Finite Group DatabasebetaFinite Group Databasebeta| order | 384 |
| isoclinism | isoclinic class of #4537 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C8 · Schur multiplier (H2) = C2 |
No aliases for this group.
| Sylow | C3 ⋊ #1315 |
116 conjugacy classes of subgroups.
| minimal degree | μ(G) = 43 |
| transitive degree | μt(G) = 192 |
A minimal faithful permutation representation — 2 generators on 43 points:
(1,2,3)(4,6)(5,8)(7,11)(9,10)(12,14)(13,19)(15,28)(16,30)(17,25)(18,27)(20,36)(21,38)(22,24)(23,35)(26,32)(29,42)(31,33)(34,40)(37,41)(39,43);(2,3)(4,5)(6,10,11,8)(7,9)(12,13,16,21,17,22,31,39,18,23,32,40,15,20,29,37)(14,24,26,41,25,35,42,38,27,36,30,43,28,19,33,34)Polycyclic presentation:
2^7,3|a^2=d,c^2=g,d^2=f,f^2=g,b^a=bc,c^a=ce,h^a=h^2,c^b=cg,d^b=deg66 conjugacy classes — view the full character table.
| maximal subgroup of | #10682551, #10682552, #10682554, … |
| maximal normal subgroup of | #10682551, #10682552, #10682554, … |
| maximal quotient of | #10681814, #10681816, #10681818, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(384, 265);