Finite Group DatabasebetaFinite Group Databasebeta| order | 384 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C24×C4 |
| direct product | D3×#495 |
| Fitting | C3×#495 ⋊ C2 |
| Sylow | C3 ⋊ C2×#495 |
592 conjugacy classes of subgroups; only the 145 normal subgroups are shown.
This group has 592 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 — 4 generators on 23 points:
(1,2,3,4)(6,11)(10,18)(12,16)(13,19)(21,22,23);(5,7,8,14,9,15,17,20)(6,10,12,13,11,18,16,19);(2,4)(5,6)(7,13)(8,16)(9,11)(10,14)(12,17)(15,19)(18,20);(22,23)66 conjugacy classes — view the full character table.
| maximal subgroup of | D3×#1360, #10706417, #10706557, … |
| maximal normal subgroup of | D3×#1360, #10706417, #10706557, … |
| maximal quotient of | D3×#1706, D3×#1707, D3×#1708, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(384, 14395);