Finite Group DatabasebetaFinite Group Databasebeta| order | 10688 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C2×C4 |
No aliases for this group.
| Sylow | C167 ⋊ #497 |
124 conjugacy classes of subgroups; only the 43 normal subgroups are shown.
This group has 124 conjugacy classes of subgroups — too many to draw. Only its 43 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=f,b^2=d,c^2=e,d^2=f,b^a=bd,c^a=ce,d^a=df,c^b=cf,g^c=g^1661178 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #497×D167, C2×#24923660, #36334580, … |
| maximal normal subgroup of | #497×D167, C2×#24923660, #36334580, … |
| maximal quotient of | #36323757, #36323758, #36323770, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(10688, 940);