Finite Group DatabasebetaFinite Group Databasebeta| order | 5504 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C8 · Schur multiplier (H2) = C22×C4 |
No aliases for this group.
| Fitting | C43×#323 ⋊ C2 |
| Sylow | C43 ⋊ #1460 |
312 conjugacy classes of subgroups; only the 81 normal subgroups are shown.
This group has 312 conjugacy classes of subgroups — too many to draw. Only its 81 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=e,c^2=fg,e^2=g,b^a=bd,d^a=df,e^b=ef,h^c=h^42506 conjugacy classes — view the full character table.
| maximal subgroup of | #25005844, #25005846, #25005849, … |
| maximal normal subgroup of | #25005844, #25005846, #25005849, … |
| maximal quotient of | #24984563, #24984565, #24984570, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(5504, 2829);