Finite Group DatabasebetaFinite Group Databasebeta| order | 384 |
| automorphism | ? |
| homology | Abelianization (H1) = C42 · Schur multiplier (H2) = C4 |
| unambiguous semidirect product | C3⋊#1309 |
| Sylow | C3 ⋊ #1309 |
146 conjugacy classes of subgroups.
| minimal degree | μ(G) = 19 |
| transitive degree | μt(G) = 192 |
A minimal faithful permutation representation — 2 generators on 19 points:
(1,2,3)(5,8)(6,10)(12,13,14,17,15,16,18,19);(2,3)(4,5,6,9,7,8,10,11)(13,16)(14,18)Polycyclic presentation:
2^7,3|a^2=d,b^2=e,d^2=f,e^2=g,b^a=bc,c^a=cf,e^a=eg,h^a=h^2,c^b=cg,d^b=df54 conjugacy classes — view the full character table.
| maximal subgroup of | #10682730, #10682731, #10682808, … |
| maximal normal subgroup of | #10682730, #10682731, #10682808, … |
| maximal quotient of | #10681762, #10681763, #10681783, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(384, 288);