Finite Group DatabasebetaFinite Group Databasebeta| order | 384 |
| isoclinism | isoclinic class of Dic6 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C42 · Schur multiplier (H2) = C26×C4 |
| direct product | C2×C4×(C2×D3)⋊C4 |
| Fitting | C22×C3×C42 ⋊ C2 |
| Sylow | C3 ⋊ C2×C4×C22⋊C4 |
1360 conjugacy classes of subgroups.
| minimal degree | μ(G) = 17 |
| transitive degree | μt(G) = 192 |
A minimal faithful permutation representation — 4 generators on 17 points:
(3,4,5)(7,9)(14,17,16,15);(1,2)(4,5)(6,7)(8,9);(1,2)(10,11,12,13)(14,15,16,17);(1,2)144 conjugacy classes — view the full character table.
| maximal subgroup of | C4×#4468, #10685698, #10687841, … |
| maximal normal subgroup of | C4×#4468, #10685698, #10687841, … |
| maximal quotient of | C2×C4×C3⋊#95, C42×(C2×D3)⋊C4, C2×(C2×D3)⋊#95, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(384, 14629);