Finite Group DatabasebetaFinite Group Databasebeta| order | 10624 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C24 |
No aliases for this group.
| Fitting | C4×D8×C83 ⋊ C2 |
| Sylow | C83 ⋊ #3122 |
418 conjugacy classes of subgroups.
Polycyclic presentation:
2^7,83|d^2=eg,f^2=g,b^a=be,c^a=cf,f^a=fg,d^b=dg,h^b=h^82,f^c=fg1180 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #3122×D83, C2×#24917703, #36272770, … |
| maximal normal subgroup of | #3122×D83, C2×#24917703, #36272770, … |
| maximal quotient of | #35404492, #35407491, #35407501, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(10624, 14750);