Finite Group DatabasebetaFinite Group Databasebeta| order | 384 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C42 · Schur multiplier (H2) = C22×C4 |
| direct product | Dic3×#100 |
| Sylow | C3 ⋊ C4×#100 |
360 conjugacy classes of subgroups; only the 119 normal subgroups are shown.
This group has 360 conjugacy classes of subgroups — too many to draw. Only its 119 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| minimal degree | μ(G) = 15 |
| transitive degree | μt(G) = 96 |
A minimal faithful permutation representation — 3 generators on 15 points:
(1,2,3)(9,12)(10,14);(8,9,10,13,11,12,14,15);(2,3)(4,5,6,7)66 conjugacy classes — view the full character table.
| maximal subgroup of | #10710318, Dic3×AΣL(1,𝔽16), #10710323, … |
| maximal normal subgroup of | #10710318, Dic3×AΣL(1,𝔽16), #10710323, … |
| maximal quotient of | Dic3×#323, #10685699, #10685712, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(384, 2638);