Finite Group DatabasebetaFinite Group Databasebeta| order | 5504 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C24 |
No aliases for this group.
| Fitting | C43×#336 ⋊ C2 |
| Sylow | C43 ⋊ #2014 |
474 conjugacy classes of subgroups; only the 99 normal subgroups are shown.
This group has 474 conjugacy classes of subgroups — too many to draw. Only its 99 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=g,d^2=g,e^2=g,b^a=bd,c^a=ce,d^a=dg,e^a=eg,h^a=h^42,c^b=cf,d^b=dg,e^b=eg,h^b=h^42,d^c=dg,e^c=eg,h^c=h^42872 conjugacy classes — view the full character table.
| maximal subgroup of | #24985302, #24985303, #24985339, … |
| maximal normal subgroup of | #24985302, #24985303, #24985339, … |
| maximal quotient of | #24997076, #24997118, #24997142, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(5504, 5600);