Finite Group DatabasebetaFinite Group Databasebeta| order | 10624 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C8 · Schur multiplier (H2) = C22 |
No aliases for this group.
| Sylow | C83 ⋊ #2153 |
152 conjugacy classes of subgroups.
Polycyclic presentation:
2^7,83|a^2=e,b^2=d,d^2=g,e^2=f,f^2=g,b^a=bd,d^a=dg,h^a=h^82,c^b=cg1684 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #35315921, #35315922, #35315926, … |
| maximal normal subgroup of | #35315921, #35315922, #35315926, … |
| maximal quotient of | #35315952, #35315978, #35316012, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(10624, 6276);