Finite Group DatabasebetaFinite Group Databasebeta| order | 5504 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C24 |
No aliases for this group.
| Sylow | C43 ⋊ #3120 |
372 conjugacy classes of subgroups.
Polycyclic presentation:
2^7,43|a^2=g,b^2=g,d^2=e,f^2=g,b^a=be,c^a=cf,f^a=fg,h^a=h^42,d^b=dg,f^c=fg,h^d=h^42431 conjugacy classes — view the full character table.
| maximal subgroup of | D43×#3120, C2×#19144810, #25964957, … |
| maximal normal subgroup of | D43×#3120, C2×#19144810, #25964957, … |
| maximal quotient of | #25096708, #25099674, #25099696, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(5504, 14725);