Finite Group DatabasebetaFinite Group Databasebeta| order | 5504 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C23×C4 |
| direct product | C2×#14582692 |
| Sylow | C43 ⋊ C2×#353 |
368 conjugacy classes of subgroups; only the 77 normal subgroups are shown.
This group has 368 conjugacy classes of subgroups — too many to draw. Only its 77 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
614 conjugacy classes — view the full character table.
| maximal subgroup of | #24984336, #24984337, #24984360, … |
| maximal normal subgroup of | #24984336, #24984337, #24984360, … |
| maximal quotient of | C2×#19132527, C2×#19132541, #25005867, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(5504, 6168);