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 ⋊ #1740 |
420 conjugacy classes of subgroups.
Polycyclic presentation:
2^7,43|a^2=e,b^2=f,c^2=g,b^a=bd,d^a=dg,e^b=eg,h^b=h^42884 conjugacy classes — view the full character table.
| maximal subgroup of | #25001809, #25001810, #25002058, … |
| maximal normal subgroup of | #25001809, #25001810, #25002058, … |
| maximal quotient of | #24986187, #24986193, #24986199, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(5504, 4242);