Finite Group DatabasebetaFinite Group Databasebeta| order | 5504 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C42 · Schur multiplier (H2) = C24 |
No aliases for this group.
| Sylow | C43 ⋊ #1733 |
404 conjugacy classes of subgroups.
Polycyclic presentation:
2^7,43|a^2=e,b^2=f,d^2=g,b^a=bd,d^a=dg,f^a=fg,h^a=h^42,c^b=cg884 conjugacy classes — view the full character table.
| maximal subgroup of | #25001915, #25001916, #25001920, … |
| maximal normal subgroup of | #25001915, #25001916, #25001920, … |
| maximal quotient of | #24986036, #24986042, #24986045, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(5504, 4220);