Finite Group Databasebeta

← Group #13155471

Character table — Group #13155471

Order 1728.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96C97C98C99C100C101C102C103C104C105C106C107C108C109C110C111C112C113C114C115C116C117C118C119C120
size111122222222222222444444444444444444444466668888888888889999121212121212121212121212121212121212121212121212121212121818181818182424242424242424242424243636363636365454545472727272
order122233344666666666333666666666121212121212121212128888366612121212121212122222444412121212121212122424242424242424242424242424242444666612121212121212121212121244441212888812121212
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-11111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-1-1
χ311111111111111111111111111111111111111111111111111111111-1-1-1-111-1-11111-1-1-1-11111111111111111-1-1-1-1-1-111-1-11111-1-1-1-111-1-1-1-1-1-1-1-111-1-1
χ411111111111111111111111111111111111111111111111111111111-1-1-1-1-1-111-1-1-1-111111111111111111111-1-1-1-1-1-1-1-111-1-1-1-11111-1-111-1-1-1-1-1-1-1-111
χ51111111111111111111111111111111111111111-1-1-1-11111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111111111-1-1-1-111-1-1-1-1-1-1-1-1
χ61111111111111111111111111111111111111111-1-1-1-11111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-1-11111
χ71111111111111111111111111111111111111111-1-1-1-1111111111111-1-1-1-111-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-11111-1-1-1-1-1-111-1-11111-1-111
χ81111111111111111111111111111111111111111-1-1-1-1111111111111-1-1-1-1-1-111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-1111111-1-1-1-1111111-1-1
χ91-11-1111-11-1-1-1111-1-1-1111-1-1-1-1111-1-1-1-11-1-1-1111111-1-11-1-1111-1-111-1-111-1-1i−ii−iii−i−iii−i−i11111111-1-1-1-1-1-1-1-11-111-1-1i−ii−iii−i−iii−i−ii−ii−i1-111-1-1i−ii−i
χ101-11-1111-11-1-1-1111-1-1-1111-1-1-1-1111-1-1-1-11-1-1-1111111-1-11-1-1111-1-111-1-111-1-1−ii−ii−i−iii−i−iii11111111-1-1-1-1-1-1-1-11-111-1-1−ii−ii−i−iii−i−iii−ii−ii1-111-1-1−ii−ii
χ111-11-1111-11-1-1-1111-1-1-1111-1-1-1-1111-1-1-1-11-1-1-1111111-1-11-1-1111-1-111-1-1-1-111i−i−iiii−i−i−i−iii11111111-1-1-1-1-1-1-1-1-11-1-111i−i−iiii−i−i−i−iiii−i−ii-11-1-111i−i−ii
χ121-11-1111-11-1-1-1111-1-1-1111-1-1-1-1111-1-1-1-11-1-1-1111111-1-11-1-1111-1-111-1-1-1-111−iii−i−i−iiiii−i−i11111111-1-1-1-1-1-1-1-1-11-1-111−iii−i−i−iiiii−i−i−iii−i-11-1-111−iii−i
χ131-11-1111-11-1-1-1111-1-1-1111-1-1-1-1111-1-1-1-11-1-1-11111-1-1111-1-1111-1-111-1-111-1-1i−ii−iii−i−iii−i−i-1-1-1-1-1-1-1-1111111111-111-1-1i−ii−iii−i−iii−i−i−ii−ii1-1-1-111−ii−ii
χ141-11-1111-11-1-1-1111-1-1-1111-1-1-1-1111-1-1-1-11-1-1-11111-1-1111-1-1111-1-111-1-111-1-1−ii−ii−i−iii−i−iii-1-1-1-1-1-1-1-1111111111-111-1-1−ii−ii−i−iii−i−iiii−ii−i1-1-1-111i−ii−i
χ151-11-1111-11-1-1-1111-1-1-1111-1-1-1-1111-1-1-1-11-1-1-11111-1-1111-1-1111-1-111-1-1-1-111i−i−iiii−i−i−i−iii-1-1-1-1-1-1-1-111111111-11-1-111i−i−iiii−i−i−i−iii−iii−i-1111-1-1−iii−i
χ161-11-1111-11-1-1-1111-1-1-1111-1-1-1-1111-1-1-1-11-1-1-11111-1-1111-1-1111-1-111-1-1-1-111−iii−i−i−iiiii−i−i-1-1-1-1-1-1-1-111111111-11-1-111−iii−i−i−iiiii−i−ii−i−ii-1111-1-1i−i−ii
χ172222222-2-2222222222222222222222-2-2-2-2-2-2-2-2-2-200002222-2-2-2-2-2-2-2-222220000000000000000000000000000-2-222220000000000000000-2-200000000
χ182222222-2-2222222222222222222222-2-2-2-2-2-2-2-2-2-200002222-2-2-2-2-2-2-2-2-2-2-2-2000000000000000000000000000022-2-2-2-200000000000000002200000000
χ19222222-12222-122-1-1222-1-122-1-12-1-1-1-122-1-12222220000-1-1-1-1-1-1-1-1-1-1-1-122222222-1-1-1-1-1-1-1-1000000000000000022-1-1-1-12222-1-1-1-1-1-1-1-10000-1-100000000
χ20222222-12222-122-1-1222-1-122-1-12-1-1-1-122-1-12222220000-1-1-1-1-1-1-1-1-1-1-1-12222-2-2-2-211111111000000000000000022-1-1-1-1-2-2-2-2111111110000-1-100000000
χ21222222-12222-122-1-1222-1-122-1-12-1-1-1-122-1-12222220000-1-1-1-1-1-1-1-1-1-1-1-1-2-2-2-222-2-2-1-1-1-111110000000000000000-2-2111122-2-2-1-1-1-1111100001100000000
χ22222222-12222-122-1-1222-1-122-1-12-1-1-1-122-1-12222220000-1-1-1-1-1-1-1-1-1-1-1-1-2-2-2-2-2-2221111-1-1-1-10000000000000000-2-21111-2-2221111-1-1-1-100001100000000
χ23222222-1-2-222-122-1-1222-1-122-1-12-1-1-1-1-2-211-2-2-2-2-2-20000-1-1-1-11111111122220000−i3i3−i3i3−i3i3−i3i30000000000000000-2-2-1-1-1-10000−i3i3−i3i3−i3i3−i3i300001100000000
χ24222222-1-2-222-122-1-1222-1-122-1-12-1-1-1-1-2-211-2-2-2-2-2-20000-1-1-1-11111111122220000i3−i3i3−i3i3−i3i3−i30000000000000000-2-2-1-1-1-10000i3−i3i3−i3i3−i3i3−i300001100000000
χ25222222-1-2-222-122-1-1222-1-122-1-12-1-1-1-1-2-211-2-2-2-2-2-20000-1-1-1-111111111-2-2-2-20000−i3i3−i3i3i3−i3i3−i300000000000000002211110000−i3i3−i3i3i3−i3i3−i30000-1-100000000
χ26222222-1-2-222-122-1-1222-1-122-1-12-1-1-1-1-2-211-2-2-2-2-2-20000-1-1-1-111111111-2-2-2-20000i3−i3i3−i3−i3i3−i3i300000000000000002211110000i3−i3i3−i3−i3i3−i3i30000-1-100000000
χ2722222-12222-122-1222-1-12-1-1-12-1-12-12-12-122-1-12-1-1-12222-1-1-1-12-12-1-1-1-1-1000000220000222222-1-1-1-1-1-122-1-1-1-1-1-100000000-1-10000-1-1-1-1002200000000-1-1
χ2822222-12222-122-1222-1-12-1-1-12-1-12-12-12-122-1-12-1-1-12222-1-1-1-12-12-1-1-1-1-1000000-2-20000-2-2-2-222-1-1-1-1-1-122-1-1-1-1-1-100000000110000111100-2-20000000011
χ2922222-12222-122-1222-1-12-1-1-12-1-12-12-12-122-1-12-1-1-1-2-2-2-2-1-1-1-12-12-1-1-1-1-10000002200002222-2-2111111-2-211111100000000-1-10000-1-1-1-100-2-20000000011
χ3022222-12222-122-1222-1-12-1-1-12-1-12-12-12-122-1-12-1-1-1-2-2-2-2-1-1-1-12-12-1-1-1-1-1000000-2-20000-2-2-2-2-2-2111111-2-2111111000000001100001111002200000000-1-1
χ312222-12222-122-1222-12-1-12-1-1-12-1-12-12-1222-1-1-12-1-12222-1-1-1-1-12-12-1-1-1-10000220022220000-1-122-1-1-1-1-1-122-1-1-1-1000000-1-100-1-1-1-100002200000000-1-100
χ322222-12222-122-1222-12-1-12-1-1-12-1-12-12-1222-1-1-12-1-12222-1-1-1-1-12-12-1-1-1-10000-2-200-2-2-2-20000-1-122-1-1-1-1-1-122-1-1-1-1000000110011110000-2-2000000001100
χ332222-12222-122-1222-12-1-12-1-1-12-1-12-12-1222-1-1-12-1-1-2-2-2-2-1-1-1-1-12-12-1-1-1-1000022002222000011-2-2111111-2-21111000000-1-100-1-1-1-10000-2-2000000001100
χ342222-12222-122-1222-12-1-12-1-1-12-1-12-12-1222-1-1-12-1-1-2-2-2-2-1-1-1-1-12-12-1-1-1-10000-2-200-2-2-2-2000011-2-2111111-2-211110000001100111100002200000000-1-100
χ3522-2-222200222-2-2-2-2-2-22222-222-2-2-2-2-200000000002−22−222-2-2000000002-22-20000000000002−22−222−2−22−22−222−2−2002-22-20000000000000000002−22−20000
χ3622-2-222200222-2-2-2-2-2-22222-222-2-2-2-2-200000000002−22−222-2-200000000-22-220000000000002−22−222−2−22−22−222−2−200-22-22000000000000000000−22−220000
χ3722-2-222200222-2-2-2-2-2-22222-222-2-2-2-2-20000000000−22−2222-2-2000000002-22-2000000000000−22−22−2−222−22−22−2−222002-22-2000000000000000000−22−220000
χ3822-2-222200222-2-2-2-2-2-22222-222-2-2-2-2-20000000000−22−2222-2-200000000-22-22000000000000−22−22−2−222−22−22−2−22200-22-220000000000000000002−22−20000
χ392-22-22222-2-2-2-2222-2-2-2222-2-2-2-2222-2-222-2222-2-2-2-200002-2-22-2-222-2-22222-2-20000000000000000000000000000-2222-2-20000000000000000-2200000000
χ402-22-22222-2-2-2-2222-2-2-2222-2-2-2-2222-2-222-2222-2-2-2-200002-2-22-2-222-2-222-2-22200000000000000000000000000002-2-2-22200000000000000002-200000000
χ412-22-222-12-2-2-2122-11-2-22-1-1-2-2112-1-111221-122-2-2-2-20000-111-111-1-111-1-122-2-200003−3−333−3−330000000000000000-22-1-11100003−3−333−3−3300001-100000000
χ422-22-222-12-2-2-2122-11-2-22-1-1-2-2112-1-111221-122-2-2-2-20000-111-111-1-111-1-122-2-20000−333−3−333−30000000000000000-22-1-1110000−333−3−333−300001-100000000
χ432-22-222-12-2-2-2122-11-2-22-1-1-2-2112-1-111221-122-2-2-2-20000-111-111-1-111-1-1-2-22200003−3−33−333−300000000000000002-211-1-100003−3−33−333−30000-1100000000
χ442-22-222-12-2-2-2122-11-2-22-1-1-2-2112-1-111221-122-2-2-2-20000-111-111-1-111-1-1-2-2220000−333−33−3−3300000000000000002-211-1-10000−333−33−3−330000-1100000000
χ452-22-222-1-22-2-2122-11-2-22-1-1-2-2112-1-111-2-2-11-2-222220000-111-1-1-111-1-11122-2-22i−2i2i−2i−i−iii−i−iii00000000000000002-2-1-1112i−2i2i−2i−i−iii−i−iii0000-1100000000
χ462-22-222-1-22-2-2122-11-2-22-1-1-2-2112-1-111-2-2-11-2-222220000-111-1-1-111-1-11122-2-2−2i2i−2i2iii−i−iii−i−i00000000000000002-2-1-111−2i2i−2i2iii−i−iii−i−i0000-1100000000
χ472-22-222-1-22-2-2122-11-2-22-1-1-2-2112-1-111-2-2-11-2-222220000-111-1-1-111-1-111-2-2222i−2i−2i2i−i−iiiii−i−i0000000000000000-2211-1-12i−2i−2i2i−i−iiiii−i−i00001-100000000
χ482-22-222-1-22-2-2122-11-2-22-1-1-2-2112-1-111-2-2-11-2-222220000-111-1-1-111-1-111-2-222−2i2i2i−2iii−i−i−i−iii0000000000000000-2211-1-1−2i2i2i−2iii−i−i−i−iii00001-100000000
χ492-22-22-12-22-21-22-12-2-21-12-111-21-12-1-21-212-2112-1-1-122-2-2-111-12-1-21-1-1110000002i−2i00002i2i−2i−2i22-1-1-1-1-1-1-2-211111100000000−ii0000−i−iii002i−2i00000000−ii
χ502-22-22-12-22-21-22-12-2-21-12-111-21-12-1-21-212-2112-1-1-122-2-2-111-12-1-21-1-111000000−2i2i0000−2i−2i2i2i22-1-1-1-1-1-1-2-211111100000000i−i0000ii−i−i00−2i2i00000000i−i
χ512-22-22-12-22-21-22-12-2-21-12-111-21-12-1-21-212-2112-1-1-1-2-222-111-12-1-21-1-1110000002i−2i00002i2i−2i−2i-2-211111122-1-1-1-1-1-100000000−ii0000−i−iii00−2i2i00000000i−i
χ522-22-22-12-22-21-22-12-2-21-12-111-21-12-1-21-212-2112-1-1-1-2-222-111-12-1-21-1-111000000−2i2i0000−2i−2i2i2i-2-211111122-1-1-1-1-1-100000000i−i0000ii−i−i002i−2i00000000−ii
χ532-22-2-122-221-2-2-122-21-2-1-12111-2-1-121-21-22-211-12-1-122-2-2-111-1-121-2-1-11100002i−2i002i2i−2i−2i0000-1-122-1-1-1-111-2-21111000000−ii00−i−iii00002i−2i00000000−ii00
χ542-22-2-122-221-2-2-122-21-2-1-12111-2-1-121-21-22-211-12-1-122-2-2-111-1-121-2-1-1110000−2i2i00−2i−2i2i2i0000-1-122-1-1-1-111-2-21111000000i−i00ii−i−i0000−2i2i00000000i−i00
χ552-22-2-122-221-2-2-122-21-2-1-12111-2-1-121-21-22-211-12-1-1-2-222-111-1-121-2-1-11100002i−2i002i2i−2i−2i000011-2-21111-1-122-1-1-1-1000000−ii00−i−iii0000−2i2i00000000i−i00
χ562-22-2-122-221-2-2-122-21-2-1-12111-2-1-121-21-22-211-12-1-1-2-222-111-1-121-2-1-1110000−2i2i00−2i−2i2i2i000011-2-21111-1-122-1-1-1-1000000i−i00ii−i−i00002i−2i00000000−ii00
χ572-2-2222200-2-2-2-2-2-2222222-22-2-2-2-2-22200000000002−2−222-22-2000000002-2-220000000000002−22−222−2−2−22−22−2−222002-2-220000000000000000002−2−220000
χ582-2-2222200-2-2-2-2-2-2222222-22-2-2-2-2-22200000000002−2−222-22-200000000-222-20000000000002−22−222−2−2−22−22−2−22200-222-2000000000000000000−222−20000
χ592-2-2222200-2-2-2-2-2-2222222-22-2-2-2-2-2220000000000−222−22-22-2000000002-2-22000000000000−22−22−2−2222−22−222−2−2002-2-22000000000000000000−222−20000
χ602-2-2222200-2-2-2-2-2-2222222-22-2-2-2-2-2220000000000−222−22-22-200000000-222-2000000000000−22−22−2−2222−22−222−2−200-222-20000000000000000002−2−220000
χ6144444-24-4-44-244-2444-2-24-2-2-24-2-24-24-2-42-4-422-42220000-2-2-2-2-42-4222220000000000000000000000000000000000000000000000000000000000000000
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χ6344444-2-2444-2-24-2-2-24-2-2-21-2-2-21-2-21-214-2-2-2-2-24-2-2-200001111-21-211111000000-4-400002222000000000000000000000000220000-1-1-1-100000000000000
χ6444444-2-2-4-44-2-24-2-2-24-2-2-21-2-2-21-2-21-21-422222-4222000011112-12-1-1-1-1-1000000000000−2i32i3−2i32i3000000000000000000000000000000i3−i3i3−i300000000000000
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χ684444-24-244-24-2-24-2-2-24-21-2-2-21-2-21-21-2-24-2-2-2-2-24-2-2000011111-21-211110000-4-4002222000000000000000000000000002200-1-1-1-1000000000000000000
χ694444-24-2-4-4-24-2-24-2-2-24-21-2-2-21-2-21-21-22-422222-42200001111-12-12-1-1-1-100000000−2i32i3−2i32i3000000000000000000000000000000i3−i3i3−i3000000000000000000
χ704444-24-2-4-4-24-2-24-2-2-24-21-2-2-21-2-21-21-22-422222-42200001111-12-12-1-1-1-1000000002i3−2i32i3−2i3000000000000000000000000000000−i3i3−i3i3000000000000000000
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χ724444-2-2444-2-24-2-244-2-21-2-211-2-21-2-2-2-2-2-24411-2-211-4-4-4-41111-2-2-2-2111100000000000000002222-1-1-1-12222-1-1-1-100000000000000000000000000000000
χ734444-2-24-4-4-2-24-2-244-2-21-2-211-2-21-2-2-2-222-4-4-1-122-1-1000011112222-1-1-1-1000000000000000000003i−3i3i−3i00003i−3i3i−3i00000000000000000000000000000000
χ744444-2-24-4-4-2-24-2-244-2-21-2-211-2-21-2-2-2-222-4-4-1-122-1-1000011112222-1-1-1-100000000000000000000−3i3i−3i3i0000−3i3i−3i3i00000000000000000000000000000000
χ7544-4-444-20044-2-4-422-4-44-2-24-4-2-2-4222200000000000000-2-222000000004-44-4000000000000000000000000000000-22-2200000000000000000000000000
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χ7844-4-44-24004-24-42-4-4-42-24-2-224-22-42-420000000000−2222−2222-2-222000000000000000000000000−22222−222−2−2−22222−222−2−200000000000000000000000000000000
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Here ζ is a primitive root of unity of order 24 (ζ24 = 1); i = ζ6.