Finite Group DatabasebetaFinite Group Databasebeta| order | 5504 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C25 |
| direct product | C2×#14583118 |
| Sylow | C43 ⋊ C2×#464 |
500 conjugacy classes of subgroups; only the 157 normal subgroups are shown.
This group has 500 conjugacy classes of subgroups — too many to draw. Only its 157 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
626 conjugacy classes — view the full character table.
| maximal subgroup of | #24992936, #24992942, C4×#14583118, … |
| maximal normal subgroup of | #24992936, #24992942, C4×#14583118, … |
| maximal quotient of | C2×#19134008, C2×#19134022, C2×#19134036, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(5504, 13951);