Finite Group DatabasebetaFinite Group Databasebeta| order | 10688 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C23 |
No aliases for this group.
| Fitting | C2×M16×C167 ⋊ C2 |
| Sylow | C167 ⋊ #407 |
190 conjugacy classes of subgroups.
Polycyclic presentation:
2^6,167|a^2=e,e^2=f,b^a=bd,c^a=cf,g^b=g^1661688 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #36322073, #36324057, #36324060, … |
| maximal normal subgroup of | #36322073, #36324057, #36324060, … |
| maximal quotient of | #36322464, #36322467, #36322470, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(10688, 512);