Finite Group DatabasebetaFinite Group Databasebeta| order | 10688 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C24 |
No aliases for this group.
| Sylow | C167 ⋊ #533 |
222 conjugacy classes of subgroups.
Polycyclic presentation:
2^6,167|a^2=f,c^2=f,d^2=e,b^a=be,c^a=cf,g^a=g^1662684 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #36322540, #36322542, #36322558, … |
| maximal normal subgroup of | #36322540, #36322542, #36322558, … |
| maximal quotient of | #36326545, #36326615, #36326621, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(10688, 1106);