Finite Group DatabasebetaFinite Group Databasebeta| order | 5504 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C23 |
No aliases for this group.
| Sylow | C43 ⋊ #2025 |
294 conjugacy classes of subgroups; only the 85 normal subgroups are shown.
This group has 294 conjugacy classes of subgroups — too many to draw. Only its 85 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
Polycyclic presentation:
2^7,43|a^2=d,b^2=dg,e^2=g,b^a=bd,c^a=ce,e^a=eg,c^b=cf,h^b=h^42,e^c=eg620 conjugacy classes — view the full character table.
| maximal subgroup of | D43×#2025, C2×#19135739, #25123887, … |
| maximal normal subgroup of | D43×#2025, C2×#19135739, #25123887, … |
| maximal quotient of | #24999585, #24999595, #24999622, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(5504, 5654);