Finite Group DatabasebetaFinite Group Databasebeta| order | 384 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C26 |
No aliases for this group.
| Fitting | C3×#452 ⋊ C2 |
| Sylow | C3 ⋊ #3011 |
700 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)(11,22)(15,29)(19,33)(23,35)(27,38)(30,36)(32,39)(34,37);(5,7)(8,11)(9,15)(10,19)(12,23)(13,22)(14,27)(16,30)(17,29)(18,32)(20,34)(21,33)(24,36)(25,37)(26,35)(28,38)(31,39);(2,3)(8,10,13,21)(9,14,17,28)(11,19,22,33)(12,25,26,20)(15,27,29,38)(16,31,24,18)(23,37,35,34)(30,39,36,32);(4,5)(6,7)(8,9,13,17)(10,18,21,31)(11,15,22,29)(12,24,26,16)(14,25,28,20)(19,32,33,39)(23,36,35,30)(27,37,38,34)Polycyclic presentation:
2^7,3|a^2=g,b^2=g,e^2=g,b^a=be,c^a=cf,e^a=eg,e^b=eg,h^b=h^2,d^c=dg,h^d=h^251 conjugacy classes — view the full character table.
| maximal subgroup of | D3×#3011, C2×#80230, #11661650, … |
| maximal normal subgroup of | D3×#3011, C2×#80230, #11661650, … |
| maximal quotient of | #10768377, #10768379, #10768465, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(384, 12806);