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 ⋊ #384 |
186 conjugacy classes of subgroups.
Polycyclic presentation:
2^6,167|a^2=f,b^2=d,c^2=e,b^a=bd,c^a=ce,g^a=g^1662684 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #36322022, #36324138, #36324139, … |
| maximal normal subgroup of | #36322022, #36324138, #36324139, … |
| maximal quotient of | #36322368, #36322403, #36324290, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(10688, 419);