Finite Group DatabasebetaFinite Group Databasebeta| order | 5504 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C42 · Schur multiplier (H2) = C22×C4 |
No aliases for this group.
| Sylow | C43 ⋊ #1776 |
272 conjugacy classes of subgroups; only the 129 normal subgroups are shown.
This group has 272 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|a^2=e,b^2=f,c^2=de,d^2=g,e^2=g,b^a=bd,c^a=cg,h^a=h^42,d^b=dg,e^b=eg884 conjugacy classes — view the full character table.
| maximal subgroup of | D43×#1776, C2×#19134493, #25094656, … |
| maximal normal subgroup of | D43×#1776, C2×#19134493, #25094656, … |
| maximal quotient of | #24987795, #24987800, #24987816, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(5504, 4408);