Finite Group DatabasebetaFinite Group Databasebeta| order | 384 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C23 |
| direct product | D3×#361 |
| Fitting | C3×#361 ⋊ C2 |
| Sylow | C3 ⋊ C2×#361 |
256 conjugacy classes of subgroups; only the 67 normal subgroups are shown.
This group has 256 conjugacy classes of subgroups — too many to draw. Only its 67 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| minimal degree | μ(G) = 19 |
| transitive degree | μt(G) = 48 |
A minimal faithful permutation representation — 3 generators on 19 points:
(2,6)(3,12)(4,15)(7,8)(9,16)(10,11)(13,14)(17,18,19);(1,2,4,8,5,10,15,9)(3,11,13,7,14,6,12,16);(18,19)48 conjugacy classes — view the full character table.
| maximal subgroup of | C2×D3×#361, D3×#2148, #10948150, … |
| maximal normal subgroup of | C2×D3×#361, D3×#2148, #10948150, … |
| maximal quotient of | D3×#1333, #10704960, #10705191, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(384, 1831);