Finite Group Databasebeta

← Group #13169302

Character table — Group #13169302

Order 1728.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96C97C98C99C100C101C102C103C104C105C106C107C108
size111122222222222244444444444444444444466888888888888812121212121212121212121212121212121212121212121212181824242424242424242424242424243636363636363654547272727272108
order12223336666666663334666666666121212121212121244366612121212121212121244444121212121212121212121212121212121212121244121212121212121212121212121222444121222661212124
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111111111111111111111111-1-111111-1-111111111111111-1-111-1-1-111111-1-1-1-11-11-1-1-1-1-1-11-11-1-1-1
χ31111111111111111111111111111111111111111111111111111-1111-1-1-1111111111111111111-1-1-1-1111-1-1-1-1-11111-1-1-111-1-1-1-1-1-1-111-1
χ41111111111111111111111111111111111111111111111111111-11-1-1-1-1-111-1-11111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11-1-1-11111-11-1-1-11
χ51111111111111111111111111111111111111-1-111111111111111-111111-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111111111-11-1-1-111-1-1-11-1-1-1-1
χ61111111111111111111111111111111111111-1-111111111111111-1-1-1111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-111111-1-1-1-1-1-1-111-1-111-1-1-1111
χ71111111111111111111111111111111111111-1-11111111111111-1-111-1-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111-1-1-1-1-111111-11-1-1-1-1111-11-1-11
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
χ91111111111111111111-1111111111-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1-11-11-1-1111111-1-1-1-1111111-1-1-1-1111-1-11-1-1-1-11111-1-11-1-11-111111-1-11-1-1
χ101111111111111111111-1111111111-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1-11-1-11-11111-1-1-1-1-1-1111111-1-1-1-1-1-11-11-11-1-1-111-1-11111-1-11-1-1-1-111-1-111
χ111111111111111111111-1111111111-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-11-11-1-11111-1-1-1-1111111-1-1-1-1-1-1-11-11-1111-1-111-1-1-1111-1-1-1-1-1-1111-11
χ121111111111111111111-1111111111-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-111-1-111-1-1-1-1-1-1111111-1-1-1-111-111-11111-1-1-1-111-1-11-111111-1-11-11-1
χ131111111111111111111-1111111111-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1111-1-111-1-1111111-1-1-1-1-1-11111111-1-11-1-1-1-11111-1-1-1-11-1111-1-1-1-11-111
χ141111111111111111111-1111111111-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-111-11-111-1-1-1-11111-1-1-1-1-1-11111-1-11-11-11-1-1-111-1-111-1111-1-1-111-1111-1-1
χ151111111111111111111-1111111111-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-111-11-1-1-1-1111111-1-1-1-1-1-11111-1-1-11-11-1111-1-111-1-111-1-11-1-11111-1-11-1
χ161111111111111111111-1111111111-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-11-111-1-1-1-1-1-11111-1-1-1-1-1-1111111-111-11111-1-1-1-1111-1-11-111-1-11-1-11-11
χ17222222-122-12-122-122-1-122-12-1-1-1-1-1222-1-1-1-1-1-122-1-1-1-1222-1-1-1-1-1-12200222-1-10022-1-122-1-1-1-1-1-1-1-100-1-10002-1-1-1-10000202000000-10-1000
χ18222222-122-12-122-122-1-122-12-1-1-1-1-1222-1-1-1-1-1-122-1-1-1-1222-1-1-1-1-1-1-2200-2-2-2-1-10022-1-122-1-1-1-1-1-1-1-10011000-211110000-20-2000000101000
χ19222222-122-12-122-122-1-122-12-1-1-1-1-1222-1-1-1-1-1-1-2-2-1-1-1-1222-1-1-1-1-1-12-2002221100-2-211-2-21111111100-1-10002-1-1-1-10000-20-2000000101000
χ20222222-122-12-122-122-1-122-12-1-1-1-1-1222-1-1-1-1-1-1-2-2-1-1-1-1222-1-1-1-1-1-1-2-200-2-2-21100-2-211-2-2111111110011000-211110000202000000-10-1000
χ21222222-122-12-122-122-1-1-22-12-1-1-1-1-12-2-211111122-1-1-1-1-2-2-21111112-200-222-1-100-2-21122-1-1-1-1111100-11000-211-1-1000020-2000000-101000
χ22222222-122-12-122-122-1-1-22-12-1-1-1-1-12-2-211111122-1-1-1-1-2-2-2111111-2-2002-2-2-1-100-2-21122-1-1-1-11111001-10002-1-1110000-20200000010-1000
χ23222222-122-12-122-122-1-1-22-12-1-1-1-1-12-2-2111111-2-2-1-1-1-1-2-2-21111112200-222110022-1-1-2-21111-1-1-1-100-11000-211-1-10000-20200000010-1000
χ24222222-122-12-122-122-1-1-22-12-1-1-1-1-12-2-2111111-2-2-1-1-1-1-2-2-2111111-22002-2-2110022-1-1-2-21111-1-1-1-1001-10002-1-111000020-2000000-101000
χ2522222-122-12-122-122-12-12-1-1-1222-1-1-12222222200-1-1-1-1-1-1-1-1-1-1-1-1-120222-1-100-1-1000000000000002222-122-1-1-1-1-1-1-1-1-102000-1-1000-10000
χ2622222-122-12-122-122-12-12-1-1-1222-1-1-12222222200-1-1-1-1-1-1-1-1-1-1-1-1-120-2-22-1-1001100000000000000-2-2221-2-2-1-1-1-1-111110-20001100010000
χ2722222-122-12-122-122-12-12-1-1-1222-1-1-12222222200-1-1-1-1-1-1-1-1-1-1-1-1-1-2022-21100-1-100000000000000-2-2-2-2-12211111-1-1-1-10-20001100010000
χ2822222-122-12-122-122-12-12-1-1-1222-1-1-12222222200-1-1-1-1-1-1-1-1-1-1-1-1-1-20-2-2-21100110000000000000022-2-21-2-211111111102000-1-1000-10000
χ2922222-122-12-122-122-12-1-2-1-1-1222-1-1-1-2-2-2-2-2-2-2-200-1-1-1-1111111111202-2-2-1-100-1-100000000000000222-212-2111-1-1-1-1110-2000-1-100010000
χ3022222-122-12-122-122-12-1-2-1-1-1222-1-1-1-2-2-2-2-2-2-2-200-1-1-1-111111111120-22-2-1-1001100000000000000-2-22-2-1-22111-1-111-1-10200011000-10000
χ3122222-122-12-122-122-12-1-2-1-1-1222-1-1-1-2-2-2-2-2-2-2-200-1-1-1-1111111111-202-221100-1-100000000000000-2-2-2212-2-1-1-111-1-1110200011000-10000
χ3222222-122-12-122-122-12-1-2-1-1-1222-1-1-1-2-2-2-2-2-2-2-200-1-1-1-1111111111-20-2221100110000000000000022-22-1-22-1-1-11111-1-10-2000-1-100010000
χ332222-122-12222-122-1-1-122-12-1-1-1-122-1-1-122-1-1-1-122-1-1-1-12-1-122-1-1-1-102220002222-1-122-1-1-1-1-1-1-1-1-1-100002-1-100000-1-1-1-1000220000000-1-10
χ342222-122-12222-122-1-1-122-12-1-1-1-122-1-1-122-1-1-1-122-1-1-1-12-1-122-1-1-1-102-2-200022-2-2-1-122-1-1-1-1-1-1-1-1-1-10000-211000001111000-2-20000000110
χ352222-122-12222-122-1-1-122-12-1-1-1-122-1-1-122-1-1-1-1-2-2-1-1-1-12-1-122-1-1-1-10-222000-2-22211-2-2111111111100002-1-100000-1-1-1-1000-2-20000000110
χ362222-122-12222-122-1-1-122-12-1-1-1-122-1-1-122-1-1-1-1-2-2-1-1-1-12-1-122-1-1-1-10-2-2-2000-2-2-2-211-2-211111111110000-211000001111000220000000-1-10
χ372222-122-12222-122-1-1-12-2-12-1-1-1-122-111-2-2111122-1-1-1-1-211-2-211110-22-2000222211-2-2-1-1-1-1-1-111110000-2-1100000-1-1110002-20000000-110
χ382222-122-12222-122-1-1-12-2-12-1-1-1-122-111-2-2111122-1-1-1-1-211-2-211110-2-2200022-2-211-2-2-1-1-1-1-1-11111000021-10000011-1-1000-2200000001-10
χ392222-122-12222-122-1-1-12-2-12-1-1-1-122-111-2-21111-2-2-1-1-1-1-211-2-21111022-2000-2-222-1-122111111-1-1-1-10000-2-1100000-1-111000-2200000001-10
χ402222-122-12222-122-1-1-12-2-12-1-1-1-122-111-2-21111-2-2-1-1-1-1-211-2-2111102-22000-2-2-2-2-1-122111111-1-1-1-1000021-10000011-1-10002-20000000-110
χ412-22-2222-2-2-22-22-22-22220-22-2-22-2-2-22000000002i−2i22-2-200000000000000002i−2i0000002i−2i2i2i−2i−2i00002i−2i00000000000000000002i−2i2-2000000
χ422-22-2222-2-2-22-22-22-22220-22-2-22-2-2-22000000002i−2i22-2-200000000000000002i−2i0000002i−2i2i2i−2i−2i0000−2i2i0000000000000000000−2i2i-22000000
χ432-22-2222-2-2-22-22-22-22220-22-2-22-2-2-2200000000−2i2i22-2-20000000000000000−2i2i000000−2i2i−2i−2i2i2i00002i−2i00000000000000000002i−2i-22000000
χ442-22-2222-2-2-22-22-22-22220-22-2-22-2-2-2200000000−2i2i22-2-20000000000000000−2i2i000000−2i2i−2i−2i2i2i0000−2i2i0000000000000000000−2i2i2-2000000
χ4544444-2-24-2-2-2-24-2-24-2-214-21-2-2-2-211-244-2-2-2-2-2-2001111-2-2-211111140004-2-200000000000000000000-2-2000-211110000000000000000000
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χ4744444-2-24-2-2-2-24-2-24-2-21-4-21-2-2-2-211-2-4-4222222001111222-1-1-1-1-1-14000-4-2-200000000000000000000-220002-1-1110000000000000000000
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χ494444-24-2-24-24-2-24-2-2-21-24-2-2-2111-2-2-2-2-2-2-211114411114-2-2-2-211110400000-2-200-2-2-2-2-2-2111111110000000000000000000000000000000
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χ524444-24-2-24-24-2-24-2-2-21-2-4-2-2-2111-2-2-22222-1-1-1-1-4-41111-42222-1-1-1-104000002200-2-2-2-222-1-1-1-111110000000000000000000000000000000
χ534444-2-24-2-24-24-2-24-21-2-241-21-2-2-2-2-21-2-244-2-2-2-2001111-211-2-21111004400000-2-2000000000000000000-2-2-2000001111000000000000000
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χ934-4-44-24-22-42-4-2242-2-21-20-222-1-11-2220023−23−333−3001-11-100023−23−333−30000000000023−230000-333-3−333−30000000000000000000000000000000
χ944-4-44-24-22-42-4-2242-2-21-20-222-1-11-2220023−23−333−3001-11-100023−23−333−300000000000−232300003-3-333−3−330000000000000000000000000000000
χ954-4-44-24-22-42-4-2242-2-21-20-222-1-11-22200−23233−3−33001-11-1000−23233−3−330000000000023−2300003-3-33−333−30000000000000000000000000000000
χ964-4-44-24-22-42-4-2242-2-21-20-222-1-11-22200−23233−3−33001-11-1000−23233−3−3300000000000−23230000-333-33−3−330000000000000000000000000000000
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
χ9988-8-88-4-48-4-444-844-8-4-4204-2-4-444-22400000000002-2-2200000000000000000000000000000000000000000000000000000000000000000
χ10088-8-8-4-4-4-4-4-44444442220-2-222-2-2-22-2−4i34i3002i32i3−2i3−2i300-111-102i3−2i300−i3−i3i3i300000000000000000000000000000000000000000000000000000000
χ10188-8-8-4-4-4-4-4-44444442220-2-222-2-2-22-24i3−4i300−2i3−2i32i32i300-111-10−2i32i300i3i3−i3−i300000000000000000000000000000000000000000000000000000000
χ1028-88-88-4-4-844-4484-4-8-4-4204244-44-2-2-4000000000022-2-200000000000000000000000000000000000000000000000000000000000000000
χ1038-88-8-4-4844-8-4-8-44842-4-40-2-4-24-44442000000000022-2-200000000000000000000000000000000000000000000000000000000000000000
χ1048-88-8-4-4-4444-44-44-442220-22-2-22-2-2-2200006i−6i6i−6i00-1-11100000−3i3i−3i3i00000000000000000000000000000000000000000000000000000000
χ1058-88-8-4-4-4444-44-44-442220-22-2-22-2-2-220000−6i6i−6i6i00-1-111000003i−3i3i−3i00000000000000000000000000000000000000000000000000000000
χ1068-8-88-4-4844-8484-4-8-42-4-4024-244-4-44-200000000002-22-200000000000000000000000000000000000000000000000000000000000000000
χ1078-8-88-4-4-44444-44-44-422202-2-2-2-222-2-20043−43−232323−2300-11-11000−23233−3−3300000000000000000000000000000000000000000000000000000000
χ1088-8-88-4-4-44444-44-44-422202-2-2-2-222-2-200−434323−23−232300-11-1100023−23−333−300000000000000000000000000000000000000000000000000000000

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