Finite Group DatabasebetaFinite Group Databasebeta| order | 10688 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C23 |
No aliases for this group.
| Fitting | H(5,𝔽2)×C167 ⋊ C2 |
| Sylow | C167 ⋊ #453 |
168 conjugacy classes of subgroups.
Polycyclic presentation:
2^6,167|d^2=f,b^a=bd,c^a=ce,d^a=df,g^a=g^166,d^b=df,e^b=ef,d^c=df1427 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #36326120, #36326132, #36326142, … |
| maximal normal subgroup of | #36326120, #36326132, #36326142, … |
| maximal quotient of | #36323056, #36323061, #36323084, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(10688, 717);