Finite Group Databasebeta

← Group #13155608

Character table — Group #13155608

Order 1728.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96C97C98C99C100C101C102C103C104C105C106C107C108C109C110C111C112C113C114
size11112222222222222244444444444444444488888888888888999912121212121212121212121212121818181818181818181818181818242424242424242424242424242424242424242436363636363636363636108108
order1222333446666666663336666666661212121212123666121212121212121212124444222244666612121212448888888812121212666666666666661212121212121212242424242424242444
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111111111111111111111-1-1111111111111-1-1-1-1-1-1-1-11111-1-111-1-11111-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1
χ3111111111111111111111111111111111111111111111111111111-1-111-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1111111-1-111-1-1-1-11111-1-1-1-1-1-111-1-1-1-1-1-1-1-111
χ4111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111-1-1
χ511111111111111111111111111111111111111111111111111-1-1-1-11111-1-11111-1-1-1-1-1-11111-1-1-1-1-1-1-1-111111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1
χ611111111111111111111111111111111111111111111111111-1-1-1-111-1-1-1-11111-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-111-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111
χ711111111111111111111111111111111111111111111111111-1-1-1-1-1-11111-1-1-1-11111-1-1-1-1-1-11111-1-1-1-111-1-111-1-1-1-11111111111-1-1-1-1-1-11111-1-1
χ811111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-111-1-1-1-11111-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111-1-11111-1-1-1-111
χ911-1-11111-1-1-1-1111-1-1-1111-1-1-1-1-1111-111-1-11-11-1-11111-1-1-111-1-1ii−i−i1-11-1i−i11-1-1ii−i−ii−i11-1-1ii−i−iii−i−i1-11-11-111-1-111-1-1i−iii−i−ii−i11-1-1ii−i−ii−i
χ1011-1-11111-1-1-1-1111-1-1-1111-1-1-1-1-1111-111-1-11-11-1-11111-1-1-111-1-1ii−i−i1-1-11i−i11-1-1ii−i−ii−i-1-111−i−iiiii−i−i-111-1-1111-1-1-1-111i−iii−i−ii−i-1-111−i−iii−ii
χ1111-1-11111-1-1-1-1111-1-1-1111-1-1-1-1-1111-111-1-11-11-1-11111-1-1-111-1-1ii−i−i-111-1−ii-1-111−i−iiii−i-1-111−i−iiiii−i−i1-1-111-1-1-11111-1-1−ii−i−iiii−i-1-111−i−iiii−i
χ1211-1-11111-1-1-1-1111-1-1-1111-1-1-1-1-1111-111-1-11-11-1-11111-1-1-111-1-1ii−i−i-11-11−ii-1-111−i−iiii−i11-1-1ii−i−iii−i−i-11-11-11-1-111-1-111−ii−i−iiii−i11-1-1ii−i−i−ii
χ1311-1-11111-1-1-1-1111-1-1-1111-1-1-1-1-1111-111-1-11-11-1-11111-1-1-111-1-1−i−iii1-11-1−ii11-1-1−i−iii−ii11-1-1−i−iii−i−iii1-11-11-111-1-111-1-1−ii−i−iii−ii11-1-1−i−iii−ii
χ1411-1-11111-1-1-1-1111-1-1-1111-1-1-1-1-1111-111-1-11-11-1-11111-1-1-111-1-1−i−iii1-1-11−ii11-1-1−i−iii−ii-1-111ii−i−i−i−iii-111-1-1111-1-1-1-111−ii−i−iii−ii-1-111ii−i−ii−i
χ1511-1-11111-1-1-1-1111-1-1-1111-1-1-1-1-1111-111-1-11-11-1-11111-1-1-111-1-1−i−iii-111-1i−i-1-111ii−i−i−ii-1-111ii−i−i−i−iii1-1-111-1-1-11111-1-1i−iii−i−i−ii-1-111ii−i−i−ii
χ1611-1-11111-1-1-1-1111-1-1-1111-1-1-1-1-1111-111-1-11-11-1-11111-1-1-111-1-1−i−iii-11-11i−i-1-111ii−i−i−ii11-1-1−i−iii−i−iii-11-11-11-1-111-1-111i−iii−i−i−ii11-1-1−i−iiii−i
χ172222222-2-2222222222222222222222-2-2-2-2-2-22222-2-2-2-2-2-2-2-2-2-2222200000000000000-2-200000000222200000000000000000000-2-20000000000
χ182222222-2-2222222222222222222222-2-2-2-2-2-22222-2-2-2-2-2-2-2-2-2-2-2-2-2-2000000000000002200000000-2-2-2-200000000000000000000220000000000
χ19222222-1222-1-122-12222-1-12-1-1-1-12-1-12222-1-12-1-1-1-12-1-12-1-1-1-1-1-10000222200222200000022220000000022-1-1-1-1-1-1-1-1-1-1-1-100000000-1-1-1-1000000
χ20222222-1222-1-122-12222-1-12-1-1-1-12-1-12222-1-12-1-1-1-12-1-12-1-1-1-1-1-1000022-2-2002222000000-2-2-2-200000000-2-2-1-111-1-1-1-11111000000001111000000
χ21222222-1222-1-122-12222-1-12-1-1-1-12-1-12222-1-12-1-1-1-12-1-12-1-1-1-1-1-10000-2-22200-2-2-2-2000000-2-2-2-2000000002211-1-11111-1-1-1-1000000001111000000
χ22222222-1222-1-122-12222-1-12-1-1-1-12-1-12222-1-12-1-1-1-12-1-12-1-1-1-1-1-10000-2-2-2-200-2-2-2-2000000222200000000-2-211111111111100000000-1-1-1-1000000
χ2322222-12222222-122-1-1-12-1-122-1-1-12-1-12-1-1222-1-1-1-1-12-1-12-1-1-1-1-12222220022-1-1-1-1-1-1-1-12200000000-1-1-1-1002200-1-1-1-1000022-1-1-1-1-1-10000000000
χ2422222-12222222-122-1-1-12-1-122-1-1-12-1-12-1-1222-1-1-1-1-12-1-12-1-1-1-1-12222-2-200-2-2111111112200000000-1-1-1-100-2-20011110000-2-21111-1-10000000000
χ2522222-12222222-122-1-1-12-1-122-1-1-12-1-12-1-1222-1-1-1-1-12-1-12-1-1-1-1-1-2-2-2-22200-2-2-1-1-1-11111-2-2000000001111002200-1-1-1-10000-2-21111110000000000
χ2622222-12222222-122-1-1-12-1-122-1-1-12-1-12-1-1222-1-1-1-1-12-1-12-1-1-1-1-1-2-2-2-2-2-200221111-1-1-1-1-2-200000000111100-2-2001111000022-1-1-1-1110000000000
χ2722222-12-2-22222-122-1-1-12-1-122-1-1-12-1-1-211-2-2-2-1-1-1-11-211-2111112222000000−i3i3−i3i3−i3i3−i3i3-2-200000000-1-1-1-1000000−i3i3−i3i3000000−i3i3−i3i3110000000000
χ2822222-12-2-22222-122-1-1-12-1-122-1-1-12-1-1-211-2-2-2-1-1-1-11-211-2111112222000000i3−i3i3−i3i3−i3i3−i3-2-200000000-1-1-1-1000000i3−i3i3−i3000000i3−i3i3−i3110000000000
χ2922222-12-2-22222-122-1-1-12-1-122-1-1-12-1-1-211-2-2-2-1-1-1-11-211-211111-2-2-2-2000000−i3i3−i3i3i3−i3i3−i322000000001111000000−i3i3−i3i3000000i3−i3i3−i3-1-10000000000
χ3022222-12-2-22222-122-1-1-12-1-122-1-1-12-1-1-211-2-2-2-1-1-1-11-211-211111-2-2-2-2000000i3−i3i3−i3−i3i3−i3i322000000001111000000i3−i3i3−i3000000−i3i3−i3i3-1-10000000000
χ312222-12222-122-122-122-1-12-1-1-122-1-12-1-12222-1-1-1-1-1-1-12-1-12-1-1-1-100000022220000222200000022220000-1-100220000-1-1-1-1-1-1-1-1-1-1000000-1-1-1-100
χ322222-12222-122-122-122-1-12-1-1-122-1-12-1-12222-1-1-1-1-1-1-12-1-12-1-1-1-100000022-2-20000-2-2-2-2000000-2-2-2-20000-1-100220000-1-1-1-1111111000000111100
χ332222-12222-122-122-122-1-12-1-1-122-1-12-1-12222-1-1-1-1-1-1-12-1-12-1-1-1-1000000-2-22200002222000000-2-2-2-200001100-2-200001111-1-1-1-1-1-1000000111100
χ342222-12222-122-122-122-1-12-1-1-122-1-12-1-12222-1-1-1-1-1-1-12-1-12-1-1-1-1000000-2-2-2-20000-2-2-2-2000000222200001100-2-200001111111111000000-1-1-1-100
χ3522-2-2222-22-2-2-2222-2-2-2222-2-2-2-2-2222-2-2-222-222-2-22-2-2-2222-2-2222i2i−2i−2i00000000000000−2i2i000000002i2i−2i−2i00000000000000000000−2i2i0000000000
χ3622-2-2222-22-2-2-2222-2-2-2222-2-2-2-2-2222-2-2-222-222-2-22-2-2-2222-2-222−2i−2i2i2i000000000000002i−2i00000000−2i−2i2i2i000000000000000000002i−2i0000000000
χ3722-2-222-12-2-21122-1-2-2-22-1-1-211112-1-1-222-21-1-2-111-12-1-1-211-1-11100002-22-20022-2-200000022-2-2000000002-2-11-11-1-111-1-11100000000-1-111000000
χ3822-2-222-12-2-21122-1-2-2-22-1-1-211112-1-1-222-21-1-2-111-12-1-1-211-1-11100002-2-220022-2-2000000-2-22200000000-22-111-1-1-11111-1-10000000011-1-1000000
χ3922-2-222-12-2-21122-1-2-2-22-1-1-211112-1-1-222-21-1-2-111-12-1-1-211-1-1110000-222-200-2-222000000-2-222000000002-21-1-1111-1-1-1-1110000000011-1-1000000
χ4022-2-222-12-2-21122-1-2-2-22-1-1-211112-1-1-222-21-1-2-111-12-1-1-211-1-1110000-22-2200-2-22200000022-2-200000000-221-11-111-1-111-1-100000000-1-111000000
χ4122-2-22-122-2-2-2-22-12-211-12-11-2-211-12-112-11-22-2-111-1-12-11-21-1-1112i2i−2i−2i2-2002i−2i-1-111−i−iii2i−2i00000000−i−iii002-200-1-11100002i−2i−i−iii−ii0000000000
χ4222-2-22-122-2-2-2-22-12-211-12-11-2-211-12-112-11-22-2-111-1-12-11-21-1-1112i2i−2i−2i-2200−2i2i11-1-1ii−i−i2i−2i00000000−i−iii00-220011-1-10000−2i2iii−i−i−ii0000000000
χ4322-2-22-122-2-2-2-22-12-211-12-11-2-211-12-112-11-22-2-111-1-12-11-21-1-111−2i−2i2i2i2-200−2i2i-1-111ii−i−i−2i2i00000000ii−i−i002-200-1-1110000−2i2iii−i−ii−i0000000000
χ4422-2-22-122-2-2-2-22-12-211-12-11-2-211-12-112-11-22-2-111-1-12-11-21-1-111−2i−2i2i2i-22002i−2i11-1-1−i−iii−2i2i00000000ii−i−i00-220011-1-100002i−2i−i−iiii−i0000000000
χ4522-2-22-12-22-2-2-22-12-211-12-11-2-211-12-11-21-12-22-111-11-21-12-111-1-12i2i−2i−2i000000−i3i3i3−i33−3−33−2i2i00000000−i−iii000000−i3i3i3−i30000003−3−33i−i0000000000
χ4622-2-22-12-22-2-2-22-12-211-12-11-2-211-12-11-21-12-22-111-11-21-12-111-1-12i2i−2i−2i000000i3−i3−i3i3−333−3−2i2i00000000−i−iii000000i3−i3−i3i3000000−333−3i−i0000000000
χ4722-2-22-12-22-2-2-22-12-211-12-11-2-211-12-11-21-12-22-111-11-21-12-111-1-1−2i−2i2i2i000000−i3i3i3−i3−333−32i−2i00000000ii−i−i000000−i3i3i3−i3000000−333−3−ii0000000000
χ4822-2-22-12-22-2-2-22-12-211-12-11-2-211-12-11-21-12-22-111-11-21-12-111-1-1−2i−2i2i2i000000i3−i3−i3i33−3−332i−2i00000000ii−i−i000000i3−i3−i3i30000003−3−33−ii0000000000
χ4922-2-2-1222-21-2-2-1221-2-2-1-12111-2-2-1-121-12-2-221-111-1-1-1211-2-1-1110000002-22i−2i00002i2i−2i−2i0000002i2i−2i−2i0000-11002-20000-1-111−ii−i−iii000000−i−iii00
χ5022-2-2-1222-21-2-2-1221-2-2-1-12111-2-2-1-121-12-2-221-111-1-1-1211-2-1-1110000002-2−2i2i0000−2i−2i2i2i000000−2i−2i2i2i0000-11002-20000-1-111i−iii−i−i000000ii−i−i00
χ5122-2-2-1222-21-2-2-1221-2-2-1-12111-2-2-1-121-12-2-221-111-1-1-1211-2-1-111000000-222i−2i00002i2i−2i−2i000000−2i−2i2i2i00001-100-22000011-1-1−ii−i−iii000000ii−i−i00
χ5222-2-2-1222-21-2-2-1221-2-2-1-12111-2-2-1-121-12-2-221-111-1-1-1211-2-1-111000000-22−2i2i0000−2i−2i2i2i0000002i2i−2i−2i00001-100-22000011-1-1i−iii−i−i000000−i−iii00
χ532-22-22220022-2-2-2-2-22-222222-22-2-2-2-2-200000022-2-200000000002i−2i2i−2i00000000000000002−22−2−i2i2−i2i22i−2i2i−2i00000000000000000000002−22−2−i2i2−i2i200
χ542-22-22220022-2-2-2-2-22-222222-22-2-2-2-2-200000022-2-200000000002i−2i2i−2i0000000000000000−22−22i2−i2i2−i22i−2i2i−2i0000000000000000000000−22−22i2−i2i2−i200
χ552-22-22220022-2-2-2-2-22-222222-22-2-2-2-2-200000022-2-20000000000−2i2i−2i2i00000000000000002−22−2i2−i2i2−i2−2i2i−2i2i00000000000000000000002−22−2i2−i2i2−i200
χ562-22-22220022-2-2-2-2-22-222222-22-2-2-2-2-200000022-2-20000000000−2i2i−2i2i0000000000000000−22−22−i2i2−i2i2−2i2i−2i2i0000000000000000000000−22−22−i2i2−i2i200
χ572-2-2222200-2-22-2-2-22-22222-2-22-22-2-2-220000002-22-200000000002-2-2200000000000000002−2−22−222−22-2-2200000000000000000000002−2−22−222−200
χ582-2-2222200-2-22-2-2-22-22222-2-22-22-2-2-220000002-22-200000000002-2-220000000000000000−222−22−2−222-2-220000000000000000000000−222−22−2−2200
χ592-2-2222200-2-22-2-2-22-22222-2-22-22-2-2-220000002-22-20000000000-222-200000000000000002−2−222−2−22-222-200000000000000000000002−2−222−2−2200
χ602-2-2222200-2-22-2-2-22-22222-2-22-22-2-2-220000002-22-20000000000-222-20000000000000000−222−2−222−2-222-20000000000000000000000−222−2−222−200
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χ7644-4-44-2-24-4-4224-2-2-422-2-21222-1-1-2-2124-222-2-41-1-11-2-2122-111-1-100004-40000-2-22200000000000000000000-220011-1-10000000000000000000000
χ7744-4-44-2-24-4-4224-2-2-422-2-21222-1-1-2-2124-222-2-41-1-11-2-2122-111-1-10000-44000022-2-2000000000000000000002-200-1-1110000000000000000000000
χ7844-4-44-2-2-44-4224-2-2-422-2-21222-1-1-2-212-42-2-2241-1-1122-1-2-21-1-1110000000000−2i32i32i3−2i3000000000000000000000000i3−i3−i3i30000000000000000000000
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χ8144-4-4-24-24-4222-24-22-4-4-21-22-1-122-21-22-24-42-221-1-11-21-22-1211-1-10000004-4000000000000000000000000-2200-22000011-1-1000000000000000000
χ8244-4-4-24-24-4222-24-22-4-4-21-22-1-122-21-22-24-42-221-1-11-21-22-1211-1-1000000-440000000000000000000000002-2002-20000-1-111000000000000000000
χ8344-4-4-24-2-44222-24-22-4-4-21-22-1-122-21-222-44-22-21-1-112-12-21-2-1-1110000000000000000000000000000000000000000003-3-33000000000000000000
χ8444-4-4-24-2-44222-24-22-4-4-21-22-1-122-21-222-44-22-21-1-112-12-21-2-1-111000000000000000000000000000000000000000000-333-3000000000000000000
χ8544-4-4-2-244-42-4-4-2-242221-2-2-122221-2-2-1-2-22-4421-1-111-2-2-12211-1-1000000004i−4i0000−2i−2i2i2i0000000000000000000000000000−2i2iii−i−i000000000000
χ8644-4-4-2-244-42-4-4-2-242221-2-2-122221-2-2-1-2-22-4421-1-111-2-2-12211-1-100000000−4i4i00002i2i−2i−2i00000000000000000000000000002i−2i−i−iii000000000000
χ8744-4-4-2-24-442-4-4-2-242221-2-2-122221-2-2-122-24-4-21-1-11-1221-2-2-1-1110000000000000023−23−2323000000000000000000000000000000−333−3000000000000
χ8844-4-4-2-24-442-4-4-2-242221-2-2-122221-2-2-122-24-4-21-1-11-1221-2-2-1-11100000000000000−232323−230000000000000000000000000000003−3−33000000000000
χ894-44-444-2004-22-4-42-44-44-2-24-22-22-422-4000000-2-22200000000000000000000000000000022−2222−22000000000000000000000000000000−22−22000000
χ904-44-444-2004-22-4-42-44-44-2-24-22-22-422-4000000-2-222000000000000000000000000000000−2222−22220000000000000000000000000000002−22−2000000
χ914-44-44-240044-4-42-4-4-22-24-2-24-4-222-422000000-2-22200000000004i−4i4i−4i000000000000000000000000−2i2i−2i2i00000000000000000000000000000000
χ924-44-44-240044-4-42-4-4-22-24-2-24-4-222-422000000-2-2220000000000−4i4i−4i4i0000000000000000000000002i−2i2i−2i00000000000000000000000000000000
χ934-44-4-24400-24-42-4-424-4-2-24-2-224-422-42000000-2-2220000000000000000000000000000000000−2i22i2−2i22i2000000000000000000000000000000i2−i2i2−i200
χ944-44-4-24400-24-42-4-424-4-2-24-2-224-422-42000000-2-22200000000000000000000000000000000002i2−2i22i2−2i2000000000000000000000000000000−i2i2−i2i200
χ954-4-4444-200-42-2-4-424-444-2-2-42-22-2-4224000000-22-2200000000000000000000000000000022−22−2222000000000000000000000000000000−222−2000000
χ964-4-4444-200-42-2-4-424-444-2-2-42-22-2-4224000000-22-22000000000000000000000000000000−222222−220000000000000000000000000000002−2−22000000
χ974-4-444-2400-4-44-42-442-2-24-22-442-22-42-2000000-22-2200000000004-4-44000000000000000000000000-222-200000000000000000000000000000000
χ984-4-444-2400-4-44-42-442-2-24-22-442-22-42-2000000-22-220000000000-444-40000000000000000000000002-2-2200000000000000000000000000000000
χ994-4-44-244002-442-4-4-2-44-2-2422-2-4422-4-2000000-22-22000000000000000000000000000000000022−22−2222000000000000000000000000000000−222−200
χ1004-4-44-244002-442-4-4-2-44-2-2422-2-4422-4-2000000-22-220000000000000000000000000000000000−222222−220000000000000000000000000000002−2−2200
χ1018888-4-4-488-4-4-4-4-4-4-4-4-4222222222222-4-4-4-4-4-4-1-1-1-1222222-1-1-1-10000000000000000000000000000000000000000000000000000000000000000
χ1028888-4-4-4-8-8-4-4-4-4-4-4-4-4-4222222222222444444-1-1-1-1-2-2-2-2-2-211110000000000000000000000000000000000000000000000000000000000000000
χ10388-8-8-4-4-48-8444-4-4-4444222-2-2-2-2-2222-2-4-444-44-111-1222-2-2-2-1-1110000000000000000000000000000000000000000000000000000000000000000
χ10488-8-8-4-4-4-88444-4-4-4444222-2-2-2-2-2222-244-4-44-4-111-1-2-2-222211-1-10000000000000000000000000000000000000000000000000000000000000000
χ1058-88-88-4-4008-44-844-8-44-4-42-4-442-244-2400000022-2-200000000000000000000000000000000000000000000000000000000000000000000000000
χ1068-88-8-48-400-4-444-8448-8-42-4-42-2-444-24400000022-2-200000000000000000000000000000000000000000000000000000000000000000000000000
χ1078-88-8-4-4800-48-844-84-442-4-42-44-44-244-200000022-2-200000000000000000000000000000000000000000000000000000000000000000000000000
χ1088-88-8-4-4-400-4-444444-4422222-22-2-2-2-2-2000000-1-11100000033−3333−330000000000000000000000000000000000000000000000000000000000000000
χ1098-88-8-4-4-400-4-444444-4422222-22-2-2-2-2-2000000-1-111000000−3333−33330000000000000000000000000000000000000000000000000000000000000000
χ1108-8-888-4-400-84-4-84484-4-4-4244-4-2244-2-40000002-22-200000000000000000000000000000000000000000000000000000000000000000000000000
χ1118-8-88-48-40044-44-84-4-88-42-44-224-44-24-40000002-22-200000000000000000000000000000000000000000000000000000000000000000000000000
χ1128-8-88-4-48004-8844-8-44-42-4-4-24-44-4-24420000002-22-200000000000000000000000000000000000000000000000000000000000000000000000000
χ1138-8-88-4-4-40044-4444-44-4222-2-22-22-2-2-22000000-11-1100000033−33−33330000000000000000000000000000000000000000000000000000000000000000
χ1148-8-88-4-4-40044-4444-44-4222-2-22-22-2-2-22000000-11-11000000−333333−330000000000000000000000000000000000000000000000000000000000000000

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