Finite Group Databasebeta

← Group #13172209

Character table — Group #13172209

Order 1728.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96C97C98C99C100C101C102C103C104C105C106C107C108C109C110C111C112C113C114C115C116C117C118C119C120C121C122C123C124C125C126C127C128C129C130C131C132C133C134C135C136C137C138C139C140C141C142C143C144C145C146C147C148C149C150C151C152C153C154C155C156
size11112222222222224444444444446666668888121212121212121212121212121212121212121212121212181818181818272727273636363636361111222222222222444444444444666666888812121212121212121212121212121212121212121212121218181818181827272727363636363636
order122233366666666633366666666644444436661212121212121212121212121212121212121212121212124444444444121212121212222266666666666666666666666644444466661212121212121212121212121212121212121212121212124444444444121212121212
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111-1-111111111-1-1-1-1111111111111-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-11111111111111111111111111111111111-1-111111111-1-1-1-1111111111111-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-111
χ3111111111111111111111111111111-1-111111111-1-1111111-1-11111-1-1-1-11111-1-111-1-1-1-1-1-111-1-1-1-1111111111111111111111111111111-1-111111111-1-1111111-1-11111-1-1-1-11111-1-111-1-1-1-1-1-111-1-1-1-1
χ4111111111111111111111111111111-1-1-1-1111111-1-1-1-1-1-111-1-11111-1-1-1-1-1-1-1-1-1-1-1-1111111-1-111-1-1111111111111111111111111111111-1-1-1-1111111-1-1-1-1-1-111-1-11111-1-1-1-1-1-1-1-1-1-1-1-1111111-1-111-1-1
χ51111111111111111111111111111-1-111111111-1-1111111-1-111-1-1-1-111111111-1-1-1-111-1-1-1-1-1-111-1-11111111111111111111111111111-1-111111111-1-1111111-1-111-1-1-1-111111111-1-1-1-111-1-1-1-1-1-111-1-1
χ61111111111111111111111111111-1-111-1-11111-1-111-1-1-1-1-1-111-1-1-1-11111-1-1-1-1-1-111-1-1111111-1-1-1-11111111111111111111111111111-1-111-1-11111-1-111-1-1-1-1-1-111-1-1-1-11111-1-1-1-1-1-111-1-1111111-1-1-1-1
χ71111111111111111111111111111-1-1-1-1111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-1-11111-1-1-1-1111111111111111111111111111111-1-1-1-1111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-1-11111-1-1-1-111
χ81111111111111111111111111111-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-1-11111111111111111111111111111111111-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-1-1111111
χ911-1-1111-1-1-1-111-1-111111-1-1-1-1-111-11-11-1i−i11-1-11-11-1ii−i−i1-11-111-1-111-1-1ii−i−i1-1i−ii−iii−i−ii−ii−i1-111-1-1111-1-1-1-111-1-111111-1-1-1-1-111-11-11-1i−i11-1-11-11-1ii−i−i1-11-111-1-111-1-1ii−i−i1-1i−ii−iii−i−ii−ii−i1-1
χ1011-1-1111-1-1-1-111-1-111111-1-1-1-1-111-11-11-1−ii11-1-11-11-1−i−iii1-11-111-1-111-1-1−i−iii1-1−ii−ii−i−iii−ii−ii1-111-1-1111-1-1-1-111-1-111111-1-1-1-1-111-11-11-1−ii11-1-11-11-1−i−iii1-11-111-1-111-1-1−i−iii1-1−ii−ii−i−iii−ii−ii1-1
χ1111-1-1111-1-1-1-111-1-111111-1-1-1-1-111-11-1-11i−i11-1-11-1-11ii−i−i1-1-1111-1-1-1-111ii−i−i-11i−i−ii−i−iiii−i−ii-1111-1-1111-1-1-1-111-1-111111-1-1-1-1-111-11-1-11i−i11-1-11-1-11ii−i−i1-1-1111-1-1-1-111ii−i−i-11i−i−ii−i−iiii−i−ii-11
χ1211-1-1111-1-1-1-111-1-111111-1-1-1-1-111-11-1-11−ii11-1-11-1-11−i−iii1-1-1111-1-1-1-111−i−iii-11−iii−iii−i−i−iii−i-1111-1-1111-1-1-1-111-1-111111-1-1-1-1-111-11-1-11−ii11-1-11-1-11−i−iii1-1-1111-1-1-1-111−i−iii-11−iii−iii−i−i−iii−i-11
χ1311-1-1111-1-1-1-111-1-111111-1-1-1-1-111-1-111-1i−i11-1-1-111-1ii−i−i-111-1-1-11111-1-1ii−i−i-11−iii−i−i−iii−iii−i-1111-1-1111-1-1-1-111-1-111111-1-1-1-1-111-1-111-1i−i11-1-1-111-1ii−i−i-111-1-1-11111-1-1ii−i−i-11−iii−i−i−iii−iii−i-11
χ1411-1-1111-1-1-1-111-1-111111-1-1-1-1-111-1-111-1−ii11-1-1-111-1−i−iii-111-1-1-11111-1-1−i−iii-11i−i−iiii−i−ii−i−ii-1111-1-1111-1-1-1-111-1-111111-1-1-1-1-111-1-111-1−ii11-1-1-111-1−i−iii-111-1-1-11111-1-1−i−iii-11i−i−iiii−i−ii−i−ii-11
χ1511-1-1111-1-1-1-111-1-111111-1-1-1-1-111-1-11-11i−i11-1-1-11-11ii−i−i-11-11-1-111-1-111ii−i−i1-1−ii−iiii−i−i−ii−ii1-111-1-1111-1-1-1-111-1-111111-1-1-1-1-111-1-11-11i−i11-1-1-11-11ii−i−i-11-11-1-111-1-111ii−i−i1-1−ii−iiii−i−i−ii−ii1-1
χ1611-1-1111-1-1-1-111-1-111111-1-1-1-1-111-1-11-11−ii11-1-1-11-11−i−iii-11-11-1-111-1-111−i−iii1-1i−ii−i−i−iiii−ii−i1-111-1-1111-1-1-1-111-1-111111-1-1-1-1-111-1-11-11−ii11-1-1-11-11−i−iii-11-11-1-111-1-111−i−iii1-1i−ii−i−i−iiii−ii−i1-1
χ17222222-1222-12-12-122-1-1-122-1-1-12-1-1002222-1-1-1-100-1-12-12-100220000-1-1-1-1-1-1-1-1000022000000-1-100222222-1222-12-12-122-1-1-122-1-1-12-1-1002222-1-1-1-100-1-12-12-100220000-1-1-1-1-1-1-1-1000022000000-1-100
χ18222222-1222-12-12-122-1-1-122-1-1-12-1-10022-2-2-1-1-1-100-1-1-21-2100220000-1-1-1-111110000-2-20000001100222222-1222-12-12-122-1-1-122-1-1-12-1-10022-2-2-1-1-1-100-1-1-21-2100220000-1-1-1-111110000-2-20000001100
χ19222222-1222-12-12-122-1-1-122-1-1-12-1-100-2-222-1-1-1-100112-12-100-2-200001111-1-1-1-10000-2-20000001100222222-1222-12-12-122-1-1-122-1-1-12-1-100-2-222-1-1-1-100112-12-100-2-200001111-1-1-1-10000-2-20000001100
χ20222222-1222-12-12-122-1-1-122-1-1-12-1-100-2-2-2-2-1-1-1-10011-21-2100-2-2000011111111000022000000-1-100222222-1222-12-12-122-1-1-122-1-1-12-1-100-2-2-2-2-1-1-1-10011-21-2100-2-2000011111111000022000000-1-100
χ2122222-1222-12-12-122-12-1-1-1-122-1-12-1220022-1-1-1-1-1-100-12-122200-1-1-1-10000-1-1-1-10022000000-1-1000022222-1222-12-12-122-12-1-1-1-122-1-12-1220022-1-1-1-1-1-100-12-122200-1-1-1-10000-1-1-1-10022000000-1-10000
χ2222222-1222-12-12-122-12-1-1-1-122-1-12-12200-2-2-1-1-1-1-1-1001-21-22200-1-1-1-10000111100-2-200000011000022222-1222-12-12-122-12-1-1-1-122-1-12-12200-2-2-1-1-1-1-1-1001-21-22200-1-1-1-10000111100-2-2000000110000
χ2322222-1222-12-12-122-12-1-1-1-122-1-12-1-2-20022-1-1-1-11100-12-12-2-20011110000-1-1-1-100-2-200000011000022222-1222-12-12-122-12-1-1-1-122-1-12-1-2-20022-1-1-1-11100-12-12-2-20011110000-1-1-1-100-2-2000000110000
χ2422222-1222-12-12-122-12-1-1-1-122-1-12-1-2-200-2-2-1-1-1-111001-21-2-2-2001111000011110022000000-1-1000022222-1222-12-12-122-12-1-1-1-122-1-12-1-2-200-2-2-1-1-1-111001-21-2-2-2001111000011110022000000-1-10000
χ252222-122-1-1222222-1-1-122-1-1-1-12-1-12222200-1-1-1-122220000-1-1-1-1-1-1-1-1-1-1-1-1000022000000000000-1-12222-122-1-1222222-1-1-122-1-1-1-12-1-12222200-1-1-1-122220000-1-1-1-1-1-1-1-1-1-1-1-1000022000000000000-1-1
χ262222-122-1-1222222-1-1-122-1-1-1-12-1-1222-2-200-1-1-1-122-2-20000-1-111-1-1-1-111110000-2-2000000000000112222-122-1-1222222-1-1-122-1-1-1-12-1-1222-2-200-1-1-1-122-2-20000-1-111-1-1-1-111110000-2-200000000000011
χ272222-122-1-1222222-1-1-122-1-1-1-12-1-12-2-22200-1-1-1-1-2-222000011-1-11111-1-1-1-10000-2-2000000000000112222-122-1-1222222-1-1-122-1-1-1-12-1-12-2-22200-1-1-1-1-2-222000011-1-11111-1-1-1-10000-2-200000000000011
χ282222-122-1-1222222-1-1-122-1-1-1-12-1-12-2-2-2-200-1-1-1-1-2-2-2-20000111111111111000022000000000000-1-12222-122-1-1222222-1-1-122-1-1-1-12-1-12-2-2-2-200-1-1-1-1-2-2-2-20000111111111111000022000000000000-1-1
χ2922-2-222-1-2-2-212-1-2122-1-1-1-2-21112-11002-22i−2i-1-11100-112i−i−2ii002-20000-1-111−i−iii00002i−2i000000−ii0022-2-222-1-2-2-212-1-2122-1-1-1-2-21112-11002-22i−2i-1-11100-112i−i−2ii002-20000-1-111−i−iii00002i−2i000000−ii00
χ3022-2-222-1-2-2-212-1-2122-1-1-1-2-21112-11002-2−2i2i-1-11100-11−2ii2i−i002-20000-1-111ii−i−i0000−2i2i000000i−i0022-2-222-1-2-2-212-1-2122-1-1-1-2-21112-11002-2−2i2i-1-11100-11−2ii2i−i002-20000-1-111ii−i−i0000−2i2i000000i−i00
χ3122-2-222-1-2-2-212-1-2122-1-1-1-2-21112-1100-222i−2i-1-111001-12i−i−2ii00-22000011-1-1−i−iii0000−2i2i000000i−i0022-2-222-1-2-2-212-1-2122-1-1-1-2-21112-1100-222i−2i-1-111001-12i−i−2ii00-22000011-1-1−i−iii0000−2i2i000000i−i00
χ3222-2-222-1-2-2-212-1-2122-1-1-1-2-21112-1100-22−2i2i-1-111001-1−2ii2i−i00-22000011-1-1ii−i−i00002i−2i000000−ii0022-2-222-1-2-2-212-1-2122-1-1-1-2-21112-1100-22−2i2i-1-111001-1−2ii2i−i00-22000011-1-1ii−i−i00002i−2i000000−ii00
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χ3922-2-2-12211-2-222-2-2-1-1-1221111-2-1-1-2-222-200-1-111-222-200001-1-1111-1-1-1-1110000-220000000000001-122-2-2-12211-2-222-2-2-1-1-1221111-2-1-1-2-222-200-1-111-222-200001-1-1111-1-1-1-1110000-220000000000001-1
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χ1202-22-22222-2-2-2-2-222-2222-22-22-2-2-2-220000002-22-2000000000000000000000000000000−2i2i−2i2i000000-22-22-2-2-2-222222-2-22-2-2-22-22-22222-2000000-22-220000000000000000000000000000002i−2i2i−2i000000
χ1212-2-22222-2222-2-2-2-2-2222-2-22-222-2-2-20000002-2-220000000000000000000000000000002-2-22000000-222-2-2-2-22-2-2-222222-2-2-222-22-2-2222000000-222-2000000000000000000000000000000-222-2000000
χ1222-2-22222-2222-2-2-2-2-2222-2-22-222-2-2-20000002-2-22000000000000000000000000000000-222-2000000-222-2-2-2-22-2-2-222222-2-2-222-22-2-2222000000-222-20000000000000000000000000000002-2-22000000
χ12344444-2-244-2-2-2-2-2-24-2-211-2-2-2-21-2-2100004411110000-2-2-2-200000000000011110000000000000000-4-4-4-4-422-4-4222222-422-1-12222-122-10000-4-4-1-1-1-100002222000000000000-1-1-1-10000000000000000
χ12444444-2-244-2-2-2-2-2-24-2-211-2-2-2-21-2-210000-4-4111100002222000000000000-1-1-1-10000000000000000-4-4-4-4-422-4-4222222-422-1-12222-122-1000044-1-1-1-10000-2-2-2-200000000000011110000000000000000
χ1254444-24-2-2-24-24-24-2-2-21-2-2-2-211-2-21-2004400111100-2-2000000-2-20000111100000000000000000000-4-4-4-42-4222-42-42-4222-12222-1-122-1200-4-400-1-1-1-10022000000220000-1-1-1-100000000000000000000
χ1264444-24-2-2-24-24-24-2-2-21-2-2-2-211-2-21-200-4-40011110022000000220000-1-1-1-100000000000000000000-4-4-4-42-4222-42-42-4222-12222-1-122-12004400-1-1-1-100-2-2000000-2-20000111100000000000000000000
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χ1284444-2-24-2-2-24-24-24-21-2-2-211-2-2-21-2-2-4-400001111220000002200-1-1-1-1000000000000000000000000-4-4-4-422-4222-42-42-42-1222-1-1222-122440000-1-1-1-1-2-2000000-2-2001111000000000000000000000000
χ12944-4-44-2-2-4-422-2-2224-2-2112222-1-2-2-100004i−4i11-1-10000−2i−2i2i2i000000000000ii−i−i0000000000000000-4-444-42244-2-222-2-2-422-1-1-2-2-2-212210000−4i4i-1-11100002i2i−2i−2i000000000000−i−iii0000000000000000
χ13044-4-44-2-2-4-422-2-2224-2-2112222-1-2-2-10000−4i4i11-1-100002i2i−2i−2i000000000000−i−iii0000000000000000-4-444-42244-2-222-2-2-422-1-1-2-2-2-2122100004i−4i-1-1110000−2i−2i2i2i000000000000ii−i−i0000000000000000
χ13144-4-4-24-222-424-2-42-2-21-2-222-1-12-212004-40011-1-100-22000000-22000011-1-100000000000000000000-4-4442-42-2-24-2-424-222-122-2-211-22-1-200-4400-1-111002-20000002-20000-1-11100000000000000000000
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χ13344-4-4-2-24222-4-242-4-21-2-2-2-1-12221-224-4000011-1-1-22000000-220011-1-1000000000000000000000000-4-44422-4-2-2-242-4-242-122211-2-2-2-12-2-440000-1-1112-20000002-200-1-111000000000000000000000000
χ13444-4-4-2-24222-4-242-4-21-2-2-2-1-12221-22-44000011-1-12-20000002-200-1-111000000000000000000000000-4-44422-4-2-2-242-4-242-122211-2-2-2-12-24-40000-1-111-22000000-220011-1-1000000000000000000000000
χ1354-44-444-24-4-42-424-2-44-2-224-4-222-42-2000000-22-220000000000000000000000000000000000000000-44-44-4-42-444-24-2-424-422-2-442-2-24-220000002-22-20000000000000000000000000000000000000000
χ1364-44-44-244-42-42-4-24-4-24-22-224-422-4-2000000-22-220000000000000000000000000000000000000000-44-44-42-4-44-24-242-442-42-22-2-44-2-2420000002-22-20000000000000000000000000000000000000000
χ1374-44-44-2-24-42222-2-2-4-2-21-1-22-22-12210000001-11-1000000000000000000003-33-30000000000000000-44-44-422-44-2-2-2-222422-112-22-21-2-2-1000000-11-1100000000000000000000-33-330000000000000000
χ1384-44-44-2-24-42222-2-2-4-2-21-1-22-22-12210000001-11-100000000000000000000-33-330000000000000000-44-44-422-44-2-2-2-222422-112-22-21-2-2-1000000-11-11000000000000000000003-33-30000000000000000
χ1394-44-4-244-22-4-4-4-4442-2-24-4-22-22-4224000000-22-220000000000000000000000000000000000000000-44-442-4-42-24444-4-4-222-442-22-24-2-2-40000002-22-20000000000000000000000000000000000000000
χ1404-44-4-24-2-22-42-424-22-21-22-221-122-1-20000001-11-100000000000000003i−3i3i−3i00000000000000000000-44-442-422-24-24-2-42-22-12-22-2-11-2-212000000-11-110000000000000000−3i3i−3i3i00000000000000000000
χ1414-44-4-24-2-22-42-424-22-21-22-221-122-1-20000001-11-10000000000000000−3i3i−3i3i00000000000000000000-44-442-422-24-24-2-42-22-12-22-2-11-2-212000000-11-1100000000000000003i−3i3i−3i00000000000000000000
χ1424-44-4-2-24-222-42-4-2421-2-221-1-222-12-20000001-11-10000000000003i−3i3i−3i000000000000000000000000-44-4422-42-2-24-242-4-2-122-2-112-2-21-22000000-11-11000000000000−3i3i−3i3i000000000000000000000000
χ1434-44-4-2-24-222-42-4-2421-2-221-1-222-12-20000001-11-1000000000000−3i3i−3i3i000000000000000000000000-44-4422-42-2-24-242-4-2-122-2-112-2-21-22000000-11-110000000000003i−3i3i−3i000000000000000000000000
χ1444-4-4444-2-444-2-42-42-44-2-22-442-2-2-422000000-222-20000000000000000000000000000000000000000-444-4-4-424-4-424-24-24-422-24-4-2224-2-20000002-2-220000000000000000000000000000000000000000
χ1454-4-444-24-44-242-42-4-4-24-222-2-44-22-42000000-222-20000000000000000000000000000000000000000-444-4-42-44-42-4-24-2442-42-2-224-42-24-20000002-2-220000000000000000000000000000000000000000
χ1464-4-444-2-2-44-2-22222-4-2-21-12-22-2122-10000001-1-11000000000000000000003i−3i−3i3i0000000000000000-444-4-4224-422-2-2-2-2422-11-22-22-1-2-21000000-111-100000000000000000000−3i3i3i−3i0000000000000000
χ1474-4-444-2-2-44-2-22222-4-2-21-12-22-2122-10000001-1-1100000000000000000000−3i3i3i−3i0000000000000000-444-4-4224-422-2-2-2-2422-11-22-22-1-2-21000000-111-1000000000000000000003i−3i−3i3i0000000000000000
χ1484-4-44-2442-244-4-4-4-42-2-24-42-22-2422-4000000-222-20000000000000000000000000000000000000000-444-42-4-4-22-4-44444-222-44-22-22-4-2-240000002-2-220000000000000000000000000000000000000000
χ1494-4-44-24-22-24-2-42-422-21-222-2-11-22-120000001-1-1100000000000000003i−3i−3i3i00000000000000000000-444-42-42-22-424-24-2-22-12-2-221-12-21-2000000-111-10000000000000000−3i3i3i−3i00000000000000000000
χ1504-4-44-24-22-24-2-42-422-21-222-2-11-22-120000001-1-110000000000000000−3i3i3i−3i00000000000000000000-444-42-42-22-424-24-2-22-12-2-221-12-21-2000000-111-100000000000000003i−3i−3i3i00000000000000000000
χ1514-4-44-2-242-2-242-42-421-2-22-112-2-2-1220000001-1-110000000000003i−3i−3i3i000000000000000000000000-444-422-4-222-4-24-24-2-122-21-1-2221-2-2000000-111-1000000000000−3i3i3i−3i000000000000000000000000
χ1524-4-44-2-242-2-242-42-421-2-22-112-2-2-1220000001-1-11000000000000−3i3i3i−3i000000000000000000000000-444-422-4-222-4-24-24-2-122-21-1-2221-2-2000000-111-10000000000003i−3i−3i3i000000000000000000000000
χ1538888-4-4-4-4-4-4-4-4-4-4-4-4222222222222000000-1-1-1-10000000000000000000000000000000000000000-8-8-8-8444444444444-2-2-2-2-2-2-2-2-2-2-2-200000011110000000000000000000000000000000000000000
χ15488-8-8-4-4-44444-4-444-42222-2-2-2-2-222-2000000-1-1110000000000000000000000000000000000000000-8-888444-4-4-4-444-4-44-2-2-2-222222-2-2200000011-1-10000000000000000000000000000000000000000
χ1558-88-8-4-4-4-444444-4-44222-22-22-2-2-2-22000000-11-110000000000000000000000000000000000000000-88-884444-4-4-4-4-444-4-2-2-22-22-22222-20000001-11-10000000000000000000000000000000000000000
χ1568-8-88-4-4-44-4-4-444444222-2-22-222-2-2-2000000-111-10000000000000000000000000000000000000000-888-8444-4444-4-4-4-4-4-2-2-222-22-2-22220000001-1-110000000000000000000000000000000000000000

Here i is the imaginary unit (i² = −1).