Finite Group DatabasebetaFinite Group Databasebeta| order | 10624 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C24 |
No aliases for this group.
| Fitting | #520×C83 ⋊ C2 |
| Sylow | C83 ⋊ #3124 |
384 conjugacy classes of subgroups.
Polycyclic presentation:
2^7,83|b^2=g,d^2=eg,f^2=g,b^a=be,c^a=cf,f^a=fg,h^a=h^82,d^b=dg,f^c=fg1426 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #3124×D83, C2×#24917725, #36272775, … |
| maximal normal subgroup of | #3124×D83, C2×#24917725, #36272775, … |
| maximal quotient of | #35404514, #35407480, #35407525, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(10624, 14772);