Finite Group DatabasebetaFinite Group Databasebeta| order | 10624 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C24 |
No aliases for this group.
| Fitting | #486×C83 ⋊ C2 |
| Sylow | C83 ⋊ #3361 |
362 conjugacy classes of subgroups; only the 115 normal subgroups are shown.
This group has 362 conjugacy classes of subgroups — too many to draw. Only its 115 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=g,b^2=eg,d^2=e,f^2=g,b^a=be,c^a=cf,f^a=fg,h^a=h^82,d^b=de,h^b=h^82,f^c=fg,h^c=h^82937 conjugacy classes — view the full character table.
| maximal subgroup of | #35394260, #35394267, #35394395, … |
| maximal normal subgroup of | #35394260, #35394267, #35394395, … |
| maximal quotient of | #35421005, #35421223, #35423351, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(10624, 17175);