Finite Group DatabasebetaFinite Group Databasebeta| order | 10624 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C24 |
No aliases for this group.
| Fitting | #441×C83 ⋊ C2 |
| Sylow | C83 ⋊ #3181 |
366 conjugacy classes of subgroups.
Polycyclic presentation:
2^7,83|a^2=g,c^2=f,d^2=e,f^2=g,b^a=be,c^a=cf,f^a=fg,h^b=h^82,d^c=dg,h^c=h^82934 conjugacy classes — view the full character table.
| maximal subgroup of | #3181×D83, C2×#24918170, #36274333, … |
| maximal normal subgroup of | #3181×D83, C2×#24918170, #36274333, … |
| maximal quotient of | #35404992, #35408730, #35408734, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(10624, 15217);