Finite Group DatabasebetaFinite Group Databasebeta| order | 10688 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C2×C4 |
No aliases for this group.
| Fitting | #102×C167 ⋊ C2 |
| Sylow | C167 ⋊ #486 |
118 conjugacy classes of subgroups; only the 41 normal subgroups are shown.
This group has 118 conjugacy classes of subgroups — too many to draw. Only its 41 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=e,c^2=d,d^2=f,e^2=f,b^a=bd,c^a=ce,d^a=df,e^a=ef,g^c=g^1661184 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #486×D167, C2×#24923614, #36334458, … |
| maximal normal subgroup of | #486×D167, C2×#24923614, #36334458, … |
| maximal quotient of | #36324264, #36324818, #36324819, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(10688, 894);