Finite Group DatabasebetaFinite Group Databasebeta| order | 10624 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C2 |
No aliases for this group.
| Sylow | C83 ⋊ #2165 |
128 conjugacy classes of subgroups.
Polycyclic presentation:
2^7,83|a^2=e,c^2=d,e^2=f,f^2=g,b^a=bd,c^a=cf,d^a=dg,h^a=h^82,e^b=eg,e^c=eg1672 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #35291464, #35291465, #35291467, … |
| maximal normal subgroup of | #35291464, #35291465, #35291467, … |
| maximal quotient of | #35319420, #35319470, #35319738, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(10624, 6322);