Finite Group DatabasebetaFinite Group Databasebeta| order | 5504 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C22 |
No aliases for this group.
| Sylow | C43 ⋊ #2070 |
196 conjugacy classes of subgroups; only the 65 normal subgroups are shown.
This group has 196 conjugacy classes of subgroups — too many to draw. Only its 65 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=de,b^2=d,c^2=g,d^2=g,b^a=bd,c^a=ce,d^a=dg,e^a=eg,f^a=fg,c^b=cf,f^b=fg,h^b=h^42,d^c=dg485 conjugacy classes — view the full character table.
| maximal subgroup of | D43×#2070, C2×#19135996, #25125322, … |
| maximal normal subgroup of | D43×#2070, C2×#19135996, #25125322, … |
| maximal quotient of | #25001229, #25001231, #25001233, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(5504, 5911);