Finite Group DatabasebetaFinite Group Databasebeta| order | 5504 |
| automorphism | ? |
| homology | Abelianization (H1) = C4×C8 · Schur multiplier (H2) = C23 |
No aliases for this group.
| Sylow | C43 ⋊ #1277 |
180 conjugacy classes of subgroups; only the 113 normal subgroups are shown.
This group has 180 conjugacy classes of subgroups — too many to draw. Only its 113 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,c^2=f,d^2=g,e^2=f,b^a=bc,c^a=cf,e^a=ef,h^a=h^421400 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #24983364, #24983365, #24983367, … |
| maximal normal subgroup of | #24983364, #24983365, #24983367, … |
| maximal quotient of | #24983125, #24983131, #24983135, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(5504, 2345);