Finite Group DatabasebetaFinite Group Databasebeta| order | 5504 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C25 |
No aliases for this group.
| Fitting | C43×#417 ⋊ C2 |
| Sylow | C43 ⋊ #3061 |
484 conjugacy classes of subgroups; only the 133 normal subgroups are shown.
This group has 484 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|b^2=eg,d^2=g,e^2=g,b^a=be,c^a=cf,e^a=eg,h^b=h^42,d^c=dg,h^c=h^42494 conjugacy classes — view the full character table.
| maximal subgroup of | #25132559, #25132563, #25132570, … |
| maximal normal subgroup of | #25132559, #25132563, #25132570, … |
| maximal quotient of | #25079689, #25079728, #25079783, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(5504, 14179);