Finite Group Databasebeta

← Group #13169392

Character table — Group #13169392

Order 1728.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96C97C98C99C100C101C102C103C104C105C106C107C108
size111122222222222244444444444444444444466888888888888812121212121212121212121212121212121212121212121212181824242424242424242424242424243636363636363654547272727272108
order1222333666666666333466666666612121212121212124436661212121212121212124444412121212121212121212121212121212121212124412121212121212121212121212124444412124412121212122
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111111111111111111-1-11111111111-1-11111111111-1-1111-1-1-11111-1-1-1-11-1-1-11-1-1-1-111-1-1-1-1
χ31111111111111111111111111111111111111111111111111111-1111-11111-1-111111111111111-1-1-1-1-1111-1-1-1-11111-111-1-1-1-1-1-1-1-1-111-1
χ41111111111111111111111111111111111111111111111111111-1-1-11-11111-1-111-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11-11111-1-11-1-11
χ51111111111111111111111111111111111111-1-11111111111111111-11-1-1-1-111-1-111-1-1-1-1-1-1-1-1-1-11111111111111111-1-1-11-111-1-1-1-11-1-1-1
χ61111111111111111111111111111111111111-1-111111111111111-1-1-11-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111-1-1-11111-1-1-1-1-111-1-1-1-111-1-1-1111
χ71111111111111111111111111111111111111-1-11111111111111-111-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111-1-1-1-111111-1-1-11-1-11111-1-1-11
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
χ91111111111111111111-1111111111-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1-111-1-1-111-1-1-1-1-1-111111111-1-1-1-1-1-111-1-11-1-1-11111-1-111-11-1-1-1-1-11-111-11
χ101111111111111111111-1111111111-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1-11-11-1-111-1-1-1-1-1-1-1-1111111-1-1-1-11111-11-11-1-111-1-1111-11-1-111111-1-1-11-1
χ111111111111111111111-1111111111-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1-1-11-1-1111-1-111-1-111111111-1-1-1-111-1-11-11-111-1-111-1-1-11-1-111111-11-11-1-1
χ121111111111111111111-1111111111-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-11-1111-1-111-1-1-1-1111111-1-1-1-1-1-1-1-111-1111-1-1-1-111-1-1111-1-1-1-1-111-111
χ131111111111111111111-1111111111-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-111-11-1-1-111-1-11111-1-1-1-1-1-11111-1-111-1-11-1-1-11111-1-1-1-1111-1-111-111-11-1
χ141111111111111111111-1111111111-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-11-111-1-1-111-1-111-1-1-1-1-1-1-1-111111111-11-11-1-111-1-111-11-1-1111-1-1-11-11-11
χ151111111111111111111-1111111111-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-11-111-1-111111111-1-1-1-1-1-1111111-1-11-11-111-1-111-1-11-11-1-111-1-11-1-1-111
χ161111111111111111111-1111111111-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1111-1-1111111-1-1-1-1-1-1-1-11111-1-1-1-111-1111-1-1-1-11111-11-1-1-1111-111-1-1
χ17222222-1222-12-12-122-1-122-12-1-1-1-1-1222-1-1-1-1-1-122-1-1-1-1222-1-1-1-1-1-120022-1-12222-1-10022-1-1-1-1-1-1-1-1002-1-1000-1-1-1-10000200020000-1-10000
χ18222222-1222-12-12-122-1-122-12-1-1-1-1-1222-1-1-1-1-1-122-1-1-1-1222-1-1-1-1-1-1-2002-2-1-122-2-2-1-10022-1-1-1-1-1-1-1-100-21100011110000-2000-20000110000
χ19222222-1222-12-12-122-1-122-12-1-1-1-1-1222-1-1-1-1-1-1-2-2-1-1-1-1222-1-1-1-1-1-1200-2211-2-2221100-2-211111111002-1-1000-1-1-1-10000-2000-20000110000
χ20222222-1222-12-12-122-1-122-12-1-1-1-1-1222-1-1-1-1-1-1-2-2-1-1-1-1222-1-1-1-1-1-1-200-2-211-2-2-2-21100-2-21111111100-21100011110000200020000-1-10000
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χ22222222-1222-12-12-122-1-1-22-12-1-1-1-1-12-2-211111122-1-1-1-1-2-2-2111111-200-22-1-1-2-222110022-1-1-1-1111100-21-1000-1-1110000-2000200001-10000
χ23222222-1222-12-12-122-1-1-22-12-1-1-1-1-12-2-2111111-2-2-1-1-1-1-2-2-21111112002-21122-2-2-1-100-2-21111-1-1-1-1002-1100011-1-10000-2000200001-10000
χ24222222-1222-12-12-122-1-1-22-12-1-1-1-1-12-2-2111111-2-2-1-1-1-1-2-2-2111111-20022112222-1-100-2-21111-1-1-1-100-21-1000-1-11100002000-20000-110000
χ2522222-1222-12-12-122-12-12-1-1-1222-1-1-12222222200-1-1-1-1-1-1-1-1-1-1-1-1-1222020000-1-100-1-1000000000022-122-122-1-1-1-1-1-1-1-100020-1-10000-1000
χ2622222-1222-12-12-122-12-12-1-1-1222-1-1-12222222200-1-1-1-1-1-1-1-1-1-1-1-1-12-2-2020000-1-100110000000000-2-2-1221-2-2-1-1-1-11111000-201100001000
χ2722222-1222-12-12-122-12-12-1-1-1222-1-1-12222222200-1-1-1-1-1-1-1-1-1-1-1-1-1-2220-200001100-1-10000000000-2-21-2-2-1221111-1-1-1-1000-201100001000
χ2822222-1222-12-12-122-12-12-1-1-1222-1-1-12222222200-1-1-1-1-1-1-1-1-1-1-1-1-1-2-2-20-200001100110000000000221-2-21-2-21111111100020-1-10000-1000
χ2922222-1222-12-12-122-12-1-2-1-1-1222-1-1-1-2-2-2-2-2-2-2-200-1-1-1-111111111122-20-200001100-1-10000000000-2-2-12-212-211-1-1-1-11100020110000-1000
χ3022222-1222-12-12-122-12-1-2-1-1-1222-1-1-1-2-2-2-2-2-2-2-200-1-1-1-11111111112-220-20000110011000000000022-12-2-1-2211-1-111-1-1000-20-1-100001000
χ3122222-1222-12-12-122-12-1-2-1-1-1222-1-1-1-2-2-2-2-2-2-2-200-1-1-1-1111111111-22-2020000-1-100-1-10000000000221-2212-2-1-111-1-111000-20-1-100001000
χ3222222-1222-12-12-122-12-1-2-1-1-1222-1-1-1-2-2-2-2-2-2-2-200-1-1-1-1111111111-2-22020000-1-100110000000000-2-21-22-1-22-1-11111-1-100020110000-1000
χ332222-122-1-1222222-1-1-122-12-1-1-1-122-1-1-122-1-1-1-122-1-1-1-12-1-122-1-1-1-10222022-1-1002222-1-1-1-1-1-1-1-1-1-1000002-1-10000-1-1-1-1022000000000-1-10
χ342222-122-1-1222222-1-1-122-12-1-1-1-122-1-1-122-1-1-1-122-1-1-1-12-1-122-1-1-1-10-2-22022-1-10022-2-2-1-1-1-1-1-1-1-1-1-100000-211000011110-2-2000000000110
χ352222-122-1-1222222-1-1-122-12-1-1-1-122-1-1-122-1-1-1-1-2-2-1-1-1-12-1-122-1-1-1-1022-20-2-21100-2-2221111111111000002-1-10000-1-1-1-10-2-2000000000110
χ362222-122-1-1222222-1-1-122-12-1-1-1-122-1-1-122-1-1-1-1-2-2-1-1-1-12-1-122-1-1-1-10-2-2-20-2-21100-2-2-2-2111111111100000-21100001111022000000000-1-10
χ372222-122-1-1222222-1-1-12-2-12-1-1-1-122-111-2-2111122-1-1-1-1-211-2-2111102-2-20221100-2-222-1-1-1-1-1-1111100000-2-110000-1-11102-2000000000-110
χ382222-122-1-1222222-1-1-12-2-12-1-1-1-122-111-2-2111122-1-1-1-1-211-2-211110-22-20221100-2-2-2-2-1-1-1-1-1-111110000021-1000011-1-10-220000000001-10
χ392222-122-1-1222222-1-1-12-2-12-1-1-1-122-111-2-21111-2-2-1-1-1-1-211-2-2111102-220-2-2-1-1002222111111-1-1-1-100000-2-110000-1-1110-220000000001-10
χ402222-122-1-1222222-1-1-12-2-12-1-1-1-122-111-2-21111-2-2-1-1-1-1-211-2-211110-2220-2-2-1-10022-2-2111111-1-1-1-10000021-1000011-1-102-2000000000-110
χ412-22-2222-2-2-22-2-22-222220-22-2-22-2-2-22000000002-222-2-2000000000000002-2000000002-222-2-200002i−2i00000000000000000002i−2i2i−2i000000
χ422-22-2222-2-2-22-2-22-222220-22-2-22-2-2-22000000002-222-2-2000000000000002-2000000002-222-2-20000−2i2i0000000000000000000−2i2i−2i2i000000
χ432-22-2222-2-2-22-2-22-222220-22-2-22-2-2-2200000000-2222-2-200000000000000-2200000000-22-2-22200002i−2i00000000000000000002i−2i−2i2i000000
χ442-22-2222-2-2-22-2-22-222220-22-2-22-2-2-2200000000-2222-2-200000000000000-2200000000-22-2-2220000−2i2i0000000000000000000−2i2i2i−2i000000
χ4544444-2-244-2-2-2-2-2-24-2-214-21-2-2-2-211-244-2-2-2-2-2-2001111-2-2-2111111400040000-2-20000000000000000-2-2-200011110000000000000000000
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χ494444-24-2-2-24-24-24-2-2-21-24-2-2-2111-2-2-2-2-2-2-211114411114-2-2-2-2111100040-2-2-2-200-2-200-2-2111111110000000000000000000000000000000
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χ934-4-44-24-22-242-42-4-22-21-20-222-1-11-2220023−23−333−3001-11-100023−23−333−30000000−2i32i300000000−3i3i3i−3ii3−i3−i3i30000000000000000000000000000000
χ944-4-44-24-22-242-42-4-22-21-20-222-1-11-2220023−23−333−3001-11-100023−23−333−300000002i3−2i3000000003i−3i−3i3i−i3i3i3−i30000000000000000000000000000000
χ954-4-44-24-22-242-42-4-22-21-20-222-1-11-22200−23233−3−33001-11-1000−23233−3−330000000−2i32i3000000003i−3i−3i3ii3−i3−i3i30000000000000000000000000000000
χ964-4-44-24-22-242-42-4-22-21-20-222-1-11-22200−23233−3−33001-11-1000−23233−3−3300000002i3−2i300000000−3i3i3i−3i−i3i3i3−i30000000000000000000000000000000
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
χ9988-8-88-4-48-844-4-444-8-4-4204-2-4-444-22400000000002-2-2200000000000000000000000000000000000000000000000000000000000000000
χ10088-8-8-4-4-4-4444-4-44442220-2-222-2-2-22-2−4i34i3002i32i3−2i3−2i300-111-102i3−2i300−i3−i3i3i300000000000000000000000000000000000000000000000000000000
χ10188-8-8-4-4-4-4444-4-44442220-2-222-2-2-22-24i3−4i300−2i3−2i32i32i300-111-10−2i32i300i3i3−i3−i300000000000000000000000000000000000000000000000000000000
χ1028-88-88-4-4-8-84-444-448-4-4204244-44-2-2-4000000000022-2-200000000000000000000000000000000000000000000000000000000000000000
χ1038-88-8-4-4844484-8-4-8-42-4-40-2-4-24-44442000000000022-2-200000000000000000000000000000000000000000000000000000000000000000
χ1048-88-8-4-4-4444-444-44-42220-22-2-22-2-2-2200006i−6i6i−6i00-1-11100000−3i3i−3i3i00000000000000000000000000000000000000000000000000000000
χ1058-88-8-4-4-4444-444-44-42220-22-2-22-2-2-220000−6i6i−6i6i00-1-111000003i−3i3i−3i00000000000000000000000000000000000000000000000000000000
χ1068-8-88-4-484-4-4-84-84842-4-4024-244-4-44-200000000002-22-200000000000000000000000000000000000000000000000000000000000000000
χ1078-8-88-4-4-44-4-44444-4422202-2-2-2-222-2-20043−43−232323−2300-11-11000−23233−3−3300000000000000000000000000000000000000000000000000000000
χ1088-8-88-4-4-44-4-44444-4422202-2-2-2-222-2-200−434323−23−232300-11-1100023−23−333−300000000000000000000000000000000000000000000000000000000

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