Finite Group DatabasebetaFinite Group Databasebeta| order | 5504 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C25 |
No aliases for this group.
| Fitting | C43×#427 ⋊ C2 |
| Sylow | C43 ⋊ #3054 |
500 conjugacy classes of subgroups; only the 141 normal subgroups are shown.
This group has 500 conjugacy classes of subgroups — too many to draw. Only its 141 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^c=h^42620 conjugacy classes — view the full character table.
| maximal subgroup of | #25013575, #25013631, #25015367, … |
| maximal normal subgroup of | #25013575, #25013631, #25015367, … |
| maximal quotient of | #25079112, #25079140, #25079181, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(5504, 14120);