Finite Group DatabasebetaFinite Group Databasebeta| order | 5504 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C25 |
No aliases for this group.
| Fitting | C8×D4×C43 ⋊ C2 |
| Sylow | C43 ⋊ #3283 |
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|a^2=g,c^2=g,e^2=g,b^a=be,c^a=cf,d^a=dg,e^a=eg,h^a=h^42,d^b=de,e^b=eg,h^b=h^42,e^d=eg,h^d=h^42875 conjugacy classes — view the full character table.
| maximal subgroup of | #25010040, #25010044, #25010068, … |
| maximal normal subgroup of | #25010040, #25010044, #25010068, … |
| maximal quotient of | #25087506, #25087521, #25087536, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(5504, 16232);