Finite Group DatabasebetaFinite Group Databasebeta| order | 5504 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4 · Schur multiplier (H2) = C25 |
| direct product | C2×#14582939 |
| Sylow | C43 ⋊ C2×#428 |
536 conjugacy classes of subgroups; only the 269 normal subgroups are shown.
This group has 536 conjugacy classes of subgroups — too many to draw. Only its 269 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
884 conjugacy classes — view the full character table.
| maximal subgroup of | #25002675, #25002677, #25002696, … |
| maximal normal subgroup of | #25002675, #25002677, #25002696, … |
| maximal quotient of | C2×#19133345, C2×#19133360, #25065624, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(5504, 13093);