Finite Group DatabasebetaFinite Group Databasebeta| order | 5504 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C24 |
| direct product | C2×#14582642 |
| Fitting | C2×C4⋊C8×C43 ⋊ C2 |
| Sylow | C43 ⋊ C2×#331 |
360 conjugacy classes of subgroups; only the 117 normal subgroups are shown.
This group has 360 conjugacy classes of subgroups — too many to draw. Only its 117 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
878 conjugacy classes — view the full character table.
| maximal subgroup of | #24987536, C4×#14582642, #24987549, … |
| maximal normal subgroup of | #24987536, C4×#14582642, #24987549, … |
| maximal quotient of | C2×#19132415, #24984571, #24984873, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(5504, 3150);