Finite Group DatabasebetaFinite Group Databasebeta| order | 384 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C23 |
No aliases for this group.
| Fitting | C3×#350 ⋊ C2 |
| Sylow | C3 ⋊ #2195 |
206 conjugacy classes of subgroups; only the 49 normal subgroups are shown.
This group has 206 conjugacy classes of subgroups — too many to draw. Only its 49 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| minimal degree | μ(G) = 67 |
| transitive degree | μt(G) = 192 |
A minimal faithful permutation representation — 3 generators on 67 points:
(1,2,3)(4,7,11,26)(5,13,17,39)(6,19,22,51)(8,24,31,58)(9,32,10,25)(12,35,37,63)(14,38,42,55)(15,43,16,23)(18,45,46,66)(20,48,34,61)(21,50,33,49)(27,54,41,65)(28,56,59,67)(29,60,30,57)(36,62,44,53)(40,64,52,47);(2,3)(4,6)(5,12)(7,19)(8,28)(9,21)(10,33)(11,22)(13,35)(14,40)(15,36)(16,44)(17,37)(18,27)(20,30)(23,53)(24,56)(25,49)(26,51)(29,34)(31,59)(32,50)(38,64)(39,63)(41,46)(42,52)(43,62)(45,54)(47,55)(48,57)(58,67)(60,61)(65,66);(2,3)(4,5,11,17)(6,18,22,46)(7,23,26,43)(8,27,31,41)(9,16,10,15)(12,34,37,20)(13,32,39,25)(14,29,42,30)(19,47,51,64)(21,52,33,40)(24,55,58,38)(28,44,59,36)(35,56,63,67)(45,50,66,49)(48,53,61,62)(54,60,65,57)Polycyclic presentation:
2^7,3|a^2=g,c^2=g,d^2=fg,e^2=g,f^2=g,b^a=bd,c^a=ce,d^a=df,e^a=eg,f^a=fg,h^a=h^2,d^b=df,f^b=fg,h^b=h^2,e^c=eg51 conjugacy classes — view the full character table.
| maximal subgroup of | D3×#2195, C2×#69129, #10949138, … |
| maximal normal subgroup of | D3×#2195, C2×#69129, #10949138, … |
| maximal quotient of | #10707342, #10707348, #10707686, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(384, 1705);