(C167⋊C8), … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(10688, 1309);