Finite Group DatabasebetaFinite Group Databasebeta| order | 10688 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4 · Schur multiplier (H2) = C25 |
No aliases for this group.
| Fitting | C2×M16×C167 ⋊ C2 |
| Sylow | C167 ⋊ #568 |
258 conjugacy classes of subgroups; only the 147 normal subgroups are shown.
This group has 258 conjugacy classes of subgroups — too many to draw. Only its 147 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,e^2=f,d^a=df,c^b=cf,g^c=g^1661694 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #36324356, #36324359, #36324375, … |
| maximal normal subgroup of | #36324356, #36324359, #36324375, … |
| maximal quotient of | #36332555, #36332556, #36332563, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(10688, 1315);