Finite Group DatabasebetaFinite Group Databasebeta| order | 5504 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C24 |
No aliases for this group.
| Sylow | C43 ⋊ #3349 |
336 conjugacy classes of subgroups.
Polycyclic presentation:
2^7,43|a^2=e,b^2=g,c^2=e,d^2=g,f^2=g,b^a=be,c^a=cf,f^a=fg,h^a=h^42,c^b=cg,d^b=de,f^c=fg554 conjugacy classes — view the full character table.
| maximal subgroup of | D43×#3349, C2×#19147125, #25975251, … |
| maximal normal subgroup of | D43×#3349, C2×#19147125, #25975251, … |
| maximal quotient of | #25112924, #25112960, #25114287, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(5504, 17040);