Finite Group DatabasebetaFinite Group Databasebeta| order | 384 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4 · Schur multiplier (H2) = C24×C4 |
| direct product | Dic3×#124 |
| Sylow | C3 ⋊ C4×#124 |
652 conjugacy classes of subgroups; only the 249 normal subgroups are shown.
This group has 652 conjugacy classes of subgroups — too many to draw. Only its 249 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:
(1,2,3)(8,10,11,9)(13,17)(16,19);(8,9,11,10)(12,14,15,18)(13,16,17,19);(9,10)(12,13)(14,16)(15,17)(18,19);(2,3)(4,5,6,7)84 conjugacy classes — view the full character table.
| maximal subgroup of | Dic3×#329, #10686111, #10686119, … |
| maximal normal subgroup of | Dic3×#329, #10686111, #10686119, … |
| maximal quotient of | Dic3×#388, Dic3×#390, Dic3×#391, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(384, 15528);