Finite Group DatabasebetaFinite Group Databasebeta| order | 10624 |
| automorphism | ? |
| homology | Abelianization (H1) = C43 · Schur multiplier (H2) = C2×C42 |
No aliases for this group.
| Sylow | C83 ⋊ #1726 |
328 conjugacy classes of subgroups.
Polycyclic presentation:
2^7,83|a^2=d,b^2=e,c^2=f,d^2=g,h^a=h^82,c^b=cg1720 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #35294842, #35294846, #35294850, … |
| maximal normal subgroup of | #35294842, #35294846, #35294850, … |
| maximal quotient of | #35293758, #35293761, #35293767, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(10624, 4197);