Finite Group DatabasebetaFinite Group Databasebeta| order | 10624 |
| automorphism | ? |
| homology | Abelianization (H1) = C82 · Schur multiplier (H2) = C22×C4 |
| unambiguous semidirect product | C83⋊#1273 |
| Sylow | C83 ⋊ #1273 |
212 conjugacy classes of subgroups.
Polycyclic presentation:
2^7,83|a^2=d,b^2=e,d^2=f,e^2=g,b^a=bc,h^b=h^822704 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #35291176, #35291177, #35291189, … |
| maximal normal subgroup of | #35291176, #35291177, #35291189, … |
| maximal quotient of | C83⋊#7014, #35290931, #35290932, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(10624, 2337);