C3:D32 - GroupNames

class	1	2A	2B	2C	3	4	6A	6B	6C	8A	8B	12	16A	16B	16C	16D	24A	24B	32A	32B	32C	32D	32E	32F	32G	32H	48A	48B	48C	48D
size	1	1	16	48	2	2	2	16	16	2	2	4	2	2	2	2	4	4	6	6	6	6	6	6	6	6	4	4	4	4
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	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	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	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	1	linear of order 2
ρ₅	2	2	2	0	-1	2	-1	-1	-1	2	2	-1	2	2	2	2	-1	-1	0	0	0	0	0	0	0	0	-1	-1	-1	-1	orthogonal lifted from S₃
ρ₆	2	2	0	0	2	2	2	0	0	2	2	2	-2	-2	-2	-2	2	2	0	0	0	0	0	0	0	0	-2	-2	-2	-2	orthogonal lifted from D₄
ρ₇	2	2	-2	0	-1	2	-1	1	1	2	2	-1	2	2	2	2	-1	-1	0	0	0	0	0	0	0	0	-1	-1	-1	-1	orthogonal lifted from D₆
ρ₈	2	2	0	0	2	-2	2	0	0	0	0	-2	√2	-√2	√2	-√2	0	0	-ζ₁₆⁷+ζ₁₆	-ζ₁₆⁵+ζ₁₆³	ζ₁₆⁵-ζ₁₆³	ζ₁₆⁵-ζ₁₆³	ζ₁₆⁷-ζ₁₆	ζ₁₆⁷-ζ₁₆	-ζ₁₆⁷+ζ₁₆	-ζ₁₆⁵+ζ₁₆³	-√2	√2	-√2	√2	orthogonal lifted from D₁₆
ρ₉	2	2	0	0	2	-2	2	0	0	0	0	-2	√2	-√2	√2	-√2	0	0	ζ₁₆⁷-ζ₁₆	ζ₁₆⁵-ζ₁₆³	-ζ₁₆⁵+ζ₁₆³	-ζ₁₆⁵+ζ₁₆³	-ζ₁₆⁷+ζ₁₆	-ζ₁₆⁷+ζ₁₆	ζ₁₆⁷-ζ₁₆	ζ₁₆⁵-ζ₁₆³	-√2	√2	-√2	√2	orthogonal lifted from D₁₆
ρ₁₀	2	2	0	0	2	2	2	0	0	-2	-2	2	0	0	0	0	-2	-2	-√2	√2	√2	√2	-√2	-√2	-√2	√2	0	0	0	0	orthogonal lifted from D₈
ρ₁₁	2	2	0	0	2	2	2	0	0	-2	-2	2	0	0	0	0	-2	-2	√2	-√2	-√2	-√2	√2	√2	√2	-√2	0	0	0	0	orthogonal lifted from D₈
ρ₁₂	2	-2	0	0	2	0	-2	0	0	√2	-√2	0	ζ₃₂¹⁰-ζ₃₂⁶	-ζ₃₂³⁰+ζ₃₂¹⁸	-ζ₃₂¹⁰+ζ₃₂⁶	ζ₃₂³⁰-ζ₃₂¹⁸	√2	-√2	ζ₃₂¹¹-ζ₃₂⁵	ζ₃₂¹⁵-ζ₃₂	-ζ₃₂²⁵+ζ₃₂²³	ζ₃₂²⁵-ζ₃₂²³	-ζ₃₂¹³+ζ₃₂³	ζ₃₂¹³-ζ₃₂³	-ζ₃₂¹¹+ζ₃₂⁵	-ζ₃₂¹⁵+ζ₃₂	ζ₃₂³⁰-ζ₃₂¹⁸	ζ₃₂¹⁰-ζ₃₂⁶	-ζ₃₂³⁰+ζ₃₂¹⁸	-ζ₃₂¹⁰+ζ₃₂⁶	orthogonal lifted from D₃₂
ρ₁₃	2	-2	0	0	2	0	-2	0	0	√2	-√2	0	-ζ₃₂¹⁰+ζ₃₂⁶	ζ₃₂³⁰-ζ₃₂¹⁸	ζ₃₂¹⁰-ζ₃₂⁶	-ζ₃₂³⁰+ζ₃₂¹⁸	√2	-√2	ζ₃₂¹³-ζ₃₂³	-ζ₃₂²⁵+ζ₃₂²³	-ζ₃₂¹⁵+ζ₃₂	ζ₃₂¹⁵-ζ₃₂	ζ₃₂¹¹-ζ₃₂⁵	-ζ₃₂¹¹+ζ₃₂⁵	-ζ₃₂¹³+ζ₃₂³	ζ₃₂²⁵-ζ₃₂²³	-ζ₃₂³⁰+ζ₃₂¹⁸	-ζ₃₂¹⁰+ζ₃₂⁶	ζ₃₂³⁰-ζ₃₂¹⁸	ζ₃₂¹⁰-ζ₃₂⁶	orthogonal lifted from D₃₂
ρ₁₄	2	2	0	0	2	-2	2	0	0	0	0	-2	-√2	√2	-√2	√2	0	0	-ζ₁₆⁵+ζ₁₆³	ζ₁₆⁷-ζ₁₆	-ζ₁₆⁷+ζ₁₆	-ζ₁₆⁷+ζ₁₆	ζ₁₆⁵-ζ₁₆³	ζ₁₆⁵-ζ₁₆³	-ζ₁₆⁵+ζ₁₆³	ζ₁₆⁷-ζ₁₆	√2	-√2	√2	-√2	orthogonal lifted from D₁₆
ρ₁₅	2	2	0	0	2	-2	2	0	0	0	0	-2	-√2	√2	-√2	√2	0	0	ζ₁₆⁵-ζ₁₆³	-ζ₁₆⁷+ζ₁₆	ζ₁₆⁷-ζ₁₆	ζ₁₆⁷-ζ₁₆	-ζ₁₆⁵+ζ₁₆³	-ζ₁₆⁵+ζ₁₆³	ζ₁₆⁵-ζ₁₆³	-ζ₁₆⁷+ζ₁₆	√2	-√2	√2	-√2	orthogonal lifted from D₁₆
ρ₁₆	2	-2	0	0	2	0	-2	0	0	√2	-√2	0	-ζ₃₂¹⁰+ζ₃₂⁶	ζ₃₂³⁰-ζ₃₂¹⁸	ζ₃₂¹⁰-ζ₃₂⁶	-ζ₃₂³⁰+ζ₃₂¹⁸	√2	-√2	-ζ₃₂¹³+ζ₃₂³	ζ₃₂²⁵-ζ₃₂²³	ζ₃₂¹⁵-ζ₃₂	-ζ₃₂¹⁵+ζ₃₂	-ζ₃₂¹¹+ζ₃₂⁵	ζ₃₂¹¹-ζ₃₂⁵	ζ₃₂¹³-ζ₃₂³	-ζ₃₂²⁵+ζ₃₂²³	-ζ₃₂³⁰+ζ₃₂¹⁸	-ζ₃₂¹⁰+ζ₃₂⁶	ζ₃₂³⁰-ζ₃₂¹⁸	ζ₃₂¹⁰-ζ₃₂⁶	orthogonal lifted from D₃₂
ρ₁₇	2	-2	0	0	2	0	-2	0	0	√2	-√2	0	ζ₃₂¹⁰-ζ₃₂⁶	-ζ₃₂³⁰+ζ₃₂¹⁸	-ζ₃₂¹⁰+ζ₃₂⁶	ζ₃₂³⁰-ζ₃₂¹⁸	√2	-√2	-ζ₃₂¹¹+ζ₃₂⁵	-ζ₃₂¹⁵+ζ₃₂	ζ₃₂²⁵-ζ₃₂²³	-ζ₃₂²⁵+ζ₃₂²³	ζ₃₂¹³-ζ₃₂³	-ζ₃₂¹³+ζ₃₂³	ζ₃₂¹¹-ζ₃₂⁵	ζ₃₂¹⁵-ζ₃₂	ζ₃₂³⁰-ζ₃₂¹⁸	ζ₃₂¹⁰-ζ₃₂⁶	-ζ₃₂³⁰+ζ₃₂¹⁸	-ζ₃₂¹⁰+ζ₃₂⁶	orthogonal lifted from D₃₂
ρ₁₈	2	-2	0	0	2	0	-2	0	0	-√2	√2	0	-ζ₃₂³⁰+ζ₃₂¹⁸	-ζ₃₂¹⁰+ζ₃₂⁶	ζ₃₂³⁰-ζ₃₂¹⁸	ζ₃₂¹⁰-ζ₃₂⁶	-√2	√2	-ζ₃₂²⁵+ζ₃₂²³	ζ₃₂¹¹-ζ₃₂⁵	ζ₃₂¹³-ζ₃₂³	-ζ₃₂¹³+ζ₃₂³	ζ₃₂¹⁵-ζ₃₂	-ζ₃₂¹⁵+ζ₃₂	ζ₃₂²⁵-ζ₃₂²³	-ζ₃₂¹¹+ζ₃₂⁵	ζ₃₂¹⁰-ζ₃₂⁶	-ζ₃₂³⁰+ζ₃₂¹⁸	-ζ₃₂¹⁰+ζ₃₂⁶	ζ₃₂³⁰-ζ₃₂¹⁸	orthogonal lifted from D₃₂
ρ₁₉	2	-2	0	0	2	0	-2	0	0	-√2	√2	0	ζ₃₂³⁰-ζ₃₂¹⁸	ζ₃₂¹⁰-ζ₃₂⁶	-ζ₃₂³⁰+ζ₃₂¹⁸	-ζ₃₂¹⁰+ζ₃₂⁶	-√2	√2	ζ₃₂¹⁵-ζ₃₂	-ζ₃₂¹³+ζ₃₂³	ζ₃₂¹¹-ζ₃₂⁵	-ζ₃₂¹¹+ζ₃₂⁵	ζ₃₂²⁵-ζ₃₂²³	-ζ₃₂²⁵+ζ₃₂²³	-ζ₃₂¹⁵+ζ₃₂	ζ₃₂¹³-ζ₃₂³	-ζ₃₂¹⁰+ζ₃₂⁶	ζ₃₂³⁰-ζ₃₂¹⁸	ζ₃₂¹⁰-ζ₃₂⁶	-ζ₃₂³⁰+ζ₃₂¹⁸	orthogonal lifted from D₃₂
ρ₂₀	2	-2	0	0	2	0	-2	0	0	-√2	√2	0	-ζ₃₂³⁰+ζ₃₂¹⁸	-ζ₃₂¹⁰+ζ₃₂⁶	ζ₃₂³⁰-ζ₃₂¹⁸	ζ₃₂¹⁰-ζ₃₂⁶	-√2	√2	ζ₃₂²⁵-ζ₃₂²³	-ζ₃₂¹¹+ζ₃₂⁵	-ζ₃₂¹³+ζ₃₂³	ζ₃₂¹³-ζ₃₂³	-ζ₃₂¹⁵+ζ₃₂	ζ₃₂¹⁵-ζ₃₂	-ζ₃₂²⁵+ζ₃₂²³	ζ₃₂¹¹-ζ₃₂⁵	ζ₃₂¹⁰-ζ₃₂⁶	-ζ₃₂³⁰+ζ₃₂¹⁸	-ζ₃₂¹⁰+ζ₃₂⁶	ζ₃₂³⁰-ζ₃₂¹⁸	orthogonal lifted from D₃₂
ρ₂₁	2	-2	0	0	2	0	-2	0	0	-√2	√2	0	ζ₃₂³⁰-ζ₃₂¹⁸	ζ₃₂¹⁰-ζ₃₂⁶	-ζ₃₂³⁰+ζ₃₂¹⁸	-ζ₃₂¹⁰+ζ₃₂⁶	-√2	√2	-ζ₃₂¹⁵+ζ₃₂	ζ₃₂¹³-ζ₃₂³	-ζ₃₂¹¹+ζ₃₂⁵	ζ₃₂¹¹-ζ₃₂⁵	-ζ₃₂²⁵+ζ₃₂²³	ζ₃₂²⁵-ζ₃₂²³	ζ₃₂¹⁵-ζ₃₂	-ζ₃₂¹³+ζ₃₂³	-ζ₃₂¹⁰+ζ₃₂⁶	ζ₃₂³⁰-ζ₃₂¹⁸	ζ₃₂¹⁰-ζ₃₂⁶	-ζ₃₂³⁰+ζ₃₂¹⁸	orthogonal lifted from D₃₂
ρ₂₂	2	2	0	0	-1	2	-1	√-3	-√-3	2	2	-1	-2	-2	-2	-2	-1	-1	0	0	0	0	0	0	0	0	1	1	1	1	complex lifted from C₃⋊D₄
ρ₂₃	2	2	0	0	-1	2	-1	-√-3	√-3	2	2	-1	-2	-2	-2	-2	-1	-1	0	0	0	0	0	0	0	0	1	1	1	1	complex lifted from C₃⋊D₄
ρ₂₄	4	4	0	0	-2	4	-2	0	0	-4	-4	-2	0	0	0	0	2	2	0	0	0	0	0	0	0	0	0	0	0	0	orthogonal lifted from D₄⋊S₃, Schur index 2
ρ₂₅	4	4	0	0	-2	-4	-2	0	0	0	0	2	2√2	-2√2	2√2	-2√2	0	0	0	0	0	0	0	0	0	0	√2	-√2	√2	-√2	orthogonal lifted from C₃⋊D₁₆, Schur index 2
ρ₂₆	4	4	0	0	-2	-4	-2	0	0	0	0	2	-2√2	2√2	-2√2	2√2	0	0	0	0	0	0	0	0	0	0	-√2	√2	-√2	√2	orthogonal lifted from C₃⋊D₁₆, Schur index 2
ρ₂₇	4	-4	0	0	-2	0	2	0	0	2√2	-2√2	0	2ζ₁₆⁵-2ζ₁₆³	-2ζ₁₆¹⁵+2ζ₁₆⁹	-2ζ₁₆⁵+2ζ₁₆³	2ζ₁₆¹⁵-2ζ₁₆⁹	-√2	√2	0	0	0	0	0	0	0	0	ζ₁₆⁷-ζ₁₆	-ζ₁₆⁵+ζ₁₆³	-ζ₁₆⁷+ζ₁₆	ζ₁₆⁵-ζ₁₆³	orthogonal faithful, Schur index 2
ρ₂₈	4	-4	0	0	-2	0	2	0	0	-2√2	2√2	0	-2ζ₁₆¹⁵+2ζ₁₆⁹	-2ζ₁₆⁵+2ζ₁₆³	2ζ₁₆¹⁵-2ζ₁₆⁹	2ζ₁₆⁵-2ζ₁₆³	√2	-√2	0	0	0	0	0	0	0	0	-ζ₁₆⁵+ζ₁₆³	-ζ₁₆⁷+ζ₁₆	ζ₁₆⁵-ζ₁₆³	ζ₁₆⁷-ζ₁₆	orthogonal faithful, Schur index 2
ρ₂₉	4	-4	0	0	-2	0	2	0	0	2√2	-2√2	0	-2ζ₁₆⁵+2ζ₁₆³	2ζ₁₆¹⁵-2ζ₁₆⁹	2ζ₁₆⁵-2ζ₁₆³	-2ζ₁₆¹⁵+2ζ₁₆⁹	-√2	√2	0	0	0	0	0	0	0	0	-ζ₁₆⁷+ζ₁₆	ζ₁₆⁵-ζ₁₆³	ζ₁₆⁷-ζ₁₆	-ζ₁₆⁵+ζ₁₆³	orthogonal faithful, Schur index 2
ρ₃₀	4	-4	0	0	-2	0	2	0	0	-2√2	2√2	0	2ζ₁₆¹⁵-2ζ₁₆⁹	2ζ₁₆⁵-2ζ₁₆³	-2ζ₁₆¹⁵+2ζ₁₆⁹	-2ζ₁₆⁵+2ζ₁₆³	√2	-√2	0	0	0	0	0	0	0	0	ζ₁₆⁵-ζ₁₆³	ζ₁₆⁷-ζ₁₆	-ζ₁₆⁵+ζ₁₆³	-ζ₁₆⁷+ζ₁₆	orthogonal faithful, Schur index 2

Smallest permutation representation of C₃⋊D₃₂
►On 96 points

Generators in S₉₆

(1 78 49)(2 50 79)(3 80 51)(4 52 81)(5 82 53)(6 54 83)(7 84 55)(8 56 85)(9 86 57)(10 58 87)(11 88 59)(12 60 89)(13 90 61)(14 62 91)(15 92 63)(16 64 93)(17 94 33)(18 34 95)(19 96 35)(20 36 65)(21 66 37)(22 38 67)(23 68 39)(24 40 69)(25 70 41)(26 42 71)(27 72 43)(28 44 73)(29 74 45)(30 46 75)(31 76 47)(32 48 77)

(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 89 90 91 92 93 94 95 96)

(2 32)(3 31)(4 30)(5 29)(6 28)(7 27)(8 26)(9 25)(10 24)(11 23)(12 22)(13 21)(14 20)(15 19)(16 18)(33 94)(34 93)(35 92)(36 91)(37 90)(38 89)(39 88)(40 87)(41 86)(42 85)(43 84)(44 83)(45 82)(46 81)(47 80)(48 79)(49 78)(50 77)(51 76)(52 75)(53 74)(54 73)(55 72)(56 71)(57 70)(58 69)(59 68)(60 67)(61 66)(62 65)(63 96)(64 95)

G:=sub<Sym(96)| (1,78,49)(2,50,79)(3,80,51)(4,52,81)(5,82,53)(6,54,83)(7,84,55)(8,56,85)(9,86,57)(10,58,87)(11,88,59)(12,60,89)(13,90,61)(14,62,91)(15,92,63)(16,64,93)(17,94,33)(18,34,95)(19,96,35)(20,36,65)(21,66,37)(22,38,67)(23,68,39)(24,40,69)(25,70,41)(26,42,71)(27,72,43)(28,44,73)(29,74,45)(30,46,75)(31,76,47)(32,48,77), (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)(65,66,67,68,69,70,71,72,73,74,75,76,77,78,79,80,81,82,83,84,85,86,87,88,89,90,91,92,93,94,95,96), (2,32)(3,31)(4,30)(5,29)(6,28)(7,27)(8,26)(9,25)(10,24)(11,23)(12,22)(13,21)(14,20)(15,19)(16,18)(33,94)(34,93)(35,92)(36,91)(37,90)(38,89)(39,88)(40,87)(41,86)(42,85)(43,84)(44,83)(45,82)(46,81)(47,80)(48,79)(49,78)(50,77)(51,76)(52,75)(53,74)(54,73)(55,72)(56,71)(57,70)(58,69)(59,68)(60,67)(61,66)(62,65)(63,96)(64,95)>;

G:=Group( (1,78,49)(2,50,79)(3,80,51)(4,52,81)(5,82,53)(6,54,83)(7,84,55)(8,56,85)(9,86,57)(10,58,87)(11,88,59)(12,60,89)(13,90,61)(14,62,91)(15,92,63)(16,64,93)(17,94,33)(18,34,95)(19,96,35)(20,36,65)(21,66,37)(22,38,67)(23,68,39)(24,40,69)(25,70,41)(26,42,71)(27,72,43)(28,44,73)(29,74,45)(30,46,75)(31,76,47)(32,48,77), (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)(65,66,67,68,69,70,71,72,73,74,75,76,77,78,79,80,81,82,83,84,85,86,87,88,89,90,91,92,93,94,95,96), (2,32)(3,31)(4,30)(5,29)(6,28)(7,27)(8,26)(9,25)(10,24)(11,23)(12,22)(13,21)(14,20)(15,19)(16,18)(33,94)(34,93)(35,92)(36,91)(37,90)(38,89)(39,88)(40,87)(41,86)(42,85)(43,84)(44,83)(45,82)(46,81)(47,80)(48,79)(49,78)(50,77)(51,76)(52,75)(53,74)(54,73)(55,72)(56,71)(57,70)(58,69)(59,68)(60,67)(61,66)(62,65)(63,96)(64,95) );

G=PermutationGroup([[(1,78,49),(2,50,79),(3,80,51),(4,52,81),(5,82,53),(6,54,83),(7,84,55),(8,56,85),(9,86,57),(10,58,87),(11,88,59),(12,60,89),(13,90,61),(14,62,91),(15,92,63),(16,64,93),(17,94,33),(18,34,95),(19,96,35),(20,36,65),(21,66,37),(22,38,67),(23,68,39),(24,40,69),(25,70,41),(26,42,71),(27,72,43),(28,44,73),(29,74,45),(30,46,75),(31,76,47),(32,48,77)], [(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),(65,66,67,68,69,70,71,72,73,74,75,76,77,78,79,80,81,82,83,84,85,86,87,88,89,90,91,92,93,94,95,96)], [(2,32),(3,31),(4,30),(5,29),(6,28),(7,27),(8,26),(9,25),(10,24),(11,23),(12,22),(13,21),(14,20),(15,19),(16,18),(33,94),(34,93),(35,92),(36,91),(37,90),(38,89),(39,88),(40,87),(41,86),(42,85),(43,84),(44,83),(45,82),(46,81),(47,80),(48,79),(49,78),(50,77),(51,76),(52,75),(53,74),(54,73),(55,72),(56,71),(57,70),(58,69),(59,68),(60,67),(61,66),(62,65),(63,96),(64,95)]])

Matrix representation of C₃⋊D₃₂ ►in GL₄(𝔽₉₇) generated by

1	0	0	0
0	1	0	0
0	0	96	1
0	0	96	0

67	59	0	0
74	84	0	0
0	0	82	56
0	0	41	15

1	0	0	0
94	96	0	0
0	0	0	1
0	0	1	0

G:=sub<GL(4,GF(97))| [1,0,0,0,0,1,0,0,0,0,96,96,0,0,1,0],[67,74,0,0,59,84,0,0,0,0,82,41,0,0,56,15],[1,94,0,0,0,96,0,0,0,0,0,1,0,0,1,0] >;

C₃⋊D₃₂ in GAP, Magma, Sage, TeX

C_3\rtimes D_{32}

% in TeX

G:=Group("C3:D32");

// GroupNames label

G:=SmallGroup(192,78);

// by ID

G=gap.SmallGroup(192,78);

# by ID

G:=PCGroup([7,-2,-2,-2,-2,-2,-2,-3,85,254,135,142,675,346,192,1684,851,102,6278]);

// Polycyclic

G:=Group<a,b,c|a^3=b^32=c^2=1,b*a*b^-1=c*a*c=a^-1,c*b*c=b^-1>;

// generators/relations

Export

Subgroup lattice of C₃⋊D₃₂ in TeX
Character table of C₃⋊D₃₂ in TeX

G = C3⋊D32 order 192 = 26·3

The semidirect product of C3 and D32 acting via D32/D16=C2

G = C₃⋊D₃₂ order 192 = 2⁶·3

The semidirect product of C₃ and D₃₂ acting via D₃₂/D₁₆=C₂