Finite Group DatabasebetaFinite Group Databasebeta| order | 5504 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C23×C4 |
No aliases for this group.
| Fitting | C43×#542 ⋊ C2 |
| Sylow | C43 ⋊ #3224 |
408 conjugacy classes of subgroups.
Polycyclic presentation:
2^7,43|b^2=eg,f^2=g,b^a=be,c^a=cf,d^a=de,f^a=fg,c^b=ce,d^b=dg,f^c=fg,h^c=h^42488 conjugacy classes — view the full character table.
| maximal subgroup of | D43×#3224, C2×#19145683, #25968002, … |
| maximal normal subgroup of | D43×#3224, C2×#19145683, #25968002, … |
| maximal quotient of | #25105965, #25106368, #25107202, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(5504, 15598);