Finite Group DatabasebetaFinite Group Databasebeta| order | 10688 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4 · Schur multiplier (H2) = C24×C4 |
| direct product | C2×#19128789 |
| Fitting | C2×C42×C167 ⋊ C2 |
| Sylow | C167 ⋊ C2×#117 |
330 conjugacy classes of subgroups.
2696 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #36322450, #36322470, #36323833, … |
| maximal normal subgroup of | #36322450, #36322470, #36323833, … |
| maximal quotient of | C2×#24923115, C2×C4×(C2×D167)⋊C4, C2×C4×Dic167⋊C4, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(10688, 1003);