Finite Group DatabasebetaFinite Group Databasebeta| order | 10688 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C23 |
No aliases for this group.
| Fitting | C2×C4⋊C4×C167 ⋊ C2 |
| Sylow | C167 ⋊ #397 |
170 conjugacy classes of subgroups; only the 57 normal subgroups are shown.
This group has 170 conjugacy classes of subgroups — too many to draw. Only its 57 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
Polycyclic presentation:
2^6,167|a^2=e,c^2=d,b^a=bd,c^a=ce,c^b=cf,g^b=g^1661682 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #36323122, #36323127, #36323149, … |
| maximal normal subgroup of | #36323122, #36323127, #36323149, … |
| maximal quotient of | #36322380, #36322386, #36322397, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(10688, 475);