Finite Group DatabasebetaFinite Group Databasebeta| order | 384 |
| isoclinism | isoclinic class of #4519 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C4 · Schur multiplier (H2) = C1 |
No aliases for this group.
| Sylow | C3 ⋊ #1425 |
50 conjugacy classes of subgroups.
| minimal degree | μ(G) = 67 |
| transitive degree | μt(G) = 192 |
A minimal faithful permutation representation — 2 generators on 67 points:
(2,3)(4,6,18,45,9,21,26,33,8,20,37,61,29,51,28,50,11,23,47,66,31,53,27,49,10,22,46,65,25,48,7,19)(5,12,24,43,15,35,56,54,32,60,58,67,59,63,39,44,16,36,57,64,40,62,38,42,14,34,55,52,30,41,13,17);(1,2,3)(4,5,8,14,11,16,10,32)(6,17,20,42,23,44,22,54)(7,24,26,55,28,57,27,58)(9,30,29,40,31,59,25,15)(12,33,34,50,36,49,60,19)(13,37,38,47,39,46,56,18)(21,52,51,64,53,67,48,43)(35,45,41,61,62,66,63,65)Polycyclic presentation:
2^7,3|a^2=d,b^2=ce,c^2=ef,d^2=g,e^2=fg,f^2=g,b^a=bc,c^a=ce,e^a=ef,f^a=fg,h^b=h^260 conjugacy classes — view the full character table.
| maximal subgroup of | D3×#1425, C2×#67581, #10715699, … |
| maximal normal subgroup of | D3×#1425, C2×#67581, #10715699, … |
| maximal quotient of | #10682863, #10682865, #10682889, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(384, 157);