Finite Group DatabasebetaFinite Group Databasebeta| order | 5504 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4 · Schur multiplier (H2) = C25 |
No aliases for this group.
| Sylow | C43 ⋊ #2911 |
492 conjugacy classes of subgroups; only the 293 normal subgroups are shown.
This group has 492 conjugacy classes of subgroups — too many to draw. Only its 293 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=f,b^2=e,d^2=g,e^2=g,b^a=be,e^a=eg,h^a=h^42,c^b=cg884 conjugacy classes — view the full character table.
| maximal subgroup of | #25002672, #25002674, #25002707, … |
| maximal normal subgroup of | #25002672, #25002674, #25002707, … |
| maximal quotient of | #25065581, #25065620, #25065632, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(5504, 13100);