Finite Group Databasebeta

← Group #13170512

Character table — Group #13170512

Order 1728.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96C97C98C99C100C101C102C103C104C105C106C107C108C109C110C111C112C113C114C115C116C117C118C119C120C121C122C123C124C125C126C127C128C129C130C131C132C133C134C135C136C137C138C139C140C141C142C143C144C145C146C147C148C149C150C151C152C153C154C155C156
size11112222222222224444444444446666668888121212121212121212121212121212121212121212121212181818181818272727273636363636361111222222222222444444444444666666888812121212121212121212121212121212121212121212121218181818181827272727363636363636
order1244333666121212121212333666121212121212224488361212666666661212121212121212242424242424242424888888886122424242422446666661212121212126666661212121212122244886612126666666612121212121212122424242424242424248888888861224242424
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111-1-111111111111111111111-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-111-1-1-1-111111111111111111111111111111111-1-111111111111111111111-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-111-1-1-1-1
χ311111111111111111111111111111-11-11111111-11-111-1-11-11-111-1-111111111-1-111-1-1-1-1-1-1-1-111-1-111111111111111111111111111111-11-11111111-11-111-1-11-11-111-1-111111111-1-111-1-1-1-1-1-1-1-111-1-1
χ411111111111111111111111111111-11-1-1-111111-11-111-1-11-11-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-1-11111111111111111111111111111111-11-1-1-111111-11-111-1-11-11-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-1-111
χ51111111111111111111111111111-11-11111111-11-11-1-111-11-11-1-11111111111-1-1-1-111-1-1-1-1-1-1-1-1111111111111111111111111111111-11-11111111-11-11-1-111-11-11-1-11111111111-1-1-1-111-1-1-1-1-1-1-1-111
χ61111111111111111111111111111-11-11-1-11111-11-11-1-111-11-11-1-111-1-1-1-1-1-1-1-1-1-111-1-11111-1-111-1-11111111111111111111111111111-11-11-1-11111-11-11-1-111-11-11-1-111-1-1-1-1-1-1-1-1-1-111-1-11111-1-111-1-1
χ71111111111111111111111111111-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111-1-1-1-1111111-1-1-1-11111111111111111111111111111-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111-1-1-1-1111111-1-1-1-1
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
χ911-1-1111111-1-1-1-1-1-1111111-1-1-1-1-1-111-1-1i−i11-1-111111111-1-1-1-1-1-1-1-1ii−i−iii−i−i-11i−ii−iii−i−i-11i−ii−i11-1-1111111-1-1-1-1-1-1111111-1-1-1-1-1-111-1-1i−i11-1-111111111-1-1-1-1-1-1-1-1ii−i−iii−i−i-11i−ii−iii−i−i-11i−ii−i
χ1011-1-1111111-1-1-1-1-1-1111111-1-1-1-1-1-111-1-1−ii11-1-111111111-1-1-1-1-1-1-1-1−i−iii−i−iii-11−ii−ii−i−iii-11−ii−ii11-1-1111111-1-1-1-1-1-1111111-1-1-1-1-1-111-1-1−ii11-1-111111111-1-1-1-1-1-1-1-1−i−iii−i−iii-11−ii−ii−i−iii-11−ii−ii
χ1111-1-1111111-1-1-1-1-1-1111111-1-1-1-1-1-11-1-11i−i11-1-11-11-111-1-1-11-11-1-111ii−i−iii−i−i1-1i−i−ii−i−iii1-1i−i−ii11-1-1111111-1-1-1-1-1-1111111-1-1-1-1-1-11-1-11i−i11-1-11-11-111-1-1-11-11-1-111ii−i−iii−i−i1-1i−i−ii−i−iii1-1i−i−ii
χ1211-1-1111111-1-1-1-1-1-1111111-1-1-1-1-1-11-1-11−ii11-1-11-11-111-1-1-11-11-1-111−i−iii−i−iii1-1−iii−iii−i−i1-1−iii−i11-1-1111111-1-1-1-1-1-1111111-1-1-1-1-1-11-1-11−ii11-1-11-11-111-1-1-11-11-1-111−i−iii−i−iii1-1−iii−iii−i−i1-1−iii−i
χ1311-1-1111111-1-1-1-1-1-1111111-1-1-1-1-1-1-111-1i−i11-1-1-11-11-1-1111-11-111-1-1ii−i−iii−i−i1-1−iii−i−i−iii1-1−iii−i11-1-1111111-1-1-1-1-1-1111111-1-1-1-1-1-1-111-1i−i11-1-1-11-11-1-1111-11-111-1-1ii−i−iii−i−i1-1−iii−i−i−iii1-1−iii−i
χ1411-1-1111111-1-1-1-1-1-1111111-1-1-1-1-1-1-111-1−ii11-1-1-11-11-1-1111-11-111-1-1−i−iii−i−iii1-1i−i−iiii−i−i1-1i−i−ii11-1-1111111-1-1-1-1-1-1111111-1-1-1-1-1-1-111-1−ii11-1-1-11-11-1-1111-11-111-1-1−i−iii−i−iii1-1i−i−iiii−i−i1-1i−i−ii
χ1511-1-1111111-1-1-1-1-1-1111111-1-1-1-1-1-1-1-111i−i11-1-1-1-1-1-1-1-1-1-111111111ii−i−iii−i−i-11−ii−iiii−i−i-11−ii−ii11-1-1111111-1-1-1-1-1-1111111-1-1-1-1-1-1-1-111i−i11-1-1-1-1-1-1-1-1-1-111111111ii−i−iii−i−i-11−ii−iiii−i−i-11−ii−ii
χ1611-1-1111111-1-1-1-1-1-1111111-1-1-1-1-1-1-1-111−ii11-1-1-1-1-1-1-1-1-1-111111111−i−iii−i−iii-11i−ii−i−i−iii-11i−ii−i11-1-1111111-1-1-1-1-1-1111111-1-1-1-1-1-1-1-111−ii11-1-1-1-1-1-1-1-1-1-111111111−i−iii−i−iii-11i−ii−i−i−iii-11i−ii−i
χ17222222-122-1-1-122222-1-12-1-1-1-1-1-122222200-1-1-1-122-1-1-1-1-1-122-1-1-1-1-1-1000000002200000000-1-10000222222-122-1-1-122222-1-12-1-1-1-1-1-122222200-1-1-1-122-1-1-1-1-1-122-1-1-1-1-1-1000000002200000000-1-10000
χ18222222-122-1-1-122222-1-12-1-1-1-1-1-1222-22-200-1-1-1-12-2-11-1-1112-2-11-1-11100000000-2-200000000110000222222-122-1-1-122222-1-12-1-1-1-1-1-1222-22-200-1-1-1-12-2-11-1-1112-2-11-1-11100000000-2-200000000110000
χ19222222-122-1-1-122222-1-12-1-1-1-1-1-122-22-2200-1-1-1-1-221-111-1-1-221-111-1-100000000-2-200000000110000222222-122-1-1-122222-1-12-1-1-1-1-1-122-22-2200-1-1-1-1-221-111-1-1-221-111-1-100000000-2-200000000110000
χ20222222-122-1-1-122222-1-12-1-1-1-1-1-122-2-2-2-200-1-1-1-1-2-2111111-2-2111111000000002200000000-1-10000222222-122-1-1-122222-1-12-1-1-1-1-1-122-2-2-2-200-1-1-1-1-2-2111111-2-2111111000000002200000000-1-10000
χ2122222-122-122222-1-1-12-1-12-122-1-1-1-1020222-1-1-1-10-10200-1-10-10200-1-12-12-1-1-1-1-100002200000000-1-122222-122-122222-1-1-12-1-12-122-1-1-1-1020222-1-1-1-10-10200-1-10-10200-1-12-12-1-1-1-1-100002200000000-1-1
χ2222222-122-122222-1-1-12-1-12-122-1-1-1-10202-2-2-1-1-1-10-10200-1-10-10200-1-1-21-2111110000-2-2000000001122222-122-122222-1-1-12-1-12-122-1-1-1-10202-2-2-1-1-1-10-10200-1-10-10200-1-1-21-2111110000-2-20000000011
χ2322222-122-122222-1-1-12-1-12-122-1-1-1-10-20-222-1-1-1-1010-20011010-200112-12-1-1-1-1-10000-2-2000000001122222-122-122222-1-1-12-1-12-122-1-1-1-10-20-222-1-1-1-1010-20011010-200112-12-1-1-1-1-10000-2-20000000011
χ2422222-122-122222-1-1-12-1-12-122-1-1-1-10-20-2-2-2-1-1-1-1010-20011010-20011-21-21111100002200000000-1-122222-122-122222-1-1-12-1-12-122-1-1-1-10-20-2-2-2-1-1-1-1010-20011010-20011-21-21111100002200000000-1-1
χ252222-122-12222-1-122-1-12-1-12-1-122-1-1202022-1-1-1-1-1020-1-100-1020-1-100-12-12-1-1-1-1002200000000-1-1002222-122-12222-1-122-1-12-1-12-1-122-1-1202022-1-1-1-1-1020-1-100-1020-1-100-12-12-1-1-1-1002200000000-1-100
χ262222-122-12222-1-122-1-12-1-12-1-122-1-12020-2-2-1-1-1-1-1020-1-100-1020-1-1001-21-2111100-2-20000000011002222-122-12222-1-122-1-12-1-12-1-122-1-12020-2-2-1-1-1-1-1020-1-100-1020-1-1001-21-2111100-2-2000000001100
χ272222-122-12222-1-122-1-12-1-12-1-122-1-1-20-2022-1-1-1-110-20110010-201100-12-12-1-1-1-100-2-20000000011002222-122-12222-1-122-1-12-1-12-1-122-1-1-20-2022-1-1-1-110-20110010-201100-12-12-1-1-1-100-2-2000000001100
χ282222-122-12222-1-122-1-12-1-12-1-122-1-1-20-20-2-2-1-1-1-110-20110010-2011001-21-21111002200000000-1-1002222-122-12222-1-122-1-12-1-12-1-122-1-1-20-20-2-2-1-1-1-110-20110010-2011001-21-21111002200000000-1-100
χ2922-2-222-122-111-2-2-2-22-1-12-1-11111-2-222-2-200-1-11122-1-1-1-1-1-1-2-211111100000000-22000000001-1000022-2-222-122-111-2-2-2-22-1-12-1-11111-2-222-2-200-1-11122-1-1-1-1-1-1-2-211111100000000-22000000001-10000
χ3022-2-222-122-111-2-2-2-22-1-12-1-11111-2-22-2-2200-1-1112-2-11-1-111-221-111-1-1000000002-200000000-11000022-2-222-122-111-2-2-2-22-1-12-1-11111-2-22-2-2200-1-1112-2-11-1-111-221-111-1-1000000002-200000000-110000
χ3122-2-222-122-111-2-2-2-22-1-12-1-11111-2-2-222-200-1-111-221-111-1-12-2-11-1-111000000002-200000000-11000022-2-222-122-111-2-2-2-22-1-12-1-11111-2-2-222-200-1-111-221-111-1-12-2-11-1-111000000002-200000000-110000
χ3222-2-222-122-111-2-2-2-22-1-12-1-11111-2-2-2-22200-1-111-2-211111122-1-1-1-1-1-100000000-22000000001-1000022-2-222-122-111-2-2-2-22-1-12-1-11111-2-2-2-22200-1-111-2-211111122-1-1-1-1-1-100000000-22000000001-10000
χ3322-2-22-122-12-2-2-2-211-12-1-12-1-2-21111020-22i−2i-1-1110-10200-1-1010-200112i−i−2ii−i−iii00002i−2i00000000−ii22-2-22-122-12-2-2-2-211-12-1-12-1-2-21111020-22i−2i-1-1110-10200-1-1010-200112i−i−2ii−i−iii00002i−2i00000000−ii
χ3422-2-22-122-12-2-2-2-211-12-1-12-1-2-21111020-2−2i2i-1-1110-10200-1-1010-20011−2ii2i−iii−i−i0000−2i2i00000000i−i22-2-22-122-12-2-2-2-211-12-1-12-1-2-21111020-2−2i2i-1-1110-10200-1-1010-20011−2ii2i−iii−i−i0000−2i2i00000000i−i
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χ3622-2-22-122-12-2-2-2-211-12-1-12-1-2-211110-202−2i2i-1-111010-200110-10200-1-1−2ii2i−iii−i−i00002i−2i00000000−ii22-2-22-122-12-2-2-2-211-12-1-12-1-2-211110-202−2i2i-1-111010-200110-10200-1-1−2ii2i−iii−i−i00002i−2i00000000−ii
χ3722-2-2-122-122-2-211-2-2-1-12-1-1211-2-21120-202i−2i-1-111-1020-1-10010-201100−i2ii−2i−i−iii002i−2i00000000−ii0022-2-2-122-122-2-211-2-2-1-12-1-1211-2-21120-202i−2i-1-111-1020-1-10010-201100−i2ii−2i−i−iii002i−2i00000000−ii00
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χ422-22i−2i222-2-2-22i−2i2i−2i2i−2i222-2-2-22i−2i2i−2i2i−2i0000002-22i−2i000000000000000000000000000000−2ζ32ζ3−2ζ2ζ0000002-22i−2i222-2-2-22i−2i2i−2i2i−2i222-2-2-22i−2i2i−2i2i−2i0000002-22i−2i000000000000000000000000000000−2ζ32ζ3−2ζ2ζ000000
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χ484444-24-2-24-2-2-2-2-244-21-2-21-211-2-2-2-2-40-400011112020-1-1002020-1-1000000000000000000000000004444-24-2-24-2-2-2-2-244-21-2-21-211-2-2-2-2-40-400011112020-1-1002020-1-100000000000000000000000000
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χ13144-4-4-24-2-24-22222-4-4-21-2-21-2-1-1222240-400011-1-1-20-2011002020-1-100000000000000000000000000-4-4442-422-42-2-2-2-2442-122-1211-2-2-2-2-404000-1-1112020-1-100-20-201100000000000000000000000000
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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
χ15488-8-8-4-4-4-4-4-4444444222222-2-2-2-2-2-2000000-1-1110000000000000000000000000000000000000000-8-888444444-4-4-4-4-4-4-2-2-2-2-2-222222200000011-1-10000000000000000000000000000000000000000
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Here ζ is a primitive root of unity of order 8 (ζ8 = 1); i = ζ2.