Finite Group DatabasebetaFinite Group Databasebeta| order | 384 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C3×C8 · Schur multiplier (H2) = C23 |
| direct product | A4×C22⋊C8 |
| unambiguous semidirect product | (C22×C22⋊C8)⋊C3 |
| Fitting, Sylow | C22×C22⋊C8 ⋊ C3 |
262 conjugacy classes of subgroups; only the 48 normal subgroups are shown.
This group has 262 conjugacy classes of subgroups — too many to draw. Only its 48 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) = 48 |
A minimal faithful permutation representation — 2 generators on 16 points:
(2,3,4)(6,8);(1,4)(2,3)(5,6)(7,8)(9,13,15,10,12,16,11,14)80 conjugacy classes — view the full character table.
| maximal subgroup of | A4×#323, A4×#324, A4×#327, … |
| maximal normal subgroup of | A4×#323, A4×#324, A4×#327, … |
| maximal quotient of | A4×#323, A4×#324, #17352⋊C3, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(384, 5803);