Finite Group DatabasebetaFinite Group Databasebeta| order | 5504 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C23 |
No aliases for this group.
| Fitting | C43×D4⋊C8 ⋊ C2 |
| Sylow | C43 ⋊ #1492 |
276 conjugacy classes of subgroups; only the 75 normal subgroups are shown.
This group has 276 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=e,d^2=f,e^2=g,b^a=bd,c^a=cg,d^a=df,c^b=cg,d^b=df,h^c=h^42632 conjugacy classes — view the full character table.
| maximal subgroup of | D43×#1492, C2×#19133044, #25063207, … |
| maximal normal subgroup of | D43×#1492, C2×#19133044, #25063207, … |
| maximal quotient of | #24984946, #24984948, #24984951, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(5504, 2959);