Finite Group DatabasebetaFinite Group Databasebeta| order | 10688 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C4 · Schur multiplier (H2) = C22 |
No aliases for this group.
| Fitting | C22⋊C8×C167 ⋊ C2 |
| Sylow | C167 ⋊ #327 |
90 conjugacy classes of subgroups.
Polycyclic presentation:
2^6,167|a^2=d,c^2=f,b^a=bc,c^a=ce,g^a=g^166,c^b=cf,d^b=def,g^b=g^1661679 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #327×D167, C2×#24923004, #36322623, … |
| maximal normal subgroup of | #327×D167, C2×#24923004, #36322623, … |
| maximal quotient of | #36321958, #36321960, #36322018, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(10688, 284);