Finite Group DatabasebetaFinite Group Databasebeta| order | 10688 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4 · Schur multiplier (H2) = C24×C4 |
| direct product | C2×#19128791 |
| Sylow | C167 ⋊ C2×#117 |
330 conjugacy classes of subgroups.
2696 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #36323834, #36323836, C2×#24923025, … |
| maximal normal subgroup of | #36323834, #36323836, C2×#24923025, … |
| maximal quotient of | C2×#24923115, C2×C4×C22⋊Dic167, C2×C4×C4⋊Dic167, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(10688, 1005);