Finite Group DatabasebetaFinite Group Databasebeta| order | 10688 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C22×C4 |
No aliases for this group.
| Sylow | C167 ⋊ #410 |
158 conjugacy classes of subgroups.
Polycyclic presentation:
2^6,167|a^2=e,c^2=f,b^a=bd,d^a=df,g^a=g^166,e^b=ef1682 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #36322258, #36322259, #36322267, … |
| maximal normal subgroup of | #36322258, #36322259, #36322267, … |
| maximal quotient of | #36322452, #36322459, #36322462, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(10688, 523);