Finite Group DatabasebetaFinite Group Databasebeta| order | 5504 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C24 |
No aliases for this group.
| Fitting | C43×#389 ⋊ C2 |
| Sylow | C43 ⋊ #2041 |
402 conjugacy classes of subgroups; only the 93 normal subgroups are shown.
This group has 402 conjugacy classes of subgroups — too many to draw. Only its 93 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
Polycyclic presentation:
2^7,43|c^2=d,e^2=g,f^2=g,b^a=bd,c^a=ce,e^a=eg,f^a=fg,h^a=h^42,c^b=cf,e^b=eg,f^b=fg,h^b=h^42,e^c=eg,f^c=fg620 conjugacy classes — view the full character table.
| maximal subgroup of | #24985300, #24985303, #24985306, … |
| maximal normal subgroup of | #24985300, #24985303, #24985306, … |
| maximal quotient of | #24999921, #24999926, #24999957, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(5504, 5744);