Aliases: Dic5.A4, SL2(𝔽3)⋊2D5, C5⋊(C4.A4), Q8⋊2D5⋊C3, (C5×Q8).C6, Q8.(C3×D5), C2.2(D5×A4), C10.1(C2×A4), (C5×SL2(𝔽3))⋊2C2, SmallGroup(240,108)
Series: Derived ►Chief ►Lower central ►Upper central
| C1 — C2 — C10 — C5×Q8 — C5×SL2(𝔽3) — Dic5.A4 |
| C5×Q8 — Dic5.A4 |
Generators and relations for Dic5.A4
G = < a,b,c,d,e | a10=e3=1, b2=c2=d2=a5, bab-1=a-1, ac=ca, ad=da, ae=ea, bc=cb, bd=db, be=eb, dcd-1=a5c, ece-1=a5cd, ede-1=c >
Character table of Dic5.A4
| class | 1 | 2A | 2B | 3A | 3B | 4A | 4B | 4C | 5A | 5B | 6A | 6B | 10A | 10B | 12A | 12B | 12C | 12D | 15A | 15B | 15C | 15D | 20A | 20B | 30A | 30B | 30C | 30D | |
| size | 1 | 1 | 30 | 4 | 4 | 5 | 5 | 6 | 2 | 2 | 4 | 4 | 2 | 2 | 20 | 20 | 20 | 20 | 8 | 8 | 8 | 8 | 12 | 12 | 8 | 8 | 8 | 8 | |
| 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 | 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 | linear of order 2 |
| ρ3 | 1 | 1 | 1 | ζ3 | ζ32 | 1 | 1 | 1 | 1 | 1 | ζ32 | ζ3 | 1 | 1 | ζ3 | ζ32 | ζ3 | ζ32 | ζ3 | ζ3 | ζ32 | ζ32 | 1 | 1 | ζ32 | ζ3 | ζ32 | ζ3 | linear of order 3 |
| ρ4 | 1 | 1 | -1 | ζ32 | ζ3 | -1 | -1 | 1 | 1 | 1 | ζ3 | ζ32 | 1 | 1 | ζ6 | ζ65 | ζ6 | ζ65 | ζ32 | ζ32 | ζ3 | ζ3 | 1 | 1 | ζ3 | ζ32 | ζ3 | ζ32 | linear of order 6 |
| ρ5 | 1 | 1 | 1 | ζ32 | ζ3 | 1 | 1 | 1 | 1 | 1 | ζ3 | ζ32 | 1 | 1 | ζ32 | ζ3 | ζ32 | ζ3 | ζ32 | ζ32 | ζ3 | ζ3 | 1 | 1 | ζ3 | ζ32 | ζ3 | ζ32 | linear of order 3 |
| ρ6 | 1 | 1 | -1 | ζ3 | ζ32 | -1 | -1 | 1 | 1 | 1 | ζ32 | ζ3 | 1 | 1 | ζ65 | ζ6 | ζ65 | ζ6 | ζ3 | ζ3 | ζ32 | ζ32 | 1 | 1 | ζ32 | ζ3 | ζ32 | ζ3 | linear of order 6 |
| ρ7 | 2 | 2 | 0 | 2 | 2 | 0 | 0 | 2 | -1+√5/2 | -1-√5/2 | 2 | 2 | -1-√5/2 | -1+√5/2 | 0 | 0 | 0 | 0 | -1-√5/2 | -1+√5/2 | -1-√5/2 | -1+√5/2 | -1+√5/2 | -1-√5/2 | -1-√5/2 | -1+√5/2 | -1+√5/2 | -1-√5/2 | orthogonal lifted from D5 |
| ρ8 | 2 | 2 | 0 | 2 | 2 | 0 | 0 | 2 | -1-√5/2 | -1+√5/2 | 2 | 2 | -1+√5/2 | -1-√5/2 | 0 | 0 | 0 | 0 | -1+√5/2 | -1-√5/2 | -1+√5/2 | -1-√5/2 | -1-√5/2 | -1+√5/2 | -1+√5/2 | -1-√5/2 | -1-√5/2 | -1+√5/2 | orthogonal lifted from D5 |
| ρ9 | 2 | -2 | 0 | -1 | -1 | 2i | -2i | 0 | 2 | 2 | 1 | 1 | -2 | -2 | -i | -i | i | i | -1 | -1 | -1 | -1 | 0 | 0 | 1 | 1 | 1 | 1 | complex lifted from C4.A4 |
| ρ10 | 2 | -2 | 0 | -1 | -1 | -2i | 2i | 0 | 2 | 2 | 1 | 1 | -2 | -2 | i | i | -i | -i | -1 | -1 | -1 | -1 | 0 | 0 | 1 | 1 | 1 | 1 | complex lifted from C4.A4 |
| ρ11 | 2 | -2 | 0 | ζ65 | ζ6 | -2i | 2i | 0 | 2 | 2 | ζ32 | ζ3 | -2 | -2 | ζ4ζ3 | ζ4ζ32 | ζ43ζ3 | ζ43ζ32 | ζ65 | ζ65 | ζ6 | ζ6 | 0 | 0 | ζ32 | ζ3 | ζ32 | ζ3 | complex lifted from C4.A4 |
| ρ12 | 2 | -2 | 0 | ζ6 | ζ65 | 2i | -2i | 0 | 2 | 2 | ζ3 | ζ32 | -2 | -2 | ζ43ζ32 | ζ43ζ3 | ζ4ζ32 | ζ4ζ3 | ζ6 | ζ6 | ζ65 | ζ65 | 0 | 0 | ζ3 | ζ32 | ζ3 | ζ32 | complex lifted from C4.A4 |
| ρ13 | 2 | -2 | 0 | ζ65 | ζ6 | 2i | -2i | 0 | 2 | 2 | ζ32 | ζ3 | -2 | -2 | ζ43ζ3 | ζ43ζ32 | ζ4ζ3 | ζ4ζ32 | ζ65 | ζ65 | ζ6 | ζ6 | 0 | 0 | ζ32 | ζ3 | ζ32 | ζ3 | complex lifted from C4.A4 |
| ρ14 | 2 | -2 | 0 | ζ6 | ζ65 | -2i | 2i | 0 | 2 | 2 | ζ3 | ζ32 | -2 | -2 | ζ4ζ32 | ζ4ζ3 | ζ43ζ32 | ζ43ζ3 | ζ6 | ζ6 | ζ65 | ζ65 | 0 | 0 | ζ3 | ζ32 | ζ3 | ζ32 | complex lifted from C4.A4 |
| ρ15 | 2 | 2 | 0 | -1-√-3 | -1+√-3 | 0 | 0 | 2 | -1-√5/2 | -1+√5/2 | -1+√-3 | -1-√-3 | -1+√5/2 | -1-√5/2 | 0 | 0 | 0 | 0 | ζ32ζ54+ζ32ζ5 | ζ32ζ53+ζ32ζ52 | ζ3ζ54+ζ3ζ5 | ζ3ζ53+ζ3ζ52 | -1-√5/2 | -1+√5/2 | ζ3ζ54+ζ3ζ5 | ζ32ζ53+ζ32ζ52 | ζ3ζ53+ζ3ζ52 | ζ32ζ54+ζ32ζ5 | complex lifted from C3×D5 |
| ρ16 | 2 | 2 | 0 | -1+√-3 | -1-√-3 | 0 | 0 | 2 | -1+√5/2 | -1-√5/2 | -1-√-3 | -1+√-3 | -1-√5/2 | -1+√5/2 | 0 | 0 | 0 | 0 | ζ3ζ53+ζ3ζ52 | ζ3ζ54+ζ3ζ5 | ζ32ζ53+ζ32ζ52 | ζ32ζ54+ζ32ζ5 | -1+√5/2 | -1-√5/2 | ζ32ζ53+ζ32ζ52 | ζ3ζ54+ζ3ζ5 | ζ32ζ54+ζ32ζ5 | ζ3ζ53+ζ3ζ52 | complex lifted from C3×D5 |
| ρ17 | 2 | 2 | 0 | -1+√-3 | -1-√-3 | 0 | 0 | 2 | -1-√5/2 | -1+√5/2 | -1-√-3 | -1+√-3 | -1+√5/2 | -1-√5/2 | 0 | 0 | 0 | 0 | ζ3ζ54+ζ3ζ5 | ζ3ζ53+ζ3ζ52 | ζ32ζ54+ζ32ζ5 | ζ32ζ53+ζ32ζ52 | -1-√5/2 | -1+√5/2 | ζ32ζ54+ζ32ζ5 | ζ3ζ53+ζ3ζ52 | ζ32ζ53+ζ32ζ52 | ζ3ζ54+ζ3ζ5 | complex lifted from C3×D5 |
| ρ18 | 2 | 2 | 0 | -1-√-3 | -1+√-3 | 0 | 0 | 2 | -1+√5/2 | -1-√5/2 | -1+√-3 | -1-√-3 | -1-√5/2 | -1+√5/2 | 0 | 0 | 0 | 0 | ζ32ζ53+ζ32ζ52 | ζ32ζ54+ζ32ζ5 | ζ3ζ53+ζ3ζ52 | ζ3ζ54+ζ3ζ5 | -1+√5/2 | -1-√5/2 | ζ3ζ53+ζ3ζ52 | ζ32ζ54+ζ32ζ5 | ζ3ζ54+ζ3ζ5 | ζ32ζ53+ζ32ζ52 | complex lifted from C3×D5 |
| ρ19 | 3 | 3 | 1 | 0 | 0 | -3 | -3 | -1 | 3 | 3 | 0 | 0 | 3 | 3 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | -1 | -1 | 0 | 0 | 0 | 0 | orthogonal lifted from C2×A4 |
| ρ20 | 3 | 3 | -1 | 0 | 0 | 3 | 3 | -1 | 3 | 3 | 0 | 0 | 3 | 3 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | -1 | -1 | 0 | 0 | 0 | 0 | orthogonal lifted from A4 |
| ρ21 | 4 | -4 | 0 | -2 | -2 | 0 | 0 | 0 | -1-√5 | -1+√5 | 2 | 2 | 1-√5 | 1+√5 | 0 | 0 | 0 | 0 | 1-√5/2 | 1+√5/2 | 1-√5/2 | 1+√5/2 | 0 | 0 | -1+√5/2 | -1-√5/2 | -1-√5/2 | -1+√5/2 | orthogonal faithful |
| ρ22 | 4 | -4 | 0 | -2 | -2 | 0 | 0 | 0 | -1+√5 | -1-√5 | 2 | 2 | 1+√5 | 1-√5 | 0 | 0 | 0 | 0 | 1+√5/2 | 1-√5/2 | 1+√5/2 | 1-√5/2 | 0 | 0 | -1-√5/2 | -1+√5/2 | -1+√5/2 | -1-√5/2 | orthogonal faithful |
| ρ23 | 4 | -4 | 0 | 1-√-3 | 1+√-3 | 0 | 0 | 0 | -1-√5 | -1+√5 | -1-√-3 | -1+√-3 | 1-√5 | 1+√5 | 0 | 0 | 0 | 0 | -ζ3ζ54-ζ3ζ5 | -ζ3ζ53-ζ3ζ52 | -ζ32ζ54-ζ32ζ5 | -ζ32ζ53-ζ32ζ52 | 0 | 0 | ζ32ζ54+ζ32ζ5 | ζ3ζ53+ζ3ζ52 | ζ32ζ53+ζ32ζ52 | ζ3ζ54+ζ3ζ5 | complex faithful |
| ρ24 | 4 | -4 | 0 | 1-√-3 | 1+√-3 | 0 | 0 | 0 | -1+√5 | -1-√5 | -1-√-3 | -1+√-3 | 1+√5 | 1-√5 | 0 | 0 | 0 | 0 | -ζ3ζ53-ζ3ζ52 | -ζ3ζ54-ζ3ζ5 | -ζ32ζ53-ζ32ζ52 | -ζ32ζ54-ζ32ζ5 | 0 | 0 | ζ32ζ53+ζ32ζ52 | ζ3ζ54+ζ3ζ5 | ζ32ζ54+ζ32ζ5 | ζ3ζ53+ζ3ζ52 | complex faithful |
| ρ25 | 4 | -4 | 0 | 1+√-3 | 1-√-3 | 0 | 0 | 0 | -1-√5 | -1+√5 | -1+√-3 | -1-√-3 | 1-√5 | 1+√5 | 0 | 0 | 0 | 0 | -ζ32ζ54-ζ32ζ5 | -ζ32ζ53-ζ32ζ52 | -ζ3ζ54-ζ3ζ5 | -ζ3ζ53-ζ3ζ52 | 0 | 0 | ζ3ζ54+ζ3ζ5 | ζ32ζ53+ζ32ζ52 | ζ3ζ53+ζ3ζ52 | ζ32ζ54+ζ32ζ5 | complex faithful |
| ρ26 | 4 | -4 | 0 | 1+√-3 | 1-√-3 | 0 | 0 | 0 | -1+√5 | -1-√5 | -1+√-3 | -1-√-3 | 1+√5 | 1-√5 | 0 | 0 | 0 | 0 | -ζ32ζ53-ζ32ζ52 | -ζ32ζ54-ζ32ζ5 | -ζ3ζ53-ζ3ζ52 | -ζ3ζ54-ζ3ζ5 | 0 | 0 | ζ3ζ53+ζ3ζ52 | ζ32ζ54+ζ32ζ5 | ζ3ζ54+ζ3ζ5 | ζ32ζ53+ζ32ζ52 | complex faithful |
| ρ27 | 6 | 6 | 0 | 0 | 0 | 0 | 0 | -2 | -3-3√5/2 | -3+3√5/2 | 0 | 0 | -3+3√5/2 | -3-3√5/2 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 1+√5/2 | 1-√5/2 | 0 | 0 | 0 | 0 | orthogonal lifted from D5×A4 |
| ρ28 | 6 | 6 | 0 | 0 | 0 | 0 | 0 | -2 | -3+3√5/2 | -3-3√5/2 | 0 | 0 | -3-3√5/2 | -3+3√5/2 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 1-√5/2 | 1+√5/2 | 0 | 0 | 0 | 0 | orthogonal lifted from D5×A4 |
►On 80 points
Generators in S80
(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)
(1 46 6 41)(2 45 7 50)(3 44 8 49)(4 43 9 48)(5 42 10 47)(11 54 16 59)(12 53 17 58)(13 52 18 57)(14 51 19 56)(15 60 20 55)(21 64 26 69)(22 63 27 68)(23 62 28 67)(24 61 29 66)(25 70 30 65)(31 74 36 79)(32 73 37 78)(33 72 38 77)(34 71 39 76)(35 80 40 75)
(1 14 6 19)(2 15 7 20)(3 16 8 11)(4 17 9 12)(5 18 10 13)(21 31 26 36)(22 32 27 37)(23 33 28 38)(24 34 29 39)(25 35 30 40)(41 56 46 51)(42 57 47 52)(43 58 48 53)(44 59 49 54)(45 60 50 55)(61 71 66 76)(62 72 67 77)(63 73 68 78)(64 74 69 79)(65 75 70 80)
(1 24 6 29)(2 25 7 30)(3 26 8 21)(4 27 9 22)(5 28 10 23)(11 36 16 31)(12 37 17 32)(13 38 18 33)(14 39 19 34)(15 40 20 35)(41 66 46 61)(42 67 47 62)(43 68 48 63)(44 69 49 64)(45 70 50 65)(51 76 56 71)(52 77 57 72)(53 78 58 73)(54 79 59 74)(55 80 60 75)
(11 21 31)(12 22 32)(13 23 33)(14 24 34)(15 25 35)(16 26 36)(17 27 37)(18 28 38)(19 29 39)(20 30 40)(51 61 71)(52 62 72)(53 63 73)(54 64 74)(55 65 75)(56 66 76)(57 67 77)(58 68 78)(59 69 79)(60 70 80)
G:=sub<Sym(80)| (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), (1,46,6,41)(2,45,7,50)(3,44,8,49)(4,43,9,48)(5,42,10,47)(11,54,16,59)(12,53,17,58)(13,52,18,57)(14,51,19,56)(15,60,20,55)(21,64,26,69)(22,63,27,68)(23,62,28,67)(24,61,29,66)(25,70,30,65)(31,74,36,79)(32,73,37,78)(33,72,38,77)(34,71,39,76)(35,80,40,75), (1,14,6,19)(2,15,7,20)(3,16,8,11)(4,17,9,12)(5,18,10,13)(21,31,26,36)(22,32,27,37)(23,33,28,38)(24,34,29,39)(25,35,30,40)(41,56,46,51)(42,57,47,52)(43,58,48,53)(44,59,49,54)(45,60,50,55)(61,71,66,76)(62,72,67,77)(63,73,68,78)(64,74,69,79)(65,75,70,80), (1,24,6,29)(2,25,7,30)(3,26,8,21)(4,27,9,22)(5,28,10,23)(11,36,16,31)(12,37,17,32)(13,38,18,33)(14,39,19,34)(15,40,20,35)(41,66,46,61)(42,67,47,62)(43,68,48,63)(44,69,49,64)(45,70,50,65)(51,76,56,71)(52,77,57,72)(53,78,58,73)(54,79,59,74)(55,80,60,75), (11,21,31)(12,22,32)(13,23,33)(14,24,34)(15,25,35)(16,26,36)(17,27,37)(18,28,38)(19,29,39)(20,30,40)(51,61,71)(52,62,72)(53,63,73)(54,64,74)(55,65,75)(56,66,76)(57,67,77)(58,68,78)(59,69,79)(60,70,80)>;
G:=Group( (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), (1,46,6,41)(2,45,7,50)(3,44,8,49)(4,43,9,48)(5,42,10,47)(11,54,16,59)(12,53,17,58)(13,52,18,57)(14,51,19,56)(15,60,20,55)(21,64,26,69)(22,63,27,68)(23,62,28,67)(24,61,29,66)(25,70,30,65)(31,74,36,79)(32,73,37,78)(33,72,38,77)(34,71,39,76)(35,80,40,75), (1,14,6,19)(2,15,7,20)(3,16,8,11)(4,17,9,12)(5,18,10,13)(21,31,26,36)(22,32,27,37)(23,33,28,38)(24,34,29,39)(25,35,30,40)(41,56,46,51)(42,57,47,52)(43,58,48,53)(44,59,49,54)(45,60,50,55)(61,71,66,76)(62,72,67,77)(63,73,68,78)(64,74,69,79)(65,75,70,80), (1,24,6,29)(2,25,7,30)(3,26,8,21)(4,27,9,22)(5,28,10,23)(11,36,16,31)(12,37,17,32)(13,38,18,33)(14,39,19,34)(15,40,20,35)(41,66,46,61)(42,67,47,62)(43,68,48,63)(44,69,49,64)(45,70,50,65)(51,76,56,71)(52,77,57,72)(53,78,58,73)(54,79,59,74)(55,80,60,75), (11,21,31)(12,22,32)(13,23,33)(14,24,34)(15,25,35)(16,26,36)(17,27,37)(18,28,38)(19,29,39)(20,30,40)(51,61,71)(52,62,72)(53,63,73)(54,64,74)(55,65,75)(56,66,76)(57,67,77)(58,68,78)(59,69,79)(60,70,80) );
G=PermutationGroup([[(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)], [(1,46,6,41),(2,45,7,50),(3,44,8,49),(4,43,9,48),(5,42,10,47),(11,54,16,59),(12,53,17,58),(13,52,18,57),(14,51,19,56),(15,60,20,55),(21,64,26,69),(22,63,27,68),(23,62,28,67),(24,61,29,66),(25,70,30,65),(31,74,36,79),(32,73,37,78),(33,72,38,77),(34,71,39,76),(35,80,40,75)], [(1,14,6,19),(2,15,7,20),(3,16,8,11),(4,17,9,12),(5,18,10,13),(21,31,26,36),(22,32,27,37),(23,33,28,38),(24,34,29,39),(25,35,30,40),(41,56,46,51),(42,57,47,52),(43,58,48,53),(44,59,49,54),(45,60,50,55),(61,71,66,76),(62,72,67,77),(63,73,68,78),(64,74,69,79),(65,75,70,80)], [(1,24,6,29),(2,25,7,30),(3,26,8,21),(4,27,9,22),(5,28,10,23),(11,36,16,31),(12,37,17,32),(13,38,18,33),(14,39,19,34),(15,40,20,35),(41,66,46,61),(42,67,47,62),(43,68,48,63),(44,69,49,64),(45,70,50,65),(51,76,56,71),(52,77,57,72),(53,78,58,73),(54,79,59,74),(55,80,60,75)], [(11,21,31),(12,22,32),(13,23,33),(14,24,34),(15,25,35),(16,26,36),(17,27,37),(18,28,38),(19,29,39),(20,30,40),(51,61,71),(52,62,72),(53,63,73),(54,64,74),(55,65,75),(56,66,76),(57,67,77),(58,68,78),(59,69,79),(60,70,80)]])
Dic5.A4 is a maximal subgroup of
C5⋊U2(𝔽3) SL2(𝔽3).F5 CSU2(𝔽3)⋊D5 Dic5.6S4 Dic5.7S4 GL2(𝔽3)⋊D5 SL2(𝔽3).11D10 Dic10.A4 D5×C4.A4
Dic5.A4 is a maximal quotient of
Dic5×SL2(𝔽3)
Matrix representation of Dic5.A4 ►in GL4(𝔽61) generated by
| 60 | 0 | 0 | 0 |
| 0 | 60 | 0 | 0 |
| 0 | 0 | 1 | 2 |
| 0 | 0 | 38 | 16 |
| 50 | 0 | 0 | 0 |
| 0 | 50 | 0 | 0 |
| 0 | 0 | 14 | 12 |
| 0 | 0 | 60 | 47 |
| 0 | 1 | 0 | 0 |
| 60 | 0 | 0 | 0 |
| 0 | 0 | 1 | 0 |
| 0 | 0 | 0 | 1 |
| 48 | 47 | 0 | 0 |
| 47 | 13 | 0 | 0 |
| 0 | 0 | 1 | 0 |
| 0 | 0 | 0 | 1 |
| 1 | 0 | 0 | 0 |
| 47 | 13 | 0 | 0 |
| 0 | 0 | 1 | 0 |
| 0 | 0 | 0 | 1 |
G:=sub<GL(4,GF(61))| [60,0,0,0,0,60,0,0,0,0,1,38,0,0,2,16],[50,0,0,0,0,50,0,0,0,0,14,60,0,0,12,47],[0,60,0,0,1,0,0,0,0,0,1,0,0,0,0,1],[48,47,0,0,47,13,0,0,0,0,1,0,0,0,0,1],[1,47,0,0,0,13,0,0,0,0,1,0,0,0,0,1] >;
Dic5.A4 in GAP, Magma, Sage, TeX
{\rm Dic}_5.A_4 % in TeX
G:=Group("Dic5.A4"); // GroupNames label
G:=SmallGroup(240,108);
// by ID
G=gap.SmallGroup(240,108);
# by ID
G:=PCGroup([6,-2,-3,-2,2,-5,-2,720,170,374,81,543,261,2884]);
// Polycyclic
G:=Group<a,b,c,d,e|a^10=e^3=1,b^2=c^2=d^2=a^5,b*a*b^-1=a^-1,a*c=c*a,a*d=d*a,a*e=e*a,b*c=c*b,b*d=d*b,b*e=e*b,d*c*d^-1=a^5*c,e*c*e^-1=a^5*c*d,e*d*e^-1=c>;
// generators/relations
Export
Subgroup lattice of Dic5.A4 in TeX
Character table of Dic5.A4 in TeX