Finite Group DatabasebetaFinite Group Databasebeta| order | 384 |
| automorphism | ? |
| homology | Abelianization (H1) = C3×C42 · Schur multiplier (H2) = C22 |
| direct product | A4×#97 |
| unambiguous semidirect product | (C22×#97)⋊C3 |
| Fitting, Sylow | C22×#97 ⋊ C3 |
180 conjugacy classes of subgroups; only the 54 normal subgroups are shown.
This group has 180 conjugacy classes of subgroups — too many to draw. Only its 54 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| minimal degree | μ(G) = 16 |
| transitive degree | μt(G) = 96 |
A minimal faithful permutation representation — 2 generators on 16 points:
(1,4,3,2)(6,7,8)(10,13)(14,16);(5,8)(6,7)(9,14,15,10,12,16,11,13)80 conjugacy classes — view the full character table.
| maximal subgroup of | A4×#329, A4×#330, A4×#347, … |
| maximal normal subgroup of | A4×#329, A4×#330, A4×#347, … |
| maximal quotient of | A4×#322, #17320⋊C3, A4×#336, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(384, 5800);