Finite Group DatabasebetaFinite Group Databasebeta| order | 10688 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C24 |
No aliases for this group.
| Fitting | C2×C4⋊C4×C167 ⋊ C2 |
| Sylow | C167 ⋊ #539 |
218 conjugacy classes of subgroups; only the 95 normal subgroups are shown.
This group has 218 conjugacy classes of subgroups — too many to draw. Only its 95 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=f,c^2=e,b^a=be,c^a=cf,d^a=de,g^a=g^166,c^b=ce1682 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #36323065, #36323069, #36323099, … |
| maximal normal subgroup of | #36323065, #36323069, #36323099, … |
| maximal quotient of | #36326741, #36326772, #36326807, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(10688, 1146);