Finite Group DatabasebetaFinite Group Databasebeta| order | 384 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C3×C4 · Schur multiplier (H2) = C22 |
| direct product | A4×#107 |
| unambiguous semidirect product | (C22×#107)⋊C3 |
| Fitting, Sylow | C22×#107 ⋊ C3 |
160 conjugacy classes of subgroups; only the 42 normal subgroups are shown.
This group has 160 conjugacy classes of subgroups — too many to draw. Only its 42 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:
(6,7,8)(9,16,11,10,12,13,14,15);(1,4,3,2)(5,8)(6,7)(10,13)(11,14)(15,16)56 conjugacy classes — view the full character table.
| maximal subgroup of | A4×#357, A4×#358, A4×#366, … |
| maximal normal subgroup of | A4×#357, A4×#358, A4×#366, … |
| maximal quotient of | A4×#335, #17828⋊C3, A4×#340, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(384, 5820);