Finite Group DatabasebetaFinite Group Databasebeta| order | 5504 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C24 |
| direct product | C2×#14582685 |
| Fitting | C2×#99×C43 ⋊ C2 |
| Sylow | C43 ⋊ C2×AΣL(1,𝔽16) |
438 conjugacy classes of subgroups; only the 69 normal subgroups are shown.
This group has 438 conjugacy classes of subgroups — too many to draw. Only its 69 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
488 conjugacy classes — view the full character table.
| maximal subgroup of | #25011728, C4×#14582685, #25011743, … |
| maximal normal subgroup of | #25011728, C4×#14582685, #25011743, … |
| maximal quotient of | C2×#19132522, C2×#19132542, #25005845, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(5504, 6141);