Finite Group DatabasebetaFinite Group Databasebeta| order | 5504 |
| automorphism | ? |
| homology | Abelianization (H1) = C4×C8 · Schur multiplier (H2) = C22 |
No aliases for this group.
| Sylow | C43 ⋊ #1378 |
132 conjugacy classes of subgroups; only the 73 normal subgroups are shown.
This group has 132 conjugacy classes of subgroups — too many to draw. Only its 73 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=e,d^2=f,f^2=g,b^a=bc,e^a=eg,h^a=h^42,c^b=cg,h^b=h^42884 conjugacy classes — view the full character table.
| maximal subgroup of | D43×#1378, C2×#19132682, #25011621, … |
| maximal normal subgroup of | D43×#1378, C2×#19132682, #25011621, … |
| maximal quotient of | #24983434, #24983444, #24983451, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(5504, 2597);