Finite Group DatabasebetaFinite Group Databasebeta| order | 5504 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C23 |
| direct product | #358×D43 |
| Fitting | C43×#358 ⋊ C2 |
| Sylow | C43 ⋊ C2×#358 |
232 conjugacy classes of subgroups; only the 77 normal subgroups are shown.
This group has 232 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.
506 conjugacy classes — view the full character table.
| maximal subgroup of | C2×#358×D43, D43×#2138, D43×#2141, … |
| maximal normal subgroup of | C2×#358×D43, D43×#2138, D43×#2141, … |
| maximal quotient of | D43×#1332, #25006574, #25006626, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(5504, 6210);