Finite Group DatabasebetaFinite Group Databasebeta| order | 384 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C24×C4 |
| direct product | D3×#497 |
| Fitting | C3×#497 ⋊ C2 |
| Sylow | C3 ⋊ C2×#497 |
564 conjugacy classes of subgroups; only the 145 normal subgroups are shown.
This group has 564 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)(7,14)(10,19)(13,20)(15,18)(21,22,23);(5,7,8,15,9,14,17,18)(6,10,11,13,12,19,16,20);(2,4)(5,6,9,12)(7,13,14,20)(8,16,17,11)(10,18,19,15);(22,23)48 conjugacy classes — view the full character table.
| maximal subgroup of | D3×#1407, D3×#1659, D3×#1661, … |
| maximal normal subgroup of | D3×#1407, D3×#1659, D3×#1661, … |
| maximal quotient of | D3×#1714, D3×#1716, D3×#1718, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(384, 14444);