metacyclic, supersoluble, monomial
Aliases: C4.F11, Dic22⋊C5, C44.1C10, Dic11.C10, C11⋊C5⋊Q8, C11⋊(C5×Q8), C11⋊C20.C2, C2.3(C2×F11), C22.1(C2×C10), (C4×C11⋊C5).1C2, (C2×C11⋊C5).1C22, SmallGroup(440,7)
Series: Derived ►Chief ►Lower central ►Upper central
Generators and relations for C4.F11
G = < a,b,c | a4=b11=1, c10=a2, ab=ba, cac-1=a-1, cbc-1=b6 >
Character table of C4.F11
| class | 1 | 2 | 4A | 4B | 4C | 5A | 5B | 5C | 5D | 10A | 10B | 10C | 10D | 11 | 20A | 20B | 20C | 20D | 20E | 20F | 20G | 20H | 20I | 20J | 20K | 20L | 22 | 44A | 44B | |
| size | 1 | 1 | 2 | 22 | 22 | 11 | 11 | 11 | 11 | 11 | 11 | 11 | 11 | 10 | 22 | 22 | 22 | 22 | 22 | 22 | 22 | 22 | 22 | 22 | 22 | 22 | 10 | 10 | 10 | |
| ρ1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | trivial |
| ρ2 | 1 | 1 | -1 | 1 | -1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | -1 | -1 | -1 | -1 | -1 | -1 | -1 | 1 | 1 | 1 | -1 | 1 | -1 | -1 | linear of order 2 |
| ρ3 | 1 | 1 | -1 | -1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | -1 | -1 | -1 | 1 | 1 | 1 | 1 | -1 | -1 | -1 | -1 | -1 | 1 | -1 | -1 | linear of order 2 |
| ρ4 | 1 | 1 | 1 | -1 | -1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | -1 | 1 | 1 | -1 | -1 | -1 | -1 | 1 | -1 | -1 | -1 | 1 | 1 | 1 | 1 | linear of order 2 |
| ρ5 | 1 | 1 | 1 | 1 | 1 | ζ5 | ζ54 | ζ52 | ζ53 | ζ5 | ζ52 | ζ54 | ζ53 | 1 | ζ52 | ζ52 | ζ53 | ζ53 | ζ5 | ζ54 | ζ52 | ζ5 | ζ53 | ζ5 | ζ54 | ζ54 | 1 | 1 | 1 | linear of order 5 |
| ρ6 | 1 | 1 | 1 | 1 | 1 | ζ54 | ζ5 | ζ53 | ζ52 | ζ54 | ζ53 | ζ5 | ζ52 | 1 | ζ53 | ζ53 | ζ52 | ζ52 | ζ54 | ζ5 | ζ53 | ζ54 | ζ52 | ζ54 | ζ5 | ζ5 | 1 | 1 | 1 | linear of order 5 |
| ρ7 | 1 | 1 | 1 | -1 | -1 | ζ5 | ζ54 | ζ52 | ζ53 | ζ5 | ζ52 | ζ54 | ζ53 | 1 | -ζ52 | ζ52 | ζ53 | -ζ53 | -ζ5 | -ζ54 | -ζ52 | ζ5 | -ζ53 | -ζ5 | -ζ54 | ζ54 | 1 | 1 | 1 | linear of order 10 |
| ρ8 | 1 | 1 | 1 | 1 | 1 | ζ53 | ζ52 | ζ5 | ζ54 | ζ53 | ζ5 | ζ52 | ζ54 | 1 | ζ5 | ζ5 | ζ54 | ζ54 | ζ53 | ζ52 | ζ5 | ζ53 | ζ54 | ζ53 | ζ52 | ζ52 | 1 | 1 | 1 | linear of order 5 |
| ρ9 | 1 | 1 | -1 | 1 | -1 | ζ53 | ζ52 | ζ5 | ζ54 | ζ53 | ζ5 | ζ52 | ζ54 | 1 | ζ5 | -ζ5 | -ζ54 | -ζ54 | -ζ53 | -ζ52 | -ζ5 | -ζ53 | ζ54 | ζ53 | ζ52 | -ζ52 | 1 | -1 | -1 | linear of order 10 |
| ρ10 | 1 | 1 | -1 | -1 | 1 | ζ54 | ζ5 | ζ53 | ζ52 | ζ54 | ζ53 | ζ5 | ζ52 | 1 | -ζ53 | -ζ53 | -ζ52 | ζ52 | ζ54 | ζ5 | ζ53 | -ζ54 | -ζ52 | -ζ54 | -ζ5 | -ζ5 | 1 | -1 | -1 | linear of order 10 |
| ρ11 | 1 | 1 | -1 | -1 | 1 | ζ52 | ζ53 | ζ54 | ζ5 | ζ52 | ζ54 | ζ53 | ζ5 | 1 | -ζ54 | -ζ54 | -ζ5 | ζ5 | ζ52 | ζ53 | ζ54 | -ζ52 | -ζ5 | -ζ52 | -ζ53 | -ζ53 | 1 | -1 | -1 | linear of order 10 |
| ρ12 | 1 | 1 | 1 | 1 | 1 | ζ52 | ζ53 | ζ54 | ζ5 | ζ52 | ζ54 | ζ53 | ζ5 | 1 | ζ54 | ζ54 | ζ5 | ζ5 | ζ52 | ζ53 | ζ54 | ζ52 | ζ5 | ζ52 | ζ53 | ζ53 | 1 | 1 | 1 | linear of order 5 |
| ρ13 | 1 | 1 | 1 | -1 | -1 | ζ54 | ζ5 | ζ53 | ζ52 | ζ54 | ζ53 | ζ5 | ζ52 | 1 | -ζ53 | ζ53 | ζ52 | -ζ52 | -ζ54 | -ζ5 | -ζ53 | ζ54 | -ζ52 | -ζ54 | -ζ5 | ζ5 | 1 | 1 | 1 | linear of order 10 |
| ρ14 | 1 | 1 | 1 | -1 | -1 | ζ53 | ζ52 | ζ5 | ζ54 | ζ53 | ζ5 | ζ52 | ζ54 | 1 | -ζ5 | ζ5 | ζ54 | -ζ54 | -ζ53 | -ζ52 | -ζ5 | ζ53 | -ζ54 | -ζ53 | -ζ52 | ζ52 | 1 | 1 | 1 | linear of order 10 |
| ρ15 | 1 | 1 | -1 | 1 | -1 | ζ5 | ζ54 | ζ52 | ζ53 | ζ5 | ζ52 | ζ54 | ζ53 | 1 | ζ52 | -ζ52 | -ζ53 | -ζ53 | -ζ5 | -ζ54 | -ζ52 | -ζ5 | ζ53 | ζ5 | ζ54 | -ζ54 | 1 | -1 | -1 | linear of order 10 |
| ρ16 | 1 | 1 | -1 | -1 | 1 | ζ5 | ζ54 | ζ52 | ζ53 | ζ5 | ζ52 | ζ54 | ζ53 | 1 | -ζ52 | -ζ52 | -ζ53 | ζ53 | ζ5 | ζ54 | ζ52 | -ζ5 | -ζ53 | -ζ5 | -ζ54 | -ζ54 | 1 | -1 | -1 | linear of order 10 |
| ρ17 | 1 | 1 | -1 | -1 | 1 | ζ53 | ζ52 | ζ5 | ζ54 | ζ53 | ζ5 | ζ52 | ζ54 | 1 | -ζ5 | -ζ5 | -ζ54 | ζ54 | ζ53 | ζ52 | ζ5 | -ζ53 | -ζ54 | -ζ53 | -ζ52 | -ζ52 | 1 | -1 | -1 | linear of order 10 |
| ρ18 | 1 | 1 | -1 | 1 | -1 | ζ52 | ζ53 | ζ54 | ζ5 | ζ52 | ζ54 | ζ53 | ζ5 | 1 | ζ54 | -ζ54 | -ζ5 | -ζ5 | -ζ52 | -ζ53 | -ζ54 | -ζ52 | ζ5 | ζ52 | ζ53 | -ζ53 | 1 | -1 | -1 | linear of order 10 |
| ρ19 | 1 | 1 | -1 | 1 | -1 | ζ54 | ζ5 | ζ53 | ζ52 | ζ54 | ζ53 | ζ5 | ζ52 | 1 | ζ53 | -ζ53 | -ζ52 | -ζ52 | -ζ54 | -ζ5 | -ζ53 | -ζ54 | ζ52 | ζ54 | ζ5 | -ζ5 | 1 | -1 | -1 | linear of order 10 |
| ρ20 | 1 | 1 | 1 | -1 | -1 | ζ52 | ζ53 | ζ54 | ζ5 | ζ52 | ζ54 | ζ53 | ζ5 | 1 | -ζ54 | ζ54 | ζ5 | -ζ5 | -ζ52 | -ζ53 | -ζ54 | ζ52 | -ζ5 | -ζ52 | -ζ53 | ζ53 | 1 | 1 | 1 | linear of order 10 |
| ρ21 | 2 | -2 | 0 | 0 | 0 | 2 | 2 | 2 | 2 | -2 | -2 | -2 | -2 | 2 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | -2 | 0 | 0 | symplectic lifted from Q8, Schur index 2 |
| ρ22 | 2 | -2 | 0 | 0 | 0 | 2ζ54 | 2ζ5 | 2ζ53 | 2ζ52 | -2ζ54 | -2ζ53 | -2ζ5 | -2ζ52 | 2 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | -2 | 0 | 0 | complex lifted from C5×Q8 |
| ρ23 | 2 | -2 | 0 | 0 | 0 | 2ζ52 | 2ζ53 | 2ζ54 | 2ζ5 | -2ζ52 | -2ζ54 | -2ζ53 | -2ζ5 | 2 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | -2 | 0 | 0 | complex lifted from C5×Q8 |
| ρ24 | 2 | -2 | 0 | 0 | 0 | 2ζ53 | 2ζ52 | 2ζ5 | 2ζ54 | -2ζ53 | -2ζ5 | -2ζ52 | -2ζ54 | 2 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | -2 | 0 | 0 | complex lifted from C5×Q8 |
| ρ25 | 2 | -2 | 0 | 0 | 0 | 2ζ5 | 2ζ54 | 2ζ52 | 2ζ53 | -2ζ5 | -2ζ52 | -2ζ54 | -2ζ53 | 2 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | -2 | 0 | 0 | complex lifted from C5×Q8 |
| ρ26 | 10 | 10 | -10 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | -1 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | -1 | 1 | 1 | orthogonal lifted from C2×F11 |
| ρ27 | 10 | 10 | 10 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | -1 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | -1 | -1 | -1 | orthogonal lifted from F11 |
| ρ28 | 10 | -10 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | -1 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 1 | √11 | -√11 | symplectic faithful, Schur index 2 |
| ρ29 | 10 | -10 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | -1 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 1 | -√11 | √11 | symplectic faithful, Schur index 2 |
►On 88 points
Generators in S88
(1 7 3 5)(2 6 4 8)(9 72 19 82)(10 83 20 73)(11 74 21 84)(12 85 22 75)(13 76 23 86)(14 87 24 77)(15 78 25 88)(16 69 26 79)(17 80 27 70)(18 71 28 81)(29 65 39 55)(30 56 40 66)(31 67 41 57)(32 58 42 68)(33 49 43 59)(34 60 44 50)(35 51 45 61)(36 62 46 52)(37 53 47 63)(38 64 48 54)
(1 12 55 20 24 16 63 51 67 28 59)(2 64 13 52 56 68 21 9 25 60 17)(3 22 65 10 14 26 53 61 57 18 49)(4 54 23 62 66 58 11 19 15 50 27)(5 75 39 83 87 79 47 35 31 71 43)(6 48 76 36 40 32 84 72 88 44 80)(7 85 29 73 77 69 37 45 41 81 33)(8 38 86 46 30 42 74 82 78 34 70)
(1 2 3 4)(5 6 7 8)(9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28)(29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48)(49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68)(69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88)
G:=sub<Sym(88)| (1,7,3,5)(2,6,4,8)(9,72,19,82)(10,83,20,73)(11,74,21,84)(12,85,22,75)(13,76,23,86)(14,87,24,77)(15,78,25,88)(16,69,26,79)(17,80,27,70)(18,71,28,81)(29,65,39,55)(30,56,40,66)(31,67,41,57)(32,58,42,68)(33,49,43,59)(34,60,44,50)(35,51,45,61)(36,62,46,52)(37,53,47,63)(38,64,48,54), (1,12,55,20,24,16,63,51,67,28,59)(2,64,13,52,56,68,21,9,25,60,17)(3,22,65,10,14,26,53,61,57,18,49)(4,54,23,62,66,58,11,19,15,50,27)(5,75,39,83,87,79,47,35,31,71,43)(6,48,76,36,40,32,84,72,88,44,80)(7,85,29,73,77,69,37,45,41,81,33)(8,38,86,46,30,42,74,82,78,34,70), (1,2,3,4)(5,6,7,8)(9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28)(29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,48)(49,50,51,52,53,54,55,56,57,58,59,60,61,62,63,64,65,66,67,68)(69,70,71,72,73,74,75,76,77,78,79,80,81,82,83,84,85,86,87,88)>;
G:=Group( (1,7,3,5)(2,6,4,8)(9,72,19,82)(10,83,20,73)(11,74,21,84)(12,85,22,75)(13,76,23,86)(14,87,24,77)(15,78,25,88)(16,69,26,79)(17,80,27,70)(18,71,28,81)(29,65,39,55)(30,56,40,66)(31,67,41,57)(32,58,42,68)(33,49,43,59)(34,60,44,50)(35,51,45,61)(36,62,46,52)(37,53,47,63)(38,64,48,54), (1,12,55,20,24,16,63,51,67,28,59)(2,64,13,52,56,68,21,9,25,60,17)(3,22,65,10,14,26,53,61,57,18,49)(4,54,23,62,66,58,11,19,15,50,27)(5,75,39,83,87,79,47,35,31,71,43)(6,48,76,36,40,32,84,72,88,44,80)(7,85,29,73,77,69,37,45,41,81,33)(8,38,86,46,30,42,74,82,78,34,70), (1,2,3,4)(5,6,7,8)(9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28)(29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,48)(49,50,51,52,53,54,55,56,57,58,59,60,61,62,63,64,65,66,67,68)(69,70,71,72,73,74,75,76,77,78,79,80,81,82,83,84,85,86,87,88) );
G=PermutationGroup([[(1,7,3,5),(2,6,4,8),(9,72,19,82),(10,83,20,73),(11,74,21,84),(12,85,22,75),(13,76,23,86),(14,87,24,77),(15,78,25,88),(16,69,26,79),(17,80,27,70),(18,71,28,81),(29,65,39,55),(30,56,40,66),(31,67,41,57),(32,58,42,68),(33,49,43,59),(34,60,44,50),(35,51,45,61),(36,62,46,52),(37,53,47,63),(38,64,48,54)], [(1,12,55,20,24,16,63,51,67,28,59),(2,64,13,52,56,68,21,9,25,60,17),(3,22,65,10,14,26,53,61,57,18,49),(4,54,23,62,66,58,11,19,15,50,27),(5,75,39,83,87,79,47,35,31,71,43),(6,48,76,36,40,32,84,72,88,44,80),(7,85,29,73,77,69,37,45,41,81,33),(8,38,86,46,30,42,74,82,78,34,70)], [(1,2,3,4),(5,6,7,8),(9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28),(29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,48),(49,50,51,52,53,54,55,56,57,58,59,60,61,62,63,64,65,66,67,68),(69,70,71,72,73,74,75,76,77,78,79,80,81,82,83,84,85,86,87,88)]])
Matrix representation of C4.F11 ►in GL12(𝔽661)
| 1 | 659 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 |
| 1 | 660 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 |
| 0 | 0 | 1 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 |
| 0 | 0 | 0 | 1 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 |
| 0 | 0 | 0 | 0 | 1 | 0 | 0 | 0 | 0 | 0 | 0 | 0 |
| 0 | 0 | 0 | 0 | 0 | 1 | 0 | 0 | 0 | 0 | 0 | 0 |
| 0 | 0 | 0 | 0 | 0 | 0 | 1 | 0 | 0 | 0 | 0 | 0 |
| 0 | 0 | 0 | 0 | 0 | 0 | 0 | 1 | 0 | 0 | 0 | 0 |
| 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 1 | 0 | 0 | 0 |
| 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 1 | 0 | 0 |
| 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 1 | 0 |
| 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 1 |
| 1 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 |
| 0 | 1 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 |
| 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 660 |
| 0 | 0 | 1 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 660 |
| 0 | 0 | 0 | 1 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 660 |
| 0 | 0 | 0 | 0 | 1 | 0 | 0 | 0 | 0 | 0 | 0 | 660 |
| 0 | 0 | 0 | 0 | 0 | 1 | 0 | 0 | 0 | 0 | 0 | 660 |
| 0 | 0 | 0 | 0 | 0 | 0 | 1 | 0 | 0 | 0 | 0 | 660 |
| 0 | 0 | 0 | 0 | 0 | 0 | 0 | 1 | 0 | 0 | 0 | 660 |
| 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 1 | 0 | 0 | 660 |
| 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 1 | 0 | 660 |
| 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 1 | 660 |
| 515 | 83 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 |
| 226 | 146 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 |
| 0 | 0 | 565 | 0 | 565 | 0 | 565 | 316 | 96 | 0 | 0 | 96 |
| 0 | 0 | 220 | 96 | 565 | 0 | 0 | 96 | 0 | 0 | 565 | 96 |
| 0 | 0 | 0 | 0 | 565 | 565 | 0 | 0 | 316 | 96 | 565 | 96 |
| 0 | 0 | 565 | 316 | 0 | 565 | 0 | 96 | 96 | 0 | 565 | 0 |
| 0 | 0 | 0 | 96 | 565 | 565 | 565 | 96 | 0 | 316 | 0 | 0 |
| 0 | 0 | 0 | 0 | 220 | 0 | 565 | 96 | 96 | 96 | 565 | 0 |
| 0 | 0 | 0 | 96 | 0 | 565 | 565 | 0 | 96 | 0 | 220 | 96 |
| 0 | 0 | 565 | 96 | 565 | 220 | 0 | 0 | 96 | 96 | 0 | 0 |
| 0 | 0 | 565 | 96 | 0 | 0 | 565 | 0 | 0 | 96 | 565 | 316 |
| 0 | 0 | 565 | 0 | 0 | 565 | 220 | 96 | 0 | 96 | 0 | 96 |
G:=sub<GL(12,GF(661))| [1,1,0,0,0,0,0,0,0,0,0,0,659,660,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,0,0,1],[1,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,660,660,660,660,660,660,660,660,660,660],[515,226,0,0,0,0,0,0,0,0,0,0,83,146,0,0,0,0,0,0,0,0,0,0,0,0,565,220,0,565,0,0,0,565,565,565,0,0,0,96,0,316,96,0,96,96,96,0,0,0,565,565,565,0,565,220,0,565,0,0,0,0,0,0,565,565,565,0,565,220,0,565,0,0,565,0,0,0,565,565,565,0,565,220,0,0,316,96,0,96,96,96,0,0,0,96,0,0,96,0,316,96,0,96,96,96,0,0,0,0,0,0,96,0,316,96,0,96,96,96,0,0,0,565,565,565,0,565,220,0,565,0,0,0,96,96,96,0,0,0,96,0,316,96] >;
C4.F11 in GAP, Magma, Sage, TeX
C_4.F_{11} % in TeX
G:=Group("C4.F11"); // GroupNames label
G:=SmallGroup(440,7);
// by ID
G=gap.SmallGroup(440,7);
# by ID
G:=PCGroup([5,-2,-2,-5,-2,-11,100,221,106,10004,2264]);
// Polycyclic
G:=Group<a,b,c|a^4=b^11=1,c^10=a^2,a*b=b*a,c*a*c^-1=a^-1,c*b*c^-1=b^6>;
// generators/relations
Export
Subgroup lattice of C4.F11 in TeX
Character table of C4.F11 in TeX