Finite Group Databasebeta

← Group #11780652

Character table — Group #11780652

Order 1152.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75
size111122222222444444444444444448888888888888888888888888242424242424242424244848484848484872727272
order122233666666344466612121212121212121212881212121212121224242424242424242424242424242424244488242424244612121212122488
χ1111111111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-111-1-1111-1-1-1-1
χ3111111111111111111111111111111111111111111111111111111-1-111111111-1-111-1-1-1-1-1-1-1
χ4111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111
χ511111111111111111111111111111-1-11111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-11111-1-111-1-1
χ611111111111111111111111111111-1-11111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1111111-11-1-11-1-1-1-111
χ711111111111111111111111111111-1-11111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-11-111-111-1-111
χ811111111111111111111111111111-1-11111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111-1-1-1-11111-1-1
χ922222222222222-2-222222222222-2-200-2-2-2-2-2-2-200000000000000002-2000000000200-2000000
χ1022222222222222-2-222222222222-2-200-2-2-2-2-2-2-20000000000000000-22000000000-2002000000
χ112222222222222-22-2222-2-2-2-2-2-2-2-222002-2-222-2-20000000000000000000000000000000002-200
χ122222222222222-22-2222-2-2-2-2-2-2-2-222002-2-222-2-2000000000000000000000000000000000-2200
χ132222222222222-2-22222-2-2-2-2-2-2-2-2-2-200-222-2-2220000000000000000002-2000000002-20000000
χ142222222222222-2-22222-2-2-2-2-2-2-2-2-2-200-222-2-222000000000000000000-2200000000-220000000
χ1522222-12-1-122-1-1222-1-1-122-1-1-1-1-1-12222-12-1-1-1-1-12222-1-1-1-1-1-1-1-1-1-1-1-122000000002-100-1-1-10000
χ1622222-12-1-122-1-1222-1-1-122-1-1-1-1-1-12222-12-1-1-1-1-12222-1-1-1-1-1-1-1-1-1-1-1-1-2-200000000-21001110000
χ1722222-12-1-122-1-1222-1-1-122-1-1-1-1-1-122-2-2-12-1-1-1-1-1-2-2-2-21111111111112200000000-2-100-1110000
χ1822222-12-1-122-1-1222-1-1-122-1-1-1-1-1-122-2-2-12-1-1-1-1-1-2-2-2-2111111111111-2-20000000021001-1-10000
χ1922222-12-1-122-1-12-2-2-1-1-122-1-1-1-1-1-1-2-2001-2111110000−i3−i3−i3−i3−i3−i3i3i3i3i3i3i32-2000000000-1001−i3i30000
χ2022222-12-1-122-1-12-2-2-1-1-122-1-1-1-1-1-1-2-2001-2111110000−i3−i3−i3−i3−i3−i3i3i3i3i3i3i3-22000000000100-1i3−i30000
χ2122222-12-1-122-1-12-2-2-1-1-122-1-1-1-1-1-1-2-2001-2111110000i3i3i3i3i3i3−i3−i3−i3−i3−i3−i32-2000000000-1001i3−i30000
χ2222222-12-1-122-1-12-2-2-1-1-122-1-1-1-1-1-1-2-2001-2111110000i3i3i3i3i3i3−i3−i3−i3−i3−i3−i3-22000000000100-1−i3i30000
χ232222-12-122-1-12-1222-1-1-1-1-122-1-1-1-1-1-1222-12-1-1-1-1-1-1-1-122-1-1-1-122-1-1-1-1002222-1-1-1-100-1-10000000
χ242222-12-122-1-12-1222-1-1-1-1-122-1-1-1-1-1-1222-12-1-1-1-1-1-1-1-122-1-1-1-122-1-1-1-100-2-2-2-2111100110000000
χ252222-12-122-1-12-1222-1-1-1-1-122-1-1-1-1-1-1-2-22-12-1-1-1-11111-2-21111-2-211110022-2-2111100-1-10000000
χ262222-12-122-1-12-1222-1-1-1-1-122-1-1-1-1-1-1-2-22-12-1-1-1-11111-2-21111-2-2111100-2-222-1-1-1-100110000000
χ272222-12-122-1-12-1-2-22-1-1-111-2-211111100-2-1211-1-133−3−30033−3−30033−3−3002-20033−3−300-110000000
χ282222-12-122-1-12-1-2-22-1-1-111-2-211111100-2-1211-1-133−3−30033−3−30033−3−300-2200−3−333001-10000000
χ292222-12-122-1-12-1-2-22-1-1-111-2-211111100-2-1211-1-1−3−33300−3−33300−3−333002-200−3−33300-110000000
χ302222-12-122-1-12-1-2-22-1-1-111-2-211111100-2-1211-1-1−3−33300−3−33300−3−33300-220033−3−3001-10000000
χ3144444-24-2-244-2-2-44-4-2-2-2-4-42222224400-2-42-2-2220000000000000000000000000000000000000
χ3244444-24-2-244-2-2-4-44-2-2-2-4-4222222-4-40024-222-2-20000000000000000000000000000000000000
χ334444-24-244-2-24-24-4-4-2-2-2-2-244-2-2-2-22200-42-422220000000000000000000000000000000000000
χ344444-24-244-2-24-2-44-4-2-2-222-4-42222-2-20042-4-2-2220000000000000000000000000000000000000
χ354444-2-2-2-2-2-2-2-21444111-2-2-2-21111-2-244-2-2-21111-2-2-2-2-2-21111-2-21111000000000000000000000
χ364444-2-2-2-2-2-2-2-21444111-2-2-2-21111-2-2-4-4-2-2-21111222222-1-1-1-122-1-1-1-1000000000000000000000
χ374444-2-2-2-2-2-2-2-214-4-4111-2-2-2-211112200222-1-1-1-10000−2i3−2i3i3i3i3i32i32i3−i3−i3−i3−i3000000000000000000000
χ384444-2-2-2-2-2-2-2-214-4-4111-2-2-2-211112200222-1-1-1-100002i32i3−i3−i3−i3−i3−2i3−2i3i3i3i3i3000000000000000000000
χ394444-2-2-2-2-2-2-2-21-44-41112222-1-1-1-1-2-200-22211-1-10000003i3i−3i−3i00−3i−3i3i3i000000000000000000000
χ404444-2-2-2-2-2-2-2-21-44-41112222-1-1-1-1-2-200-22211-1-1000000−3i−3i3i3i003i3i−3i−3i000000000000000000000
χ414444-2-2-2-2-2-2-2-21-4-441112222-1-1-1-122002-2-2-1-1112323−23−2300−3−33300−3−333000000000000000000000
χ424444-2-2-2-2-2-2-2-21-4-441112222-1-1-1-122002-2-2-1-111−23−2323230033−3−30033−3−3000000000000000000000
χ4344-4-44444-4-4-4-440004-4-40000000000000000000000000000000000000000000000000000002-2
χ4444-4-44444-4-4-4-440004-4-4000000000000000000000000000000000000000000000000000000-22
χ454-44-444-4-444-4-44000-44-40000000000000000000000000000000000000002i−2i2i−2i2i−2i00000000000
χ464-44-444-4-444-4-44000-44-4000000000000000000000000000000000000000−2i2i−2i2i−2i2i00000000000
χ474-44-4-242-44-22-4-20002-2223−23002323−23−2300000000000000000000000000000002i−2iζ2+ζ7−ζ10+ζ11−ζ2−ζ7+ζ10−ζ11−ζ2+ζ7+ζ10+ζ11ζ2−ζ7−ζ10−ζ1100000000000
χ484-44-4-242-44-22-4-20002-2223−23002323−23−230000000000000000000000000000000−2i2i−ζ2−ζ7+ζ10−ζ11ζ2+ζ7−ζ10+ζ11ζ2−ζ7−ζ10−ζ11−ζ2+ζ7+ζ10+ζ1100000000000
χ494-44-4-242-44-22-4-20002-22−232300−23−23232300000000000000000000000000000002i−2i−ζ2+ζ7+ζ10+ζ11ζ2−ζ7−ζ10−ζ11ζ2+ζ7−ζ10+ζ11−ζ2−ζ7+ζ10−ζ1100000000000
χ504-44-4-242-44-22-4-20002-22−232300−23−2323230000000000000000000000000000000−2i2iζ2−ζ7−ζ10−ζ11−ζ2+ζ7+ζ10+ζ11−ζ2−ζ7+ζ10−ζ11ζ2+ζ7−ζ10+ζ1100000000000
χ514-4-4444-4-4-4-4444000-4-4400000000002-200000002-22-22-22-22-22-22-22-2000000000000000000000
χ524-4-4444-4-4-4-4444000-4-440000000000-220000000-22-22-22-22-22-22-22-22000000000000000000000
χ534-4-444-2-422-44-2-200022-200−2i32i3−2i32i3−2i32i3002-200000002-22-2−1−i31+i3−1−i31+i3−1−i31+i3−1+i31−i3−1+i31−i3−1+i31−i3000000000000000000000
χ544-4-444-2-422-44-2-200022-200−2i32i3−2i32i3−2i32i300-220000000-22-221+i3−1−i31+i3−1−i31+i3−1−i31−i3−1+i31−i3−1+i31−i3−1+i3000000000000000000000
χ554-4-444-2-422-44-2-200022-2002i3−2i32i3−2i32i3−2i3002-200000002-22-2−1+i31−i3−1+i31−i3−1+i31−i3−1−i31+i3−1−i31+i3−1−i31+i3000000000000000000000
χ564-4-444-2-422-44-2-200022-2002i3−2i32i3−2i32i3−2i300-220000000-22-221−i3−1+i31−i3−1+i31−i3−1+i31+i3−1−i31+i3−1−i31+i3−1−i3000000000000000000000
χ574-4-44-242-4-42-24-200022-20000000023−232-200023−2300−1+31−3−1−31+32-2−1+31−3−1−31+32-2−1+31−3−1−31+3000000000000000000000
χ584-4-44-242-4-42-24-200022-20000000023−23-2200023−23001−3−1+31+3−1−3-221−3−1+31+3−1−3-221−3−1+31+3−1−3000000000000000000000
χ594-4-44-242-4-42-24-200022-200000000−23232-2000−232300−1−31+3−1+31−32-2−1−31+3−1+31−32-2−1−31+3−1+31−3000000000000000000000
χ604-4-44-242-4-42-24-200022-200000000−2323-22000−2323001+3−1−31−3−1+3-221+3−1−31−3−1+3-221+3−1−31−3−1+3000000000000000000000
χ614-4-44-2-22222-2-21000-1-1100−2i32i3i3−i3i3−i323−232-2000−333i−3i−1+31−3−1−31+3−1−i31+i3ζ2−ζ7−2ζ11−ζ2+ζ7+2ζ11ζ2+ζ7+2ζ11−ζ2−ζ7−2ζ11−1+i31−i32ζ7+ζ10+ζ11−2ζ7−ζ10−ζ11−2ζ7+ζ10−ζ112ζ7−ζ10+ζ11000000000000000000000
χ624-4-44-2-22222-2-21000-1-1100−2i32i3i3−i3i3−i323−23-22000−333i−3i1−3−1+31+3−1−31+i3−1−i3−ζ2+ζ7+2ζ11ζ2−ζ7−2ζ11−ζ2−ζ7−2ζ11ζ2+ζ7+2ζ111−i3−1+i3−2ζ7−ζ10−ζ112ζ7+ζ10+ζ112ζ7−ζ10+ζ11−2ζ7+ζ10−ζ11000000000000000000000
χ634-4-44-2-22222-2-21000-1-1100−2i32i3i3−i3i3−i3−23232-20003−3−3i3i−1−31+3−1+31−3−1−i31+i3ζ2+ζ7+2ζ11−ζ2−ζ7−2ζ11ζ2−ζ7−2ζ11−ζ2+ζ7+2ζ11−1+i31−i3−2ζ7+ζ10−ζ112ζ7−ζ10+ζ112ζ7+ζ10+ζ11−2ζ7−ζ10−ζ11000000000000000000000
χ644-4-44-2-22222-2-21000-1-1100−2i32i3i3−i3i3−i3−2323-220003−3−3i3i1+3−1−31−3−1+31+i3−1−i3−ζ2−ζ7−2ζ11ζ2+ζ7+2ζ11−ζ2+ζ7+2ζ11ζ2−ζ7−2ζ111−i3−1+i32ζ7−ζ10+ζ11−2ζ7+ζ10−ζ11−2ζ7−ζ10−ζ112ζ7+ζ10+ζ11000000000000000000000
χ654-4-44-2-22222-2-21000-1-11002i3−2i3−i3i3−i3i323−232-2000−33−3i3i−1+31−3−1−31+3−1+i31−i32ζ7+ζ10+ζ11−2ζ7−ζ10−ζ11−2ζ7+ζ10−ζ112ζ7−ζ10+ζ11−1−i31+i3ζ2−ζ7−2ζ11−ζ2+ζ7+2ζ11ζ2+ζ7+2ζ11−ζ2−ζ7−2ζ11000000000000000000000
χ664-4-44-2-22222-2-21000-1-11002i3−2i3−i3i3−i3i323−23-22000−33−3i3i1−3−1+31+3−1−31−i3−1+i3−2ζ7−ζ10−ζ112ζ7+ζ10+ζ112ζ7−ζ10+ζ11−2ζ7+ζ10−ζ111+i3−1−i3−ζ2+ζ7+2ζ11ζ2−ζ7−2ζ11−ζ2−ζ7−2ζ11ζ2+ζ7+2ζ11000000000000000000000
χ674-4-44-2-22222-2-21000-1-11002i3−2i3−i3i3−i3i3−23232-20003−33i−3i−1−31+3−1+31−3−1+i31−i3−2ζ7+ζ10−ζ112ζ7−ζ10+ζ112ζ7+ζ10+ζ11−2ζ7−ζ10−ζ11−1−i31+i3ζ2+ζ7+2ζ11−ζ2−ζ7−2ζ11ζ2−ζ7−2ζ11−ζ2+ζ7+2ζ11000000000000000000000
χ684-4-44-2-22222-2-21000-1-11002i3−2i3−i3i3−i3i3−2323-220003−33i−3i1+3−1−31−3−1+31−i3−1+i32ζ7−ζ10+ζ11−2ζ7+ζ10−ζ11−2ζ7−ζ10−ζ112ζ7+ζ10+ζ111+i3−1−i3−ζ2−ζ7−2ζ11ζ2+ζ7+2ζ11−ζ2+ζ7+2ζ11ζ2−ζ7−2ζ11000000000000000000000
χ6988-8-88-48-44-8-84-4000-44400000000000000000000000000000000000000000000000000000000
χ7088-8-8-48-48-844-8-4000-44400000000000000000000000000000000000000000000000000000000
χ7188-8-8-4-4-4-4444420002-2-200006i−6i−6i6i000000000000000000000000000000000000000000000000
χ7288-8-8-4-4-4-4444420002-2-20000−6i6i6i−6i000000000000000000000000000000000000000000000000
χ738-88-88-4-84-48-84-40004-4400000000000000000000000000000000000000000000000000000000
χ748-88-8-4-444-4-4442000-22-243−4300−23−232323000000000000000000000000000000000000000000000000
χ758-88-8-4-444-4-4442000-22-2−4343002323−23−23000000000000000000000000000000000000000000000000

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