Finite Group DatabasebetaFinite Group Databasebeta| order | 10688 |
| automorphism | ? |
| homology | Abelianization (H1) = C4×C8 · Schur multiplier (H2) = C4 |
No aliases for this group.
| Sylow | C167 ⋊ #322 |
66 conjugacy classes of subgroups.
Polycyclic presentation:
2^6,167|a^2=c,b^2=d,c^2=e,d^2=f,b^a=be,g^b=g^1662696 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #36322058, #36322060, #36322113, … |
| maximal normal subgroup of | #36322058, #36322060, #36322113, … |
| maximal quotient of | C167⋊#1273, #36322056, #36322058, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(10688, 270);