Finite Group DatabasebetaFinite Group Databasebeta| order | 10624 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C25 |
No aliases for this group.
| Fitting | #466×C83 ⋊ C2 |
| Sylow | C83 ⋊ #3186 |
520 conjugacy classes of subgroups; only the 121 normal subgroups are shown.
This group has 520 conjugacy classes of subgroups — too many to draw. Only its 121 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
Polycyclic presentation:
2^7,83|f^2=g,b^a=be,c^a=cf,d^a=de,f^a=fg,c^b=ce,f^c=fg,h^d=h^82934 conjugacy classes — view the full character table.
| maximal subgroup of | #35316499, #35316502, #35316516, … |
| maximal normal subgroup of | #35316499, #35316502, #35316516, … |
| maximal quotient of | #35413404, #35414673, #35415530, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(10624, 15257);