Finite Group Databasebeta

← Group #13139020

Character table — Group #13139020

Order 1728.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96C97C98C99C100C101C102C103C104C105C106C107C108C109C110C111C112C113C114C115C116
size1111111122222222222244446666666666666666666666661212121212121212121212121212121212121212181818181818181818181818181818181818181818181818363636363636363636363636363636363636363636363636
order124488882346881212242424246122424336666121212121212242424242424242424242424366661212121212242424242424242424244444888812121212121212122424242424242424224466668888121212122424242424242424
χ111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ311111111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11-11-111-1-111-1-111-1-11111-1-1-1-1
χ411111111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11-11-1-111-1-111-1-111-1-1-1-11111
χ51111-1-1-1-11111-1-111-1-1-1-111-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-11111-1-1-1-111111111-1-1-1-1-1-1-1-11-11-111-1-1-1-11111-1-1-1-1-1-11111
χ61111-1-1-1-11111-1-111-1-1-1-111-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-11111-1-1-1-111111111-1-1-1-1-1-1-1-1-11-11-1-11111-1-1-1-1111111-1-1-1-1
χ71111-1-1-1-11111-1-111-1-1-1-111-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-11111111111111111-1-1-1-11111-1-1-1-1-1-1-1-1
χ81111-1-1-1-11111-1-111-1-1-1-111-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-11111-1-1-1-111111111
χ911-1-1ii−i−i-1111i−i-1-1ii−i−i-11i−i111-1-11-1-111-1-1iiii−i−i−i−iii−i−i1-1-1-11111-1-1i−iiiii−i−i−i−iii−i−i11-1-1iiii−i−i−i−i1111-1-1-1-111-1-11111i−ii−i-1-1-1-1ii−i−iii−i−i
χ1011-1-1ii−i−i-1111i−i-1-1ii−i−i-11i−i111-1-11-1-111-1-1iiii−i−i−i−iii−i−i1-1-1-11111-1-1i−iiiii−i−i−i−iii−i−i11-1-1iiii−i−i−i−i1111-1-1-1-1-1-111-1-1-1-1−ii−ii1111−i−iii−i−iii
χ1111-1-1ii−i−i-1111i−i-1-1ii−i−i-11i−i111-1-11-1-111-1-1iiii−i−i−i−iii−i−i1-1-1-11111-1-1i−iiiii−i−i−i−i−i−iii-1-111−i−i−i−iiiii-1-1-1-111111-1-1111-1-1i−i−ii-1-111ii−i−i−i−iii
χ1211-1-1ii−i−i-1111i−i-1-1ii−i−i-11i−i111-1-11-1-111-1-1iiii−i−i−i−iii−i−i1-1-1-11111-1-1i−iiiii−i−i−i−i−i−iii-1-111−i−i−i−iiiii-1-1-1-11111-111-1-1-111−iii−i11-1-1−i−iiiii−i−i
χ1311-1-1−i−iii-1111−ii-1-1−i−iii-11−ii111-1-11-1-111-1-1−i−i−i−iiiii−i−iii1-1-1-11111-1-1−ii−i−i−i−iiiiiii−i−i-1-111iiii−i−i−i−i-1-1-1-111111-1-1111-1-1−iii−i-1-111−i−iiiii−i−i
χ1411-1-1−i−iii-1111−ii-1-1−i−iii-11−ii111-1-11-1-111-1-1−i−i−i−iiiii−i−iii1-1-1-11111-1-1−ii−i−i−i−iiiiiii−i−i-1-111iiii−i−i−i−i-1-1-1-11111-111-1-1-111i−i−ii11-1-1ii−i−i−i−iii
χ1511-1-1−i−iii-1111−ii-1-1−i−iii-11−ii111-1-11-1-111-1-1−i−i−i−iiiii−i−iii1-1-1-11111-1-1−ii−i−i−i−iiiii−i−iii11-1-1−i−i−i−iiiii1111-1-1-1-111-1-11111−ii−ii-1-1-1-1−i−iii−i−iii
χ1611-1-1−i−iii-1111−ii-1-1−i−iii-11−ii111-1-11-1-111-1-1−i−i−i−iiiii−i−iii1-1-1-11111-1-1−ii−i−i−i−iiiii−i−iii11-1-1−i−i−i−iiiii1111-1-1-1-1-1-111-1-1-1-1i−ii−i1111ii−i−iii−i−i
χ172222222222222222222222222-1222-12222-1-122222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1000000000000000000000000020200-1-1002200-1-10000-1-1-1-1
χ182222222222222222222222222-1222-12222-1-122222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-10000000000000000000000000-20-2001100-2-2001100001111
χ19222222222222222222222222-12-1-1-12-1-1-1-122-1-1-1-1-1-1-1-12222-12-1-1-12-1-1-1-122-1-1-1-1-1-1-1-122222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1000000000000000000000000
χ20222222222222222222222222-12-1-1-12-1-1-1-122-1-1-1-1-1-1-1-12222-12-1-1-12-1-1-1-122-1-1-1-1-1-1-1-1-2-2-2-2-2-2-2-21111111111111111000000000000000000000000
χ2122222222-22-22-2-2222222-2-2-2-2222-2-2222-2-22222-2-222-2-222222-2-2-22-2-2-222-2-222-2-222-2-2000000000000000000000000000000000000000000000000
χ2222222222-22-22-2-2222222-2-2-2-22-12-2-2-122-2-2-1-122-2-222-2-2-1-1-1-1-1111-1111-1-111-1-111-1-111000000000000000000000000000000−i3i3000000−i3i30000−i3i3−i3i3
χ2322222222-22-22-2-2222222-2-2-2-22-12-2-2-122-2-2-1-122-2-222-2-2-1-1-1-1-1111-1111-1-111-1-111-1-111000000000000000000000000000000i3−i3000000i3−i30000i3−i3i3−i3
χ2422222222-22-22-2-2222222-2-2-2-2-12-1112-1-11122-1-111-1-1112222-1-211-1-211-1-1-2-2-1-111-1-1110000000033−3−333−3−333−3−333−3−3000000000000000000000000
χ2522222222-22-22-2-2222222-2-2-2-2-12-1112-1-11122-1-111-1-1112222-1-211-1-211-1-1-2-2-1-111-1-11100000000−3−333−3−333−3−333−3−333000000000000000000000000
χ262222-2-2-2-22222-2-222-2-2-2-222-2-22-1222-12222-1-1-2-2-2-2-2-2-2-21111-1-1-1-1-1-1-1-1-1-11111111111000000000000000000000000020200-1-100-2-200-1-100001111
χ272222-2-2-2-22222-2-222-2-2-2-222-2-22-1222-12222-1-1-2-2-2-2-2-2-2-21111-1-1-1-1-1-1-1-1-1-111111111110000000000000000000000000-20-20011002200110000-1-1-1-1
χ282222-2-2-2-22222-2-222-2-2-2-222-2-2-12-1-1-12-1-1-1-12211111111-2-2-2-2-12-1-1-12-1-1-1-1-2-2111111112222-2-2-2-2-1-1-1-1-1-1-1-111111111000000000000000000000000
χ292222-2-2-2-22222-2-222-2-2-2-222-2-2-12-1-1-12-1-1-1-12211111111-2-2-2-2-12-1-1-12-1-1-1-1-2-211111111-2-2-2-2222211111111-1-1-1-1-1-1-1-1000000000000000000000000
χ302222-2-2-2-2-22-222222-2-2-2-2-2-222222-2-2222-2-222-2-222-2-222-2-2-2-22-2-2-22-2-2-22222-2-222-2-222000000000000000000000000000000000000000000000000
χ312222-2-2-2-2-22-222222-2-2-2-2-2-2222-12-2-2-122-2-2-1-1-2-222-2-2221111-1111-1111-1-1-1-111-1-111-1-1000000000000000000000000000000−i3i3000000−i3i30000i3−i3i3−i3
χ322222-2-2-2-2-22-222222-2-2-2-2-2-2222-12-2-2-122-2-2-1-1-2-222-2-2221111-1111-1111-1-1-1-111-1-111-1-1000000000000000000000000000000i3−i3000000i3−i30000−i3i3−i3i3
χ332222-2-2-2-2-22-222222-2-2-2-2-2-222-12-1112-1-1112211-1-111-1-1-2-2-2-2-1-211-1-211-1-12211-1-111-1-10000000033−3−333−3−3−3−333−3−333000000000000000000000000
χ342222-2-2-2-2-22-222222-2-2-2-2-2-222-12-1112-1-1112211-1-111-1-1-2-2-2-2-1-211-1-211-1-12211-1-111-1-100000000−3−333−3−33333−3−333−3−3000000000000000000000000
χ3522-2-22i2i−2i−2i22-22−2i2i-2-22i2i−2i−2i2-2−2i2i222222-2-2-2-2-2-22i2i−2i−2i−2i−2i2i2i2i2i−2i−2i22222-2-2-2-2-2−2i2i2i2i−2i−2i−2i−2i2i2i000000000000000000000000000000000000000000000000
χ3622-2-22i2i−2i−2i22-22−2i2i-2-22i2i−2i−2i2-2−2i2i2-1222-1-2-2-2-2112i2i−2i−2i−2i−2i2i2i−i−iii-1-1-1-1-111111i−i−i−iiiii−i−i000000000000000000000000000000−i3i3000000i3−i300003−3−33
χ3722-2-22i2i−2i−2i22-22−2i2i-2-22i2i−2i−2i2-2−2i2i2-1222-1-2-2-2-2112i2i−2i−2i−2i−2i2i2i−i−iii-1-1-1-1-111111i−i−i−iiiii−i−i000000000000000000000000000000i3−i3000000−i3i30000−333−3
χ3822-2-22i2i−2i−2i22-22−2i2i-2-22i2i−2i−2i2-2−2i2i-12-1-1-121111-2-2−i−iiiii−i−i2i2i−2i−2i-12-1-1-1-21111−2i2i−i−iiiii−i−i00000000−i3−i3i3i3i3i3−i3−i3−3−33333−3−3000000000000000000000000
χ3922-2-22i2i−2i−2i22-22−2i2i-2-22i2i−2i−2i2-2−2i2i-12-1-1-121111-2-2−i−iiiii−i−i2i2i−2i−2i-12-1-1-1-21111−2i2i−i−iiiii−i−i00000000i3i3−i3−i3−i3−i3i3i333−3−3−3−333000000000000000000000000
χ4022-2-22i2i−2i−2i-22222i−2i-2-22i2i−2i−2i-222i−2i2-12-2-2-1-2-222112i2i2i2i−2i−2i−2i−2i−i−iii-1111-1-1-1-111−ii−i−i−i−iiiii000000000000000000000000020-200-1-1002i−2i00110000−i−iii
χ4122-2-22i2i−2i−2i-22222i−2i-2-22i2i−2i−2i-222i−2i2-12-2-2-1-2-222112i2i2i2i−2i−2i−2i−2i−i−iii-1111-1-1-1-111−ii−i−i−i−iiiii0000000000000000000000000-202001100−2i2i00-1-10000ii−i−i
χ4222-2-22i2i−2i−2i-22222i−2i-2-22i2i−2i−2i-222i−2i-12-111211-1-1-2-2−i−i−i−iiiii2i2i−2i−2i-1-211-12-1-1112i−2i−i−i−i−iiiii2i2i−2i−2i22-2-2−i−i−i−iiiii-1-1-1-11111000000000000000000000000
χ4322-2-22i2i−2i−2i-22222i−2i-2-22i2i−2i−2i-222i−2i-12-111211-1-1-2-2−i−i−i−iiiii2i2i−2i−2i-1-211-12-1-1112i−2i−i−i−i−iiiii−2i−2i2i2i-2-222iiii−i−i−i−i1111-1-1-1-1000000000000000000000000
χ4422-2-2−2i−2i2i2i22-222i−2i-2-2−2i−2i2i2i2-22i−2i222222-2-2-2-2-2-2−2i−2i2i2i2i2i−2i−2i−2i−2i2i2i22222-2-2-2-2-22i−2i−2i−2i2i2i2i2i−2i−2i000000000000000000000000000000000000000000000000
χ4522-2-2−2i−2i2i2i22-222i−2i-2-2−2i−2i2i2i2-22i−2i2-1222-1-2-2-2-211−2i−2i2i2i2i2i−2i−2iii−i−i-1-1-1-1-111111−iiii−i−i−i−iii000000000000000000000000000000−i3i3000000i3−i30000−333−3
χ4622-2-2−2i−2i2i2i22-222i−2i-2-2−2i−2i2i2i2-22i−2i2-1222-1-2-2-2-211−2i−2i2i2i2i2i−2i−2iii−i−i-1-1-1-1-111111−iiii−i−i−i−iii000000000000000000000000000000i3−i3000000−i3i300003−3−33
χ4722-2-2−2i−2i2i2i22-222i−2i-2-2−2i−2i2i2i2-22i−2i-12-1-1-121111-2-2ii−i−i−i−iii−2i−2i2i2i-12-1-1-1-211112i−2iii−i−i−i−iii00000000−i3−i3i3i3i3i3−i3−i333−3−3−3−333000000000000000000000000
χ4822-2-2−2i−2i2i2i22-222i−2i-2-2−2i−2i2i2i2-22i−2i-12-1-1-121111-2-2ii−i−i−i−iii−2i−2i2i2i-12-1-1-1-211112i−2iii−i−i−i−iii00000000i3i3−i3−i3−i3−i3i3i3−3−33333−3−3000000000000000000000000
χ4922-2-2−2i−2i2i2i-2222−2i2i-2-2−2i−2i2i2i-22−2i2i2-12-2-2-1-2-22211−2i−2i−2i−2i2i2i2i2iii−i−i-1111-1-1-1-111i−iiiii−i−i−i−i000000000000000000000000020-200-1-100−2i2i00110000ii−i−i
χ5022-2-2−2i−2i2i2i-2222−2i2i-2-2−2i−2i2i2i-22−2i2i2-12-2-2-1-2-22211−2i−2i−2i−2i2i2i2i2iii−i−i-1111-1-1-1-111i−iiiii−i−i−i−i0000000000000000000000000-2020011002i−2i00-1-10000−i−iii
χ5122-2-2−2i−2i2i2i-2222−2i2i-2-2−2i−2i2i2i-22−2i2i-12-111211-1-1-2-2iiii−i−i−i−i−2i−2i2i2i-1-211-12-1-111−2i2iiiii−i−i−i−i2i2i−2i−2i-2-222−i−i−i−iiiii1111-1-1-1-1000000000000000000000000
χ5222-2-2−2i−2i2i2i-2222−2i2i-2-2−2i−2i2i2i-22−2i2i-12-111211-1-1-2-2iiii−i−i−i−i−2i−2i2i2i-1-211-12-1-111−2i2iiiii−i−i−i−i−2i−2i2i2i22-2-2iiii−i−i−i−i-1-1-1-11111000000000000000000000000
χ532-22i−2i2ζ7+2ζ23−2ζ7−2ζ23−2ζ5−2ζ132ζ5+2ζ13020-2002i−2i2ζ7+2ζ23−2ζ7−2ζ23−2ζ5−2ζ132ζ5+2ζ13000022-200-22i−2i002i−2i2ζ7+2ζ23−2ζ7−2ζ2300−2ζ5−2ζ132ζ5+2ζ13002ζ7+2ζ23−2ζ7−2ζ23−2ζ5−2ζ132ζ5+2ζ132000-20002i−2i002ζ7+2ζ23−2ζ7−2ζ2300−2ζ5−2ζ132ζ5+2ζ13001+i−1−i1−i−1+i2−2−i2i21+i−1−i1+i−1−i1−i−1+i1−i−1+i2−22−2−i2i2−i2i2000000000000000000000000
χ542-22i−2i2ζ7+2ζ23−2ζ7−2ζ23−2ζ5−2ζ132ζ5+2ζ13020-2002i−2i2ζ7+2ζ23−2ζ7−2ζ23−2ζ5−2ζ132ζ5+2ζ13000022-200-22i−2i002i−2i2ζ7+2ζ23−2ζ7−2ζ2300−2ζ5−2ζ132ζ5+2ζ13002ζ7+2ζ23−2ζ7−2ζ23−2ζ5−2ζ132ζ5+2ζ132000-20002i−2i002ζ7+2ζ23−2ζ7−2ζ2300−2ζ5−2ζ132ζ5+2ζ1300−1−i1+i−1+i1−i−22i2−i2−1−i1+i−1−i1+i−1+i1−i−1+i1−i−22−22i2−i2i2−i2000000000000000000000000
χ552-22i−2i2ζ7+2ζ23−2ζ7−2ζ23−2ζ5−2ζ132ζ5+2ζ13020-2002i−2i2ζ7+2ζ23−2ζ7−2ζ23−2ζ5−2ζ132ζ5+2ζ130000-121−i3i3-2−ii3−32i−2i−ζ7−ζ23ζ7+ζ23ζ5−ζ13−ζ5+ζ13ζ5+ζ13−ζ5−ζ13−ζ7+ζ23ζ7−ζ232ζ7+2ζ23−2ζ7−2ζ23−2ζ5−2ζ132ζ5+2ζ13-10−i3i3103−3−ii00−ζ7−ζ23ζ7+ζ23ζ5−ζ13−ζ5+ζ13ζ5+ζ13−ζ5−ζ13−ζ7+ζ23ζ7−ζ231+i−1−i1−i−1+i2−2−i2i2−ζ4+ζ14ζ4−ζ14−ζ20+ζ22ζ20−ζ22−ζ20−ζ22ζ20+ζ22−ζ4−ζ14ζ4+ζ14ζ13−ζ23−ζ13+ζ23ζ5−ζ7−ζ5+ζ7ζ5+ζ7−ζ5−ζ7ζ13+ζ23−ζ13−ζ23000000000000000000000000
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Here ζ is a primitive root of unity of order 24 (ζ24 = 1); i = ζ6.