Finite Group DatabasebetaFinite Group Databasebeta| order | 10624 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C25 |
No aliases for this group.
| Sylow | C83 ⋊ #1780 |
612 conjugacy classes of subgroups.
Polycyclic presentation:
2^7,83|a^2=f,f^2=g,b^a=bd,c^a=ce,h^a=h^82,c^b=cg1684 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #35291678, #35291680, #35291686, … |
| maximal normal subgroup of | #35291678, #35291680, #35291686, … |
| maximal quotient of | #35295752, #35295755, #35295758, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(10624, 4422);