Finite Group DatabasebetaFinite Group Databasebeta| order | 5504 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C24 |
No aliases for this group.
| Fitting | C2×C4×D4×C43 ⋊ C2 |
| Sylow | C43 ⋊ #3114 |
450 conjugacy classes of subgroups; only the 129 normal subgroups are shown.
This group has 450 conjugacy classes of subgroups — too many to draw. Only its 129 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
Polycyclic presentation:
2^7,43|d^2=eg,f^2=g,b^a=be,c^a=cf,f^a=fg,h^a=h^42,d^c=dg,f^c=fg872 conjugacy classes — view the full character table.
| maximal subgroup of | #24994704, #24994710, #25069179, … |
| maximal normal subgroup of | #24994704, #24994710, #25069179, … |
| maximal quotient of | #25096648, #25099613, #25099628, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(5504, 14648);