Finite Group Databasebeta

← Group #11780692

Character table — Group #11780692

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
χ112222222222222-22-2222-2-2-2-2-2-2-2-222002-2-222-2-20000000000000000000000000000000002-200
χ122222222222222-22-2222-2-2-2-2-2-2-2-222002-2-222-2-2000000000000000000000000000000000-2200
χ132222222222222-2-22222-2-2-2-2-2-2-2-2-2-200-222-2-22200000000000000002-20000000002-200000000
χ142222222222222-2-22222-2-2-2-2-2-2-2-2-2-200-222-2-2220000000000000000-22000000000-2200000000
χ1522222-1-1-122-12-1222-1-1-1-1-122-1-1-1-1-1-12222-1-1-1-1-12222-1-1-1-1-1-1-1-1-1-1-1-1220022-1-1-1-10-1-100000000
χ1622222-1-1-122-12-1222-1-1-1-1-122-1-1-1-1-1-12222-1-1-1-1-12222-1-1-1-1-1-1-1-1-1-1-1-1-2-200-2-2111101100000000
χ1722222-1-1-122-12-1222-1-1-1-1-122-1-1-1-1-1-1-2-222-1-1-1-1-1-2-2-2-21111111111112200-2-211110-1-100000000
χ1822222-1-1-122-12-1222-1-1-1-1-122-1-1-1-1-1-1-2-222-1-1-1-1-1-2-2-2-2111111111111-2-20022-1-1-1-101100000000
χ1922222-1-1-122-12-1-2-22-1-1-111-2-211111100-22-111-1-10000333333−3−3−3−3−3−32-2000033−3−30-1100000000
χ2022222-1-1-122-12-1-2-22-1-1-111-2-211111100-22-111-1-10000333333−3−3−3−3−3−3-220000−3−33301-100000000
χ2122222-1-1-122-12-1-2-22-1-1-111-2-211111100-22-111-1-10000−3−3−3−3−3−33333332-20000−3−3330-1100000000
χ2222222-1-1-122-12-1-2-22-1-1-111-2-211111100-22-111-1-10000−3−3−3−3−3−3333333-22000033−3−301-100000000
χ232222-1222-1-12-1-1222-1-1-122-1-1-1-1-1-12222-1-12-1-1-1-1-1-1-1-122-1-1-1-122-1-1-1-10022000000200-1-1-1-10000
χ242222-1222-1-12-1-1222-1-1-122-1-1-1-1-1-12222-1-12-1-1-1-1-1-1-1-122-1-1-1-122-1-1-1-100-2-2000000-20011110000
χ252222-1222-1-12-1-1222-1-1-122-1-1-1-1-1-122-2-2-1-12-1-1-1-11111-2-21111-2-211110022000000-200-1-1110000
χ262222-1222-1-12-1-1222-1-1-122-1-1-1-1-1-122-2-2-1-12-1-1-1-11111-2-21111-2-2111100-2-200000020011-1-10000
χ272222-1222-1-12-1-12-2-2-1-1-122-1-1-1-1-1-1-2-20011-21111−i3−i3i3i300−i3−i3i3i300−i3−i3i3i3002-2000000000-11−i3i30000
χ282222-1222-1-12-1-12-2-2-1-1-122-1-1-1-1-1-1-2-20011-21111−i3−i3i3i300−i3−i3i3i300−i3−i3i3i300-220000000001-1i3−i30000
χ292222-1222-1-12-1-12-2-2-1-1-122-1-1-1-1-1-1-2-20011-21111i3i3−i3−i300i3i3−i3−i300i3i3−i3−i3002-2000000000-11i3−i30000
χ302222-1222-1-12-1-12-2-2-1-1-122-1-1-1-1-1-1-2-20011-21111i3i3−i3−i300i3i3−i3−i300i3i3−i3−i300-220000000001-1−i3i30000
χ3144444-2-2-244-24-24-4-4-2-2-2-2-244-2-2-2-22200-4-4222220000000000000000000000000000000000000
χ3244444-2-2-244-24-2-44-4-2-2-222-4-42222-2-2004-42-2-2220000000000000000000000000000000000000
χ334444-2444-2-24-2-2-44-4-2-2-2-4-42222224400-22-4-2-2220000000000000000000000000000000000000
χ344444-2444-2-24-2-2-4-44-2-2-2-4-4222222-4-4002-2422-2-20000000000000000000000000000000000000
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
χ394444-2-2-2-2-2-2-2-21-44-41112222-1-1-1-1-2-200-22211-1-10000003i3i−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
χ414444-2-2-2-2-2-2-2-21-4-441112222-1-1-1-122002-2-2-1-11100002323−3−3−3−3−23−233333000000000000000000000
χ424444-2-2-2-2-2-2-2-21-4-441112222-1-1-1-122002-2-2-1-1110000−23−2333332323−3−3−3−3000000000000000000000
χ4344-4-4444-4-4-4-4440004-4-400000000002i−2i00000002i−2i2i−2i2i−2i2i−2i2i−2i2i−2i2i−2i2i−2i000000000000000000000
χ4444-4-4444-4-4-4-4440004-4-40000000000−2i2i0000000−2i2i−2i2i−2i2i−2i2i−2i2i−2i2i−2i2i−2i2i000000000000000000000
χ4544-4-44-2-22-4-424-2000-2220000000023−232i−2i00023−23002i−2i2i−2i−ζ2+ζ7+ζ10+ζ11ζ2−ζ7−ζ10−ζ11−ζ2+ζ7+ζ10+ζ11ζ2−ζ7−ζ10−ζ11−ζ2+ζ7+ζ10+ζ11ζ2−ζ7−ζ10−ζ11ζ2+ζ7−ζ10+ζ11−ζ2−ζ7+ζ10−ζ11ζ2+ζ7−ζ10+ζ11−ζ2−ζ7+ζ10−ζ11ζ2+ζ7−ζ10+ζ11−ζ2−ζ7+ζ10−ζ11000000000000000000000
χ4644-4-44-2-22-4-424-2000-2220000000023−23−2i2i00023−2300−2i2i−2i2iζ2−ζ7−ζ10−ζ11−ζ2+ζ7+ζ10+ζ11ζ2−ζ7−ζ10−ζ11−ζ2+ζ7+ζ10+ζ11ζ2−ζ7−ζ10−ζ11−ζ2+ζ7+ζ10+ζ11−ζ2−ζ7+ζ10−ζ11ζ2+ζ7−ζ10+ζ11−ζ2−ζ7+ζ10−ζ11ζ2+ζ7−ζ10+ζ11−ζ2−ζ7+ζ10−ζ11ζ2+ζ7−ζ10+ζ11000000000000000000000
χ4744-4-44-2-22-4-424-2000-22200000000−23232i−2i000−2323002i−2i2i−2iζ2+ζ7−ζ10+ζ11−ζ2−ζ7+ζ10−ζ11ζ2+ζ7−ζ10+ζ11−ζ2−ζ7+ζ10−ζ11ζ2+ζ7−ζ10+ζ11−ζ2−ζ7+ζ10−ζ11−ζ2+ζ7+ζ10+ζ11ζ2−ζ7−ζ10−ζ11−ζ2+ζ7+ζ10+ζ11ζ2−ζ7−ζ10−ζ11−ζ2+ζ7+ζ10+ζ11ζ2−ζ7−ζ10−ζ11000000000000000000000
χ4844-4-44-2-22-4-424-2000-22200000000−2323−2i2i000−232300−2i2i−2i2i−ζ2−ζ7+ζ10−ζ11ζ2+ζ7−ζ10+ζ11−ζ2−ζ7+ζ10−ζ11ζ2+ζ7−ζ10+ζ11−ζ2−ζ7+ζ10−ζ11ζ2+ζ7−ζ10+ζ11ζ2−ζ7−ζ10−ζ11−ζ2+ζ7+ζ10+ζ11ζ2−ζ7−ζ10−ζ11−ζ2+ζ7+ζ10+ζ11ζ2−ζ7−ζ10−ζ11−ζ2+ζ7+ζ10+ζ11000000000000000000000
χ4944-4-4-244-422-4-2-2000-22200−2i32i3−2i3−2i32i32i3002i−2i00000002ζ7−2ζ72ζ11−2ζ112i−2i2ζ7−2ζ72ζ11−2ζ112i−2i2ζ7−2ζ72ζ11−2ζ11000000000000000000000
χ5044-4-4-244-422-4-2-2000-22200−2i32i3−2i3−2i32i32i300−2i2i0000000−2ζ72ζ7−2ζ112ζ11−2i2i−2ζ72ζ7−2ζ112ζ11−2i2i−2ζ72ζ7−2ζ112ζ11000000000000000000000
χ5144-4-4-244-422-4-2-2000-222002i3−2i32i32i3−2i3−2i3002i−2i00000002ζ11−2ζ112ζ7−2ζ72i−2i2ζ11−2ζ112ζ7−2ζ72i−2i2ζ11−2ζ112ζ7−2ζ7000000000000000000000
χ5244-4-4-244-422-4-2-2000-222002i3−2i32i32i3−2i3−2i300−2i2i0000000−2ζ112ζ11−2ζ72ζ7−2i2i−2ζ112ζ11−2ζ72ζ7−2i2i−2ζ112ζ11−2ζ72ζ7000000000000000000000
χ5344-4-4-2-2-22222-210001-1-100−2i32i3i3i3−i3−i323−232i−2i000−333i−3i2ζ7−2ζ72ζ11−2ζ11−ζ2+ζ7+ζ10+ζ11ζ2−ζ7−ζ10−ζ11−ζ2−ζ7−2ζ10ζ2+ζ7+2ζ102ζ2+ζ10−ζ11−2ζ2−ζ10+ζ11ζ2+ζ7−ζ10+ζ11−ζ2−ζ7+ζ10−ζ11ζ2−ζ7+2ζ10−ζ2+ζ7−2ζ10−2ζ2−ζ10−ζ112ζ2+ζ10+ζ11000000000000000000000
χ5444-4-4-2-2-22222-210001-1-100−2i32i3i3i3−i3−i323−23−2i2i000−333i−3i−2ζ72ζ7−2ζ112ζ11ζ2−ζ7−ζ10−ζ11−ζ2+ζ7+ζ10+ζ11ζ2+ζ7+2ζ10−ζ2−ζ7−2ζ10−2ζ2−ζ10+ζ112ζ2+ζ10−ζ11−ζ2−ζ7+ζ10−ζ11ζ2+ζ7−ζ10+ζ11−ζ2+ζ7−2ζ10ζ2−ζ7+2ζ102ζ2+ζ10+ζ11−2ζ2−ζ10−ζ11000000000000000000000
χ5544-4-4-2-2-22222-210001-1-100−2i32i3i3i3−i3−i3−23232i−2i0003−3−3i3i2ζ7−2ζ72ζ11−2ζ11ζ2+ζ7−ζ10+ζ11−ζ2−ζ7+ζ10−ζ11ζ2−ζ7+2ζ10−ζ2+ζ7−2ζ10−2ζ2−ζ10−ζ112ζ2+ζ10+ζ11−ζ2+ζ7+ζ10+ζ11ζ2−ζ7−ζ10−ζ11−ζ2−ζ7−2ζ10ζ2+ζ7+2ζ102ζ2+ζ10−ζ11−2ζ2−ζ10+ζ11000000000000000000000
χ5644-4-4-2-2-22222-210001-1-100−2i32i3i3i3−i3−i3−2323−2i2i0003−3−3i3i−2ζ72ζ7−2ζ112ζ11−ζ2−ζ7+ζ10−ζ11ζ2+ζ7−ζ10+ζ11−ζ2+ζ7−2ζ10ζ2−ζ7+2ζ102ζ2+ζ10+ζ11−2ζ2−ζ10−ζ11ζ2−ζ7−ζ10−ζ11−ζ2+ζ7+ζ10+ζ11ζ2+ζ7+2ζ10−ζ2−ζ7−2ζ10−2ζ2−ζ10+ζ112ζ2+ζ10−ζ11000000000000000000000
χ5744-4-4-2-2-22222-210001-1-1002i3−2i3−i3−i3i3i323−232i−2i000−33−3i3i2ζ11−2ζ112ζ7−2ζ7−ζ2+ζ7+ζ10+ζ11ζ2−ζ7−ζ10−ζ112ζ2+ζ10−ζ11−2ζ2−ζ10+ζ11−ζ2−ζ7−2ζ10ζ2+ζ7+2ζ10ζ2+ζ7−ζ10+ζ11−ζ2−ζ7+ζ10−ζ11−2ζ2−ζ10−ζ112ζ2+ζ10+ζ11ζ2−ζ7+2ζ10−ζ2+ζ7−2ζ10000000000000000000000
χ5844-4-4-2-2-22222-210001-1-1002i3−2i3−i3−i3i3i323−23−2i2i000−33−3i3i−2ζ112ζ11−2ζ72ζ7ζ2−ζ7−ζ10−ζ11−ζ2+ζ7+ζ10+ζ11−2ζ2−ζ10+ζ112ζ2+ζ10−ζ11ζ2+ζ7+2ζ10−ζ2−ζ7−2ζ10−ζ2−ζ7+ζ10−ζ11ζ2+ζ7−ζ10+ζ112ζ2+ζ10+ζ11−2ζ2−ζ10−ζ11−ζ2+ζ7−2ζ10ζ2−ζ7+2ζ10000000000000000000000
χ5944-4-4-2-2-22222-210001-1-1002i3−2i3−i3−i3i3i3−23232i−2i0003−33i−3i2ζ11−2ζ112ζ7−2ζ7ζ2+ζ7−ζ10+ζ11−ζ2−ζ7+ζ10−ζ11−2ζ2−ζ10−ζ112ζ2+ζ10+ζ11ζ2−ζ7+2ζ10−ζ2+ζ7−2ζ10−ζ2+ζ7+ζ10+ζ11ζ2−ζ7−ζ10−ζ112ζ2+ζ10−ζ11−2ζ2−ζ10+ζ11−ζ2−ζ7−2ζ10ζ2+ζ7+2ζ10000000000000000000000
χ6044-4-4-2-2-22222-210001-1-1002i3−2i3−i3−i3i3i3−2323−2i2i0003−33i−3i−2ζ112ζ11−2ζ72ζ7−ζ2−ζ7+ζ10−ζ11ζ2+ζ7−ζ10+ζ112ζ2+ζ10+ζ11−2ζ2−ζ10−ζ11−ζ2+ζ7−2ζ10ζ2−ζ7+2ζ10ζ2−ζ7−ζ10−ζ11−ζ2+ζ7+ζ10+ζ11−2ζ2−ζ10+ζ112ζ2+ζ10−ζ11ζ2+ζ7+2ζ10−ζ2−ζ7−2ζ10000000000000000000000
χ614-44-444-4-44-44-44000-44-40000000000000000000000000000000000000000000000000000002i−2i
χ624-44-444-4-44-44-44000-44-4000000000000000000000000000000000000000000000000000000−2i2i
χ634-4-4444-44-44-4-44000-4-440000000000000000000000000000000000000002i−2i2i−2i2i−2i00000000000
χ644-4-4444-44-44-4-44000-4-44000000000000000000000000000000000000000−2i2i−2i2i−2i2i00000000000
χ654-4-444-22-2-442-4-200022-223−230023−2323−2300000000000000000000000000000002i−2iζ2+ζ7−ζ10+ζ11−ζ2−ζ7+ζ10−ζ11−ζ2+ζ7+ζ10+ζ11ζ2−ζ7−ζ10−ζ1100000000000
χ664-4-444-22-2-442-4-200022-223−230023−2323−230000000000000000000000000000000−2i2i−ζ2−ζ7+ζ10−ζ11ζ2+ζ7−ζ10+ζ11ζ2−ζ7−ζ10−ζ11−ζ2+ζ7+ζ10+ζ1100000000000
χ674-4-444-22-2-442-4-200022-2−232300−2323−232300000000000000000000000000000002i−2i−ζ2+ζ7+ζ10+ζ11ζ2−ζ7−ζ10−ζ11ζ2+ζ7−ζ10+ζ11−ζ2−ζ7+ζ10−ζ1100000000000
χ684-4-444-22-2-442-4-200022-2−232300−2323−23230000000000000000000000000000000−2i2iζ2−ζ7−ζ10−ζ11−ζ2+ζ7+ζ10+ζ11−ζ2−ζ7+ζ10−ζ11ζ2+ζ7−ζ10+ζ1100000000000
χ698-88-88-4448-8-4-8-40004-4400000000000000000000000000000000000000000000000000000000
χ708-88-8-48-8-8-4484-40004-4400000000000000000000000000000000000000000000000000000000
χ718-88-8-4-444-44-442000-22-200006i−6i−6i6i000000000000000000000000000000000000000000000000
χ728-88-8-4-444-44-442000-22-20000−6i6i6i−6i000000000000000000000000000000000000000000000000
χ738-8-88-48-884-4-84-400044-400000000000000000000000000000000000000000000000000000000
χ748-8-88-4-44-44-4442000-2-2243−4300−2323−2323000000000000000000000000000000000000000000000000
χ758-8-88-4-44-44-4442000-2-22−43430023−2323−23000000000000000000000000000000000000000000000000

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