Finite Group DatabasebetaFinite Group Databasebeta| order | 5504 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C8 · Schur multiplier (H2) = C22×C4 |
No aliases for this group.
| Sylow | C43 ⋊ #1461 |
248 conjugacy classes of subgroups; only the 81 normal subgroups are shown.
This group has 248 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,b^2=f,c^2=fg,e^2=g,b^a=bd,d^a=df,e^b=ef,h^c=h^42506 conjugacy classes — view the full character table.
| maximal subgroup of | #25005868, #25005870, #25005876, … |
| maximal normal subgroup of | #25005868, #25005870, #25005876, … |
| maximal quotient of | #24984567, #24984573, #24984641, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(5504, 2832);