Finite Group Databasebeta

← Group #10693018

Character table — Group #10693018

Order 768.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75
size111122222222222222224444444444488888888888888888888888888161616161616242424242424242448484848
order12222222344446661212121224466661212121244444444612121212121212121212121212121212128824242424444444444488
χ1111111111111111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1
χ311111111111111111111111111111111111-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-111-1-1
χ411111111111111111111111111111111111-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-111
χ51111111111111111111111111111111-1-1-1-1111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-111111111-1-1-1-1
χ61111111111111111111111111111111-1-1-1-1111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-11111
χ71111111111111111111111111111111-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-111
χ81111111111111111111111111111111-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-1-1111111-1-1
χ9111111-1-11-1-1-1-1111-1-1-1-1-11111-1-111-1-111-1-1ii−i−i-111111-1-1-1-1iiii−i−i−i−ii−iii−i−i11-1-1ii−i−i1-1i−i
χ10111111-1-11-1-1-1-1111-1-1-1-1-11111-1-111-1-111-1-1ii−i−i-111111-1-1-1-1iiii−i−i−i−ii−iii−i−i-1-111−i−iii-11−ii
χ11111111-1-11-1-1-1-1111-1-1-1-1-11111-1-111-1-111-1-1−i−iii-111111-1-1-1-1−i−i−i−iiiii−ii−i−iii11-1-1−i−iii1-1−ii
χ12111111-1-11-1-1-1-1111-1-1-1-1-11111-1-111-1-111-1-1−i−iii-111111-1-1-1-1−i−i−i−iiiii−ii−i−iii-1-111ii−i−i-11i−i
χ13111111-1-11-1-1-1-1111-1-1-1-1-11111-1-111-1-1-1-111ii−i−i-11-1-1-1-11111iiii−i−i−i−i−ii−i−iii11-1-1ii−i−i-11−ii
χ14111111-1-11-1-1-1-1111-1-1-1-1-11111-1-111-1-1-1-111ii−i−i-11-1-1-1-11111iiii−i−i−i−i−ii−i−iii-1-111−i−iii1-1i−i
χ15111111-1-11-1-1-1-1111-1-1-1-1-11111-1-111-1-1-1-111−i−iii-11-1-1-1-11111−i−i−i−iiiiii−iii−i−i11-1-1−i−iii-11i−i
χ16111111-1-11-1-1-1-1111-1-1-1-1-11111-1-111-1-1-1-111−i−iii-11-1-1-1-11111−i−i−i−iiiiii−iii−i−i-1-111ii−i−i1-1−ii
χ17222222222-2-2-2-2222-2-2-2-22-2-22222-2-2-2-2000000002-200000000000000000000002-22-200000000
χ18222222222-2-2-2-2222-2-2-2-22-2-22222-2-2-2-2000000002-20000000000000000000000-22-2200000000
χ1922222222-12222-1-1-1-1-1-1-1222-1-1-1-1-1-1-1-122222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-122-1-1-1-1000000000000
χ2022222222-12222-1-1-1-1-1-1-1222-1-1-1-1-1-1-1-12222-2-2-2-2-1-1-1-1-1-1-1-1-1-111111111-2-21111000000000000
χ2122222222-12222-1-1-1-1-1-1-1222-1-1-1-1-1-1-1-1-2-2-2-22222-1-111111111-1-1-1-1-1-1-1-1-2-21111000000000000
χ2222222222-12222-1-1-1-1-1-1-1222-1-1-1-1-1-1-1-1-2-2-2-2-2-2-2-2-1-1111111111111111122-1-1-1-1000000000000
χ23222222-2-2222222222222-2-2-222-2-2-2-22200000000-2-200000000000000000000002-2-2200000000
χ24222222-2-2222222222222-2-2-222-2-2-2-22200000000-2-20000000000000000000000-222-200000000
χ25222222-2-2-1-2-2-2-2-1-1-11111-222-1-111-1-11122-2-22i2i−2i−2i1-1-1-1-1-11111−i−i−i−iiiii2i−2i−i−iii000000000000
χ26222222-2-2-1-2-2-2-2-1-1-11111-222-1-111-1-11122-2-2−2i−2i2i2i1-1-1-1-1-11111iiii−i−i−i−i−2i2iii−i−i000000000000
χ27222222-2-2-1-2-2-2-2-1-1-11111-222-1-111-1-111-2-2222i2i−2i−2i1-11111-1-1-1-1−i−i−i−iiiii−2i2iii−i−i000000000000
χ28222222-2-2-1-2-2-2-2-1-1-11111-222-1-111-1-111-2-222−2i−2i2i2i1-11111-1-1-1-1iiii−i−i−i−i2i−2i−i−iii000000000000
χ292222-2-222222-2-22222222-22-2-2-22222-2-200002-22-2-2-20000000022-2-222-2-2000000000000000000
χ302222-2-222222-2-22222222-22-2-2-22222-2-20000-22-22-2-200000000-2-222-2-222000000000000000000
χ312222-2-2222-2-222222-2-2-2-2-2-22-2-222-2-22200000000-22000000000000000000000000002-22-20000
χ322222-2-2222-2-222222-2-2-2-2-2-22-2-222-2-22200000000-2200000000000000000000000000-22-220000
χ332222-2-222-122-2-2-1-1-1-1-1-1-1-22-211-1-1-1-11100002-22-211−i3−i3i3i3−i3−i3i3i3-1-111-1-11100−i3i3−i3i3000000000000
χ342222-2-222-122-2-2-1-1-1-1-1-1-1-22-211-1-1-1-11100002-22-211i3i3−i3−i3i3i3−i3−i3-1-111-1-11100i3−i3i3−i3000000000000
χ352222-2-222-122-2-2-1-1-1-1-1-1-1-22-211-1-1-1-1110000-22-2211−i3−i3i3i3−i3−i3i3i311-1-111-1-100i3−i3i3−i3000000000000
χ362222-2-222-122-2-2-1-1-1-1-1-1-1-22-211-1-1-1-1110000-22-2211i3i3−i3−i3i3i3−i3−i311-1-111-1-100−i3i3−i3i3000000000000
χ372222-2-2-2-2222-2-222222222-22-2-2-2-2-2-2-2-20000000022000000000000000000000000002i−2i−2i2i0000
χ382222-2-2-2-2222-2-222222222-22-2-2-2-2-2-2-2-2000000002200000000000000000000000000−2i2i2i−2i0000
χ392222-2-2-2-22-2-222222-2-2-2-222-2-2-2-2-2222200002i−2i−2i2i2-2000000002i2i−2i−2i−2i−2i2i2i000000000000000000
χ402222-2-2-2-22-2-222222-2-2-2-222-2-2-2-2-222220000−2i2i2i−2i2-200000000−2i−2i2i2i2i2i−2i−2i000000000000000000
χ412222-2-2-2-2-1-2-222-1-1-1111122-21111-1-1-1-100002i−2i−2i2i-11−i3−i3i3i3i3i3−i3−i3−i−iiiii−i−i003−3−33000000000000
χ422222-2-2-2-2-1-2-222-1-1-1111122-21111-1-1-1-100002i−2i−2i2i-11i3i3−i3−i3−i3−i3i3i3−i−iiiii−i−i00−333−3000000000000
χ432222-2-2-2-2-1-2-222-1-1-1111122-21111-1-1-1-10000−2i2i2i−2i-11−i3−i3i3i3i3i3−i3−i3ii−i−i−i−iii00−333−3000000000000
χ442222-2-2-2-2-1-2-222-1-1-1111122-21111-1-1-1-10000−2i2i2i−2i-11i3i3−i3−i3−i3−i3i3i3ii−i−i−i−iii003−3−33000000000000
χ4544444444-2-4-4-4-4-2-2-222224-4-4-2-2-2-2222200000000-220000000000000000000000000000000000
χ46444444-4-4-24444-2-2-2-2-2-2-2-4-4-4-2-22222-2-200000000220000000000000000000000000000000000
χ474444-4-444-2-4-444-2-2-22222-4-4422-2-222-2-2000000002-20000000000000000000000000000000000
χ484444-4-4-4-4-244-4-4-2-2-2-2-2-2-24-442222222200000000-2-20000000000000000000000000000000000
χ494-44-4004-4400004-4-40000000004-400002i−2i2i−2i0000002i−2i2i−2i2i−2i2i−2i00000000000000000000000000
χ504-44-4004-4400004-4-40000000004-40000−2i2i−2i2i000000−2i2i−2i2i−2i2i−2i2i00000000000000000000000000
χ514-44-4004-4-20000-222−2i3−2i32i32i300000-22−2i32i3002i−2i2i−2i0000002ζ7−2ζ72ζ11−2ζ112ζ7−2ζ72ζ11−2ζ1100000000000000000000000000
χ524-44-4004-4-20000-222−2i3−2i32i32i300000-22−2i32i300−2i2i−2i2i000000−2ζ72ζ7−2ζ112ζ11−2ζ72ζ7−2ζ112ζ1100000000000000000000000000
χ534-44-4004-4-20000-2222i32i3−2i3−2i300000-222i3−2i3002i−2i2i−2i0000002ζ11−2ζ112ζ7−2ζ72ζ11−2ζ112ζ7−2ζ700000000000000000000000000
χ544-44-4004-4-20000-2222i32i3−2i3−2i300000-222i3−2i300−2i2i−2i2i000000−2ζ112ζ11−2ζ72ζ7−2ζ112ζ11−2ζ72ζ700000000000000000000000000
χ554-44-400-44400004-4-4000000000-4400002i−2i−2i2i0000002i−2i2i−2i−2i2i−2i2i00000000000000000000000000
χ564-44-400-44400004-4-4000000000-440000−2i2i2i−2i000000−2i2i−2i2i2i−2i2i−2i00000000000000000000000000
χ574-44-400-44-20000-222−2i3−2i32i32i3000002-22i3−2i3002i−2i−2i2i0000002ζ11−2ζ112ζ7−2ζ7−2ζ112ζ11−2ζ72ζ700000000000000000000000000
χ584-44-400-44-20000-222−2i3−2i32i32i3000002-22i3−2i300−2i2i2i−2i000000−2ζ112ζ11−2ζ72ζ72ζ11−2ζ112ζ7−2ζ700000000000000000000000000
χ594-44-400-44-20000-2222i32i3−2i3−2i3000002-2−2i32i3002i−2i−2i2i0000002ζ7−2ζ72ζ11−2ζ11−2ζ72ζ7−2ζ112ζ1100000000000000000000000000
χ604-44-400-44-20000-2222i32i3−2i3−2i3000002-2−2i32i300−2i2i2i−2i000000−2ζ72ζ7−2ζ112ζ112ζ7−2ζ72ζ11−2ζ1100000000000000000000000000
χ614-4-444-40044i−4i4i−4i-44-44i−4i4i−4i0004-400004i−4i00000000000000000000000000000000000000000000
χ624-4-444-4004−4i4i−4i4i-44-4−4i4i−4i4i0004-40000−4i4i00000000000000000000000000000000000000000000
χ634-4-444-400-24i−4i4i−4i2-22−2i2i−2i2i000-220000−2i2i000000000000000000−ζ2+ζ7+ζ10−ζ11ζ2−ζ7−ζ10+ζ11−ζ2+ζ7+ζ10−ζ11ζ2−ζ7−ζ10+ζ11−ζ2−ζ7+ζ10+ζ11ζ2+ζ7−ζ10−ζ11−ζ2−ζ7+ζ10+ζ11ζ2+ζ7−ζ10−ζ11000000000000000000
χ644-4-444-400-24i−4i4i−4i2-22−2i2i−2i2i000-220000−2i2i000000000000000000ζ2−ζ7−ζ10+ζ11−ζ2+ζ7+ζ10−ζ11ζ2−ζ7−ζ10+ζ11−ζ2+ζ7+ζ10−ζ11ζ2+ζ7−ζ10−ζ11−ζ2−ζ7+ζ10+ζ11ζ2+ζ7−ζ10−ζ11−ζ2−ζ7+ζ10+ζ11000000000000000000
χ654-4-444-400-2−4i4i−4i4i2-222i−2i2i−2i000-2200002i−2i000000000000000000−ζ2−ζ7+ζ10+ζ11ζ2+ζ7−ζ10−ζ11−ζ2−ζ7+ζ10+ζ11ζ2+ζ7−ζ10−ζ11−ζ2+ζ7+ζ10−ζ11ζ2−ζ7−ζ10+ζ11−ζ2+ζ7+ζ10−ζ11ζ2−ζ7−ζ10+ζ11000000000000000000
χ664-4-444-400-2−4i4i−4i4i2-222i−2i2i−2i000-2200002i−2i000000000000000000ζ2+ζ7−ζ10−ζ11−ζ2−ζ7+ζ10+ζ11ζ2+ζ7−ζ10−ζ11−ζ2−ζ7+ζ10+ζ11ζ2−ζ7−ζ10+ζ11−ζ2+ζ7+ζ10−ζ11ζ2−ζ7−ζ10+ζ11−ζ2+ζ7+ζ10−ζ11000000000000000000
χ674-4-44-440044i−4i−4i4i-44-44i−4i4i−4i000-440000−4i4i00000000000000000000000000000000000000000000
χ684-4-44-44004−4i4i4i−4i-44-4−4i4i−4i4i000-4400004i−4i00000000000000000000000000000000000000000000
χ694-4-44-4400-24i−4i−4i4i2-22−2i2i−2i2i0002-200002i−2i000000000000000000−ζ2+ζ7+ζ10−ζ11ζ2−ζ7−ζ10+ζ11ζ2−ζ7−ζ10+ζ11−ζ2+ζ7+ζ10−ζ11−ζ2−ζ7+ζ10+ζ11ζ2+ζ7−ζ10−ζ11ζ2+ζ7−ζ10−ζ11−ζ2−ζ7+ζ10+ζ11000000000000000000
χ704-4-44-4400-24i−4i−4i4i2-22−2i2i−2i2i0002-200002i−2i000000000000000000ζ2−ζ7−ζ10+ζ11−ζ2+ζ7+ζ10−ζ11−ζ2+ζ7+ζ10−ζ11ζ2−ζ7−ζ10+ζ11ζ2+ζ7−ζ10−ζ11−ζ2−ζ7+ζ10+ζ11−ζ2−ζ7+ζ10+ζ11ζ2+ζ7−ζ10−ζ11000000000000000000
χ714-4-44-4400-2−4i4i4i−4i2-222i−2i2i−2i0002-20000−2i2i000000000000000000−ζ2−ζ7+ζ10+ζ11ζ2+ζ7−ζ10−ζ11ζ2+ζ7−ζ10−ζ11−ζ2−ζ7+ζ10+ζ11−ζ2+ζ7+ζ10−ζ11ζ2−ζ7−ζ10+ζ11ζ2−ζ7−ζ10+ζ11−ζ2+ζ7+ζ10−ζ11000000000000000000
χ724-4-44-4400-2−4i4i4i−4i2-222i−2i2i−2i0002-20000−2i2i000000000000000000ζ2+ζ7−ζ10−ζ11−ζ2−ζ7+ζ10+ζ11−ζ2−ζ7+ζ10+ζ11ζ2+ζ7−ζ10−ζ11ζ2−ζ7−ζ10+ζ11−ζ2+ζ7+ζ10−ζ11−ζ2+ζ7+ζ10−ζ11ζ2−ζ7−ζ10+ζ11000000000000000000
χ7388-8-8000080000-8-8800000000000000000000000000000000000000000000000000000000000
χ7488-8-80000-4000044-443−43−43430000000000000000000000000000000000000000000000000000000
χ7588-8-80000-4000044-4−434343−430000000000000000000000000000000000000000000000000000000

Here ζ is a primitive root of unity of order 12 (ζ12 = 1); i = ζ3.