Finite Group DatabasebetaFinite Group Databasebeta| order | 384 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C42 · Schur multiplier (H2) = C24 |
| direct product | D3×#343 |
| Fitting | C3×#343 ⋊ C2 |
| Sylow | C3 ⋊ C2×#343 |
432 conjugacy classes of subgroups; only the 145 normal subgroups are shown.
This group has 432 conjugacy classes of subgroups — too many to draw. Only its 145 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)(4,5,6,7)(9,12)(10,14);(8,9,10,13,11,12,14,15);(2,3)66 conjugacy classes — view the full character table.
| maximal subgroup of | D3×#1345, D3×#1346, #10705391, … |
| maximal normal subgroup of | D3×#1345, D3×#1346, #10705391, … |
| maximal quotient of | D3×#1280, #10684782, #10684785, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(384, 1564);