Finite Group Databasebeta

← Group #13170757

Character table — Group #13170757

Order 1728.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96C97C98C99C100C101C102C103C104C105C106C107C108C109C110C111C112C113C114
size1111222222222222444444444444444666666888888888888888899991212121212121212121212121212121212121218181818181818182424242424242424242424242424242436363636363636363654547272108
order12223336666666663334666666666121222224436661212121212121212121212124444244666666661212121212121212224412121212666666661212121212121212244666612124412124
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111-1-11111111111111111-1-1-1-111-11111111111-1-1-1-1-1-111-1-1-1-1-1-1111111111-111-1-1-1-1-11-1-1-111-1-1-1-11-1-1
χ3111111111111111111111111111111111-1-11111111111111111111111-111-1-11111-1-111111111-1-1-1-11111-1-111-1-1-1-1111111111-1-111-1-1-1-1-1-1-1-1-1
χ4111111111111111111111111111111111-1-1-1-11111111111111111-1-1-1-1-11-1-1-11111-1-111-1-1-1-1-1-1-1-111-1-1-1-1-1-111-1-1-1-11-111-1-1-1-1-1-11-1-1-1-11111-111
χ51111111111111111111111111111111-1-111111111111111111111-1-1-1-11-1111-1-1-1-111-1-1111111-1-111-1-1-1-111-1-11111-11-1-11111-1-11-1-1-1-111-1-1-11-1
χ61111111111111111111111111111111-1-111-1-1111111111111111111111-1-111-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1111111-1-11111-1-1-1-1-1-1-1-11-1-111-1-1-1-111-1-11
χ71111111111111111111111111111111-1-1-1-1111111111111111111-1-1-1-1-1-11-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11-1-11111-11-1-1-111-1-1111-11
χ81111111111111111111111111111111-1-1-1-1-1-111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111-1-111-1
χ91111111111111111111-1111111111-1-11111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-111111111-1-1-1-1111111111111-1-11111-1-1-1-1-1-1-1-111-1-1-1-1-1111111-1-1-1
χ101111111111111111111-1111111111-1-11111-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111-1-111-1-1-1-111-1-1-1-1-1-1-1-11111-1-1-11-1-111-1-11-111111-1-1-1-1-111
χ111111111111111111111-1111111111-1-111-1-1111111-1-1-1-1-1-1-1-1-1-1-1-111111-1-1-1-11111-1-1-1-1-1-11111-1-1-1-111111111-1-111-1-1-1-1-1-111-111-1-1-1-1-1-1-1-1111
χ121111111111111111111-1111111111-1-111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11-11-1-11111-1-1-1-111-1-1-1-1-1-111-1-1-1-11111-1-111-11-1-111-1-111-111-1-111111-1-1
χ131111111111111111111-1111111111-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11-111-1-1-1-11111-1-11111-1-111-1-1-1-1-1-1-1-111-1-11-111-1-11111-111-1-111-1-11-11
χ141111111111111111111-1111111111-1-1-1-111-1-11111-1-1-1-1-1-1-1-1-1-1-1-11111-11111-1-1-1-1111111-1-1-1-1-1-1-1-11111-1-1-1-111-1-1111111-1-1-111-1-1-1-1-1-11111-1
χ151111111111111111111-1111111111-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1-111-1-1111111-1-1-1-1-1-111-1-1-1-1111-111-1-1111-111111-1-111-11-1
χ161111111111111111111-1111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-11111111-1-1-1-1-1-1-1-11111-1-1-1-11111111111-1-1-1-111111111-1-1-1-1-1-1-11111-1-1-1-11
χ17222222-1-1222-12-1222-1-122-1-1-1-1-12-1222222200-1-1-1-1-12-1-1-1-122-1-1-1-100002202222-1-1-1-122000000220000002-1-1-1-1-1-1-1-10-1-1000002000-1-10000-100
χ18222222-1-1222-12-1222-1-122-1-1-1-1-12-122222-2-200-1-1-1-1-12-1-1-1-122-1-1-1-10000-220-2-222-1-11122000000-2-2000000-21-1-11111-10-1-100000-2000110000100
χ19222222-1-1222-12-1222-1-122-1-1-1-1-12-1222-2-22200-1-1-1-1-12-1-1-1-122-1-1-1-100002-2022-2-211-1-1-2-2000000-2-20000002-111-1-1-1-1101100000-2000110000100
χ20222222-1-1222-12-1222-1-122-1-1-1-1-12-1222-2-2-2-200-1-1-1-1-12-1-1-1-122-1-1-1-10000-2-20-2-2-2-21111-2-200000022000000-211111111011000002000-1-10000-100
χ21222222-1-1222-12-1222-1-1-22-1-1-1-1-12-12-2-2222200-1-1-1-11-21111-2-211110000-2-202222-1-1-1-1-2-200000022000000-21-1-1-1-111101100000-2000-1-10000100
χ22222222-1-1222-12-1222-1-1-22-1-1-1-1-12-12-2-222-2-200-1-1-1-11-21111-2-2111100002-20-2-222-1-111-2-2000000-2-20000002-1-1-111-1-11011000002000110000-100
χ23222222-1-1222-12-1222-1-1-22-1-1-1-1-12-12-2-2-2-22200-1-1-1-11-21111-2-211110000-22022-2-211-1-122000000-2-2000000-2111-1-111-10-1-1000002000110000-100
χ24222222-1-1222-12-1222-1-1-22-1-1-1-1-12-12-2-2-2-2-2-200-1-1-1-11-21111-2-211110000220-2-2-2-2111122000000220000002-11111-1-1-10-1-100000-2000-1-10000100
χ2522222-1222-1-12222-1-1-122-1-122-12-1-1-1-1-1220022-1-1-1-12222-1-1-1-1-1-1-1-1222202200-1-12200-1-1-1-122-1-10000-1-1-1-100-1-1000022-1-1-1-1-1-1200-1-1000000000
χ2622222-1222-1-12222-1-1-122-1-122-12-1-1-1-1-12200-2-2-1-1-1-12222-1-1-1-1-1-1-1-1-2-2-2-202-200-1-12200-1-111-2-2110000111100-1-100002-2-1-11111-20011000000000
χ2722222-1222-1-12222-1-1-122-1-122-12-1-1-1-1-1-2-20022-1-1-1-12222-1-1-1-1-1-1-1-1-2-2-2-20-220011-2-20011-1-122-1-10000111100110000-2211-1-1-1-1-20011000000000
χ2822222-1222-1-12222-1-1-122-1-122-12-1-1-1-1-1-2-200-2-2-1-1-1-12222-1-1-1-1-1-1-1-122220-2-20011-2-2001111-2-2110000-1-1-1-100110000-2-2111111200-1-1000000000
χ2922222-1222-1-12222-1-1-12-2-1-122-12-1-1-111220022-1-1-1-1-2-2-2-21111111122220-2-200-1-12200111122-1-10000-1-1-1-100-1-10000-2-21111-1-1-20011000000000
χ3022222-1222-1-12222-1-1-12-2-1-122-12-1-1-1112200-2-2-1-1-1-1-2-2-2-211111111-2-2-2-20-2200-1-1220011-1-1-2-2110000111100-1-10000-2211-1-111200-1-1000000000
χ3122222-1222-1-12222-1-1-12-2-1-122-12-1-1-111-2-20022-1-1-1-1-2-2-2-211111111-2-2-2-202-20011-2-200-1-11122-1-100001111001100002-2-1-111-1-1200-1-1000000000
χ3222222-1222-1-12222-1-1-12-2-1-122-12-1-1-111-2-200-2-2-1-1-1-1-2-2-2-21111111122220220011-2-200-1-1-1-1-2-2110000-1-1-1-10011000022-1-1-1-111-20011000000000
χ332222-1222-1222-12-12-12-12-12-1-12-1-12-122002222-1-1-1-12-1-1-122-1-1-1-1-1-10000202-1-10000220022-1-12200220000-1200-1-1-1-10-100-1-1-1-10020000-1-1000-10
χ342222-1222-1222-12-12-12-12-12-1-12-1-12-1220022-2-2-1-1-1-12-1-1-122-1-1-1-1-1-1000020-2-1-100002200-2-211-2-200-2-20000-1200-1-1-1-10100111100-200001100010
χ352222-1222-1222-12-12-12-12-12-1-12-1-12-12200-2-222-1-1-1-12-1-1-122-1-1-1-1-1-10000-202110000-2-20022-1-12200-2-200001-20011110-100-1-1-1-100-200001100010
χ362222-1222-1222-12-12-12-12-12-1-12-1-12-12200-2-2-2-2-1-1-1-12-1-1-122-1-1-1-1-1-10000-20-2110000-2-200-2-211-2-2002200001-2001111010011110020000-1-1000-10
χ372222-1222-1222-12-12-12-1-2-12-1-12-1-12-1-2-2002222-1-1-1-1-2111-2-21111110000-20-2-1-100002200-2-2-1-122002200001-200-1-111010011-1-100-20000-1-100010
χ382222-1222-1222-12-12-12-1-2-12-1-12-1-12-1-2-20022-2-2-1-1-1-1-2111-2-21111110000-202-1-1000022002211-2-200-2-200001-200-1-1110-100-1-111002000011000-10
χ392222-1222-1222-12-12-12-1-2-12-1-12-1-12-1-2-200-2-222-1-1-1-1-2111-2-2111111000020-2110000-2-200-2-2-1-12200-2-20000-120011-1-1010011-1-1002000011000-10
χ402222-1222-1222-12-12-12-1-2-12-1-12-1-12-1-2-200-2-2-2-2-1-1-1-1-2111-2-21111110000202110000-2-2002211-2-200220000-120011-1-10-100-1-11100-20000-1-100010
χ4122-2-2222-222-2-2-22-2-22220-222-2-2-22-2-2002-2002i−2i22-2-20000000000002i2i−2i−2i000002-22-20000002i−2i2i−2i00002i2i−2i−2i002-200000000002i−2i00000000000000
χ4222-2-2222-222-2-2-22-2-22220-222-2-2-22-2-2002-200−2i2i22-2-2000000000000−2i−2i2i2i000002-22-2000000−2i2i−2i2i0000−2i−2i2i2i002-20000000000−2i2i00000000000000
χ4322-2-2222-222-2-2-22-2-22220-222-2-2-22-2-200-22002i−2i22-2-2000000000000−2i−2i2i2i00000-22-220000002i−2i2i−2i0000−2i−2i2i2i00-2200000000002i−2i00000000000000
χ4422-2-2222-222-2-2-22-2-22220-222-2-2-22-2-200-2200−2i2i22-2-20000000000002i2i−2i−2i00000-22-22000000−2i2i−2i2i00002i2i−2i−2i00-220000000000−2i2i00000000000000
χ4522-2-22-12-22-11-2-22-21-1-1201-12-21-2-1113−32-2002i−2i-1-11100003−33−333−3−32i2i−2i−2i00000-112-2003−3−i3i32i−2i−ii0000−i−iii00-110000003−3−i3i3−ii000−i3i3000000000
χ4622-2-22-12-22-11-2-22-21-1-1201-12-21-2-1113−32-200−2i2i-1-11100003−33−333−3−3−2i−2i2i2i00000-112-2003−3i3−i3−2i2ii−i0000ii−i−i00-110000003−3i3−i3i−i000i3−i3000000000
χ4722-2-22-12-22-11-2-22-21-1-1201-12-21-2-1113−3-22002i−2i-1-11100003−33−333−3−3−2i−2i2i2i000001-1-2200−33−i3i32i−2i−ii0000ii−i−i001-1000000−33−i3i3−ii000i3−i3000000000
χ4822-2-22-12-22-11-2-22-21-1-1201-12-21-2-1113−3-2200−2i2i-1-11100003−33−333−3−32i2i−2i−2i000001-1-2200−33i3−i3−2i2ii−i0000−i−iii001-1000000−33i3−i3i−i000−i3i3000000000
χ4922-2-22-12-22-11-2-22-21-1-1201-12-21-2-111−332-2002i−2i-1-1110000−33−33−3−3332i2i−2i−2i00000-112-200−33i3−i32i−2i−ii0000−i−iii00-11000000−33i3−i3−ii000i3−i3000000000
χ5022-2-22-12-22-11-2-22-21-1-1201-12-21-2-111−332-200−2i2i-1-1110000−33−33−3−333−2i−2i2i2i00000-112-200−33−i3i3−2i2ii−i0000ii−i−i00-11000000−33−i3i3i−i000−i3i3000000000
χ5122-2-22-12-22-11-2-22-21-1-1201-12-21-2-111−33-22002i−2i-1-1110000−33−33−3−333−2i−2i2i2i000001-1-22003−3i3−i32i−2i−ii0000ii−i−i001-10000003−3i3−i3−ii000−i3i3000000000
χ5222-2-22-12-22-11-2-22-21-1-1201-12-21-2-111−33-2200−2i2i-1-1110000−33−33−3−3332i2i−2i−2i000001-1-22003−3−i3i3−2i2ii−i0000−i−iii001-10000003−3−i3i3i−i000i3−i3000000000
χ532-22-2222-2-2-2222-2-2-222202-2-22-2-2-22-2000000002-22-20000000000002i−2i2i−2i00000000000000000002-22i−2i2i−2i2i−2i0000000000000000000002-22i−2i00000
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χ552-22-2222-2-2-2222-2-2-222202-2-22-2-2-22-2000000002-22-2000000000000−2i2i−2i2i00000000000000000002-2−2i2i−2i2i−2i2i0000000000000000000002-2−2i2i00000
χ562-22-2222-2-2-2222-2-2-222202-2-22-2-2-22-2000000002-22-2000000000000−2i2i−2i2i0000000000000000000-222i−2i−2i2i−2i2i000000000000000000000-222i−2i00000
χ572-2-222222-2-2-2-2-2-2222220-2-2-2-222-2-2200002-2002-2-220000000000002-2-220002-200002-20000000000002-2-2200002-200000000000000000002-2000
χ582-2-222222-2-2-2-2-2-2222220-2-2-2-222-2-2200002-2002-2-22000000000000-222-20002-200002-2000000000000-222-200002-20000000000000000000-22000
χ592-2-222222-2-2-2-2-2-2222220-2-2-2-222-2-220000-22002-2-220000000000002-2-22000-220000-220000000000002-2-220000-220000000000000000000-22000
χ602-2-222222-2-2-2-2-2-2222220-2-2-2-222-2-220000-22002-2-22000000000000-222-2000-220000-22000000000000-222-20000-2200000000000000000002-2000
χ6144444-2-2-24-2-2-24-24-2-21-24-21-2-21-2-21-2-2-24400001111-24-2-211-2-21111000004000-2-2-2-200-2-20000000000000000110000-2011000000000000000000
χ6244444-2-2-24-2-2-24-24-2-21-24-21-2-21-2-21-2-2-2-4-400001111-24-2-211-2-2111100000-4000222200220000000000000000-1-1000020-1-1000000000000000000
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χ714444-2-244-2-2-24-24-2-21-2-2-41-2-2-2-2-21-21220000441111-422222-1-1-1-1-1-1000000-4000000000022-2-2-2-200000000000000000200-1-11100000000000000
χ724444-2-244-2-2-24-24-2-21-2-2-41-2-2-2-2-21-21220000-4-41111-422222-1-1-1-1-1-100000040000000000-2-2222200000000000000000-20011-1-100000000000000
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χ7844-4-44-2-224-222-4-2-42-21-2021-22-12-2-12−2323-44000011-1-100003−3−232333−3−30000000002-22-20023−230000000000000000-11000000−33000000000000000000
χ7944-4-4-244-4-24-4-4242-4-24-2024-22-42-2-420000004i−4i-2-2220000000000000000000000000000000−2i2i4i−4i0000000000000000000000−2i2i00000000000000
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χ8444-4-4-2-24-4-2-22-424221-2-20-1-2-222212-1−23230000−4i4i11-1-10000−23233−333−3−300000000000000000−2i32i32i−2i2i−2i00000000000000000000i3−i3−ii00000000000000
χ854-44-444-22-4-44-242-4-44-2-20422-222-4-2-400000000-22-22000000000000000000000000000000000004-4000000000000000000000000000-220000000
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χ884-44-44-24-4-42-244-4-42-2-240-22-442-42-2200000000-22-22000000000000−4i4i−4i4i000000000000000000000002i−2i2i−2i000000000000000000000000000000
χ894-44-4-244-42-444-2-42-4-24-20-2-42-2-4224200000000-22-2200000000000000000000000000000000000004i−4i000000000000000000000000000−2i2i00000
χ904-44-4-244-42-444-2-42-4-24-20-2-42-2-4224200000000-22-220000000000000000000000000000000000000−4i4i0000000000000000000000000002i−2i00000
χ914-4-4444-2-2-4-4-42-42444-2-20-4222-2-2-42400004-400-222-200000000000000000004-40000-2200000000000000000000-22000000000000000000000000
χ924-4-4444-2-2-4-4-42-42444-2-20-4222-2-2-4240000-4400-222-20000000000000000000-4400002-2000000000000000000002-2000000000000000000000000
χ934-4-444-244-422-4-4-44-2-2-24022-4-4-2422-200000000-222-20000000000004-4-4400000000000000000000000-222-2000000000000000000000000000000
χ944-4-444-244-422-4-4-44-2-2-24022-4-4-2422-200000000-222-2000000000000-444-4000000000000000000000002-2-22000000000000000000000000000000
χ954-4-44-24442-4-4-42-4-24-24-202-4224-22-4-200004-400-222-20000000000000000000-2200004-400000000000000000000-22000000000000000000000000
χ964-4-44-24442-4-4-42-4-24-24-202-4224-22-4-20000-4400-222-200000000000000000002-20000-44000000000000000000002-2000000000000000000000000
χ974-4-44-24-2-22-4-4222-24-2-21022-1-1-2122-200004-4001-1-11003-300003-33-30000000-220000-22000000000000000000001-13-30000000000000000000000
χ984-4-44-24-2-22-4-4222-24-2-21022-1-1-2122-200004-4001-1-1100-330000-33-330000000-220000-22000000000000000000001-1-330000000000000000000000
χ994-4-44-24-2-22-4-4222-24-2-21022-1-1-2122-20000-44001-1-11003-300003-33-300000002-200002-200000000000000000000-11-330000000000000000000000
χ1004-4-44-24-2-22-4-4222-24-2-21022-1-1-2122-20000-44001-1-1100-330000-33-3300000002-200002-200000000000000000000-113-30000000000000000000000
χ1018888-4-4-4-4-4-4-4-4-4-4-4-42228222222222-4-4000000-1-1-1-1-4-4222222-1-1-1-10000000000000000000000000000000000000000000000000000000000000
χ1028888-4-4-4-4-4-4-4-4-4-4-4-4222-822222222244000000-1-1-1-144-2-2-2-2-2-211110000000000000000000000000000000000000000000000000000000000000
χ10388-8-8-48-44-48-844-44-8-4-4204-42-24-2-4440000000022-2-20000000000000000000000000000000000000000000000000000000000000000000000000
χ10488-8-8-4-4-44-4-4444-4442220-222-2-2-22-2-243−43000000-1-1110000−2323−232333−3−30000000000000000000000000000000000000000000000000000000000000
χ10588-8-8-4-4-44-4-4444-4442220-222-2-2-22-2-2−4343000000-1-111000023−2323−23−3−3330000000000000000000000000000000000000000000000000000000000000
χ1068-88-88-4-44-84-4-484-84-42-40-4-24-4-24424000000002-22-20000000000000000000000000000000000000000000000000000000000000000000000000
χ1078-88-8-48-444-88-4-444-8-4-420-44-224-24-44000000002-22-20000000000000000000000000000000000000000000000000000000000000000000000000
χ1088-88-8-4-48-844-48-4-8442-4-40244-444-2-4-2000000002-22-20000000000000000000000000000000000000000000000000000000000000000000000000
χ1098-88-8-4-4-4444-4-4-444422202-2-22-2-2-22-200000000-11-110000000033−33−33330000000000000000000000000000000000000000000000000000000000000
χ1108-88-8-4-4-4444-4-4-444422202-2-22-2-2-22-200000000-11-1100000000−333333−330000000000000000000000000000000000000000000000000000000000000
χ1118-8-888-4-4-4-8444-848-4-42-404-2442-44-2-4000000002-2-220000000000000000000000000000000000000000000000000000000000000000000000000
χ1128-8-88-4-488444-84-8-4-42-4-40-2444-4-4-242000000002-2-220000000000000000000000000000000000000000000000000000000000000000000000000
χ1138-8-88-4-4-4-4444444-4-42220-2-2-2-222-2-2200000000-111-1006-60000-33-330000000000000000000000000000000000000000000000000000000000000
χ1148-8-88-4-4-4-4444444-4-42220-2-2-2-222-2-2200000000-111-100-6600003-33-30000000000000000000000000000000000000000000000000000000000000

Here i is the imaginary unit (i² = −1).