Finite Group DatabasebetaFinite Group Databasebeta| order | 10688 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C24 |
No aliases for this group.
| Sylow | C167 ⋊ #381 |
218 conjugacy classes of subgroups.
Polycyclic presentation:
2^6,167|a^2=f,c^2=d,b^a=bd,c^a=ce,g^c=g^1661688 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #36322067, #36324054, #36324214, … |
| maximal normal subgroup of | #36322067, #36324054, #36324214, … |
| maximal quotient of | #36322360, #36322362, #36322385, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(10688, 410);