Finite Group DatabasebetaFinite Group Databasebeta| order | 384 |
| isoclinism | isoclinic class of Dic6 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C8 · Schur multiplier (H2) = C27 |
| direct product | C22×(C2×D3)⋊C8 |
| Fitting | C23×C3×C8 ⋊ C2 |
| Sylow | C3 ⋊ C22×C22⋊C8 |
1072 conjugacy classes of subgroups; only the 389 normal subgroups are shown.
This group has 1072 conjugacy classes of subgroups — too many to draw. Only its 389 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| minimal degree | μ(G) = 19 |
| transitive degree | μt(G) = 192 |
A minimal faithful permutation representation — 4 generators on 19 points:
(5,6,7)(9,11)(12,13,14,16,15,17,18,19);(6,7)(8,9)(10,11);(3,4);(1,2)144 conjugacy classes — view the full character table.
| maximal subgroup of | #10700403, #10700406, #10700409, … |
| maximal normal subgroup of | #10700403, #10700406, #10700409, … |
| maximal quotient of | C22×#4468, C22×#4469, C2×#70782, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(384, 16312);