Finite Group DatabasebetaFinite Group Databasebeta| order | 5504 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C2×C4 |
No aliases for this group.
| Fitting | C43×#357 ⋊ C2 |
| Sylow | C43 ⋊ #2218 |
170 conjugacy classes of subgroups; only the 47 normal subgroups are shown.
This group has 170 conjugacy classes of subgroups — too many to draw. Only its 47 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=df,d^2=fg,f^2=g,b^a=bd,c^a=ce,d^a=df,f^a=fg,c^b=cg,h^b=h^42,h^c=h^42488 conjugacy classes — view the full character table.
| maximal subgroup of | D43×#2218, C2×#19136697, #25251062, … |
| maximal normal subgroup of | D43×#2218, C2×#19136697, #25251062, … |
| maximal quotient of | #25010819, #25010870, #25010938, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(5504, 6612);