Finite Group DatabasebetaFinite Group Databasebeta| order | 10688 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C22 |
No aliases for this group.
| Fitting | #106×C167 ⋊ C2 |
| Sylow | C167 ⋊ #470 |
110 conjugacy classes of subgroups.
Polycyclic presentation:
2^6,167|a^2=f,b^2=df,d^2=f,b^a=bd,c^a=ce,d^a=df,g^a=g^166,c^b=cf,g^c=g^1661178 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #36326090, #36326359, #470×D167, … |
| maximal normal subgroup of | #36326090, #36326359, #470×D167, … |
| maximal quotient of | #36323628, #36323633, #36323662, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(10688, 808);