Finite Group DatabasebetaFinite Group Databasebeta| order | 10688 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C22 |
No aliases for this group.
| Sylow | C167 ⋊ #440 |
120 conjugacy classes of subgroups; only the 57 normal subgroups are shown.
This group has 120 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=e,d^2=f,b^a=bd,c^a=cf,d^a=df,g^a=g^166,d^b=df,g^c=g^1661184 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #440×D167, C2×#24923370, #36332933, … |
| maximal normal subgroup of | #440×D167, C2×#24923370, #36332933, … |
| maximal quotient of | SD16⋊(C167⋊C8), #36322996, #36323017, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(10688, 650);