Finite Group DatabasebetaFinite Group Databasebeta| order | 10624 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4 · Schur multiplier (H2) = C23×C4 |
No aliases for this group.
| Fitting | #423×C83 ⋊ C2 |
| Sylow | C83 ⋊ #2925 |
392 conjugacy classes of subgroups.
Polycyclic presentation:
2^7,83|a^2=f,c^2=e,f^2=g,b^a=be,h^a=h^82,d^b=dg,h^b=h^82,d^c=dg,h^c=h^821198 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #35298708, #35298712, #35298722, … |
| maximal normal subgroup of | #35298708, #35298712, #35298722, … |
| maximal quotient of | #35401904, #35401958, #35402329, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(10624, 13178);