Finite Group Databasebeta

← Group #13155430

Character table — Group #13155430

Order 1728.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96C97C98C99C100C101C102C103C104C105C106C107C108C109C110C111C112C113C114C115C116C117C118C119C120C121C122C123C124C125C126
size1111222222222222222222444444444444444444444444666666668888888888121212121212121212121212121212121212121212121212121212121212121212121212121224242424242436363636363636363636363636367272108108
order124423334666661212121212121212333666666666121212121212121212121212224466121236666121212121224446666666661212121212121212121212121212121212121212121212121266612121224446688121212121212242488
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111111111111111111111111111111111111-1-111111111111-1-1-1-1111-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-111-1-1-1-1-1-111-1-1-1-1
χ31111111111111111111111111111111111111111111111111111111111111111-1-111111-1-111111111111-1-11111111111111111-1-1-1-1-1-1-1-111-1-1-1-11111-1-1-1-1-1-1
χ41111111111111111111111111111111111111111111111111111111111111111-1-1-1-1111-1-1111111-1-1-1-11-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-11111
χ51111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-111111111111111-1-1-111-1-1-1-1-1-11111-111111111111111-1-1-1-1111111-1-1-1-1-1-111-1-1-1-1-1-111-1-1
χ61111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1111111111111-1-1-1-1-111-1-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111-1-111-1-1-1-11111-1-1-1-111
χ71111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-11111111111-1-111-1-1-1-1-1-1-1-1-1-1-11111-1-1-1111111111111-1-1-1-1-1-1-1-1-1-111-1-111-1-1-1-1-1-111-1-111
χ81111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111111111-1-1
χ911-1-1-1111111-1-1111-1-1-1-1-1-1111-1-1-11-1-1-1111111-1-111-1-1-1-11-11-111-1-11-1-1-11111-1-11-1i−i1-1-11111-1-11-1ii−i−i1-1-1iiiiii−i−i−i−i−i−i11-1-1111-1-1-11-1i−i11i−iii−i−i-1-1i−ii−i
χ1011-1-1-1111111-1-1111-1-1-1-1-1-1111-1-1-11-1-1-1111111-1-111-1-1-1-11-11-111-1-11-1-1-11111-1-11-1−ii1-1-11111-1-11-1−i−iii1-1-1−i−i−i−i−i−iiiiiii11-1-1111-1-1-11-1−ii11−ii−i−iii-1-1−ii−ii
χ1111-1-1-1111111-1-1111-1-1-1-1-1-1111-1-1-11-1-1-1111111-1-111-1-1-1-11-11-111-1-11-1-1-11111-1-1-11i−i1-1-1-1-111-1-11-1ii−i−i111iiiiii−i−i−i−i−i−i11-1-1-1-1-1111-11i−i-1-1−iiii−i−i11−ii−ii
χ1211-1-1-1111111-1-1111-1-1-1-1-1-1111-1-1-11-1-1-1111111-1-111-1-1-1-11-11-111-1-11-1-1-11111-1-1-11−ii1-1-1-1-111-1-11-1−i−iii111−i−i−i−i−i−iiiiiii11-1-1-1-1-1111-11−ii-1-1i−i−i−iii11i−ii−i
χ1311-1-1-1111111-1-1111-1-1-1-1-1-1111-1-1-11-1-1-1111111-1-111-1-1-1-1-11-11-1-1111-1-1-11111-1-11-1i−i-11111-1-111-11ii−i−i-1-1-1iiiiii−i−i−i−i−i−i-1-111111-1-1-1-11−ii-1-1i−i−i−iii11i−i−ii
χ1411-1-1-1111111-1-1111-1-1-1-1-1-1111-1-1-11-1-1-1111111-1-111-1-1-1-1-11-11-1-1111-1-1-11111-1-11-1−ii-11111-1-111-11−i−iii-1-1-1−i−i−i−i−i−iiiiiii-1-111111-1-1-1-11i−i-1-1−iiii−i−i11−iii−i
χ1511-1-1-1111111-1-1111-1-1-1-1-1-1111-1-1-11-1-1-1111111-1-111-1-1-1-1-11-11-1-1111-1-1-11111-1-1-11i−i-111-1-1-1-111-11ii−i−i-111iiiiii−i−i−i−i−i−i-1-111-1-1-11111-1−ii11−ii−i−iii-1-1−iii−i
χ1611-1-1-1111111-1-1111-1-1-1-1-1-1111-1-1-11-1-1-1111111-1-111-1-1-1-1-11-11-1-1111-1-1-11111-1-1-11−ii-111-1-1-1-111-11−i−iii-111−i−i−i−i−i−iiiiiii-1-111-1-1-11111-1i−i11i−iii−i−i-1-1i−i−ii
χ172222222-122222-12222-1-1222-1-1-1-1-12222-1-12-12222-1-1-1-1-1-12222-1-1-1-1-1-1-1-1-1-1-1-1-1-1220022-1-1-1-1-1-1-1220000-1-1-1000000000000-1-1-1-12-1-12-1-12200-1-1000000-1-10000
χ182222222-122222-12222-1-1222-1-1-1-1-12222-1-12-12222-1-1-1-1-1-12222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-2-20022-111-1-1-1-1220000-111000000000000-1-1-1-1-211-211-2-20011000000110000
χ192222222-122222-12222-1-1222-1-1-1-1-12222-1-12-12222-1-1-1-1-1-1-2-2-2-21111-1-1-1-1-1-1-1-1-1-12200-2-21-1-11111-2-200001-1-100000000000011112-1-12-1-1-2-20011000000110000
χ202222222-122222-12222-1-1222-1-1-1-1-12222-1-12-12222-1-1-1-1-1-1-2-2-2-21111-1-1-1-1-1-1-1-1-1-1-2-200-2-21111111-2-200001110000000000001111-211-2112200-1-1000000-1-10000
χ21222222-1222-1222222222-1-1-12-1222-1-1-1-12-1-12-1-1-1-12222-1-100000000-1-1-1-1-1-1-1-1-1-12222000220000002222022-1-1-1-1-1-1-1-1-1-1-1-10000-1-1-1-1-1-100000022000000-1-100
χ22222222-1222-1222222222-1-1-12-1222-1-1-1-12-1-12-1-1-1-12222-1-100000000-1-1-1-1-1-1-1-1-1-122-2-200022000000-2-2-2-20221111111111110000-1-1-1-1-1-1000000-2-20000001100
χ23222222-1222-1222222222-1-1-12-1222-1-1-1-12-1-12-1-1-1-12222-1-100000000-1-1-1-1-1-1-1-1-1-1-2-222000-2-200000022220-2-2-1-1-1-1-1-1-1-1-1-1-1-10000111111000000-2-20000001100
χ24222222-1222-1222222222-1-1-12-1222-1-1-1-12-1-12-1-1-1-12222-1-100000000-1-1-1-1-1-1-1-1-1-1-2-2-2-2000-2-2000000-2-2-2-20-2-2111111111111000011111100000022000000-1-100
χ2522222-1222-12-1-12-1-1-1-12222-1-122-1-1-12-1-1-1222-1-1-1-1-1-1-1-12222222222-12-1-1-12-1-1-1-10022-1-1200-1-1-1-1-1-1-1-1-1-120022-1-1-1-122-1-1-1-1-1-1-1-100000000220000-1-1-1-1000000
χ2622222-1222-12-1-12-1-1-1-12222-1-122-1-1-12-1-1-1222-1-1-1-1-1-1-1-12222222222-12-1-1-12-1-1-1-100-2-2-1-1200-1-1-1-1-1-11111200-2-21111-2-21111-1-1-1-100000000-2-200001111000000
χ2722222-1222-12-1-12-1-1-1-12222-1-122-1-1-12-1-1-1222-1-1-1-1-1-1-1-122-2-2-2-2-2-2-2-2-12-1-1-12-1-1-1-1002211-200111111-1-1-1-1-20022-1-1-1-122-1-1-1-1111100000000-2-200001111000000
χ2822222-1222-12-1-12-1-1-1-12222-1-122-1-1-12-1-1-1222-1-1-1-1-1-1-1-122-2-2-2-2-2-2-2-2-12-1-1-12-1-1-1-100-2-211-2001111111111-200-2-21111-2-21111111100000000220000-1-1-1-1000000
χ292222-2222-222-2-22-2-2222222222-2-2-22-2-2-222-2-2-2-222-2-222222-2-2222222-2-2-22-2-2-22200002-2-20022-2-2-220000-200000000000000-2-222000000000000000000000000
χ302222-2222-222-2-22-2-2222222222-2-2-22-2-2-222-2-2-2-222-2-22222-222-2-2-2-2-22-2-2-22-2-2-2220000-22200-2-2222-2000020000000000000022-2-2000000000000000000000000
χ312222-222-1-222-2-2-1-2-222-1-1222-1-11112-2-2-2-1-1-21-2-22211-1-1-1-12-2-22-1-1-1-1-1111-1111-1-100002-21−i3i3-1-111-2200001−i3i300000000000011-1-10−i3i30−i3i30000−i3i3000000−i3i30000
χ322222-222-1-222-2-2-1-2-222-1-1222-1-11112-2-2-2-1-1-21-2-22211-1-1-1-12-2-22-1-1-1-1-1111-1111-1-100002-21i3−i3-1-111-2200001i3−i300000000000011-1-10i3−i30i3−i30000i3−i3000000i3−i30000
χ332222-222-1-222-2-2-1-2-222-1-1222-1-11112-2-2-2-1-1-21-2-22211-1-1-1-1-222-21111-1111-1111-1-10000-22-1−i3i311-1-12-20000-1−i3i3000000000000-1-1110−i3i30−i3i30000i3−i3000000i3−i30000
χ342222-222-1-222-2-2-1-2-222-1-1222-1-11112-2-2-2-1-1-21-2-22211-1-1-1-1-222-21111-1111-1111-1-10000-22-1i3−i311-1-12-20000-1i3−i3000000000000-1-1110i3−i30i3−i30000−i3i3000000−i3i30000
χ352222-2-122-2-1211211-1-12222-1-12-211-1-211-12-2-211-1-111-1-1222-2-222222-1-211-1-211-1-10000-11-200-1-1111-13−33−3-2000033−3−30033−3−311-1-1000000000000003−33−3000000
χ362222-2-122-2-1211211-1-12222-1-12-211-1-211-12-2-211-1-111-1-1222-2-222222-1-211-1-211-1-10000-11-200-1-1111-1−33−33-20000−3−33300−3−33311-1-100000000000000−33−33000000
χ372222-2-122-2-1211211-1-12222-1-12-211-1-211-12-2-211-1-111-1-122-222-2-2-2-2-2-1-211-1-211-1-100001-120011-1-1-113−33−32000033−3−30033−3−3-1-11100000000000000−33−33000000
χ382222-2-122-2-1211211-1-12222-1-12-211-1-211-12-2-211-1-111-1-122-222-2-2-2-2-2-1-211-1-211-1-100001-120011-1-1-11−33−3320000−3−33300−3−333-1-111000000000000003−33−3000000
χ3922-2-22222-222222-2-2-2-2-2-2-2-2222222222222-2-2-2-2-2-2-2-2-2-2-2-222-2-222-2-222222-2-2-2-2-20000222002222-2-20000-200000000000000-2-2-2-2000000000000000000000000
χ4022-2-22222-222222-2-2-2-2-2-2-2-2222222222222-2-2-2-2-2-2-2-2-2-2-2-2-2-222-2-22222222-2-2-2-2-20000-2-2-200-2-2-2-22200002000000000000002222000000000000000000000000
χ4122-2-2222-1-22222-1-2-2-2-211-2-22-1-1-1-1-12222-1-1-21-2-2-2-211111122-2-2-1-111-1-1-1-1-111111000022-1−i3i3-1-1-1-1-2-200001i3−i300000000000011110−i3i30i3−i30000−i3i3000000i3−i30000
χ4222-2-2222-1-22222-1-2-2-2-211-2-22-1-1-1-1-12222-1-1-21-2-2-2-211111122-2-2-1-111-1-1-1-1-111111000022-1i3−i3-1-1-1-1-2-200001−i3i300000000000011110i3−i30−i3i30000i3−i3000000−i3i30000
χ4322-2-2222-1-22222-1-2-2-2-211-2-22-1-1-1-1-12222-1-1-21-2-2-2-2111111-2-22211-1-1-1-1-1-1-1111110000-2-21−i3i31111220000-1i3−i3000000000000-1-1-1-10−i3i30i3−i30000i3−i3000000−i3i30000
χ4422-2-2222-1-22222-1-2-2-2-211-2-22-1-1-1-1-12222-1-1-21-2-2-2-2111111-2-22211-1-1-1-1-1-1-1111110000-2-21i3−i31111220000-1−i3i3000000000000-1-1-1-10i3−i30−i3i30000−i3i3000000i3−i30000
χ4522-2-22-122-2-12-1-121111-2-2-2-2-1-122-1-1-12-1-1-12-2-211111111-2-222-2-222-2-2-12-1-1-1-211110000-1-1200-1-1-1-111−i3i3i3−i3-20000−i3−i3i3i300i3i3−i3−i3111100000000000000−i3i3i3−i3000000
χ4622-2-22-122-2-12-1-121111-2-2-2-2-1-122-1-1-12-1-1-12-2-211111111-2-222-2-222-2-2-12-1-1-1-211110000-1-1200-1-1-1-111i3−i3−i3i3-20000i3i3−i3−i300−i3−i3i3i3111100000000000000i3−i3−i3i3000000
χ4722-2-22-122-2-12-1-121111-2-2-2-2-1-122-1-1-12-1-1-12-2-211111111-2-2-2-222-2-222-12-1-1-1-21111000011-2001111-1-1−i3i3i3−i320000−i3−i3i3i300i3i3−i3−i3-1-1-1-100000000000000i3−i3−i3i3000000
χ4822-2-22-122-2-12-1-121111-2-2-2-2-1-122-1-1-12-1-1-12-2-211111111-2-2-2-222-2-222-12-1-1-1-21111000011-2001111-1-1i3−i3−i3i320000i3i3−i3−i300−i3−i3i3i3-1-1-1-100000000000000−i3i3i3−i3000000
χ4922-2-2-222-1222-2-2-122-2-211-2-22-1-11112-2-2-2-1-12-122-2-2-1-111112-22-2-1-111-1111-1-1-1-1112-2002-21-1-1-1-1112-20000-111000000000000-1-1112-1-1-2112-200-1-1000000110000
χ5022-2-2-222-1222-2-2-122-2-211-2-22-1-11112-2-2-2-1-12-122-2-2-1-111112-22-2-1-111-1111-1-1-1-111-22002-2111-1-1112-20000-1-1-1000000000000-1-111-2112-1-1-220011000000-1-10000
χ5122-2-2-222-1222-2-2-122-2-211-2-22-1-11112-2-2-2-1-12-122-2-2-1-11111-22-2211-1-1-1111-1-1-1-1112-200-22-1-1-111-1-1-22000011100000000000011-1-12-1-1-211-220011000000-1-10000
χ5222-2-2-222-1222-2-2-122-2-211-2-22-1-11112-2-2-2-1-12-122-2-2-1-11111-22-2211-1-1-1111-1-1-1-111-2200-22-11111-1-1-2200001-1-100000000000011-1-1-2112-1-12-200-1-1000000110000
χ5322-2-2-22-1222-1-2-2222-2-2-2-211-12-1-2-2-2-11112-1-12-1-11122-2-21100000000-1111-1-1-1-1112-22i−2i000220000002i2i−2i−2i0-2-2−i−i−i−i−i−iiiiiii0000-1-1-11110000002i−2i000000−ii00
χ5422-2-2-22-1222-1-2-2222-2-2-2-211-12-1-2-2-2-11112-1-12-1-11122-2-21100000000-1111-1-1-1-1112-2−2i2i00022000000−2i−2i2i2i0-2-2iiiiii−i−i−i−i−i−i0000-1-1-1111000000−2i2i000000i−i00
χ5522-2-2-22-1222-1-2-2222-2-2-2-211-12-1-2-2-2-11112-1-12-1-11122-2-21100000000-1111-1-1-1-111-222i−2i000-2-20000002i2i−2i−2i022−i−i−i−i−i−iiiiiii0000111-1-1-1000000−2i2i000000i−i00
χ5622-2-2-22-1222-1-2-2222-2-2-2-211-12-1-2-2-2-11112-1-12-1-11122-2-21100000000-1111-1-1-1-111-22−2i2i000-2-2000000−2i−2i2i2i022iiiiii−i−i−i−i−i−i0000111-1-1-10000002i−2i000000−ii00
χ5722-2-2-2-1222-12112-1-111-2-2-2-2-1-12-211-1-211-1222-1-111-1-111-2-22-22-222-2-2-1-211-12-1-111002i−2i-11-200-1-111-11−i−iii2002i2i−i−i−i−i−2i−2iiiii-1-111000000002i−2i0000−i−iii000000
χ5822-2-2-2-1222-12112-1-111-2-2-2-2-1-12-211-1-211-1222-1-111-1-111-2-22-22-222-2-2-1-211-12-1-11100−2i2i-11-200-1-111-11ii−i−i200−2i−2iiiii2i2i−i−i−i−i-1-11100000000−2i2i0000ii−i−i000000
χ5922-2-2-2-1222-12112-1-111-2-2-2-2-1-12-211-1-211-1222-1-111-1-111-2-2-22-22-2-222-1-211-12-1-111002i−2i1-120011-1-11-1−i−iii-2002i2i−i−i−i−i−2i−2iiiii11-1-100000000−2i2i0000ii−i−i000000
χ6022-2-2-2-1222-12112-1-111-2-2-2-2-1-12-211-1-211-1222-1-111-1-111-2-2-22-22-2-222-1-211-12-1-11100−2i2i1-120011-1-11-1ii−i−i-200−2i−2iiiii2i2i−i−i−i−i11-1-1000000002i−2i0000−i−iii000000
χ61444444-2-244-244-24444-2-2-2-2-2-21-2-2-2-2-2-2-2-21-2-2-2-2-2-2-2-2-2-2110000000011111111114400000-2-200000000000-2-20000000000000000-211-211000000000000000000
χ62444444-2-244-244-24444-2-2-2-2-2-21-2-2-2-2-2-2-2-21-2-2-2-2-2-2-2-2-2-211000000001111111111-4-40000022000000000002200000000000000002-1-12-1-1000000000000000000
χ6344444-24-24-24-2-2-2-2-2-2-2-2-244-21-2-211-24-2-21-24-2-2-2-2-21111-2-24444-2-2-2-21-2111-211110000-2-2-2001111-2-20000-2000000000000001111000000000000000000000000
χ6444444-24-24-24-2-2-2-2-2-2-2-2-244-21-2-211-24-2-21-24-2-2-2-2-21111-2-2-4-4-4-422221-2111-21111000022200-1-1-1-1220000200000000000000-1-1-1-1000000000000000000000000
χ6544444-2-244-2-2-2-24-2-2-2-244-2-21-2-24-2-21-211-2-2-241111-2-2-2-2-2-2000000001-2111-21111004400000000000-2-2-2-2000-2-21111-2-211110000000000000000000000000000
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Here ζ is a primitive root of unity of order 12 (ζ12 = 1); i = ζ3.