Finite Group DatabasebetaFinite Group Databasebeta| order | 10624 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C2×C4 |
No aliases for this group.
| Sylow | C83 ⋊ #1849 |
212 conjugacy classes of subgroups.
Polycyclic presentation:
2^7,83|a^2=f,b^2=d,c^2=e,d^2=g,f^2=g,b^a=bd,c^a=ce,d^a=dg,c^b=cg,h^b=h^821180 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #35291827, #35298792, #35298793, … |
| maximal normal subgroup of | #35291827, #35298792, #35298793, … |
| maximal quotient of | #35298151, #35298154, #35298156, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(10624, 4684);