Finite Group DatabasebetaFinite Group Databasebeta| order | 10624 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C2 |
No aliases for this group.
| Sylow | C83 ⋊ #2166 |
122 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,c^b=cg,e^b=eg,e^c=eg1672 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #35291498, #35291499, #35291500, … |
| maximal normal subgroup of | #35291498, #35291499, #35291500, … |
| maximal quotient of | #35319424, #35319474, #35319742, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(10624, 6326);