Finite Group DatabasebetaFinite Group Databasebeta| order | 384 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C26 |
| direct product | C2×D3×D16 |
| Fitting | C2×C3×D16 ⋊ C2 |
| Sylow | C3 ⋊ C22×D16 |
440 conjugacy classes of subgroups; only the 125 normal subgroups are shown.
This group has 440 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) = 21 |
| transitive degree | μt(G) = 96 |
A minimal faithful permutation representation — 4 generators on 21 points:
(1,2)(3,4,5)(6,7)(8,15)(9,18)(10,13)(11,14)(12,16)(17,20)(19,21);(1,2)(7,11)(8,14)(9,16)(12,20)(13,19)(15,18)(17,21);(4,5);(1,2)66 conjugacy classes — view the full character table.
| maximal subgroup of | D3×#1415, #10715628, D3×#1419, … |
| maximal normal subgroup of | D3×#1415, #10715628, D3×#1419, … |
| maximal quotient of | C2×D3×#357, C2×D3×#366, C4×D3×D16, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(384, 14592);