Finite Group DatabasebetaFinite Group Databasebeta| order | 384 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C25 |
| direct product | C2×D3×SD32 |
| Fitting | C2×C3×SD32 ⋊ C2 |
| Sylow | C3 ⋊ C22×SD32 |
400 conjugacy classes of subgroups; only the 125 normal subgroups are shown.
This group has 400 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)(7,11)(8,15)(9,16)(12,13)(14,20)(17,21)(18,19);(1,2)(6,7,10,14)(8,11,17,20)(9,18,16,13)(12,21,19,15);(4,5);(1,2)66 conjugacy classes — view the full character table.
| maximal subgroup of | C4×D3×SD32, D3×#2175, #10948551, … |
| maximal normal subgroup of | C4×D3×SD32, D3×#2175, #10948551, … |
| maximal quotient of | C2×D3×#357, C2×D3×#358, C2×D3×#367, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(384, 14596);