Finite Group DatabasebetaFinite Group Databasebeta| order | 10688 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C22 |
No aliases for this group.
| Fitting | C2×C4⋊C4×C167 ⋊ C2 |
| Sylow | C167 ⋊ #481 |
114 conjugacy classes of subgroups.
Polycyclic presentation:
2^6,167|c^2=df,e^2=f,b^a=bd,c^a=ce,e^a=ef,g^a=g^166,e^c=ef1679 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #36323156, #36323157, #36323167, … |
| maximal normal subgroup of | #36323156, #36323157, #36323167, … |
| maximal quotient of | #36324228, #36324331, #36324455, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(10688, 867);