Finite Group DatabasebetaFinite Group Databasebeta| order | 10688 |
| automorphism | ? |
| homology | Abelianization (H1) = C4×C8 · Schur multiplier (H2) = C2 |
No aliases for this group.
| Sylow | C167 ⋊ #346 |
54 conjugacy classes of subgroups.
Polycyclic presentation:
2^6,167|a^2=c,b^2=d,c^2=e,e^2=f,b^a=bf,g^b=g^1662696 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #36322273, #346×D167, C2×#24923044, … |
| maximal normal subgroup of | #36322273, #346×D167, C2×#24923044, … |
| maximal quotient of | #36322054, #36322057, #36322215, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(10688, 324);