Finite Group Databasebeta

← Group #13139975

Character table — Group #13139975

Order 1728.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96C97C98C99C100C101C102C103C104C105C106C107C108C109C110C111C112C113C114C115C116
size11111111222222222222222222226666666666666666121212121212121212121212121212121212121212121212181818181818181818181818181818181818181818181818363636363636363636363636363636363636363636363636
order12224444223446666666121212121212121233666666121212121212121236666666666612121212121212121212121288888888242424242424242424242424242424244444444412121212121212121212121212121212
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
χ311111111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-111111111-1-1-1-1-1-1-1-1
χ411111111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-111111111
χ51111-1-1-1-1-1-111111-1-1-1-1111-1-1-1-11111111111-1-1-1-1-1-1-1-11-1-1-1-111-1-1-1-1111111111-1-1-1-11111-1-1-1-111111111-1-1-1-1-1-1-1-111-1-111-1-11111-1-1-1-11111-1-1-1-1
χ61111-1-1-1-1-1-111111-1-1-1-1111-1-1-1-11111111111-1-1-1-1-1-1-1-11-1-1-1-111-1-1-1-1111111111-1-1-1-11111-1-1-1-111111111-1-1-1-1-1-1-1-1-1-111-1-111-1-1-1-11111-1-1-1-11111
χ71111-1-1-1-1-1-111111-1-1-1-1111-1-1-1-11111111111-1-1-1-1-1-1-1-11-1-1-1-111-1-1-1-1111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-11111111111-1-1-1-1111111-1-1-1-1-1-1-1-11111
χ81111-1-1-1-1-1-111111-1-1-1-1111-1-1-1-11111111111-1-1-1-1-1-1-1-11-1-1-1-111-1-1-1-1111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-111111111-1-11111-1-1-1-1-1-111111111-1-1-1-1
χ911-1-111-1-11-11-11-1-111-1-11-1-111-1-1111111-1-1-1-11111-1-1-1-1111-1-1-1-111-1-1111-1-111-1-111-1-111-1-111-1-11111-1-1-1-11111-1-1-1-1i−ii−ii−ii−iii−i−iii−i−iii−i−iii−i−i
χ1011-1-111-1-11-11-11-1-111-1-11-1-111-1-1111111-1-1-1-11111-1-1-1-1111-1-1-1-111-1-1111-1-111-1-111-1-111-1-111-1-11111-1-1-1-11111-1-1-1-1−ii−ii−ii−ii−i−iii−i−iii−i−iii−i−iii
χ1111-1-111-1-11-11-11-1-111-1-11-1-111-1-1111111-1-1-1-11111-1-1-1-1111-1-1-1-111-1-1111-1-111-1-111-1-1-1-111-1-111-1-1-1-11111-1-1-1-11111i−ii−i−ii−iiii−i−iii−i−i−i−iii−i−iii
χ1211-1-111-1-11-11-11-1-111-1-11-1-111-1-1111111-1-1-1-11111-1-1-1-1111-1-1-1-111-1-1111-1-111-1-111-1-1-1-111-1-111-1-1-1-11111-1-1-1-11111−ii−iii−ii−i−i−iii−i−iiiii−i−iii−i−i
χ1311-1-1-1-111-111-11-1-1-1-1111-1-1-1-111111111-1-1-1-1-1-1-1-111111-1-111-1-1-1-111111-1-111-1-1-1-11111-1-1-1-1111111-1-1-1-1-1-1-1-11111i−i−iii−i−iiii−i−i−i−iiiii−i−i−i−iii
χ1411-1-1-1-111-111-11-1-1-1-1111-1-1-1-111111111-1-1-1-1-1-1-1-111111-1-111-1-1-1-111111-1-111-1-1-1-11111-1-1-1-1111111-1-1-1-1-1-1-1-11111−iii−i−iii−i−i−iiiii−i−i−i−iiiii−i−i
χ1511-1-1-1-111-111-11-1-1-1-1111-1-1-1-111111111-1-1-1-1-1-1-1-111111-1-111-1-1-1-111111-1-111-1-1-1-111-1-11111-1-1-1-1-1-111111111-1-1-1-1i−i−ii−iii−iii−i−i−i−iii−i−iiiii−i−i
χ1611-1-1-1-111-111-11-1-1-1-1111-1-1-1-111111111-1-1-1-1-1-1-1-111111-1-111-1-1-1-111111-1-111-1-1-1-111-1-11111-1-1-1-1-1-111111111-1-1-1-1−iii−ii−i−ii−i−iiiii−i−iii−i−i−i−iii
χ1722222222222222222222222222222-12-122-1-122-1-122-1-1-12-12-1-1-1-1-1-1-1-12-12-1-1-1-1-1-1-1-1-10000000000000000000000000000222200000000-1-1-1-1-1-1-1-1
χ1822222222222222222222222222222-12-122-1-122-1-122-1-1-12-12-1-1-1-1-1-1-1-12-12-1-1-1-1-1-1-1-1-10000000000000000000000000000-2-2-2-20000000011111111
χ192222222222222222222222222222-12-12-1-122-1-122-1-122-1-12-12-1-1-1-1-1-1-1-12-12-1-1-1-1-1-1-1-100000000000000000000000022220000-1-1-1-1-1-1-1-100000000
χ202222222222222222222222222222-12-12-1-122-1-122-1-122-1-12-12-1-1-1-1-1-1-1-12-12-1-1-1-1-1-1-1-1000000000000000000000000-2-2-2-200001111111100000000
χ2122222222-2-22-2-222-2-2-2-22-2-22222-2-222222222222222222-2-2-2-222-2-2-2-22-2-2-2-2-2-2-2-22222000000000000000000000000000000000000000000000000
χ2222222222-2-22-2-222-2-2-2-22-2-22222-2-22-12-122-1-122-1-122-1-1-1-21-21-1-11111-1-21-211111-1-1-1-10000000000000000000000000000000000000000−i3i3−i3i3−i3i3−i3i3
χ2322222222-2-22-2-222-2-2-2-22-2-22222-2-22-12-122-1-122-1-122-1-1-1-21-21-1-11111-1-21-211111-1-1-1-10000000000000000000000000000000000000000i3−i3i3−i3i3−i3i3−i3
χ2422222222-2-22-2-222-2-2-2-22-2-22222-2-2-12-12-1-122-1-122-1-122-11-21-2-1-11111-11-21-21111-1-1-1-100000000000000000000000000000000−i3i3−i3i3−i3i3−i3i300000000
χ2522222222-2-22-2-222-2-2-2-22-2-22222-2-2-12-12-1-122-1-122-1-122-11-21-2-1-11111-11-21-21111-1-1-1-100000000000000000000000000000000i3−i3i3−i3i3−i3i3−i300000000
χ262222-2-2-2-2222-2-22222222-2-2-2-2-2-2-2-222222222-2-2-2-2-2-2-2-2222222222222-2-2-2-2-2-2-2-2-2-2-2-2000000000000000000000000000000000000000000000000
χ272222-2-2-2-2222-2-22222222-2-2-2-2-2-2-2-22-12-122-1-1-2-211-2-211-12-12-1-1-1-1-1-1-1-1-21-21111111110000000000000000000000000000000000000000−i3i3−i3i3i3−i3i3−i3
χ282222-2-2-2-2222-2-22222222-2-2-2-2-2-2-2-22-12-122-1-1-2-211-2-211-12-12-1-1-1-1-1-1-1-1-21-21111111110000000000000000000000000000000000000000i3−i3i3−i3−i3i3−i3i3
χ292222-2-2-2-2222-2-22222222-2-2-2-2-2-2-2-2-12-12-1-12211-2-211-2-2-1-12-12-1-1-1-1-1-1-11-21-21111111100000000000000000000000000000000−i3i3−i3i3i3−i3i3−i300000000
χ302222-2-2-2-2222-2-22222222-2-2-2-2-2-2-2-2-12-12-1-12211-2-211-2-2-1-12-12-1-1-1-1-1-1-11-21-21111111100000000000000000000000000000000i3−i3i3−i3−i3i3−i3i300000000
χ312222-2-2-2-2-2-222222-2-2-2-2222-2-2-2-2222-12-122-1-1-2-211-2-211-1-21-21-1-11111-12-12-1-1-1-1-11111000000000000000000000000000022-2-200000000-1-1-1-11111
χ322222-2-2-2-2-2-222222-2-2-2-2222-2-2-2-2222-12-122-1-1-2-211-2-211-1-21-21-1-11111-12-12-1-1-1-1-111110000000000000000000000000000-2-222000000001111-1-1-1-1
χ332222-2-2-2-2-2-222222-2-2-2-2222-2-2-2-222-12-12-1-12211-2-211-2-2-11-21-2-1-11111-1-12-12-1-1-1-1111100000000000000000000000022-2-20000-1-1-1-1111100000000
χ342222-2-2-2-2-2-222222-2-2-2-2222-2-2-2-222-12-12-1-12211-2-211-2-2-11-21-2-1-11111-1-12-12-1-1-1-11111000000000000000000000000-2-22200001111-1-1-1-100000000
χ3522-2-222-2-22-22-22-2-222-2-22-2-222-2-2222-12-1-2-21122-1-1-2-211-12-1-2111-1-111-12-1-21-1-111-1-11100000000000000000000000000002i−2i2i−2i00000000−i−iii−i−iii
χ3622-2-222-2-22-22-22-2-222-2-22-2-222-2-2222-12-1-2-21122-1-1-2-211-12-1-2111-1-111-12-1-21-1-111-1-1110000000000000000000000000000−2i2i−2i2i00000000ii−i−iii−i−i
χ3722-2-222-2-22-22-22-2-222-2-22-2-222-2-222-12-1211-2-2-1-12211-2-2-1-121-211-1-111-1-121-2-1-111-1-1110000000000000000000000002i−2i2i−2i0000−i−iii−i−iii00000000
χ3822-2-222-2-22-22-22-2-222-2-22-2-222-2-222-12-1211-2-2-1-12211-2-2-1-121-211-1-111-1-121-2-1-111-1-111000000000000000000000000−2i2i−2i2i0000ii−i−iii−i−i00000000
χ3922-2-222-2-2-2222-2-2-2-2-22222222-2-2-2-22222-2-2-2-22222-2-2-2-22-2-222-2-2-2-2222-2-222-2-22222-2-2000000000000000000000000000000000000000000000000
χ4022-2-222-2-2-2222-2-2-2-2-22222222-2-2-2-22-12-1-2-21122-1-1-2-211-1-212-11111-1-1-1-212-111-1-1-1-11100000000000000000000000000000000000000003−3−333−3−33
χ4122-2-222-2-2-2222-2-2-2-2-22222222-2-2-2-22-12-1-2-21122-1-1-2-211-1-212-11111-1-1-1-212-111-1-1-1-1110000000000000000000000000000000000000000−333−3−333−3
χ4222-2-222-2-2-2222-2-2-2-2-22222222-2-2-2-2-12-1211-2-2-1-12211-2-2-11-2-121111-1-1-11-2-1211-1-1-1-111000000000000000000000000000000003−3−333−3−3300000000
χ4322-2-222-2-2-2222-2-2-2-2-22222222-2-2-2-2-12-1211-2-2-1-12211-2-2-11-2-121111-1-1-11-2-1211-1-1-1-11100000000000000000000000000000000−333−3−333−300000000
χ4422-2-2-2-2222-222-2-2-222-2-2222-2-222-2-22222-2-2-2-2-2-2-2-22222222-2-2-2-222-2-22-2-222-2-222-2-222000000000000000000000000000000000000000000000000
χ4522-2-2-2-2222-222-2-2-222-2-2222-2-222-2-22-12-1-2-211-2-21122-1-1-12-1-2111-1-111-1-212-111-1-111-1-100000000000000000000000000000000000000003−3−33−333−3
χ4622-2-2-2-2222-222-2-2-222-2-2222-2-222-2-22-12-1-2-211-2-21122-1-1-12-1-2111-1-111-1-212-111-1-111-1-10000000000000000000000000000000000000000−333−33−3−33
χ4722-2-2-2-2222-222-2-2-222-2-2222-2-222-2-2-12-1211-2-211-2-2-1-122-1-121-211-1-111-11-2-1211-1-111-1-1000000000000000000000000000000003−3−33−333−300000000
χ4822-2-2-2-2222-222-2-2-222-2-2222-2-222-2-2-12-1211-2-211-2-2-1-122-1-121-211-1-111-11-2-1211-1-111-1-100000000000000000000000000000000−333−33−3−3300000000
χ4922-2-2-2-222-222-22-2-2-2-2222-2-2-2-222222-12-1-2-211-2-21122-1-1-1-212-11111-1-1-12-1-21-1-11111-1-100000000000000000000000000002i−2i−2i2i00000000−i−iiiii−i−i
χ5022-2-2-2-222-222-22-2-2-2-2222-2-2-2-222222-12-1-2-211-2-21122-1-1-1-212-11111-1-1-12-1-21-1-11111-1-10000000000000000000000000000−2i2i2i−2i00000000ii−i−i−i−iii
χ5122-2-2-2-222-222-22-2-2-2-2222-2-2-2-22222-12-1211-2-211-2-2-1-122-11-2-121111-1-1-1-121-2-1-11111-1-10000000000000000000000002i−2i−2i2i0000−i−iiiii−i−i00000000
χ5222-2-2-2-222-222-22-2-2-2-2222-2-2-2-22222-12-1211-2-211-2-2-1-122-11-2-121111-1-1-1-121-2-1-11111-1-1000000000000000000000000−2i2i2i−2i0000ii−i−i−i−iii00000000
χ532-22-22i−2i2i−2i002002-20000-2002i−2i2i−2i0022-2-22-22-22i−2i2i−2i2i−2i2i−2i200002-20000-2000000002i−2i2i−2i2−22−2−i2i2−i2i222−2−222−2−2−i2−i2i2i2−i2−i2i2i2000000000000000000000000
χ542-22-22i−2i2i−2i002002-20000-2002i−2i2i−2i0022-2-22-22-22i−2i2i−2i2i−2i2i−2i200002-20000-2000000002i−2i2i−2i−22−22i2−i2i2−i2−2−222−2−222i2i2−i2−i2i2i2−i2−i2000000000000000000000000
χ552-22-2−2i2i−2i2i002002-20000-200−2i2i−2i2i0022-2-22-22-2−2i2i−2i2i−2i2i−2i2i200002-20000-200000000−2i2i−2i2i2−22−2i2−i2i2−i222−2−222−2−2i2i2−i2−i2i2i2−i2−i2000000000000000000000000
χ562-22-2−2i2i−2i2i002002-20000-200−2i2i−2i2i0022-2-22-22-2−2i2i−2i2i−2i2i−2i2i200002-20000-200000000−2i2i−2i2i−22−22−i2i2−i2i2−2−222−2−222−i2−i2i2i2−i2−i2i2i2000000000000000000000000
χ572-2-222i−2i−2i2i00200-220000-2002i−2i−2i2i0022-2-2-22-222i−2i2i−2i−2i2i−2i2i20000-220000-2000000002i−2i−2i2i2−2−22−i2i2i2−i222−2−2−2−222−i2−i2i2i2i2i2−i2−i2000000000000000000000000
χ582-2-222i−2i−2i2i00200-220000-2002i−2i−2i2i0022-2-2-22-222i−2i2i−2i−2i2i−2i2i20000-220000-2000000002i−2i−2i2i−222−2i2−i2−i2i2−2−22222−2−2i2i2−i2−i2−i2−i2i2i2000000000000000000000000
χ592-2-22−2i2i2i−2i00200-220000-200−2i2i2i−2i0022-2-2-22-22−2i2i−2i2i2i−2i2i−2i20000-220000-200000000−2i2i2i−2i2−2−22i2−i2−i2i222−2−2−2−222i2i2−i2−i2−i2−i2i2i2000000000000000000000000
χ602-2-22−2i2i2i−2i00200-220000-200−2i2i2i−2i0022-2-2-22-22−2i2i−2i2i2i−2i2i−2i20000-220000-200000000−2i2i2i−2i−222−2−i2i2i2−i2−2−22222−2−2−i2−i2i2i2i2i2−i2−i2000000000000000000000000
χ614444444444444444444444444444-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-21-2-2-2-21111111-2-2-2-211111111000000000000000000000000000000000000000000000000
χ6244444444-4-44-4-444-4-4-4-44-4-44444-4-4-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-21222211-1-1-1-112222-1-1-1-11111000000000000000000000000000000000000000000000000
χ634444-4-4-4-4444-4-44444444-4-4-4-4-4-4-4-4-2-2-2-2-2-2-2-2222222221-2-2-2-211111112222-1-1-1-1-1-1-1-1000000000000000000000000000000000000000000000000
χ644444-4-4-4-4-4-444444-4-4-4-4444-4-4-4-444-2-2-2-2-2-2-2-2222222221222211-1-1-1-11-2-2-2-21111-1-1-1-1000000000000000000000000000000000000000000000000
χ6544-4-444-4-44-44-44-4-444-4-44-4-444-4-444-2-2-2-22222-2-2-2-222221-2-222-1-111-1-11-2-22211-1-111-1-1000000000000000000000000000000000000000000000000
χ6644-4-444-4-4-4444-4-4-4-4-44444444-4-4-4-4-2-2-2-22222-2-2-2-22222122-2-2-1-1-1-111122-2-2-1-11111-1-1000000000000000000000000000000000000000000000000
χ6744-4-4-4-4444-444-4-4-444-4-4444-4-444-4-4-2-2-2-222222222-2-2-2-21-2-222-1-111-1-1122-2-2-1-111-1-111000000000000000000000000000000000000000000000000
χ6844-4-4-4-444-444-44-4-4-4-4444-4-4-4-44444-2-2-2-222222222-2-2-2-2122-2-2-1-1-1-1111-2-22211-1-1-1-111000000000000000000000000000000000000000000000000
χ694-44-44i−4i4i−4i004004-40000-4004i−4i4i−4i004-2-424-4-224i−4i−2i2i4i−4i−2i2i-20000-220000200000000−2i2i−2i2i000000000000000000000000000000000000000000000000
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χ714-44-44i−4i4i−4i004004-40000-4004i−4i4i−4i00-2-222-22-22−2i2i−2i2i−2i2i−2i2i100001-13-33-3-100003i−3i3i−3ii−ii−i000000000000000000000000000000000000000000000000
χ724-44-44i−4i4i−4i004004-40000-4004i−4i4i−4i00-2-222-22-22−2i2i−2i2i−2i2i−2i2i100001-1-33-33-10000−3i3i−3i3ii−ii−i000000000000000000000000000000000000000000000000
χ734-44-4−4i4i−4i4i004004-40000-400−4i4i−4i4i004-2-424-4-22−4i4i2i−2i−4i4i2i−2i-20000-2200002000000002i−2i2i−2i000000000000000000000000000000000000000000000000
χ744-44-4−4i4i−4i4i004004-40000-400−4i4i−4i4i00-242-4-224-42i−2i−4i4i2i−2i−4i4i-20000-2200002000000002i−2i2i−2i000000000000000000000000000000000000000000000000
χ754-44-4−4i4i−4i4i004004-40000-400−4i4i−4i4i00-2-222-22-222i−2i2i−2i2i−2i2i−2i100001-13-33-3-10000−3i3i−3i3i−ii−ii000000000000000000000000000000000000000000000000
χ764-44-4−4i4i−4i4i004004-40000-400−4i4i−4i4i00-2-222-22-222i−2i2i−2i2i−2i2i−2i100001-1-33-33-100003i−3i3i−3i−ii−ii000000000000000000000000000000000000000000000000
χ774-4-444i−4i−4i4i00400-440000-4004i−4i−4i4i004-2-42-442-24i−4i−2i2i−4i4i2i−2i-200002-20000200000000−2i2i2i−2i000000000000000000000000000000000000000000000000
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Here ζ is a primitive root of unity of order 24 (ζ24 = 1); i = ζ6.