Finite Group DatabasebetaFinite Group Databasebeta| order | 5504 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C8 · Schur multiplier (H2) = C24 |
No aliases for this group.
| Fitting | C43×#324 ⋊ C2 |
| Sylow | C43 ⋊ #1459 |
332 conjugacy classes of subgroups; only the 81 normal subgroups are shown.
This group has 332 conjugacy classes of subgroups — too many to draw. Only its 81 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,e^2=g,b^a=bd,d^a=df,e^b=ef,h^b=h^42,h^c=h^42506 conjugacy classes — view the full character table.
| maximal subgroup of | #25005864, #25005866, #25005872, … |
| maximal normal subgroup of | #25005864, #25005866, #25005872, … |
| maximal quotient of | #24984555, #24984558, #24984628, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(5504, 2827);