Finite Group DatabasebetaFinite Group Databasebeta| order | 10688 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C24 |
No aliases for this group.
| Fitting | C4×Q8×C167 ⋊ C2 |
| Sylow | C167 ⋊ #529 |
234 conjugacy classes of subgroups; only the 101 normal subgroups are shown.
This group has 234 conjugacy classes of subgroups — too many to draw. Only its 101 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,d^2=e,b^a=be,c^a=cf,g^a=g^166,g^b=g^166,g^c=g^1661688 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #36322545, #36322550, #36322597, … |
| maximal normal subgroup of | #36322545, #36322550, #36322597, … |
| maximal quotient of | #36326534, #36326579, #36326599, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(10688, 1086);