Finite Group DatabasebetaFinite Group Databasebeta| order | 5504 |
| automorphism | ? |
| homology | Abelianization (H1) = C42 · Schur multiplier (H2) = C22 |
No aliases for this group.
| Sylow | C43 ⋊ #1394 |
172 conjugacy classes of subgroups; only the 57 normal subgroups are shown.
This group has 172 conjugacy classes of subgroups — too many to draw. Only its 57 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=d,b^2=e,c^2=g,d^2=g,b^a=bc,c^a=cf,e^a=eg,f^a=fg,d^b=dfg,h^b=h^42,d^c=dg488 conjugacy classes — view the full character table.
| maximal subgroup of | D43×#1394, C2×#19132721, #25011577, … |
| maximal normal subgroup of | D43×#1394, C2×#19132721, #25011577, … |
| maximal quotient of | #24983559, #24983600, #24983602, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(5504, 2636);