Finite Group DatabasebetaFinite Group Databasebeta| order | 384 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C3×C4 · Schur multiplier (H2) = C24 |
| direct product | C2×A4×C4⋊C4 |
| unambiguous semidirect product | (C23×C4⋊C4)⋊C3 |
| Fitting, Sylow | C23×C4⋊C4 ⋊ C3 |
568 conjugacy classes of subgroups; only the 114 normal subgroups are shown.
This group has 568 conjugacy classes of subgroups — too many to draw. Only its 114 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) = 96 |
A minimal faithful permutation representation — 3 generators on 14 points:
(3,4,5,6)(12,13,14);(4,6)(7,8,9,10)(11,14)(12,13);(1,2)80 conjugacy classes — view the full character table.
| maximal subgroup of | A4×#324, A4×#340, A4×#343, … |
| maximal normal subgroup of | A4×#324, A4×#340, A4×#343, … |
| maximal quotient of | C2×A4×#95, C4×A4×C4⋊C4, A4×#380, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(384, 18147);