Finite Group DatabasebetaFinite Group Databasebeta| order | 384 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C42 · Schur multiplier (H2) = C23×C4 |
| direct product | Dic3×#102 |
| Sylow | C3 ⋊ C4×#102 |
396 conjugacy classes of subgroups.
| minimal degree | μ(G) = 19 |
| transitive degree | μt(G) = 192 |
A minimal faithful permutation representation — 3 generators on 19 points:
(10,13)(11,16)(14,15)(17,18,19);(5,6,7,8)(9,10)(11,13)(12,15)(14,16);(1,2,3,4)(18,19)84 conjugacy classes — view the full character table.
| maximal subgroup of | C4×D3×#102, C2×Dic3×#102, C4×#4772, … |
| maximal normal subgroup of | C4×D3×#102, C2×Dic3×#102, C4×#4772, … |
| maximal quotient of | Dic3×D4⋊C8, #10685811, #10685826, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(384, 2727);