Finite Group DatabasebetaFinite Group Databasebeta| order | 384 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C4 · Schur multiplier (H2) = C2 |
No aliases for this group.
| Sylow | C3 ⋊ #1420 |
70 conjugacy classes of subgroups.
| minimal degree | μ(G) = 67 |
| transitive degree | μt(G) = 192 |
A minimal faithful permutation representation — 2 generators on 67 points:
(1,2)(4,6,11,22)(5,12,16,38)(7,24,29,53)(8,21,10,19)(9,31,33,51)(13,40,43,49)(14,44,34,36)(15,45,46,47)(17,23,50,60)(18,27,54,64)(20,25,56,32)(26,62,28,61)(30,37,41,66)(35,39,52,63)(42,55,59,67)(48,65,57,58);(2,3)(4,5,8,14,11,16,10,34)(6,17,19,48,22,50,21,57)(7,23,26,58,29,60,28,65)(9,30,25,46,33,41,32,15)(12,35,36,18,38,52,44,54)(13,39,42,64,43,63,59,27)(20,55,51,40,56,67,31,49)(24,45,61,66,53,47,62,37)Polycyclic presentation:
2^7,3|a^2=d,b^2=g,c^2=efg,d^2=g,e^2=fg,f^2=g,b^a=bc,c^a=ce,e^a=ef,f^a=fg,h^a=h^2,c^b=ceg,d^b=dg,e^b=ef,f^b=fg,h^b=h^266 conjugacy classes — view the full character table.
| maximal subgroup of | D3×#1420, C2×#67605, #10715660, … |
| maximal normal subgroup of | D3×#1420, C2×#67605, #10715660, … |
| maximal quotient of | #10682647, #10682752, #10682824, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(384, 181);