Finite Group DatabasebetaFinite Group Databasebeta| order | 5504 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C24 |
No aliases for this group.
| Fitting | C43×#485 ⋊ C2 |
| Sylow | C43 ⋊ #3201 |
390 conjugacy classes of subgroups.
Polycyclic presentation:
2^7,43|c^2=g,f^2=g,b^a=be,c^a=cf,d^a=de,f^a=fg,h^a=h^42,c^b=ce,d^b=dg,h^b=h^42,f^c=fg,h^c=h^42425 conjugacy classes — view the full character table.
| maximal subgroup of | D43×#3201, C2×#19145483, #25967326, … |
| maximal normal subgroup of | D43×#3201, C2×#19145483, #25967326, … |
| maximal quotient of | #25105703, #25105721, #25106896, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(5504, 15398);