Finite Group DatabasebetaFinite Group Databasebeta| order | 384 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C22 |
| direct product | Dic3×SD32 |
| Sylow | C3 ⋊ C4×SD32 |
162 conjugacy classes of subgroups; only the 67 normal subgroups are shown.
This group has 162 conjugacy classes of subgroups — too many to draw. Only its 67 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) = 192 |
A minimal faithful permutation representation — 3 generators on 23 points:
(6,10)(7,14)(8,15)(11,12)(13,19)(16,20)(17,18)(21,22,23);(5,6,9,13)(7,10,16,19)(8,17,15,12)(11,20,18,14);(1,2,3,4)(22,23)66 conjugacy classes — view the full character table.
| maximal subgroup of | C4×D3×SD32, C2×Dic3×SD32, C4×#4916, … |
| maximal normal subgroup of | C4×D3×SD32, C2×Dic3×SD32, C4×#4916, … |
| maximal quotient of | C3⋊C8×SD32, #10707090, #10707097, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(384, 4049);