Finite Group DatabasebetaFinite Group Databasebeta| order | 5504 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C24 |
No aliases for this group.
| Fitting | C43×#482 ⋊ C2 |
| Sylow | C43 ⋊ #3313 |
380 conjugacy classes of subgroups.
Polycyclic presentation:
2^7,43|a^2=e,b^2=g,c^2=g,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=fg,h^c=h^42,h^d=h^42428 conjugacy classes — view the full character table.
| maximal subgroup of | D43×#3313, C2×#19146664, #25973376, … |
| maximal normal subgroup of | D43×#3313, C2×#19146664, #25973376, … |
| maximal quotient of | #25112185, #25112923, #25113722, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(5504, 16579);