Finite Group DatabasebetaFinite Group Databasebeta| order | 10624 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C25 |
No aliases for this group.
| Fitting | #413×C83 ⋊ C2 |
| Sylow | C83 ⋊ #3067 |
452 conjugacy classes of subgroups.
Polycyclic presentation:
2^7,83|b^2=e,d^2=g,e^2=g,f^2=g,b^a=be,c^a=cf,e^a=eg,f^a=fg,h^b=h^82,f^c=fg,h^c=h^82934 conjugacy classes — view the full character table.
| maximal subgroup of | #35411341, #35411342, #35411352, … |
| maximal normal subgroup of | #35411341, #35411342, #35411352, … |
| maximal quotient of | #35386645, #35386673, #35386713, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(10624, 14229);