Finite Group DatabasebetaFinite Group Databasebeta| order | 384 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C4 · Schur multiplier (H2) = C2 |
No aliases for this group.
| Fitting | C3×M64 ⋊ C2 |
| Sylow | C3 ⋊ #1418 |
74 conjugacy classes of subgroups.
| minimal degree | μ(G) = 35 |
| transitive degree | μt(G) = 96 |
A minimal faithful permutation representation — 2 generators on 35 points:
(1,2)(4,5)(6,15)(7,20)(8,23)(9,11)(10,24)(12,19)(13,21)(14,26)(16,29)(17,30)(18,27)(22,25)(28,33)(31,35)(32,34);(2,3)(5,10,11,26)(6,14)(7,19)(8,21)(12,30,29,34)(13,31,23,28)(15,20,27,25)(16,22)(17,35)(18,24)(32,33)Polycyclic presentation:
2^7,3|a^2=d,c^2=efg,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×#1418, C2×#67606, #10715648, … |
| maximal normal subgroup of | D3×#1418, C2×#67606, #10715648, … |
| maximal quotient of | #10682644, #10682647, #10682743, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(384, 182);