Finite Group DatabasebetaFinite Group Databasebeta| order | 384 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C25 |
No aliases for this group.
| Fitting | C3×#464 ⋊ C2 |
| Sylow | C3 ⋊ #3044 |
458 conjugacy classes of subgroups.
| minimal degree | μ(G) = 39 |
| transitive degree | μt(G) = 192 |
A minimal faithful permutation representation — 4 generators on 39 points:
(1,2)(10,19)(14,28)(18,33)(20,35)(27,38)(29,36)(32,39)(34,37);(8,11,13,23)(9,15,17,30)(10,18,19,33)(12,25,26,22)(14,27,28,38)(16,31,24,21)(20,37,35,34)(29,39,36,32);(4,5,6,7)(8,10)(9,14)(11,18)(12,20)(13,19)(15,27)(16,29)(17,28)(21,32)(22,34)(23,33)(24,36)(25,37)(26,35)(30,38)(31,39);(2,3)(5,7)(8,9,13,17)(10,14,19,28)(11,21,23,31)(12,24,26,16)(15,25,30,22)(18,32,33,39)(20,36,35,29)(27,37,38,34)Polycyclic presentation:
2^7,3|a^2=g,b^2=e,c^2=g,f^2=g,b^a=be,c^a=cf,f^a=fg,h^a=h^2,d^b=dg,f^c=fg,h^d=h^251 conjugacy classes — view the full character table.
| maximal subgroup of | D3×#3044, C2×#80601, #11662131, … |
| maximal normal subgroup of | D3×#3044, C2×#80601, #11662131, … |
| maximal quotient of | #10780519, #10780528, #10780537, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(384, 13177);