Finite Group DatabasebetaFinite Group Databasebeta| order | 5504 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C42 · Schur multiplier (H2) = C23×C4 |
No aliases for this group.
| Sylow | C43 ⋊ #1735 |
424 conjugacy classes of subgroups.
Polycyclic presentation:
2^7,43|a^2=e,b^2=f,c^2=g,d^2=g,f^2=g,b^a=bd,d^a=dg,f^a=fg,h^b=h^42896 conjugacy classes — view the full character table.
| maximal subgroup of | #25001788, #25001789, #25001793, … |
| maximal normal subgroup of | #25001788, #25001789, #25001793, … |
| maximal quotient of | #24986055, #24986065, #24986076, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(5504, 4226);