Finite Group DatabasebetaFinite Group Databasebeta| order | 10688 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C23 |
No aliases for this group.
| 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,g^a=g^166,c^b=cf1682 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #397×D167, C2×#24923197, #36327380, … |
| maximal normal subgroup of | #397×D167, C2×#24923197, #36327380, … |
| maximal quotient of | #36322381, #36322385, #36322387, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(10688, 477);