Finite Group DatabasebetaFinite Group Databasebeta| order | 10688 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C22×C4 |
No aliases for this group.
| Sylow | C167 ⋊ #382 |
154 conjugacy classes of subgroups.
Polycyclic presentation:
2^6,167|a^2=f,b^2=e,c^2=d,b^a=bd,c^a=ce,g^a=g^1662684 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #36321997, #36321998, #36322020, … |
| maximal normal subgroup of | #36321997, #36321998, #36322020, … |
| maximal quotient of | #36322365, #36322368, #36322395, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(10688, 415);