Finite Group DatabasebetaFinite Group Databasebeta| order | 384 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C42 · Schur multiplier (H2) = C24 |
| direct product | D3×#341 |
| Fitting | C3×#341 ⋊ C2 |
| Sylow | C3 ⋊ C2×#341 |
392 conjugacy classes of subgroups; only the 145 normal subgroups are shown.
This group has 392 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) = 23 |
| transitive degree | μt(G) = 96 |
A minimal faithful permutation representation — 3 generators on 23 points:
(1,2,3,4)(5,7,9,17,10,18,8,16)(6,11,13,19,14,20,12,15)(21,22,23);(5,6,8,13,10,14,9,12)(7,15,16,11,18,19,17,20);(22,23)84 conjugacy classes — view the full character table.
| maximal subgroup of | D3×#1349, D3×#1350, #10705438, … |
| maximal normal subgroup of | D3×#1349, D3×#1350, #10705438, … |
| maximal quotient of | D3×#1277, #10684644, #10684651, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(384, 1513);