Finite Group Databasebeta

← Group #11780651

Character table — Group #11780651

Order 1152.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75
size111122222222444444444444444448888888888888888888888888242424242424242424244848484848484872727272
order12223366666634446661212121212121212121288121212121212122424242424242424242424242424242422448824242424466121212124488
χ1111111111111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111111111111111111-11-1111111-11-11-1-1-1-1-1-1-1
χ3111111111111111111111111111111111111111111111111111111-11-11-1-1-1-1-1-11-11-1111-1-1-1-1
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
χ611111111111111111111111111111-1-11111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11-11-1-1-1-1-1-1-111-11-111-1-111
χ711111111111111111111111111111-1-11111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11-11111111-1-11-11-1-1-1-111
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
χ922222222222222-2-222222222222-2-200-2-2-2-2-2-2-20000000000000000020-20000000020-2000000
χ1022222222222222-2-222222222222-2-200-2-2-2-2-2-2-200000000000000000-20200000000-202000000
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
χ132222222222222-2-22222-2-2-2-2-2-2-2-2-2-200-222-2-222000000000000000020-20000000020-20000000
χ142222222222222-2-22222-2-2-2-2-2-2-2-2-2-200-222-2-2220000000000000000-20200000000-2020000000
χ1522222-122-1-12-1-1222-1-1-122-1-1-1-1-1-12222-1-12-1-1-1-12222-1-1-1-1-1-1-1-1-1-1-1-1020200000020-10-1-1-10000
χ1622222-122-1-12-1-1222-1-1-122-1-1-1-1-1-12222-1-12-1-1-1-12222-1-1-1-1-1-1-1-1-1-1-1-10-20-2000000-20101110000
χ1722222-122-1-12-1-1222-1-1-122-1-1-1-1-1-122-2-2-1-12-1-1-1-1-2-2-2-21111111111110202000000-20-10-1110000
χ1822222-122-1-12-1-1222-1-1-122-1-1-1-1-1-122-2-2-1-12-1-1-1-1-2-2-2-21111111111110-20-200000020101-1-10000
χ1922222-122-1-12-1-12-2-2-1-1-122-1-1-1-1-1-1-2-20011-211110000−i3−i3−i3−i3−i3−i3i3i3i3i3i3i3020-200000000-101−i3i30000
χ2022222-122-1-12-1-12-2-2-1-1-122-1-1-1-1-1-1-2-20011-211110000−i3−i3−i3−i3−i3−i3i3i3i3i3i3i30-2020000000010-1i3−i30000
χ2122222-122-1-12-1-12-2-2-1-1-122-1-1-1-1-1-1-2-20011-211110000i3i3i3i3i3i3−i3−i3−i3−i3−i3−i3020-200000000-101i3−i30000
χ2222222-122-1-12-1-12-2-2-1-1-122-1-1-1-1-1-1-2-20011-211110000i3i3i3i3i3i3−i3−i3−i3−i3−i3−i30-2020000000010-1−i3i30000
χ232222-12-1-122-12-1222-1-1-1-1-122-1-1-1-1-1-12222-1-1-1-1-1-1-1-1-122-1-1-1-122-1-1-1-1202022-1-1-1-10-10-10000000
χ242222-12-1-122-12-1222-1-1-1-1-122-1-1-1-1-1-12222-1-1-1-1-1-1-1-1-122-1-1-1-122-1-1-1-1-20-20-2-2111101010000000
χ252222-12-1-122-12-1222-1-1-1-1-122-1-1-1-1-1-1-2-222-1-1-1-1-11111-2-21111-2-211112020-2-211110-10-10000000
χ262222-12-1-122-12-1222-1-1-1-1-122-1-1-1-1-1-1-2-222-1-1-1-1-11111-2-21111-2-21111-20-2022-1-1-1-101010000000
χ272222-12-1-122-12-1-2-22-1-1-111-2-211111100-22-111-1-133−3−30033−3−30033−3−320-200033−3−30-1010000000
χ282222-12-1-122-12-1-2-22-1-1-111-2-211111100-22-111-1-133−3−30033−3−30033−3−3-202000−3−333010-10000000
χ292222-12-1-122-12-1-2-22-1-1-111-2-211111100-22-111-1-1−3−33300−3−33300−3−33320-2000−3−3330-1010000000
χ302222-12-1-122-12-1-2-22-1-1-111-2-211111100-22-111-1-1−3−33300−3−33300−3−333-20200033−3−3010-10000000
χ3144444-244-2-24-2-2-44-4-2-2-2-4-42222224400-22-4-2-2220000000000000000000000000000000000000
χ3244444-244-2-24-2-2-4-44-2-2-2-4-4222222-4-4002-2422-2-20000000000000000000000000000000000000
χ334444-24-2-244-24-24-4-4-2-2-2-2-244-2-2-2-22200-4-4222220000000000000000000000000000000000000
χ344444-24-2-244-24-2-44-4-2-2-222-4-42222-2-2004-42-2-2220000000000000000000000000000000000000
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
χ4344-4-4444-44-4-4-440004-4-40000000000000000000000000000000000000002-22-22-200000000000
χ4444-4-4444-44-4-4-440004-4-4000000000000000000000000000000000000000-22-22-2200000000000
χ4544-4-4-24-224-42-4-2000-22223−23002323−23−2300000000000000000000000000000002-2−1−31+3−1+31−300000000000
χ4644-4-4-24-224-42-4-2000-22223−23002323−23−230000000000000000000000000000000-221+3−1−31−3−1+300000000000
χ4744-4-4-24-224-42-4-2000-222−232300−23−23232300000000000000000000000000000002-2−1+31−3−1−31+300000000000
χ4844-4-4-24-224-42-4-2000-222−232300−23−2323230000000000000000000000000000000-221−3−1+31+3−1−300000000000
χ494-44-444-4-4-444-44000-44-40000000000000000000000000000000000000000000000000000002i−2i
χ504-44-444-4-4-444-44000-44-4000000000000000000000000000000000000000000000000000000−2i2i
χ514-4-4444-44-4-4-444000-4-4400000000002-200000002-22-22-22-22-22-22-22-2000000000000000000000
χ524-4-4444-44-4-4-444000-4-440000000000-220000000-22-22-22-22-22-22-22-22000000000000000000000
χ534-4-444-2-4422-4-2-200022-200−2i32i3−2i32i3−2i32i3002-200000002-22-2−1−i31+i3−1−i31+i3−1−i31+i3−1+i31−i3−1+i31−i3−1+i31−i3000000000000000000000
χ544-4-444-2-4422-4-2-200022-200−2i32i3−2i32i3−2i32i300-220000000-22-221+i3−1−i31+i3−1−i31+i3−1−i31−i3−1+i31−i3−1+i31−i3−1+i3000000000000000000000
χ554-4-444-2-4422-4-2-200022-2002i3−2i32i3−2i32i3−2i3002-200000002-22-2−1+i31−i3−1+i31−i3−1+i31−i3−1−i31+i3−1−i31+i3−1−i31+i3000000000000000000000
χ564-4-444-2-4422-4-2-200022-2002i3−2i32i3−2i32i3−2i300-220000000-22-221−i3−1+i31−i3−1+i31−i3−1+i31+i3−1−i31+i3−1−i31+i3−1−i3000000000000000000000
χ574-4-44-242-2-4-424-200022-20000000023−232-200023−2300−1+31−3−1−31+32-2−1+31−3−1−31+32-2−1+31−3−1−31+3000000000000000000000
χ584-4-44-242-2-4-424-200022-20000000023−23-2200023−23001−3−1+31+3−1−3-221−3−1+31+3−1−3-221−3−1+31+3−1−3000000000000000000000
χ594-4-44-242-2-4-424-200022-200000000−23232-2000−232300−1−31+3−1+31−32-2−1−31+3−1+31−32-2−1−31+3−1+31−3000000000000000000000
χ604-4-44-242-2-4-424-200022-200000000−2323-22000−2323001+3−1−31−3−1+3-221+3−1−31−3−1+3-221+3−1−31−3−1+3000000000000000000000
χ614-4-44-2-22-2222-21000-1-1100−2i32i3i3−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
χ624-4-44-2-22-2222-21000-1-1100−2i32i3i3−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
χ634-4-44-2-22-2222-21000-1-1100−2i32i3i3−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
χ644-4-44-2-22-2222-21000-1-1100−2i32i3i3−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
χ654-4-44-2-22-2222-21000-1-11002i3−2i3−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
χ664-4-44-2-22-2222-21000-1-11002i3−2i3−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
χ674-4-44-2-22-2222-21000-1-11002i3−2i3−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
χ684-4-44-2-22-2222-21000-1-11002i3−2i3−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
χ6988-8-88-48-8-44-84-4000-44400000000000000000000000000000000000000000000000000000000
χ7088-8-8-4-4-44-444420002-2-243−4300−23−232323000000000000000000000000000000000000000000000000
χ7188-8-8-4-4-44-444420002-2-2−4343002323−23−23000000000000000000000000000000000000000000000000
χ728-88-88-4-8-84-484-40004-4400000000000000000000000000000000000000000000000000000000
χ738-88-8-4844-88-4-8-40004-4400000000000000000000000000000000000000000000000000000000
χ748-88-8-4-4444-4-442000-22-200006i−6i−6i6i000000000000000000000000000000000000000000000000
χ758-88-8-4-4444-4-442000-22-20000−6i6i6i−6i000000000000000000000000000000000000000000000000

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