Finite Group DatabasebetaFinite Group Databasebeta| order | 10624 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C24 |
No aliases for this group.
| Fitting | #440×C83 ⋊ C2 |
| Sylow | C83 ⋊ #3117 |
386 conjugacy classes of subgroups.
Polycyclic presentation:
2^7,83|c^2=g,d^2=eg,f^2=g,b^a=be,c^a=cf,f^a=fg,h^b=h^82,d^c=dg,f^c=fg934 conjugacy classes — view the full character table.
| maximal subgroup of | #3117×D83, C2×#24917632, #36272617, … |
| maximal normal subgroup of | #3117×D83, C2×#24917632, #36272617, … |
| maximal quotient of | #35404467, #35407446, #35407448, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(10624, 14679);