Finite Group DatabasebetaFinite Group Databasebeta| order | 10688 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C23 |
No aliases for this group.
| Fitting | C2×#41×C167 ⋊ C2 |
| Sylow | C167 ⋊ #449 |
162 conjugacy classes of subgroups; only the 47 normal subgroups are shown.
This group has 162 conjugacy classes of subgroups — too many to draw. Only its 47 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
Polycyclic presentation:
2^6,167|c^2=f,d^2=f,b^a=bd,c^a=ce,d^a=df,g^a=g^166,d^b=df1679 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #449×D167, C2×#24923414, #36333356, … |
| maximal normal subgroup of | #449×D167, C2×#24923414, #36333356, … |
| maximal quotient of | #36323067, #36323084, #36323135, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(10688, 694);