Finite Group DatabasebetaFinite Group Databasebeta| order | 384 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C23×C4 |
| direct product | D3×#488 |
| Fitting | C3×#488 ⋊ C2 |
| Sylow | C3 ⋊ C2×#488 |
412 conjugacy classes of subgroups; only the 125 normal subgroups are shown.
This group has 412 conjugacy classes of subgroups — too many to draw. Only its 125 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| minimal degree | μ(G) = 27 |
| transitive degree | μt(G) = 96 |
A minimal faithful permutation representation — 4 generators on 27 points:
(2,6)(5,8)(9,12,13,21,14,22,20,11)(10,16,17,15,18,19,23,24)(25,26,27);(1,3,4,7)(2,5,6,8)(9,11,20,22,14,21,13,12)(10,15,23,16,18,24,17,19);(1,2)(3,5)(4,6)(7,8)(9,10)(11,19)(12,15)(13,23)(14,18)(16,21)(17,20)(22,24);(26,27)66 conjugacy classes — view the full character table.
| maximal subgroup of | D3×#1414, C2×D3×#488, D3×#3131, … |
| maximal normal subgroup of | D3×#1414, C2×D3×#488, D3×#3131, … |
| maximal quotient of | D3×#1835, D3×#1933, D3×#1934, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(384, 14212);