Finite Group DatabasebetaFinite Group Databasebeta| order | 5504 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C24 |
No aliases for this group.
| Sylow | C43 ⋊ #2019 |
362 conjugacy classes of subgroups; only the 75 normal subgroups are shown.
This group has 362 conjugacy classes of subgroups — too many to draw. Only its 75 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=g,d^2=g,e^2=g,f^2=g,b^a=bd,c^a=ce,d^a=dg,e^a=eg,f^a=fg,h^a=h^42,c^b=cf,d^b=dg,f^b=fg,d^c=dg,e^c=eg,f^c=fg488 conjugacy classes — view the full character table.
| maximal subgroup of | D43×#2019, C2×#19135709, #25123799, … |
| maximal normal subgroup of | D43×#2019, C2×#19135709, #25123799, … |
| maximal quotient of | #24997202, #24997219, #24997270, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(5504, 5624);