Finite Group DatabasebetaFinite Group Databasebeta| order | 10688 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C8 · Schur multiplier (H2) = C23 |
| direct product | C2×C4⋊(C167⋊C8) |
| Sylow | C167 ⋊ C2×C4⋊C8 |
138 conjugacy classes of subgroups.
2696 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #36321972, #36321973, #36321978, … |
| maximal normal subgroup of | #36321972, #36321973, #36321978, … |
| maximal quotient of | C2×#24923020, C2×#24923022, #36322886, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(10688, 570);