Finite Group DatabasebetaFinite Group Databasebeta| order | 5504 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C24 |
No aliases for this group.
| Sylow | C43 ⋊ #3172 |
364 conjugacy classes of subgroups; only the 125 normal subgroups are shown.
This group has 364 conjugacy classes of subgroups — too many to draw. Only its 125 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
Polycyclic presentation:
2^7,43|a^2=g,c^2=f,d^2=e,f^2=g,b^a=be,c^a=cf,f^a=fg,h^a=h^42,c^b=cg,h^c=h^42620 conjugacy classes — view the full character table.
| maximal subgroup of | #24991503, #24991505, #25067190, … |
| maximal normal subgroup of | #24991503, #24991505, #25067190, … |
| maximal quotient of | #25097152, #25100835, #25100843, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(5504, 15117);