Finite Group DatabasebetaFinite Group Databasebeta| order | 10624 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C24 |
No aliases for this group.
| Fitting | #498×C83 ⋊ C2 |
| Sylow | C83 ⋊ #3354 |
386 conjugacy classes of subgroups; only the 117 normal subgroups are shown.
This group has 386 conjugacy classes of subgroups — too many to draw. Only its 117 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
Polycyclic presentation:
2^7,83|a^2=eg,b^2=g,c^2=e,f^2=g,b^a=be,c^a=cf,d^a=dg,f^a=fg,c^b=cg,d^b=de,h^b=h^82,f^c=fg,h^c=h^82,h^d=h^82931 conjugacy classes — view the full character table.
| maximal subgroup of | #35395308, #35395310, #35395353, … |
| maximal normal subgroup of | #35395308, #35395310, #35395353, … |
| maximal quotient of | #35420826, #35420863, #35422179, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(10624, 17104);