Finite Group DatabasebetaFinite Group Databasebeta| order | 5504 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C8 · Schur multiplier (H2) = C2×C4 |
No aliases for this group.
| Sylow | C43 ⋊ #1325 |
134 conjugacy classes of subgroups; only the 37 normal subgroups are shown.
This group has 134 conjugacy classes of subgroups — too many to draw. Only its 37 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=d,b^2=eg,c^2=g,d^2=f,b^a=bc,c^a=ce,e^a=eg,d^b=deg,h^b=h^42,d^c=dg488 conjugacy classes — view the full character table.
| maximal subgroup of | D43×#1325, C2×#19132540, #25005752, … |
| maximal normal subgroup of | D43×#1325, C2×#19132540, #25005752, … |
| maximal quotient of | #24983233, #24983240, #24983393, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(5504, 2455);