Finite Group DatabasebetaFinite Group Databasebeta| order | 10688 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C22 |
No aliases for this group.
| Fitting | C2×SD16×C167 ⋊ C2 |
| Sylow | C167 ⋊ #468 |
120 conjugacy classes of subgroups; only the 41 normal subgroups are shown.
This group has 120 conjugacy classes of subgroups — too many to draw. Only its 41 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^2=d,d^2=f,b^a=bd,c^a=ce,d^a=df,c^b=cf,g^c=g^1661178 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #468×D167, C2×#24923512, #36333742, … |
| maximal normal subgroup of | #468×D167, C2×#24923512, #36333742, … |
| maximal quotient of | #36323600, #36323607, #36323634, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(10688, 792);