Finite Group DatabasebetaFinite Group Databasebeta| order | 5504 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4 · Schur multiplier (H2) = C26 |
No aliases for this group.
| Fitting | C43×#410 ⋊ C2 |
| Sylow | C43 ⋊ #2884 |
716 conjugacy classes of subgroups; only the 209 normal subgroups are shown.
This group has 716 conjugacy classes of subgroups — too many to draw. Only its 209 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=f,c^2=g,d^2=g,b^a=be,e^a=eg,f^b=fg,d^c=dg,h^d=h^42503 conjugacy classes — view the full character table.
| maximal subgroup of | #25014188, #25014190, #25014192, … |
| maximal normal subgroup of | #25014188, #25014190, #25014192, … |
| maximal quotient of | #25062423, #25062425, #25062427, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(5504, 12972);