Finite Group DatabasebetaFinite Group Databasebeta| order | 384 |
| isoclinism | isoclinic class of #4537 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C8 · Schur multiplier (H2) = C1 |
No aliases for this group.
| Sylow | C3 ⋊ #1338 |
86 conjugacy classes of subgroups.
| minimal degree | μ(G) = 27 |
| transitive degree | μt(G) = 384 |
A minimal faithful permutation representation — 2 generators on 27 points:
(1,2,3)(4,5,7,9)(6,11,10,8)(12,14,16,17)(13,18,19,21)(15,23,24,22)(20,27,26,25);(2,3)(5,8)(6,10)(9,11)(12,13,15,20,17,18,23,25,16,19,24,26,14,21,22,27)Polycyclic presentation:
2^7,3|a^2=d,b^2=e,c^2=eg,d^2=f,f^2=g,b^a=bc,c^a=ce,h^a=h^2,c^b=ceg,d^b=dg66 conjugacy classes — view the full character table.
| maximal subgroup of | D3×#1338, C2×#67769, #10705004, … |
| maximal normal subgroup of | D3×#1338, C2×#67769, #10705004, … |
| maximal quotient of | #10681969, #10681999, #10682100, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(384, 345);