Finite Group DatabasebetaFinite Group Databasebeta| order | 10688 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C22 |
No aliases for this group.
| Fitting | C4⋊C8×C167 ⋊ C2 |
| Sylow | C167 ⋊ #474 |
108 conjugacy classes of subgroups.
Polycyclic presentation:
2^6,167|a^2=d,b^2=d,e^2=f,b^a=bd,c^a=ce,e^a=ef,g^a=g^166,e^c=ef,g^c=g^1661679 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #36323318, #36323319, #36323332, … |
| maximal normal subgroup of | #36323318, #36323319, #36323332, … |
| maximal quotient of | #36324139, #36324388, #36324710, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(10688, 830);