Finite Group DatabasebetaFinite Group Databasebeta| order | 10688 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C24 |
No aliases for this group.
| Fitting | #99×C167 ⋊ C2 |
| Sylow | C167 ⋊ B(4,𝔽2) |
198 conjugacy classes of subgroups; only the 39 normal subgroups are shown.
This group has 198 conjugacy classes of subgroups — too many to draw. Only its 39 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
Polycyclic presentation:
2^6,167|b^a=bd,c^a=ce,g^a=g^166,e^b=ef,d^c=df,g^c=g^166929 conjugacy classes — view the full character table.
| maximal subgroup of | #36326123, #36326124, #36326129, … |
| maximal normal subgroup of | #36326123, #36326124, #36326129, … |
| maximal quotient of | #36323057, #36323058, #36323062, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(10688, 737);