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 ⋊ #408 |
158 conjugacy classes of subgroups.
Polycyclic presentation:
2^6,167|a^2=e,e^2=f,b^a=bd,g^a=g^166,c^b=cf,g^b=g^1661688 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #36322075, #36324087, #36324100, … |
| maximal normal subgroup of | #36322075, #36324087, #36324100, … |
| maximal quotient of | #36322487, #36322491, #36322495, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(10688, 517);