Finite Group DatabasebetaFinite Group Databasebeta| order | 5504 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C25 |
No aliases for this group.
| Fitting | C43×#470 ⋊ C2 |
| Sylow | C43 ⋊ #3054 |
500 conjugacy classes of subgroups; only the 127 normal subgroups are shown.
This group has 500 conjugacy classes of subgroups — too many to draw. Only its 127 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
Polycyclic presentation:
2^7,43|b^2=e,d^2=g,e^2=g,b^a=be,c^a=cf,e^a=eg,h^a=h^42,c^b=cg,h^b=h^42,h^d=h^42368 conjugacy classes — view the full character table.
| maximal subgroup of | #25006746, #25006759, #25250494, … |
| maximal normal subgroup of | #25006746, #25006759, #25250494, … |
| maximal quotient of | #25079113, #25079141, #25079183, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(5504, 14121);