Finite Group DatabasebetaFinite Group Databasebeta| order | 10688 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C8 · Schur multiplier (H2) = C22 |
No aliases for this group.
| Fitting | C2×C16×C167 ⋊ C2 |
| Sylow | C167 ⋊ #504 |
84 conjugacy classes of subgroups.
Polycyclic presentation:
2^6,167|a^2=d,d^2=e,e^2=f,c^b=cf,g^c=g^1662696 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #36322279, #36322281, #36325973, … |
| maximal normal subgroup of | #36322279, #36322281, #36325973, … |
| maximal quotient of | #36325733, #36325734, #36325750, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(10688, 965);