Finite Group DatabasebetaFinite Group Databasebeta| order | 5504 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C24 |
No aliases for this group.
| Fitting | C2×C4×D4×C43 ⋊ C2 |
| Sylow | C43 ⋊ #3105 |
454 conjugacy classes of subgroups; only the 133 normal subgroups are shown.
This group has 454 conjugacy classes of subgroups — too many to draw. Only its 133 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
Polycyclic presentation:
2^7,43|d^2=eg,f^2=g,b^a=be,c^a=cf,f^a=fg,h^a=h^42,f^c=fg878 conjugacy classes — view the full character table.
| maximal subgroup of | #24991808, #24991814, #25066563, … |
| maximal normal subgroup of | #24991808, #24991814, #25066563, … |
| maximal quotient of | #25096602, #25099536, #25099580, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(5504, 14557);