Finite Group DatabasebetaFinite Group Databasebeta| order | 384 |
| isoclinism | isoclinic class of Dic6 |
| automorphism | ? |
| homology | Abelianization (H1) = C82 · Schur multiplier (H2) = C22×C4 |
| unambiguous semidirect product | C3⋊#1273 |
| Sylow | C3 ⋊ #1273 |
212 conjugacy classes of subgroups.
| minimal degree | μ(G) = 23 |
| transitive degree | μt(G) = 384 |
A minimal faithful permutation representation — 2 generators on 23 points:
(1,2,3)(5,7)(16,17,18,20,19,21,22,23);(2,3)(4,5)(6,7)(8,9,10,12,11,13,14,15)Polycyclic presentation:
2^7,3|a^2=d,b^2=e,d^2=f,e^2=g,b^a=bc,h^a=h^2144 conjugacy classes — view the full character table.
| maximal subgroup of | #10681959, #10681960, #10681972, … |
| maximal normal subgroup of | #10681959, #10681960, #10681972, … |
| maximal quotient of | C3⋊#7014, #10681714, #10681715, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(384, 229);