Finite Group DatabasebetaFinite Group Databasebeta| order | 384 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C3×C4 · Schur multiplier (H2) = C23 |
| direct product | C2×A4×M16 |
| unambiguous semidirect product | (C23×M16)⋊C3 |
| Fitting, Sylow | C23×M16 ⋊ C3 |
400 conjugacy classes of subgroups; only the 90 normal subgroups are shown.
This group has 400 conjugacy classes of subgroups — too many to draw. Only its 90 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)(12,14);(3,6)(4,5)(7,8,9,12,10,11,13,14);(1,2)80 conjugacy classes — view the full character table.
| maximal subgroup of | A4×H(3,ℤ/4), A4×#338, A4×#339, … |
| maximal normal subgroup of | A4×H(3,ℤ/4), A4×#338, A4×#339, … |
| maximal quotient of | C2×A4×#97, C4×A4×M16, C2×A4×C22⋊C8, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(384, 18201);