Finite Group DatabasebetaFinite Group Databasebeta| order | 5504 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C23×C4 |
| direct product | C2×#14583295 |
| Sylow | C43 ⋊ C2×#498 |
424 conjugacy classes of subgroups; only the 197 normal subgroups are shown.
This group has 424 conjugacy classes of subgroups — too many to draw. Only its 197 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 | #24991857, #24991858, #24991860, … |
| maximal normal subgroup of | #24991857, #24991858, #24991860, … |
| maximal quotient of | C2×#19134751, C2×#19135320, C2×#19135555, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(5504, 15007);