Finite Group DatabasebetaFinite Group Databasebeta| order | 10688 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C42 · Schur multiplier (H2) = C2×C4 |
No aliases for this group.
| Fitting | #97×C167 ⋊ C2 |
| Sylow | C167 ⋊ C4×M16 |
142 conjugacy classes of subgroups.
Polycyclic presentation:
2^6,167|a^2=d,b^2=e,d^2=f,c^a=cf,g^b=g^166,g^c=g^1661700 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #36322723, #36322725, #36322728, … |
| maximal normal subgroup of | #36322723, #36322725, #36322728, … |
| maximal quotient of | #36322417, #36322426, #36322434, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(10688, 501);