Finite Group DatabasebetaFinite Group Databasebeta| order | 384 |
| isoclinism | isoclinic class of #826 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C8 · Schur multiplier (H2) = C2 |
No aliases for this group.
| Sylow | C3 ⋊ #1332 |
98 conjugacy classes of subgroups.
| minimal degree | μ(G) = 27 |
| transitive degree | μt(G) = 384 |
A minimal faithful permutation representation — 2 generators on 27 points:
(2,3)(12,13,16,19)(14,21,23,27)(15,24,22,18)(17,25,26,20);(1,2,3)(4,5,6,8,7,9,10,11)(13,17)(14,20)(15,22)(18,27)(19,26)(21,24)(23,25)Polycyclic presentation:
2^7,3|a^2=d,b^2=g,c^2=eg,d^2=f,e^2=g,b^a=bc,c^a=ce,e^a=eg,c^b=ce,e^b=eg,h^b=h^272 conjugacy classes — view the full character table.
| maximal subgroup of | D3×#1332, C2×#67472, #10704924, … |
| maximal normal subgroup of | D3×#1332, C2×#67472, #10704924, … |
| maximal quotient of | #10681838, #10681850, #10681956, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(384, 48);