Finite Group DatabasebetaFinite Group Databasebeta| order | 384 |
| isoclinism | isoclinic class of #4519 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C4 · Schur multiplier (H2) = C2 |
No aliases for this group.
| Sylow | C3 ⋊ #1423 |
56 conjugacy classes of subgroups.
| minimal degree | μ(G) = 39 |
| transitive degree | μt(G) = 384 |
A minimal faithful permutation representation — 2 generators on 39 points:
(2,3)(8,9,15,25,11,16,28,34,22,32,36,39,35,37,21,27,13,18,30,38,23,33,20,26,12,17,29,31,19,24,10,14);(1,2,3)(4,5,6,7)(9,14)(10,15)(11,19)(12,22)(16,31)(17,34)(18,27)(20,36)(21,30)(23,35)(24,25)(26,32)(28,29)(33,39)(37,38)Polycyclic presentation:
2^7,3|a^2=d,b^2=ce,c^2=ef,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×#1423, C2×#67575, #10715688, … |
| maximal normal subgroup of | D3×#1423, C2×#67575, #10715688, … |
| maximal quotient of | #10682863, #10682887, #10683086, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(384, 151);