Finite Group DatabasebetaFinite Group Databasebeta| order | 5504 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4 · Schur multiplier (H2) = C27 |
| direct product | C22×#13063245 |
| Fitting | C22×C4⋊C4×C43 ⋊ C2 |
| Sylow | C43 ⋊ C22×#102 |
1072 conjugacy classes of subgroups; only the 349 normal subgroups are shown.
This group has 1072 conjugacy classes of subgroups — too many to draw. Only its 349 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
896 conjugacy classes — view the full character table.
| maximal subgroup of | #25002160, #25002162, #25002858, … |
| maximal normal subgroup of | #25002160, #25002162, #25002858, … |
| maximal quotient of | C22×#14582626, C2×#19133019, C2×#19132993, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(5504, 12995);