Finite Group DatabasebetaFinite Group Databasebeta| order | 384 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C3×C4 · Schur multiplier (H2) = C22 |
| direct product | A4×#100 |
| unambiguous semidirect product | (C22×#100)⋊C3 |
| Fitting, Sylow | C22×#100 ⋊ C3 |
242 conjugacy classes of subgroups; only the 36 normal subgroups are shown.
This group has 242 conjugacy classes of subgroups — too many to draw. Only its 36 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| minimal degree | μ(G) = 12 |
| transitive degree | μt(G) = 24 |
A minimal faithful permutation representation — 2 generators on 12 points:
(2,3,4)(6,9)(7,11);(1,4)(2,3)(5,10,11,6,8,12,7,9)44 conjugacy classes — view the full character table.
| maximal subgroup of | A4×AΣL(1,𝔽16), A4×#352, C2×A4×#100, … |
| maximal normal subgroup of | A4×AΣL(1,𝔽16), A4×#352, C2×A4×#100, … |
| maximal quotient of | A4×#323, #17425⋊C3, A4×#329, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(384, 5807);