Finite Group DatabasebetaFinite Group Databasebeta| order | 5504 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C23×C4 |
| direct product | C2×#14583253 |
| Sylow | C43 ⋊ C2×#488 |
412 conjugacy classes of subgroups; only the 149 normal subgroups are shown.
This group has 412 conjugacy classes of subgroups — too many to draw. Only its 149 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
632 conjugacy classes — view the full character table.
| maximal subgroup of | #24996147, #24996153, #24996154, … |
| maximal normal subgroup of | #24996147, #24996153, #24996154, … |
| maximal quotient of | C2×#19134725, C2×#19135274, C2×#19135281, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(5504, 14825);