Finite Group Databasebeta

← Group #11780653

Character table — Group #11780653

Order 1152.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75
size111122222222444444444444444448888888888888888888888888242424242424242424244848484848484872727272
order122233666666344466612121212121212121212881212121212121224242424242424242424242424242424244488242424244612121212122488
χ1111111111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111111111111111111111-1-1111111-111-1-1-1-1-1-1-1-1
χ3111111111111111111111111111111111111111111111111111111-1-111-1-1-1-1-1-11-1-11111-1-1-1-1
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
χ611111111111111111111111111111-1-11111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1111-1-111-1-111
χ711111111111111111111111111111-1-11111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-111-1-1-1-111
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
χ922222222222222-2-222222222222-2-200-2-2-2-2-2-2-20000000000000000002-20000000002-2000000
χ1022222222222222-2-222222222222-2-200-2-2-2-2-2-2-2000000000000000000-22000000000-22000000
χ112222222222222-22-2222-2-2-2-2-2-2-2-22200-2-2222-2-20000000000000000000000000000000002-200
χ122222222222222-22-2222-2-2-2-2-2-2-2-22200-2-2222-2-2000000000000000000000000000000000-2200
χ132222222222222-2-22222-2-2-2-2-2-2-2-2-2-20022-2-2-22200000000000000002-20000000002-200000000
χ142222222222222-2-22222-2-2-2-2-2-2-2-2-2-20022-2-2-2220000000000000000-22000000000-2200000000
χ1522222-12-1-12-12-1222-1-1-122-1-1-1-1-1-1-1-1222-12-1-1-1-12222-1-1-1-1-1-1-1-1-1-1-1-1220022-1-1-1-10-1-100000000
χ1622222-12-1-12-12-1222-1-1-122-1-1-1-1-1-1-1-1222-12-1-1-1-12222-1-1-1-1-1-1-1-1-1-1-1-1-2-200-2-2111101100000000
χ1722222-12-1-12-12-1222-1-1-122-1-1-1-1-1-1-1-1-2-22-12-1-1-1-1-2-2-2-21111111111112200-2-211110-1-100000000
χ1822222-12-1-12-12-1222-1-1-122-1-1-1-1-1-1-1-1-2-22-12-1-1-1-1-2-2-2-2111111111111-2-20022-1-1-1-101100000000
χ1922222-12-1-12-12-1-2-22-1-1-1-2-211111111002-1-211-1-10000333333−3−3−3−3−3−32-2000033−3−30-1100000000
χ2022222-12-1-12-12-1-2-22-1-1-1-2-211111111002-1-211-1-10000333333−3−3−3−3−3−3-220000−3−33301-100000000
χ2122222-12-1-12-12-1-2-22-1-1-1-2-211111111002-1-211-1-10000−3−3−3−3−3−33333332-20000−3−3330-1100000000
χ2222222-12-1-12-12-1-2-22-1-1-1-2-211111111002-1-211-1-10000−3−3−3−3−3−3333333-22000033−3−301-100000000
χ232222-12-122-12-1-1222-1-1-1-1-122-1-1-1-12222-12-1-1-1-1-1-1-1-1-122-1-1-1-122-1-1-1-10022000000200-1-1-1-10000
χ242222-12-122-12-1-1222-1-1-1-1-122-1-1-1-12222-12-1-1-1-1-1-1-1-1-122-1-1-1-122-1-1-1-100-2-2000000-20011110000
χ252222-12-122-12-1-1222-1-1-1-1-122-1-1-1-122-2-2-12-1-1-1-1-11111-2-21111-2-211110022000000-200-1-1110000
χ262222-12-122-12-1-1222-1-1-1-1-122-1-1-1-122-2-2-12-1-1-1-1-11111-2-21111-2-2111100-2-200000020011-1-10000
χ272222-12-122-12-1-12-2-2-1-1-1-1-122-1-1-1-1-2-2001-211111−i3−i3i3i300−i3−i3i3i300−i3−i3i3i3002-2000000000-11−i3i30000
χ282222-12-122-12-1-12-2-2-1-1-1-1-122-1-1-1-1-2-2001-211111−i3−i3i3i300−i3−i3i3i300−i3−i3i3i300-220000000001-1i3−i30000
χ292222-12-122-12-1-12-2-2-1-1-1-1-122-1-1-1-1-2-2001-211111i3i3−i3−i300i3i3−i3−i300i3i3−i3−i3002-2000000000-11i3−i30000
χ302222-12-122-12-1-12-2-2-1-1-1-1-122-1-1-1-1-2-2001-211111i3i3−i3−i300i3i3−i3−i300i3i3−i3−i300-220000000001-1−i3i30000
χ3144444-24-2-24-24-24-4-4-2-2-244-2-2-2-2-2-22200-42-422220000000000000000000000000000000000000
χ3244444-24-2-24-24-2-44-4-2-2-2-4-4222222-2-200-424-2-2220000000000000000000000000000000000000
χ334444-24-244-24-2-2-44-4-2-2-222-4-4222244002-4-2-2-2220000000000000000000000000000000000000
χ344444-24-244-24-2-2-4-44-2-2-222-4-42222-4-400-24222-2-20000000000000000000000000000000000000
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
χ374444-2-2-2-2-2-2-2-214-4-4111-2-2-2-211112200222-1-1-1-1−2i3−2i32i32i300i3i3−i3−i300i3i3−i3−i3000000000000000000000
χ384444-2-2-2-2-2-2-2-214-4-4111-2-2-2-211112200222-1-1-1-12i32i3−2i3−2i300−i3−i3i3i300−i3−i3i3i3000000000000000000000
χ394444-2-2-2-2-2-2-2-21-44-41112222-1-1-1-1-2-20022-211-1-10000003i3i−3i−3i00−3i−3i3i3i000000000000000000000
χ404444-2-2-2-2-2-2-2-21-44-41112222-1-1-1-1-2-20022-211-1-1000000−3i−3i3i3i003i3i−3i−3i000000000000000000000
χ414444-2-2-2-2-2-2-2-21-4-441112222-1-1-1-12200-2-22-1-11100002323−3−3−3−3−23−233333000000000000000000000
χ424444-2-2-2-2-2-2-2-21-4-441112222-1-1-1-12200-2-22-1-1110000−23−2333332323−3−3−3−3000000000000000000000
χ4344-4-44444-4-4-4-440004-4-400000000002-200000002-22-22-22-22-22-22-22-2000000000000000000000
χ4444-4-44444-4-4-4-440004-4-40000000000-220000000-22-22-22-22-22-22-22-22000000000000000000000
χ4544-4-44-24-22-42-4-2000-2220000000023−232-200023−23002-22-2−1+31−3−1+31−3−1+31−3−1−31+3−1−31+3−1−31+3000000000000000000000
χ4644-4-44-24-22-42-4-2000-2220000000023−23-2200023−2300-22-221−3−1+31−3−1+31−3−1+31+3−1−31+3−1−31+3−1−3000000000000000000000
χ4744-4-44-24-22-42-4-2000-22200000000−23232-2000−2323002-22-2−1−31+3−1−31+3−1−31+3−1+31−3−1+31−3−1+31−3000000000000000000000
χ4844-4-44-24-22-42-4-2000-22200000000−2323-22000−232300-22-221+3−1−31+3−1−31+3−1−31−3−1+31−3−1+31−3−1+3000000000000000000000
χ4944-4-4-24-24-42-42-2000-222−2i32i300−2i3−2i32i32i3002-20000000−1−i31+i3−1+i31−i32-2−1−i31+i3−1+i31−i32-2−1−i31+i3−1+i31−i3000000000000000000000
χ5044-4-4-24-24-42-42-2000-222−2i32i300−2i3−2i32i32i300-2200000001+i3−1−i31−i3−1+i3-221+i3−1−i31−i3−1+i3-221+i3−1−i31−i3−1+i3000000000000000000000
χ5144-4-4-24-24-42-42-2000-2222i3−2i3002i32i3−2i3−2i3002-20000000−1+i31−i3−1−i31+i32-2−1+i31−i3−1−i31+i32-2−1+i31−i3−1−i31+i3000000000000000000000
χ5244-4-4-24-24-42-42-2000-2222i3−2i3002i32i3−2i3−2i300-2200000001−i3−1+i31+i3−1−i3-221−i3−1+i31+i3−1−i3-221−i3−1+i31+i3−1−i3000000000000000000000
χ5344-4-4-2-2-2-2222210001-1-1−2i32i300i3i3−i3−i323−232-2000−333i−3i−1−i31+i3−1+i31−i3−1+31−3ζ2−ζ7−2ζ11−ζ2+ζ7+2ζ112ζ7+ζ10+ζ11−2ζ7−ζ10−ζ11−1−31+3ζ2+ζ7+2ζ11−ζ2−ζ7−2ζ11−2ζ7+ζ10−ζ112ζ7−ζ10+ζ11000000000000000000000
χ5444-4-4-2-2-2-2222210001-1-1−2i32i300i3i3−i3−i323−23-22000−333i−3i1+i3−1−i31−i3−1+i31−3−1+3−ζ2+ζ7+2ζ11ζ2−ζ7−2ζ11−2ζ7−ζ10−ζ112ζ7+ζ10+ζ111+3−1−3−ζ2−ζ7−2ζ11ζ2+ζ7+2ζ112ζ7−ζ10+ζ11−2ζ7+ζ10−ζ11000000000000000000000
χ5544-4-4-2-2-2-2222210001-1-1−2i32i300i3i3−i3−i3−23232-20003−3−3i3i−1−i31+i3−1+i31−i3−1−31+3ζ2+ζ7+2ζ11−ζ2−ζ7−2ζ11−2ζ7+ζ10−ζ112ζ7−ζ10+ζ11−1+31−3ζ2−ζ7−2ζ11−ζ2+ζ7+2ζ112ζ7+ζ10+ζ11−2ζ7−ζ10−ζ11000000000000000000000
χ5644-4-4-2-2-2-2222210001-1-1−2i32i300i3i3−i3−i3−2323-220003−3−3i3i1+i3−1−i31−i3−1+i31+3−1−3−ζ2−ζ7−2ζ11ζ2+ζ7+2ζ112ζ7−ζ10+ζ11−2ζ7+ζ10−ζ111−3−1+3−ζ2+ζ7+2ζ11ζ2−ζ7−2ζ11−2ζ7−ζ10−ζ112ζ7+ζ10+ζ11000000000000000000000
χ5744-4-4-2-2-2-2222210001-1-12i3−2i300−i3−i3i3i323−232-2000−33−3i3i−1+i31−i3−1−i31+i3−1+31−32ζ7+ζ10+ζ11−2ζ7−ζ10−ζ11ζ2−ζ7−2ζ11−ζ2+ζ7+2ζ11−1−31+3−2ζ7+ζ10−ζ112ζ7−ζ10+ζ11ζ2+ζ7+2ζ11−ζ2−ζ7−2ζ11000000000000000000000
χ5844-4-4-2-2-2-2222210001-1-12i3−2i300−i3−i3i3i323−23-22000−33−3i3i1−i3−1+i31+i3−1−i31−3−1+3−2ζ7−ζ10−ζ112ζ7+ζ10+ζ11−ζ2+ζ7+2ζ11ζ2−ζ7−2ζ111+3−1−32ζ7−ζ10+ζ11−2ζ7+ζ10−ζ11−ζ2−ζ7−2ζ11ζ2+ζ7+2ζ11000000000000000000000
χ5944-4-4-2-2-2-2222210001-1-12i3−2i300−i3−i3i3i3−23232-20003−33i−3i−1+i31−i3−1−i31+i3−1−31+3−2ζ7+ζ10−ζ112ζ7−ζ10+ζ11ζ2+ζ7+2ζ11−ζ2−ζ7−2ζ11−1+31−32ζ7+ζ10+ζ11−2ζ7−ζ10−ζ11ζ2−ζ7−2ζ11−ζ2+ζ7+2ζ11000000000000000000000
χ6044-4-4-2-2-2-2222210001-1-12i3−2i300−i3−i3i3i3−2323-220003−33i−3i1−i3−1+i31+i3−1−i31+3−1−32ζ7−ζ10+ζ11−2ζ7+ζ10−ζ11−ζ2−ζ7−2ζ11ζ2+ζ7+2ζ111−3−1+3−2ζ7−ζ10−ζ112ζ7+ζ10+ζ11−ζ2+ζ7+2ζ11ζ2−ζ7−2ζ11000000000000000000000
χ614-44-444-4-4-444-44000-44-40000000000000000000000000000000000000000000000000000002i−2i
χ624-44-444-4-4-444-44000-44-4000000000000000000000000000000000000000000000000000000−2i2i
χ634-4-4444-4-44-4-444000-4-440000000000000000000000000000000000000002-22-22-200000000000
χ644-4-4444-4-44-4-444000-4-44000000000000000000000000000000000000000-22-22-2200000000000
χ654-4-444-2-42-2-424-200022-20023−2323−2323−2300000000000000000000000000000002-2−1−31+3−1+31−300000000000
χ664-4-444-2-42-2-424-200022-20023−2323−2323−230000000000000000000000000000000-221+3−1−31−3−1+300000000000
χ674-4-444-2-42-2-424-200022-200−2323−2323−232300000000000000000000000000000002-2−1+31−3−1−31+300000000000
χ684-4-444-2-42-2-424-200022-200−2323−2323−23230000000000000000000000000000000-221−3−1+31+3−1−300000000000
χ698-88-88-4-8448-4-8-40004-4400000000000000000000000000000000000000000000000000000000
χ708-88-8-484-8-8-484-40004-4400000000000000000000000000000000000000000000000000000000
χ718-88-8-4-4444-4-442000-22-200006i−6i−6i6i000000000000000000000000000000000000000000000000
χ728-88-8-4-4444-4-442000-22-20000−6i6i6i−6i000000000000000000000000000000000000000000000000
χ738-8-88-484-884-8-4-400044-400000000000000000000000000000000000000000000000000000000
χ748-8-88-4-444-444-42000-2-220043−43−2323−2323000000000000000000000000000000000000000000000000
χ758-8-88-4-444-444-42000-2-2200−434323−2323−23000000000000000000000000000000000000000000000000

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