Finite Group DatabasebetaFinite Group Databasebeta| order | 5504 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C24 |
No aliases for this group.
| Sylow | C43 ⋊ #3363 |
336 conjugacy classes of subgroups; only the 139 normal subgroups are shown.
This group has 336 conjugacy classes of subgroups — too many to draw. Only its 139 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,b^2=e,c^2=g,d^2=e,f^2=g,b^a=be,c^a=cf,f^a=fg,h^a=h^42,d^b=de,f^c=fg,h^c=h^42875 conjugacy classes — view the full character table.
| maximal subgroup of | #25086794, #25086801, #25086854, … |
| maximal normal subgroup of | #25086794, #25086801, #25086854, … |
| maximal quotient of | Q8×#13063250, #25113405, #25115549, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(5504, 17189);