Finite Group DatabasebetaFinite Group Databasebeta| order | 5504 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C2×C4 |
No aliases for this group.
| Sylow | C43 ⋊ #1506 |
228 conjugacy classes of subgroups; only the 63 normal subgroups are shown.
This group has 228 conjugacy classes of subgroups — too many to draw. Only its 63 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,b^2=f,c^2=f,d^2=g,b^a=bd,d^a=df,c^b=cf,d^b=dg,e^b=efg,h^c=h^42431 conjugacy classes — view the full character table.
| maximal subgroup of | D43×#1506, C2×#19133105, #25063749, … |
| maximal normal subgroup of | D43×#1506, C2×#19133105, #25063749, … |
| maximal quotient of | #24984621, #24984623, #24984655, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(5504, 3020);