Finite Group Databasebeta

← Group #13169382

Character table — Group #13169382

Order 1728.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96C97C98C99C100C101C102C103C104C105C106C107C108
size111122222222222244444444444444444444466888888888888812121212121212121212121212121212121212121212121212181824242424242424242424242424243636363636363654547272727272108
order12223336666666663334666666666121212121212121244366612121212121212121224444666666661212121212121212121212124412121212121212121212121212124444412124412121212124
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111111111111111111111111-11-111111111-1-11111111111-1-1-11-11-1111-1-111-1-11-11-1-1-1-1-1-11-11-1-1-1
χ311111111111111111111111111111111111111111111111111111-11-111111111111-1-111111111-1-11-11-11-1-1-111-1-111-11-1-11-1-1-1-1-11-11-1-1
χ411111111111111111111111111111111111111111111111111111-1-1-1-111111111-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11-11111-1-1-1-111
χ51111111111111111111111111111111111111-1-11111111111111-11111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-11111111111111111-1-1-11-111-1-1-1-1-1-11-1
χ61111111111111111111111111111111111111-1-11111111111111-11-11-1-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-1-11-11-1111-1-111-1-1-11-1-11-1-111-11-11-11
χ71111111111111111111111111111111111111-1-11111111111111-1-11-11-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-11-11-11-1-1-111-1-1111-11-1-1-1-1111-11-1-11
χ81111111111111111111111111111111111111-1-11111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111-1-111111-1
χ91111111111111111111-1111111111-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-11111111111-1-11-1-111-1-1-1-1-1111111-11-1-1-1-1-1-1-11111
χ101111111111111111111-1111111111-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1-1-11-1-11-1-1-1-1-1-1-1-111111111111111-1-111-1-1-1-11111-1-11-1-1-111111-111-1-1-1
χ111111111111111111111-1111111111-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-11111-1-1-1-111-111-1-111111-1-11-1-1
χ121111111111111111111-1111111111-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-111-1-111111111-1-1-111-1-111111-1-1-1-1-1-1111-1-1-1-111-1-111
χ131111111111111111111-1111111111-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1111-1-111111111-1-111-1-1-1-1-1-1-1-1-1-11-1-111-1-1-1-1-11111-1-1111-1-11111-1-11-1
χ141111111111111111111-1111111111-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-111-1-11111111111111-1-1-1-1-1-1-1-111-1-111-1-1-1-11111-1-1-111-1-111-1-11-1-11-11
χ151111111111111111111-1111111111-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-11-111-111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-11111-1-1-1-1111-1-1-1111-1-1-111-1-11
χ161111111111111111111-1111111111-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-11-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-1-111-1-111111-1-1-1-111-11-1-1-111-1-1111-1
χ17222222-12-1222-12-122-1-122-1-1-12-12-1-122-1-1-1-1-1-122-1-1-1-1222-1-1-1-1-1-12020222-1-1-1-1-1-1220022-1-1-1-1-1-10020-10-1000-1-100-1-10200200000-10-100
χ18222222-12-1222-12-122-1-122-1-1-12-12-1-122-1-1-1-1-1-122-1-1-1-1222-1-1-1-1-1-120-20-222-1-1-1-1-1-1-2-20022-1-1-1-1-1-100-201010001100110-200-20000010100
χ19222222-12-1222-12-122-1-122-1-1-12-12-1-122-1-1-1-1-1-1-2-2-1-1-1-1222-1-1-1-1-1-1-20202-2-21111112200-2-21111110020-10-1000-1-100-1-10-200-20000010100
χ20222222-12-1222-12-122-1-122-1-1-12-12-1-122-1-1-1-1-1-1-2-2-1-1-1-1222-1-1-1-1-1-1-20-20-2-2-2111111-2-200-2-211111100-201010001100110200200000-10-100
χ21222222-12-1222-12-122-1-1-22-1-1-12-12-1-1-2-211111122-1-1-1-1-2-2-2111111-2020-2-2-2111111-2-20022-1-1-1-1-1-1002010-10001100-1-10200-20000010-100
χ22222222-12-1222-12-122-1-1-22-1-1-12-12-1-1-2-211111122-1-1-1-1-2-2-2111111-20-202-2-2111111220022-1-1-1-1-1-100-20-101000-1-100110-200200000-10100
χ23222222-12-1222-12-122-1-1-22-1-1-12-12-1-1-2-2111111-2-2-1-1-1-1-2-2-21111112020-222-1-1-1-1-1-1-2-200-2-2111111002010-10001100-1-10-200200000-10100
χ24222222-12-1222-12-122-1-1-22-1-1-12-12-1-1-2-2111111-2-2-1-1-1-1-2-2-211111120-20222-1-1-1-1-1-12200-2-211111100-20-101000-1-100110200-20000010-100
χ2522222-12-1222-12-122-12-12-12-1-1-12-12-1-1-122-1-1-1-122-1-1-1-12-1-122-1-1-1-122020-1-122-1-1-1-10022-1-122-1-1-1-1000-10-102-1-100-1-100202000000-10-1000
χ2622222-12-1222-12-122-12-12-12-1-1-12-12-1-1-122-1-1-1-122-1-1-1-12-1-122-1-1-1-12-20-20-1-122-1-1-1-100-2-2-1-122-1-1-1-10001010-211001100-20-2000000101000
χ2722222-12-1222-12-122-12-12-12-1-1-12-12-1-1-122-1-1-1-1-2-2-1-1-1-12-1-122-1-1-1-1-2202011-2-21111002211-2-21111000-10-102-1-100-1-100-20-2000000101000
χ2822222-12-1222-12-122-12-12-12-1-1-12-12-1-1-122-1-1-1-1-2-2-1-1-1-12-1-122-1-1-1-1-2-20-2011-2-2111100-2-211-2-211110001010-211001100202000000-10-1000
χ2922222-12-1222-12-122-12-1-2-12-1-1-12-12-111-2-2111122-1-1-1-1-211-2-21111-220-2011-2-211110022-1-122-1-1-1-100010-10-21100-1-10020-200000010-1000
χ3022222-12-1222-12-122-12-1-2-12-1-1-12-12-111-2-2111122-1-1-1-1-211-2-21111-2-202011-2-2111100-2-2-1-122-1-1-1-1000-10102-1-1001100-202000000-101000
χ3122222-12-1222-12-122-12-1-2-12-1-1-12-12-111-2-21111-2-2-1-1-1-1-211-2-21111220-20-1-122-1-1-1-1002211-2-2111100010-10-21100-1-100-202000000-101000
χ3222222-12-1222-12-122-12-1-2-12-1-1-12-12-111-2-21111-2-2-1-1-1-1-211-2-211112-2020-1-122-1-1-1-100-2-211-2-21111000-10102-1-100110020-200000010-1000
χ332222-12222-1-12222-1-1-122-1-122-1-1-1-122222222200-1-1-1-1-1-1-1-1-1-1-1-1-10222200000000-1-1-1-10000000022-12222-1-1-1-1-1-1-1-1-100020-1-1000000-10
χ342222-12222-1-12222-1-1-122-1-122-1-1-1-122222222200-1-1-1-1-1-1-1-1-1-1-1-1-102-22-20000000011-1-100000000-2-212-22-2-1-1-111-1-111000-201100000010
χ352222-12222-1-12222-1-1-122-1-122-1-1-1-122222222200-1-1-1-1-1-1-1-1-1-1-1-1-10-22-2200000000-1-11100000000-2-2-1-22-22111-1-111-1-1000-201100000010
χ362222-12222-1-12222-1-1-122-1-122-1-1-1-122222222200-1-1-1-1-1-1-1-1-1-1-1-1-10-2-2-2-200000000111100000000221-2-2-2-211111111100020-1-1000000-10
χ372222-12222-1-12222-1-1-12-2-1-122-1-1-1-12-2-2-2-2-2-2-2-200-1-1-1-1111111111022-2-20000000011-1-100000000-2-2-1-2-22211111-1-1-1-10002011000000-10
χ382222-12222-1-12222-1-1-12-2-1-122-1-1-1-12-2-2-2-2-2-2-2-200-1-1-1-111111111102-2-2200000000-1-1-1-100000000221-222-2111-1-1-1-111000-20-1-100000010
χ392222-12222-1-12222-1-1-12-2-1-122-1-1-1-12-2-2-2-2-2-2-2-200-1-1-1-11111111110-222-20000000011110000000022-12-2-22-1-1-11111-1-1000-20-1-100000010
χ402222-12222-1-12222-1-1-12-2-1-122-1-1-1-12-2-2-2-2-2-2-2-200-1-1-1-11111111110-2-22200000000-1-11100000000-2-2122-2-2-1-1-1-1-111110002011000000-10
χ4122-2-2222-2-2-22-2-222-22220-2-2-2-2-2-2222000000002-22-2-22000000000000000000000000002-22-222-2-22i−2i00000000000000000002i−2i2i−2i000000
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χ4322-2-2222-2-2-22-2-222-22220-2-2-2-2-2-222200000000-222-2-2200000000000000000000000000-22-22-2-2222i−2i00000000000000000002i−2i−2i2i000000
χ4422-2-2222-2-2-22-2-222-22220-2-2-2-2-2-222200000000-222-2-2200000000000000000000000000-22-22-2-222−2i2i0000000000000000000−2i2i2i−2i000000
χ4544444-2-2-2-244-2-2-2-24-2-214-2-211-2-2-2-21-2-2-2-211114411114-2-2-2-2111140000-2-2-2-211110000-2-2-2-211110000000000000000000000000000000
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χ4844444-2-2-2-244-2-2-2-24-2-21-4-2-211-2-2-2-212222-1-1-1-1-4-41111-42222-1-1-1-140000-2-2-2-2111100002222-1-1-1-10000000000000000000000000000000
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χ954-4-44-24-242-22-4-2-422-21-20-2-12-2212-1200−2323−232323−23001-11-10003−33−3−330000000000000−2i32i300000000000000000000i3−i300−3i3i000000000000000
χ964-4-44-24-242-22-4-2-422-21-20-2-12-2212-1200−2323−232323−23001-11-10003−33−3−3300000000000002i3−2i300000000000000000000−i3i3003i−3i000000000000000
χ978888-4-4-4-4-4-4-4-4-4-4-4-42228222222222-4-4-4-4222200-1-1-1-1-42222-1-1-1-100000000000000000000000000000000000000000000000000000000
χ988888-4-4-4-4-4-4-4-4-4-4-4-4222-82222222224444-2-2-2-200-1-1-1-14-2-2-2-2111100000000000000000000000000000000000000000000000000000000
χ9988-8-8-48-4-844-4-848-44-42-404-2444-2-42-400000000002-2-2200000000000000000000000000000000000000000000000000000000000000000
χ10088-8-8-4-484-84-44-8-4842-4-40-2444-242-4-400000000002-2-2200000000000000000000000000000000000000000000000000000000000000000
χ10188-8-8-4-4-4444-444-4-442220-2-2-2-2-2-2222000066-6-600-111-100000-3-33300000000000000000000000000000000000000000000000000000000
χ10288-8-8-4-4-4444-444-4-442220-2-2-2-2-2-22220000-6-66600-111-10000033-3-300000000000000000000000000000000000000000000000000000000
χ1038-88-8-48-4-8-44484-84-4-42-4042-44-4-24-24000000000022-2-200000000000000000000000000000000000000000000000000000000000000000
χ1048-88-8-4-4-44-444-4444-42220-222-22-2-2-2-243−4300−2323−232300-1-1110−2323003−33−300000000000000000000000000000000000000000000000000000000
χ1058-88-8-4-4-44-444-4444-42220-222-22-2-2-2-2−43430023−2323−2300-1-111023−2300−33−3300000000000000000000000000000000000000000000000000000000
χ1068-8-88-4-48-4-8-44484-842-4-40244-4-2-4-24400000000002-22-200000000000000000000000000000000000000000000000000000000000000000
χ1078-8-88-4-4-4-44-444-444422202-2-22-22-2-2-20043−43−232323−2300-11-11000−23233−3−3300000000000000000000000000000000000000000000000000000000
χ1088-8-88-4-4-4-44-444-444422202-2-22-22-2-2-200−434323−23−232300-11-1100023−23−333−300000000000000000000000000000000000000000000000000000000

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