Finite Group DatabasebetaFinite Group Databasebeta| order | 5504 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C23 |
No aliases for this group.
| Sylow | C43 ⋊ #2139 |
232 conjugacy classes of subgroups; only the 93 normal subgroups are shown.
This group has 232 conjugacy classes of subgroups — too many to draw. Only its 93 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=fg,f^2=g,b^a=bd,d^a=df,f^a=fg,h^a=h^42,c^b=cg,d^b=df,f^b=fg620 conjugacy classes — view the full character table.
| maximal subgroup of | #25011888, #25011893, #25012273, … |
| maximal normal subgroup of | #25011888, #25011893, #25012273, … |
| maximal quotient of | #25006342, #25006586, #25006638, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(5504, 6222);