Finite Group DatabasebetaFinite Group Databasebeta| order | 10688 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C2 |
No aliases for this group.
| Fitting | #125×C167 ⋊ C2 |
| Sylow | C167 ⋊ #478 |
102 conjugacy classes of subgroups.
Polycyclic presentation:
2^6,167|a^2=d,b^2=df,e^2=f,b^a=bd,c^a=ce,e^a=ef,e^c=ef,g^c=g^1661181 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #478×D167, C2×#24923566, #36333920, … |
| maximal normal subgroup of | #478×D167, C2×#24923566, #36333920, … |
| maximal quotient of | #36324145, #36324384, #36324398, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(10688, 846);