Finite Group Databasebeta

← Group #13155727

Character table — Group #13155727

Order 1728.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96C97C98C99C100C101C102C103C104C105C106C107C108C109C110C111C112C113C114C115C116C117C118C119C120C121C122C123C124C125C126
size111122222222222222333344444444444444444444446666666666888888888888121212121212121212121212121212121212121212121212181818182424242424242424242424243636363636363636363636363636363654545454
order12442333466612121212121288883336666666612121212121212121212128824242424242424243666661212121212122244666612121212242424242424242424242424888866666612121212121288882424242424242424242424244444
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111111111111111111111111111111-11-111-1-111-1-1111111111111-1-1-1-11-111-1-11-111-1-111-1-11111-1-1-1-1-1-1-1-1-1-1-1-1
χ3111111111111111111111111111111111111111111111111111111111111111111-11-11-1-111-1-111111111111111-1-1-1-1-11-1-111-11-1-111-1-111-1-1-1-11111-1-1-1-1-1-1-1-1
χ4111111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-11111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111
χ5111111111111111111-1-1-1-11111111111111111111111-1-1-1-1-1-1-1-1-1-1111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-11111111111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1
χ6111111111111111111-1-1-1-11111111111111111111111-1-1-1-1-1-1-1-1-1-11111111111111-11-111-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11-111-1-11-111-1-1-1-111-1-1-1-11111-1-1-1-11111
χ7111111111111111111-1-1-1-11111111111111111111111-1-1-1-1-1-1-1-1-1-1111111111111-11-11-1-111-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11-1-111-11-1-11111-1-11111-1-1-1-1-1-1-1-11111
χ8111111111111111111-1-1-1-11111111111111111111111-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-11111111111111111-1-1-1-1
χ911-1-1-11111111-1-1-1-1-1-1ii−i−i111-1-1-1-1-11111111-1-1-1-1-1-11i−iiiii−i−i−i−i1-1-1-1-111111-1-111-1-11111-1-1-1-1ii−i−iiiii−i−i−i−i11-1-1111111-1-1-1-1-1-1i−ii−iii−i−iii−i−i11-1-1ii−i−i
χ1011-1-1-11111111-1-1-1-1-1-1ii−i−i111-1-1-1-1-11111111-1-1-1-1-1-11i−iiiii−i−i−i−i1-1-1-1-111111-1-11-1-1111-1-1-1-111ii−i−iiiii−i−i−i−i-1-1111-111-1-1-11-1-111i−i−iiii−i−i−i−iii-1-111−i−iii
χ1111-1-1-11111111-1-1-1-1-1-1ii−i−i111-1-1-1-1-11111111-1-1-1-1-1-11i−iiiii−i−i−i−i1-1-1-1-111111-1-1-111-1-1-11111-1-1ii−i−iiiii−i−i−i−i-1-111-11-1-1111-111-1-1−iii−i−i−iiiii−i−i-1-111−i−iii
χ1211-1-1-11111111-1-1-1-1-1-1ii−i−i111-1-1-1-1-11111111-1-1-1-1-1-11i−iiiii−i−i−i−i1-1-1-1-111111-1-1-1-111-1-1-1-11111ii−i−iiiii−i−i−i−i11-1-1-1-1-1-1-1-1111111−ii−ii−i−iii−i−iii11-1-1ii−i−i
χ1311-1-1-11111111-1-1-1-1-1-1−i−iii111-1-1-1-1-11111111-1-1-1-1-1-11−ii−i−i−i−iiiii1-1-1-1-111111-1-111-1-11111-1-1-1-1−i−iii−i−i−i−iiiii11-1-1111111-1-1-1-1-1-1−ii−ii−i−iii−i−iii11-1-1−i−iii
χ1411-1-1-11111111-1-1-1-1-1-1−i−iii111-1-1-1-1-11111111-1-1-1-1-1-11−ii−i−i−i−iiiii1-1-1-1-111111-1-11-1-1111-1-1-1-111−i−iii−i−i−i−iiiii-1-1111-111-1-1-11-1-111−iii−i−i−iiiii−i−i-1-111ii−i−i
χ1511-1-1-11111111-1-1-1-1-1-1−i−iii111-1-1-1-1-11111111-1-1-1-1-1-11−ii−i−i−i−iiiii1-1-1-1-111111-1-1-111-1-1-11111-1-1−i−iii−i−i−i−iiiii-1-111-11-1-1111-111-1-1i−i−iiii−i−i−i−iii-1-111ii−i−i
χ1611-1-1-11111111-1-1-1-1-1-1−i−iii111-1-1-1-1-11111111-1-1-1-1-1-11−ii−i−i−i−iiiii1-1-1-1-111111-1-1-1-111-1-1-1-11111−i−iii−i−i−i−iiiii11-1-1-1-1-1-1-1-1111111i−ii−iii−i−iii−i−i11-1-1−i−iii
χ172222222-1222-1-1-1222200002-1-122-1222-1-12222-1-1-1-122-10000000000-1-1-1-1-1-1-1-1-1-1-1-12222222222220000000000002222-1-1-1-1-1-1-1-1-1-1-1-1000000000000-1-1-1-10000
χ182222222-1222-1-1-1222200002-1-122-1222-1-12222-1-1-1-122-10000000000-1-1-1-1-1-1-1-1-1-1-1-12-22-222-2-222-2-2000000000000-2-2-2-2-11-1-111-11-1-11100000000000011110000
χ192222222-1222-1-1-1222200002-1-122-1222-1-12222-1-1-1-122-10000000000-1-1-1-1-1-1-1-1-1-1-1-1-22-22-2-222-2-222000000000000-2-2-2-21-111-1-11-111-1-100000000000011110000
χ202222222-1222-1-1-1222200002-1-122-1222-1-12222-1-1-1-122-10000000000-1-1-1-1-1-1-1-1-1-1-1-1-2-2-2-2-2-2-2-2-2-2-2-20000000000002222111111111111000000000000-1-1-1-10000
χ21222222-1222-122222-1-12222-12-12-12-1-1-12-12-1-1-122-1-1-1-122222-1-122-1-1-12-1-1-1-12-1-1-1-1-1020200-1-100-1-12-12-1-1-1-1-1-1-1-1-100000200-1-10200-1-100220000-1-1-1-100000000
χ22222222-1222-122222-1-12222-12-12-12-1-1-12-12-1-1-122-1-1-1-122222-1-122-1-1-12-1-1-1-12-1-1-1-1-10-20-2001100112-12-1-1-1-1-1-1-1-1-100000-200110-2001100-2-20000111100000000
χ23222222-1222-122222-1-1-2-2-2-2-12-12-12-1-1-12-12-1-1-122-1-1-1-12-2-2-2-211-2-211-12-1-1-1-12-1-1-1-1-1020200-1-100-1-1-21-211111111100000200-1-10200-1-100-2-20000111100000000
χ24222222-1222-122222-1-1-2-2-2-2-12-12-12-1-1-12-12-1-1-122-1-1-1-12-2-2-2-211-2-211-12-1-1-1-12-1-1-1-1-10-20-200110011-21-211111111100000-200110-2001100220000-1-1-1-100000000
χ2522222-1222-12222-1-1222222-1-12-122-1-1-1-12-12-1-1-1-122-1-1222-1-122-1-122-1-12-1-1-1-12-1-1-1-12020-1-100-1-100-12-12-1-1-1-1-1-1-1-1000020-1-10020-1-1002200-1-1-1-1000000000000
χ2622222-1222-12222-1-1222222-1-12-122-1-1-1-12-12-1-1-1-122-1-1222-1-122-1-122-1-12-1-1-1-12-1-1-1-1-20-2011001100-12-12-1-1-1-1-1-1-1-10000-201100-201100-2-2001111000000000000
χ2722222-1222-12222-1-122-2-2-2-2-1-12-122-1-1-1-12-12-1-1-1-122-1-12-2-211-2-211-2-2-1-12-1-1-1-12-1-1-1-12020-1-100-1-1001-21-211111111000020-1-10020-1-100-2-2001111000000000000
χ2822222-1222-12222-1-122-2-2-2-2-1-12-122-1-1-1-12-12-1-1-1-122-1-12-2-211-2-211-2-2-1-12-1-1-1-12-1-1-1-1-20-20110011001-21-2111111110000-201100-2011002200-1-1-1-1000000000000
χ292222-2222-22222222222222222-2-2-2-2-2222-2-2-2-2222222-2-2-2222222222-2-2-2-22-2-2-2-222000000000000-2-2-2-222-2-222-2-2000000000000000000000000000000000000
χ302222-2222-2222222222-2-2-2-2222-2-2-2-2-2222-2-2-2-2222222-222-2-2-2-2-2-2-2-22-2-2-2-22-2-2-2-2220000000000002222-2-222-2-222000000000000000000000000000000000000
χ312222-22-12-22-122222-1-12222-12-1-21-211-12-1-211122-1-1-1-1-2-2-222-1-122-1-1-1-2111-1-2111-1-1000000−i3i300−i3i3-21-21-1-111-1-11100000000−i3i30000−i3i300000000−i3i3−i3i300000000
χ322222-22-12-22-122222-1-12222-12-1-21-211-12-1-211122-1-1-1-1-2-2-222-1-122-1-1-1-2111-1-2111-1-1000000i3−i300i3−i3-21-21-1-111-1-11100000000i3−i30000i3−i300000000i3−i3i3−i300000000
χ332222-22-12-22-122222-1-1-2-2-2-2-12-1-21-211-12-1-211122-1-1-1-1-222-2-211-2-211-1-2111-1-2111-1-1000000−i3i300−i3i32-12-111-1-111-1-100000000−i3i30000−i3i300000000i3−i3i3−i300000000
χ342222-22-12-22-122222-1-1-2-2-2-2-12-1-21-211-12-1-211122-1-1-1-1-222-2-211-2-211-1-2111-1-2111-1-1000000i3−i300i3−i32-12-111-1-111-1-100000000i3−i30000i3−i300000000−i3i3−i3i300000000
χ352222-2-122-2-12222-1-1222222-1-121-2-211-1-121-211-1-122-1-1-2-2-2-1-122-1-122-11-211-11-211-1-10000−i3i300−i3i3001-21-2-1-111-1-111000000−i3i30000−i3i3000000−i3i3−i3i3000000000000
χ362222-2-122-2-12222-1-1222222-1-121-2-211-1-121-211-1-122-1-1-2-2-2-1-122-1-122-11-211-11-211-1-10000i3−i300i3−i3001-21-2-1-111-1-111000000i3−i30000i3−i3000000i3−i3i3−i3000000000000
χ372222-2-122-2-12222-1-122-2-2-2-2-1-121-2-211-1-121-211-1-122-1-1-22211-2-211-2-2-11-211-11-211-1-10000−i3i300−i3i300-12-1211-1-111-1-1000000−i3i30000−i3i3000000i3−i3i3−i3000000000000
χ382222-2-122-2-12222-1-122-2-2-2-2-1-121-2-211-1-121-211-1-122-1-1-22211-2-211-2-2-11-211-11-211-1-10000i3−i300i3−i300-12-1211-1-111-1-1000000i3−i30000i3−i3000000−i3i3−i3i3000000000000
χ3922-2-22222-2222-2-2-2-2-2-22i2i−2i−2i22222222222-2-2-2-2-2-2-2-2-2-2-2−2i2i2i2i2i2i−2i−2i−2i−2i222222-2-2-2-2-2-2000000000000−2i−2i2i2i2i2i−2i−2i−2i−2i2i2i000000000000000000000000000000000000
χ4022-2-22222-2222-2-2-2-2-2-2−2i−2i2i2i22222222222-2-2-2-2-2-2-2-2-2-2-22i−2i−2i−2i−2i−2i2i2i2i2i222222-2-2-2-2-2-20000000000002i2i−2i−2i−2i−2i2i2i2i2i−2i−2i000000000000000000000000000000000000
χ4122-2-222-12-22-12-2-2-2-2112i2i−2i−2i-12-12-12-1-1-12-1-2111-2-21111-2−2i2i2i2i−i−i−2i−2iii-12-1-1-1-1-211111000000−i3i300i3−i3−2ii2i−i−i−iiiii−i−i00000000−i3i30000i3−i3000000003−3−3300000000
χ4222-2-222-12-22-12-2-2-2-2112i2i−2i−2i-12-12-12-1-1-12-1-2111-2-21111-2−2i2i2i2i−i−i−2i−2iii-12-1-1-1-1-211111000000i3−i300−i3i3−2ii2i−i−i−iiiii−i−i00000000i3−i30000−i3i300000000−333−300000000
χ4322-2-222-12-22-12-2-2-2-211−2i−2i2i2i-12-12-12-1-1-12-1-2111-2-21111-22i−2i−2i−2iii2i2i−i−i-12-1-1-1-1-211111000000−i3i300i3−i32i−i−2iiii−i−i−i−iii00000000−i3i30000i3−i300000000−333−300000000
χ4422-2-222-12-22-12-2-2-2-211−2i−2i2i2i-12-12-12-1-1-12-1-2111-2-21111-22i−2i−2i−2iii2i2i−i−i-12-1-1-1-1-211111000000i3−i300−i3i32i−i−2iiii−i−i−i−iii00000000i3−i30000−i3i3000000003−3−3300000000
χ4522-2-22-122-2-122-2-211-2-22i2i−2i−2i-1-12-122-1-1-1-121-21111-2-211-2−2i2i−i−i2i2iii−2i−2i-1-12-1-1-11-211110000−i3i300i3−i300i−2i−i2i−i−iiiii−i−i000000−i3i30000i3−i30000003−3−33000000000000
χ4622-2-22-122-2-122-2-211-2-22i2i−2i−2i-1-12-122-1-1-1-121-21111-2-211-2−2i2i−i−i2i2iii−2i−2i-1-12-1-1-11-211110000i3−i300−i3i300i−2i−i2i−i−iiiii−i−i000000i3−i30000−i3i3000000−333−3000000000000
χ4722-2-22-122-2-122-2-211-2-2−2i−2i2i2i-1-12-122-1-1-1-121-21111-2-211-22i−2iii−2i−2i−i−i2i2i-1-12-1-1-11-211110000−i3i300i3−i300−i2ii−2iii−i−i−i−iii000000−i3i30000i3−i3000000−333−3000000000000
χ4822-2-22-122-2-122-2-211-2-2−2i−2i2i2i-1-12-122-1-1-1-121-21111-2-211-22i−2iii−2i−2i−i−i2i2i-1-12-1-1-11-211110000i3−i300−i3i300−i2ii−2iii−i−i−i−iii000000i3−i30000−i3i30000003−3−33000000000000
χ4922-2-2-222-1222-111-2-2-2-200002-1-1-2-21-2-22-1-122221111-2-2-10000000000-11111-1-1-1-1-11122-2-22222-2-2-2-200000000000022-2-2-1-1-1-1-1-1111111000000000000-1-1110000
χ5022-2-2-222-1222-111-2-2-2-200002-1-1-2-21-2-22-1-122221111-2-2-10000000000-11111-1-1-1-1-1112-2-2222-2-2-2-222000000000000-2-222-11-1-1111-111-1-100000000000011-1-10000
χ5122-2-2-222-1222-111-2-2-2-200002-1-1-2-21-2-22-1-122221111-2-2-10000000000-11111-1-1-1-1-111-222-2-2-22222-2-2000000000000-2-2221-111-1-1-11-1-11100000000000011-1-10000
χ5222-2-2-222-1222-111-2-2-2-200002-1-1-2-21-2-22-1-122221111-2-2-10000000000-11111-1-1-1-1-111-2-222-2-2-2-2222200000000000022-2-2111111-1-1-1-1-1-1000000000000-1-1110000
χ5322-2-2-22-1222-12-2-2-2-2112i2i−2i−2i-12-1-21-211-12-12-1-1-1-2-2111122i−2i2i2i−i−i−2i−2iii-1-2111-12-1-1-111020-200-1-100112i−i−2ii−i−i−i−iiiii00000200-1-10-20011002i−2i0000−i−iii00000000
χ5422-2-2-22-1222-12-2-2-2-2112i2i−2i−2i-12-1-21-211-12-12-1-1-1-2-2111122i−2i2i2i−i−i−2i−2iii-1-2111-12-1-1-1110-202001100-1-12i−i−2ii−i−i−i−iiiii00000-200110200-1-100−2i2i0000ii−i−i00000000
χ5522-2-2-22-1222-12-2-2-2-211−2i−2i2i2i-12-1-21-211-12-12-1-1-1-2-211112−2i2i−2i−2iii2i2i−i−i-1-2111-12-1-1-111020-200-1-10011−2ii2i−iiiii−i−i−i−i00000200-1-10-2001100−2i2i0000ii−i−i00000000
χ5622-2-2-22-1222-12-2-2-2-211−2i−2i2i2i-12-1-21-211-12-12-1-1-1-2-211112−2i2i−2i−2iii2i2i−i−i-1-2111-12-1-1-1110-202001100-1-1−2ii2i−iiiii−i−i−i−i00000-200110200-1-1002i−2i0000−i−iii00000000
χ5722-2-2-2-1222-122-2-211-2-22i2i−2i−2i-1-121-2-211-1-12-12-1-111-2-21122i−2i−i−i2i2iii−2i−2i-11-211-1-12-1-11120-20-1-1001100−i2ii−2i−i−i−i−iiiii000020-1-100-2011002i−2i00−i−iii000000000000
χ5822-2-2-2-1222-122-2-211-2-22i2i−2i−2i-1-121-2-211-1-12-12-1-111-2-21122i−2i−i−i2i2iii−2i−2i-11-211-1-12-1-111-20201100-1-100−i2ii−2i−i−i−i−iiiii0000-20110020-1-100−2i2i00ii−i−i000000000000
χ5922-2-2-2-1222-122-2-211-2-2−2i−2i2i2i-1-121-2-211-1-12-12-1-111-2-2112−2i2iii−2i−2i−i−i2i2i-11-211-1-12-1-11120-20-1-1001100i−2i−i2iiiii−i−i−i−i000020-1-100-201100−2i2i00ii−i−i000000000000
χ6022-2-2-2-1222-122-2-211-2-2−2i−2i2i2i-1-121-2-211-1-12-12-1-111-2-2112−2i2iii−2i−2i−i−i2i2i-11-211-1-12-1-111-20201100-1-100i−2i−i2iiiii−i−i−i−i0000-20110020-1-1002i−2i00−i−iii000000000000
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χ1228-88i−8i0-4-4-40444−4i4i−4i4i−4i4i0000222000-66-2-2-200−6i6i2i−2i2i−2i2i−2i00000000000-1003-31003i−3i−ii000000000000000000000000000000000000000000000000000000000000
χ1238-8−8i8i08-4-40-8444i−4i−8i8i4i−4i0000-4-420000044-200004i−4i−2i2i4i−4i0000000000020000-20000−2i2i000000000000000000000000000000000000000000000000000000000000
χ1248-8−8i8i0-48-404-844i−4i4i−4i−8i8i0000-42-4000004-240000−2i2i4i−4i4i−4i0000000000020000-20000−2i2i000000000000000000000000000000000000000000000000000000000000
χ1258-8−8i8i0-4-4-404444i−4i4i−4i4i−4i00002220006-6-2-2-200−6i6i−2i2i−2i2i−2i2i00000000000-100-331003i−3ii−i000000000000000000000000000000000000000000000000000000000000
χ1268-8−8i8i0-4-4-404444i−4i4i−4i4i−4i0000222000-66-2-2-2006i−6i−2i2i−2i2i−2i2i00000000000-1003-3100−3i3ii−i000000000000000000000000000000000000000000000000000000000000

Here ζ is a primitive root of unity of order 24 (ζ24 = 1); i = ζ6.