Finite Group DatabasebetaFinite Group Databasebeta| order | 10688 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C2×C4 |
No aliases for this group.
| Fitting | C2×SD16×C167 ⋊ C2 |
| Sylow | C167 ⋊ #492 |
142 conjugacy classes of subgroups; only the 47 normal subgroups are shown.
This group has 142 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|b^2=d,c^2=e,d^2=f,b^a=bd,c^a=ce,d^a=df,g^c=g^1661184 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #492×D167, C2×#24923640, #36334562, … |
| maximal normal subgroup of | #492×D167, C2×#24923640, #36334562, … |
| maximal quotient of | #36323724, #36323726, #36323728, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(10688, 920);