Finite Group DatabasebetaFinite Group Databasebeta| order | 384 |
| isoclinism | isoclinic class of Dic6 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C32 · Schur multiplier (H2) = C22 |
| unambiguous semidirect product | (C2×D3)⋊C32 |
| Fitting | C2×C3×C32 ⋊ C2 |
| Sylow | C3 ⋊ C22⋊C32 |
82 conjugacy classes of subgroups.
| minimal degree | μ(G) = 39 |
| transitive degree | μt(G) = 192 |
A minimal faithful permutation representation — 2 generators on 39 points:
(2,3)(5,7);(1,2,3)(4,5)(6,7)(8,9,10,14,11,15,18,24,12,16,19,25,21,27,30,34,13,17,20,26,22,28,31,35,23,29,32,36,33,37,38,39)Polycyclic presentation:
2^7,3|a^2=d,d^2=e,e^2=f,f^2=g,b^a=bc,h^b=h^2144 conjugacy classes — view the full character table.
| maximal subgroup of | D3×C22⋊C32, C2×(C2×D3)⋊C32, #10715379, … |
| maximal normal subgroup of | D3×C22⋊C32, C2×(C2×D3)⋊C32, #10715379, … |
| maximal quotient of | #10682525, #10682585, #10682624, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(384, 170);