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## G = F16⋊C2order 480 = 25·3·5

### The semidirect product of F16 and C2 acting faithfully

Aliases: F16⋊C2, C24⋊C5⋊C6, C24⋊D5⋊C3, C22⋊A4⋊D5, C24⋊(C3×D5), SmallGroup(480,1188)

Series: Derived Chief Lower central Upper central

 Derived series C1 — C24 — C24⋊C5 — F16⋊C2
 Chief series C1 — C24 — C24⋊C5 — F16 — F16⋊C2
 Lower central C24⋊C5 — F16⋊C2
 Upper central C1

Generators and relations for F16⋊C2
G = < a,b,c,d,e,f | a2=b2=c2=d2=e15=f2=1, ab=ba, ac=ca, ad=da, eae-1=bcd, faf=abc, ebe-1=bc=cb, fbf=ede-1=bd=db, fcf=cd=dc, ece-1=a, df=fd, fef=e4 >

15C2
20C2
16C3
16C5
5C22
15C22
15C22
30C22
30C4
80C6
16D5
16C15
5C23
15C23
15C2×C4
30D4
30D4
20A4
16C3×D5
15C2×D4
15C22⋊C4
20C2×A4

Character table of F16⋊C2

 class 1 2A 2B 3A 3B 4 5A 5B 6A 6B 15A 15B 15C 15D size 1 15 20 16 16 60 32 32 80 80 32 32 32 32 ρ1 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 linear of order 2 ρ3 1 1 1 ζ3 ζ32 1 1 1 ζ3 ζ32 ζ3 ζ3 ζ32 ζ32 linear of order 3 ρ4 1 1 -1 ζ32 ζ3 -1 1 1 ζ6 ζ65 ζ32 ζ32 ζ3 ζ3 linear of order 6 ρ5 1 1 -1 ζ3 ζ32 -1 1 1 ζ65 ζ6 ζ3 ζ3 ζ32 ζ32 linear of order 6 ρ6 1 1 1 ζ32 ζ3 1 1 1 ζ32 ζ3 ζ32 ζ32 ζ3 ζ3 linear of order 3 ρ7 2 2 0 2 2 0 -1-√5/2 -1+√5/2 0 0 -1+√5/2 -1-√5/2 -1-√5/2 -1+√5/2 orthogonal lifted from D5 ρ8 2 2 0 2 2 0 -1+√5/2 -1-√5/2 0 0 -1-√5/2 -1+√5/2 -1+√5/2 -1-√5/2 orthogonal lifted from D5 ρ9 2 2 0 -1-√-3 -1+√-3 0 -1-√5/2 -1+√5/2 0 0 ζ32ζ54+ζ32ζ5 ζ32ζ53+ζ32ζ52 ζ3ζ53+ζ3ζ52 ζ3ζ54+ζ3ζ5 complex lifted from C3×D5 ρ10 2 2 0 -1+√-3 -1-√-3 0 -1+√5/2 -1-√5/2 0 0 ζ3ζ53+ζ3ζ52 ζ3ζ54+ζ3ζ5 ζ32ζ54+ζ32ζ5 ζ32ζ53+ζ32ζ52 complex lifted from C3×D5 ρ11 2 2 0 -1-√-3 -1+√-3 0 -1+√5/2 -1-√5/2 0 0 ζ32ζ53+ζ32ζ52 ζ32ζ54+ζ32ζ5 ζ3ζ54+ζ3ζ5 ζ3ζ53+ζ3ζ52 complex lifted from C3×D5 ρ12 2 2 0 -1+√-3 -1-√-3 0 -1-√5/2 -1+√5/2 0 0 ζ3ζ54+ζ3ζ5 ζ3ζ53+ζ3ζ52 ζ32ζ53+ζ32ζ52 ζ32ζ54+ζ32ζ5 complex lifted from C3×D5 ρ13 15 -1 -3 0 0 1 0 0 0 0 0 0 0 0 orthogonal faithful ρ14 15 -1 3 0 0 -1 0 0 0 0 0 0 0 0 orthogonal faithful

Permutation representations of F16⋊C2
On 16 points: primitive, doubly transitive - transitive group 16T777
Generators in S16
```(1 13)(2 16)(3 8)(4 6)(5 11)(7 15)(9 12)(10 14)
(1 3)(2 14)(4 15)(5 12)(6 7)(8 13)(9 11)(10 16)
(1 14)(2 3)(4 9)(5 7)(6 12)(8 16)(10 13)(11 15)
(1 7)(2 12)(3 6)(4 8)(5 14)(9 16)(10 11)(13 15)
(2 3 4 5 6 7 8 9 10 11 12 13 14 15 16)
(3 6)(4 10)(5 14)(8 11)(9 15)(13 16)```

`G:=sub<Sym(16)| (1,13)(2,16)(3,8)(4,6)(5,11)(7,15)(9,12)(10,14), (1,3)(2,14)(4,15)(5,12)(6,7)(8,13)(9,11)(10,16), (1,14)(2,3)(4,9)(5,7)(6,12)(8,16)(10,13)(11,15), (1,7)(2,12)(3,6)(4,8)(5,14)(9,16)(10,11)(13,15), (2,3,4,5,6,7,8,9,10,11,12,13,14,15,16), (3,6)(4,10)(5,14)(8,11)(9,15)(13,16)>;`

`G:=Group( (1,13)(2,16)(3,8)(4,6)(5,11)(7,15)(9,12)(10,14), (1,3)(2,14)(4,15)(5,12)(6,7)(8,13)(9,11)(10,16), (1,14)(2,3)(4,9)(5,7)(6,12)(8,16)(10,13)(11,15), (1,7)(2,12)(3,6)(4,8)(5,14)(9,16)(10,11)(13,15), (2,3,4,5,6,7,8,9,10,11,12,13,14,15,16), (3,6)(4,10)(5,14)(8,11)(9,15)(13,16) );`

`G=PermutationGroup([[(1,13),(2,16),(3,8),(4,6),(5,11),(7,15),(9,12),(10,14)], [(1,3),(2,14),(4,15),(5,12),(6,7),(8,13),(9,11),(10,16)], [(1,14),(2,3),(4,9),(5,7),(6,12),(8,16),(10,13),(11,15)], [(1,7),(2,12),(3,6),(4,8),(5,14),(9,16),(10,11),(13,15)], [(2,3,4,5,6,7,8,9,10,11,12,13,14,15,16)], [(3,6),(4,10),(5,14),(8,11),(9,15),(13,16)]])`

`G:=TransitiveGroup(16,777);`

On 20 points - transitive group 20T122
Generators in S20
```(1 6)(3 18)(4 19)(5 10)(8 13)(9 14)(11 16)(15 20)
(1 11)(3 8)(4 9)(5 15)(6 16)(10 20)(13 18)(14 19)
(1 11)(2 7)(4 19)(5 20)(6 16)(9 14)(10 15)(12 17)
(2 12)(3 13)(4 19)(5 15)(7 17)(8 18)(9 14)(10 20)
(1 2 3 4 5)(6 7 8 9 10 11 12 13 14 15 16 17 18 19 20)
(2 5)(3 4)(7 10)(8 14)(9 18)(12 15)(13 19)(17 20)```

`G:=sub<Sym(20)| (1,6)(3,18)(4,19)(5,10)(8,13)(9,14)(11,16)(15,20), (1,11)(3,8)(4,9)(5,15)(6,16)(10,20)(13,18)(14,19), (1,11)(2,7)(4,19)(5,20)(6,16)(9,14)(10,15)(12,17), (2,12)(3,13)(4,19)(5,15)(7,17)(8,18)(9,14)(10,20), (1,2,3,4,5)(6,7,8,9,10,11,12,13,14,15,16,17,18,19,20), (2,5)(3,4)(7,10)(8,14)(9,18)(12,15)(13,19)(17,20)>;`

`G:=Group( (1,6)(3,18)(4,19)(5,10)(8,13)(9,14)(11,16)(15,20), (1,11)(3,8)(4,9)(5,15)(6,16)(10,20)(13,18)(14,19), (1,11)(2,7)(4,19)(5,20)(6,16)(9,14)(10,15)(12,17), (2,12)(3,13)(4,19)(5,15)(7,17)(8,18)(9,14)(10,20), (1,2,3,4,5)(6,7,8,9,10,11,12,13,14,15,16,17,18,19,20), (2,5)(3,4)(7,10)(8,14)(9,18)(12,15)(13,19)(17,20) );`

`G=PermutationGroup([[(1,6),(3,18),(4,19),(5,10),(8,13),(9,14),(11,16),(15,20)], [(1,11),(3,8),(4,9),(5,15),(6,16),(10,20),(13,18),(14,19)], [(1,11),(2,7),(4,19),(5,20),(6,16),(9,14),(10,15),(12,17)], [(2,12),(3,13),(4,19),(5,15),(7,17),(8,18),(9,14),(10,20)], [(1,2,3,4,5),(6,7,8,9,10,11,12,13,14,15,16,17,18,19,20)], [(2,5),(3,4),(7,10),(8,14),(9,18),(12,15),(13,19),(17,20)]])`

`G:=TransitiveGroup(20,122);`

On 30 points - transitive group 30T112
Generators in S30
```(3 20)(4 21)(6 23)(8 25)(9 26)(10 27)(11 28)(15 17)
(1 18)(5 22)(8 25)(9 26)(11 28)(13 30)(14 16)(15 17)
(1 18)(4 21)(5 22)(7 24)(9 26)(10 27)(11 28)(12 29)
(2 19)(3 20)(4 21)(5 22)(9 26)(12 29)(13 30)(15 17)
(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)
(2 5)(3 9)(4 13)(7 10)(8 14)(12 15)(16 25)(17 29)(19 22)(20 26)(21 30)(24 27)```

`G:=sub<Sym(30)| (3,20)(4,21)(6,23)(8,25)(9,26)(10,27)(11,28)(15,17), (1,18)(5,22)(8,25)(9,26)(11,28)(13,30)(14,16)(15,17), (1,18)(4,21)(5,22)(7,24)(9,26)(10,27)(11,28)(12,29), (2,19)(3,20)(4,21)(5,22)(9,26)(12,29)(13,30)(15,17), (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), (2,5)(3,9)(4,13)(7,10)(8,14)(12,15)(16,25)(17,29)(19,22)(20,26)(21,30)(24,27)>;`

`G:=Group( (3,20)(4,21)(6,23)(8,25)(9,26)(10,27)(11,28)(15,17), (1,18)(5,22)(8,25)(9,26)(11,28)(13,30)(14,16)(15,17), (1,18)(4,21)(5,22)(7,24)(9,26)(10,27)(11,28)(12,29), (2,19)(3,20)(4,21)(5,22)(9,26)(12,29)(13,30)(15,17), (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), (2,5)(3,9)(4,13)(7,10)(8,14)(12,15)(16,25)(17,29)(19,22)(20,26)(21,30)(24,27) );`

`G=PermutationGroup([[(3,20),(4,21),(6,23),(8,25),(9,26),(10,27),(11,28),(15,17)], [(1,18),(5,22),(8,25),(9,26),(11,28),(13,30),(14,16),(15,17)], [(1,18),(4,21),(5,22),(7,24),(9,26),(10,27),(11,28),(12,29)], [(2,19),(3,20),(4,21),(5,22),(9,26),(12,29),(13,30),(15,17)], [(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)], [(2,5),(3,9),(4,13),(7,10),(8,14),(12,15),(16,25),(17,29),(19,22),(20,26),(21,30),(24,27)]])`

`G:=TransitiveGroup(30,112);`

On 30 points - transitive group 30T116
Generators in S30
```(3 30)(4 16)(6 18)(8 20)(9 21)(10 22)(11 23)(15 27)
(1 28)(5 17)(8 20)(9 21)(11 23)(13 25)(14 26)(15 27)
(1 28)(4 16)(5 17)(7 19)(9 21)(10 22)(11 23)(12 24)
(2 29)(3 30)(4 16)(5 17)(9 21)(12 24)(13 25)(15 27)
(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)
(1 28)(2 17)(3 21)(4 25)(5 29)(6 18)(7 22)(8 26)(9 30)(10 19)(11 23)(12 27)(13 16)(14 20)(15 24)```

`G:=sub<Sym(30)| (3,30)(4,16)(6,18)(8,20)(9,21)(10,22)(11,23)(15,27), (1,28)(5,17)(8,20)(9,21)(11,23)(13,25)(14,26)(15,27), (1,28)(4,16)(5,17)(7,19)(9,21)(10,22)(11,23)(12,24), (2,29)(3,30)(4,16)(5,17)(9,21)(12,24)(13,25)(15,27), (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), (1,28)(2,17)(3,21)(4,25)(5,29)(6,18)(7,22)(8,26)(9,30)(10,19)(11,23)(12,27)(13,16)(14,20)(15,24)>;`

`G:=Group( (3,30)(4,16)(6,18)(8,20)(9,21)(10,22)(11,23)(15,27), (1,28)(5,17)(8,20)(9,21)(11,23)(13,25)(14,26)(15,27), (1,28)(4,16)(5,17)(7,19)(9,21)(10,22)(11,23)(12,24), (2,29)(3,30)(4,16)(5,17)(9,21)(12,24)(13,25)(15,27), (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), (1,28)(2,17)(3,21)(4,25)(5,29)(6,18)(7,22)(8,26)(9,30)(10,19)(11,23)(12,27)(13,16)(14,20)(15,24) );`

`G=PermutationGroup([[(3,30),(4,16),(6,18),(8,20),(9,21),(10,22),(11,23),(15,27)], [(1,28),(5,17),(8,20),(9,21),(11,23),(13,25),(14,26),(15,27)], [(1,28),(4,16),(5,17),(7,19),(9,21),(10,22),(11,23),(12,24)], [(2,29),(3,30),(4,16),(5,17),(9,21),(12,24),(13,25),(15,27)], [(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)], [(1,28),(2,17),(3,21),(4,25),(5,29),(6,18),(7,22),(8,26),(9,30),(10,19),(11,23),(12,27),(13,16),(14,20),(15,24)]])`

`G:=TransitiveGroup(30,116);`

Matrix representation of F16⋊C2 in GL15(ℤ)

 1 0 0 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 0 0 0 -1 0 0 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 0 0 0 1 0 0 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 0 0 0 -1 0 0 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 0 0 0 -1 0 0 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 0 0 0 -1 0 0 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 0 0 0 1 0 0 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 0 0 0 1
,
 -1 0 0 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 0 0 0 1 0 0 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 0 0 0 1 0 0 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 0 0 0 -1 0 0 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 0 0 0 1 0 0 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 0 0 0 -1 0 0 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 0 0 0 -1 0 0 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 0 0 0 1
,
 -1 0 0 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 0 0 0 -1 0 0 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 0 0 0 -1 0 0 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 0 0 0 1 0 0 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 0 0 0 1 0 0 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 0 0 0 -1 0 0 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 0 0 0 1 0 0 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 0 0 0 1
,
 1 0 0 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 0 0 0 -1 0 0 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 0 0 0 1 0 0 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 0 0 0 -1 0 0 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 0 0 0 -1 0 0 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 0 0 0 1 0 0 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 0 0 0 1 0 0 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 0 0 0 -1
,
 0 0 0 0 0 0 1 0 0 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 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 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 1 0 0 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 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 1 0 0 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 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 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
,
 -1 0 0 0 0 0 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 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 0 -1 0 0 0 0 0 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 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 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 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 -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 0 -1 0 0 0 0 0 0 0 0 0 0 0 0 0 -1 0 0 0

`G:=sub<GL(15,Integers())| [1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,-1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,-1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,-1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,-1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,-1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,-1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,-1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,-1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1],[-1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,-1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,-1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,-1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,-1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,-1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,-1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,-1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1],[-1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,-1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,-1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,-1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,-1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,-1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,-1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,-1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1],[1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,-1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,-1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,-1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,-1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,-1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,-1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,-1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,-1],[0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0],[-1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,-1,0,0,0,0,0,0,0,0,0,0,0,0,0,-1,0,0,0,0,0,0,0,0,0,0,0,0,0,-1,0,0,0,0,0,0,0,0,0,0,0,0,0,-1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,-1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,-1,0,0,0,0,0,0,0,0,0,0,0,0,0,-1,0,0,0,0,0,0,0,0,0,0,0,0,0,-1,0,0,0,0,0,0,0,0,0,0,0,0,0,-1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,-1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,-1,0,0,0,0,0,0,0,0,0,0,0,0,0,-1,0,0,0,0,0,0,0,0,0,0,0,0,0,-1,0,0,0,0,0,0,0,0,0,0,0,0,0,-1,0,0,0] >;`

F16⋊C2 in GAP, Magma, Sage, TeX

`F_{16}\rtimes C_2`
`% in TeX`

`G:=Group("F16:C2");`
`// GroupNames label`

`G:=SmallGroup(480,1188);`
`// by ID`

`G=gap.SmallGroup(480,1188);`
`# by ID`

`G:=PCGroup([7,-2,-3,-5,-2,2,2,2,506,2523,4210,717,6836,1768,13865,1902,2749,7356,4423,755]);`
`// Polycyclic`

`G:=Group<a,b,c,d,e,f|a^2=b^2=c^2=d^2=e^15=f^2=1,a*b=b*a,a*c=c*a,a*d=d*a,e*a*e^-1=b*c*d,f*a*f=a*b*c,e*b*e^-1=b*c=c*b,f*b*f=e*d*e^-1=b*d=d*b,f*c*f=c*d=d*c,e*c*e^-1=a,d*f=f*d,f*e*f=e^4>;`
`// generators/relations`

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