Finite Group DatabasebetaFinite Group Databasebeta| order | 5504 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C24 |
No aliases for this group.
| Fitting | C43×#380 ⋊ C2 |
| Sylow | C43 ⋊ #1519 |
340 conjugacy classes of subgroups; only the 89 normal subgroups are shown.
This group has 340 conjugacy classes of subgroups — too many to draw. Only its 89 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=e,c^2=g,d^2=g,b^a=bd,c^a=cg,d^a=df,c^b=cf,d^b=dg,e^b=efg,h^b=h^42620 conjugacy classes — view the full character table.
| maximal subgroup of | #24988129, #24988130, #24988141, … |
| maximal normal subgroup of | #24988129, #24988130, #24988141, … |
| maximal quotient of | #24984583, #24984587, #24984650, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(5504, 3077);