Finite Group Databasebeta

← Group #10692830

Character table — Group #10692830

Order 768.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69
size111122222222444444444444444888888888888888888121212121616161616161616161624242424242448484848
order12222234466622444666612121212121244446888812121212121212121244444412121212242424244488884444
χ1111111111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111111111111111-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-1
χ311111111111111111111111111111111-1-1-1-11111111111111-1-1-1-1-1-1-1-1-1-111-1-1-1-111-1-1
χ411111111111111111111111111111111-1-1-1-1111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-111
χ5111111111111111111111111111-1-1-1-1111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-11111111111-1-1-1-1
χ6111111111111111111111111111-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-11111
χ7111111111111111111111111111-1-1-1-11-1-1-1-11-1-1-1-1-1-1-1-11111111111-1-1-1-111-1-1-1-1-1-111
χ8111111111111111111111111111-1-1-1-11-1-1-1-11-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1111111-1-1
χ91111111-1-1111-1-111-111-1-11111-1-111-1-1-1ii−i−i-11111-1-1-1-111-1-1i−iii−i−iii−i−i1-1ii−i−i1-1i−i
χ101111111-1-1111-1-111-111-1-11111-1-111-1-1-1ii−i−i-11111-1-1-1-1-1-111i−iii−i−iii−i−i-11−i−iii-11−ii
χ111111111-1-1111-1-111-111-1-11111-1-111-1-1-1−i−iii-11111-1-1-1-111-1-1−ii−i−iii−i−iii1-1−i−iii1-1−ii
χ121111111-1-1111-1-111-111-1-11111-1-111-1-1-1−i−iii-11111-1-1-1-1-1-111−ii−i−iii−i−iii-11ii−i−i-11i−i
χ131111111-1-1111-1-111-111-1-11111-1-1-1-111-1ii−i−i-1-1-1-1-1111111-1-1−ii−i−iiiii−i−i1-1ii−i−i-11−ii
χ141111111-1-1111-1-111-111-1-11111-1-1-1-111-1ii−i−i-1-1-1-1-11111-1-111−ii−i−iiiii−i−i-11−i−iii1-1i−i
χ151111111-1-1111-1-111-111-1-11111-1-1-1-111-1−i−iii-1-1-1-1-1111111-1-1i−iii−i−i−i−iii1-1−i−iii-11i−i
χ161111111-1-1111-1-111-111-1-11111-1-1-1-111-1−i−iii-1-1-1-1-11111-1-111i−iii−i−i−i−iii-11ii−i−i1-1−ii
χ17222222222222-2-2-2-2222-2-2-2-2-2-2220000-2000020000000022220000000000-2-200000000
χ18222222222222-2-2-2-2222-2-2-2-2-2-2220000-20000200000000-2-2-2-200000000002200000000
χ192222222-2-222222-2-2-22222-2-2-2-2-2-2000020000-20000000022-2-20000000000-2200000000
χ202222222-2-222222-2-2-22222-2-2-2-2-2-2000020000-200000000-2-22200000000002-200000000
χ21222222-122-1-1-122222-1-1-1-1-1-1-1-1-1-12222-12222-1-1-1-1-1-1-1-1-1000022-1-1-1-1-1-1-1-10000000000
χ22222222-122-1-1-122222-1-1-1-1-1-1-1-1-1-12222-1-2-2-2-2-1-1-1-1-1-1-1-1-10000-2-2111111110000000000
χ23222222-122-1-1-122222-1-1-1-1-1-1-1-1-1-1-2-2-2-2-12222-1111111110000-2-21111-1-1-1-10000000000
χ24222222-122-1-1-122222-1-1-1-1-1-1-1-1-1-1-2-2-2-2-1-2-2-2-2-111111111000022-1-1-1-111110000000000
χ25222222-1-2-2-1-1-1-2-222-2-1-111-1-1-1-11122-2-212i2i−2i−2i1-1-1-1-1111100002i−2i−i−iii−i−iii0000000000
χ26222222-1-2-2-1-1-1-2-222-2-1-111-1-1-1-11122-2-21−2i−2i2i2i1-1-1-1-111110000−2i2iii−i−iii−i−i0000000000
χ27222222-1-2-2-1-1-1-2-222-2-1-111-1-1-1-111-2-22212i2i−2i−2i11111-1-1-1-10000−2i2iii−i−i−i−iii0000000000
χ28222222-1-2-2-1-1-1-2-222-2-1-111-1-1-1-111-2-2221−2i−2i2i2i11111-1-1-1-100002i−2i−i−iiiii−i−i0000000000
χ292222-2-22222222-22-2-2-2-22222-2-2220000-20000-20000000000000000000000002-22-20000
χ302222-2-22222222-22-2-2-2-22222-2-2220000-20000-2000000000000000000000000-22-220000
χ312222-2-2222222-22-22-2-2-2-2-2-2-22222000022-22-2-20000000000000000002-22-20000000000
χ322222-2-2222222-22-22-2-2-2-2-2-2-2222200002-22-22-2000000000000000000-22-220000000000
χ332222-2-22-2-22222-2-222-2-222-2-222-2-20000-22i−2i−2i2i20000000000000000002i−2i−2i2i0000000000
χ342222-2-22-2-22222-2-222-2-222-2-222-2-20000-2−2i2i2i−2i2000000000000000000−2i2i2i−2i0000000000
χ352222-2-22-2-2222-222-22-2-2-2-222-2-2-2-200002000020000000000000000000000002i−2i−2i2i0000
χ362222-2-22-2-2222-222-22-2-2-2-222-2-2-2-20000200002000000000000000000000000−2i2i2i−2i0000
χ372222-2-2-122-1-1-1-22-22-2111111-1-1-1-10000-12-22-2133−3−333−3−30000003−33−3-11-110000000000
χ382222-2-2-122-1-1-1-22-22-2111111-1-1-1-10000-12-22-21−3−333−3−333000000−33−33-11-110000000000
χ392222-2-2-122-1-1-1-22-22-2111111-1-1-1-10000-1-22-22133−3−333−3−3000000−33−331-11-10000000000
χ402222-2-2-122-1-1-1-22-22-2111111-1-1-1-10000-1-22-221−3−333−3−3330000003−33−31-11-10000000000
χ412222-2-2-1-2-2-1-1-12-2-22211-1-111-1-111000012i−2i−2i2i-133−3−3−3−333000000i3−i3−i3i3−iii−i0000000000
χ422222-2-2-1-2-2-1-1-12-2-22211-1-111-1-111000012i−2i−2i2i-1−3−33333−3−3000000−i3i3i3−i3−iii−i0000000000
χ432222-2-2-1-2-2-1-1-12-2-22211-1-111-1-11100001−2i2i2i−2i-133−3−3−3−333000000−i3i3i3−i3i−i−ii0000000000
χ442222-2-2-1-2-2-1-1-12-2-22211-1-111-1-11100001−2i2i2i−2i-1−3−33333−3−3000000i3−i3−i3i3i−i−ii0000000000
χ45444444-244-2-2-2-4-4-4-44-2-2222222-2-2000020000-200000000000000000000000000000000
χ46444444-2-4-4-2-2-244-4-4-4-2-2-2-22222220000-20000200000000000000000000000000000000
χ474444-4-4-244-2-2-24-44-4-422-2-2-2-222-2-2000020000200000000000000000000000000000000
χ484444-4-4-2-4-4-2-2-2-444-442222-2-222220000-20000-200000000000000000000000000000000
χ494-44-44-4400-4-44000004-400000000000000000000000000004i−4i00000000000000000000
χ504-44-44-4400-4-44000004-40000000000000000000000000000−4i4i00000000000000000000
χ514-44-4-44400-4-4400000-44000000000000000000000000004i−4i0000000000000000000000
χ524-44-4-44400-4-4400000-4400000000000000000000000000−4i4i0000000000000000000000
χ534-4-440044i−4i4-4-400000000000004i−4i2-22i−2i0000002-22-22i−2i2i−2i000000000000000000000000
χ544-4-440044i−4i4-4-400000000000004i−4i-22−2i2i000000-22-22−2i2i−2i2i000000000000000000000000
χ554-4-44004−4i4i4-4-40000000000000−4i4i2-2−2i2i0000002-22-2−2i2i−2i2i000000000000000000000000
χ564-4-44004−4i4i4-4-40000000000000−4i4i-222i−2i000000-22-222i−2i2i−2i000000000000000000000000
χ574-4-4400-24i−4i-2220000000−2i32i323−2300−2i2i2-22i−2i000000−1+31−3−1−31+3ζ2+ζ7−ζ10+ζ11−ζ2−ζ7+ζ10−ζ11−ζ2+ζ7+ζ10+ζ11ζ2−ζ7−ζ10−ζ11000000000000000000000000
χ584-4-4400-24i−4i-2220000000−2i32i323−2300−2i2i-22−2i2i0000001−3−1+31+3−1−3−ζ2−ζ7+ζ10−ζ11ζ2+ζ7−ζ10+ζ11ζ2−ζ7−ζ10−ζ11−ζ2+ζ7+ζ10+ζ11000000000000000000000000
χ594-4-4400-24i−4i-22200000002i3−2i3−232300−2i2i2-22i−2i000000−1−31+3−1+31−3−ζ2+ζ7+ζ10+ζ11ζ2−ζ7−ζ10−ζ11ζ2+ζ7−ζ10+ζ11−ζ2−ζ7+ζ10−ζ11000000000000000000000000
χ604-4-4400-24i−4i-22200000002i3−2i3−232300−2i2i-22−2i2i0000001+3−1−31−3−1+3ζ2−ζ7−ζ10−ζ11−ζ2+ζ7+ζ10+ζ11−ζ2−ζ7+ζ10−ζ11ζ2+ζ7−ζ10+ζ11000000000000000000000000
χ614-4-4400-2−4i4i-2220000000−2i32i3−2323002i−2i2-2−2i2i000000−1−31+3−1+31−3ζ2−ζ7−ζ10−ζ11−ζ2+ζ7+ζ10+ζ11−ζ2−ζ7+ζ10−ζ11ζ2+ζ7−ζ10+ζ11000000000000000000000000
χ624-4-4400-2−4i4i-2220000000−2i32i3−2323002i−2i-222i−2i0000001+3−1−31−3−1+3−ζ2+ζ7+ζ10+ζ11ζ2−ζ7−ζ10−ζ11ζ2+ζ7−ζ10+ζ11−ζ2−ζ7+ζ10−ζ11000000000000000000000000
χ634-4-4400-2−4i4i-22200000002i3−2i323−23002i−2i2-2−2i2i000000−1+31−3−1−31+3−ζ2−ζ7+ζ10−ζ11ζ2+ζ7−ζ10+ζ11ζ2−ζ7−ζ10−ζ11−ζ2+ζ7+ζ10+ζ11000000000000000000000000
χ644-4-4400-2−4i4i-22200000002i3−2i323−23002i−2i-222i−2i0000001−3−1+31+3−1−3ζ2+ζ7−ζ10+ζ11−ζ2−ζ7+ζ10−ζ11−ζ2+ζ7+ζ10+ζ11ζ2−ζ7−ζ10−ζ11000000000000000000000000
χ6588-8-800800-88-8000000000000000000000000000000000000000000000000000000000
χ6688-8-800-4004-440000000000043−4300000000000000000000000000000000000000000000
χ6788-8-800-4004-4400000000000−434300000000000000000000000000000000000000000000
χ688-88-88-8-40044-400000-4400000000000000000000000000000000000000000000000000
χ698-88-8-88-40044-4000004-400000000000000000000000000000000000000000000000000

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