Finite Group DatabasebetaFinite Group Databasebeta| order | 384 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C3 · Schur multiplier (H2) = C23 |
| direct product | C2×A4×SD16 |
| unambiguous semidirect product | (C23×SD16)⋊C3 |
| Fitting, Sylow | C23×SD16 ⋊ C3 |
400 conjugacy classes of subgroups; only the 66 normal subgroups are shown.
This group has 400 conjugacy classes of subgroups — too many to draw. Only its 66 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| minimal degree | μ(G) = 14 |
| transitive degree | μt(G) = 48 |
A minimal faithful permutation representation — 3 generators on 14 points:
(1,2)(4,5,6)(8,11)(9,14)(12,13);(1,2)(3,6)(4,5)(7,8,10,13)(9,11,14,12);(1,2)56 conjugacy classes — view the full character table.
| maximal subgroup of | C4×A4×SD16, A4×#440, A4×#450, … |
| maximal normal subgroup of | C4×A4×SD16, A4×#440, A4×#450, … |
| maximal quotient of | C2×A4×#102, C2×A4×#103, C2×A4×#106, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(384, 18207);