Finite Group DatabasebetaFinite Group Databasebeta| order | 5504 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C25 |
| direct product | #508×D43 |
| Fitting | C43×#508 ⋊ C2 |
| Sylow | C43 ⋊ C2×#508 |
368 conjugacy classes of subgroups; only the 115 normal subgroups are shown.
This group has 368 conjugacy classes of subgroups — too many to draw. Only its 115 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
506 conjugacy classes — view the full character table.
| maximal subgroup of | D43×#1417, #25017050, D43×#1418, … |
| maximal normal subgroup of | D43×#1417, #25017050, D43×#1418, … |
| maximal quotient of | D43×#2138, D43×#2158, C4×D16×D43, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(5504, 17624);