Finite Group Databasebeta

← Group #13168594

Character table — Group #13168594

Order 1728.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96C97C98C99C100C101C102C103C104C105C106C107C108
size111122222222222244444444444444444444466888888888888812121212121212121212121212121212121212121212121212181824242424242424242424242424243636363636363654547272727272108
order122233366666666633346666666661212121212121212443666121212121212121212222446612121212121212121212121212121212121244666666666661212124444412124412121212124
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111111111111111111111111-11-11111111111-1-111111111-1-1-1111-1-1-11111-1-1-1-111-1-1-1-1-1-1-1-1-111-1
χ31111111111111111111111111111111111111111111111111111-1-1111-1-1111111111111111111-1-11-1-1-1111-1-1-1-11111-1-11-1-1-1-1-11-11-1-1-1
χ41111111111111111111111111111111111111111111111111111-1-1-11-1-1-111111111-1-11111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111-11-1-1-11
χ51111111111111111111111111111111111111-1-11111111111111111-1111-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-11111111111111111-1-1-1-1111-1-1-11-1-1-1-1
χ61111111111111111111111111111111111111-1-1111111111111111-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111-1-1-11111-1-1-11-1-11-1-1-1111-11-1-11
χ71111111111111111111111111111111111111-1-11111111111111-1-11-11-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-11-1-1-1111-1-1-1-1111-111-1-1-1-111-1-1-1111
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
χ91111111111111111111-1111111111-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1-11-11-1-11111-1-1-1-111-1-11111-1-1-1-1-1-111-1-111111-1-1-1-1-1-11-111-1-1-1-111-11-11
χ101111111111111111111-1111111111-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1-11-1-1-111111-1-1-1-111111111-1-1-1-111-11-1-1-1-1-111-1-111111-1-1-11111-1-111-1-1
χ111111111111111111111-1111111111-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1-1-111-1-1-1-111-1-1-1-111-1-11111-1-1-1-1111-111111-1-111-1-1-1-1-111-111111-1-1-11-1
χ121111111111111111111-1111111111-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1-1-11-1-11-1-111-1-1-1-111111111-1-1-1-1-1-1-1-111-1-1-1-1-1111111-11-11-1-1-1-1-111-111
χ131111111111111111111-1111111111-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-11-111-111-1-11111-1-1-1-1-1-1-1-11111-1-111-1-111111-1-1-1-1-11-11-11-1-111-111-11-1
χ141111111111111111111-1111111111-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-11-1-11111-1-11111-1-111-1-1-1-1111111-11-1-1-1-1-111-1-1111-1-111-111-1-11-1-1-111
χ151111111111111111111-1111111111-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1111-1-1-1-1-11111-1-1-1-1-1-1-1-11111111-111111-1-111-1-1-111-1-1-111-1-1-1-111-11
χ161111111111111111111-1111111111-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-11-111-1-1-1-11111-1-111-1-1-1-11111-1-1-1-111-1-1-1-1-111111-11-111-1-11111-11-1-1
χ17222222-1-12222-12-122-1-12-1-1-12-1-122-12222222200-1-1-1-1-1-1-1-1-1-1-1-1-122202-1-100000000-1-10000000022222-1-1-1-1-1-1-1-12-1-100002-1-1000-10000
χ18222222-1-12222-12-122-1-12-1-1-12-1-122-12222222200-1-1-1-1-1-1-1-1-1-1-1-1-122-20-2-1-1000000001100000000-2-2-222-1111-1-1-1-1-2110000-21100010000
χ19222222-1-12222-12-122-1-12-1-1-12-1-122-12222222200-1-1-1-1-1-1-1-1-1-1-1-1-1-2-22021100000000-1-100000000-2-22-2-21-1-1-111112-1-10000-21100010000
χ20222222-1-12222-12-122-1-12-1-1-12-1-122-12222222200-1-1-1-1-1-1-1-1-1-1-1-1-1-2-2-20-21100000000110000000022-2-2-211111111-21100002-1-1000-10000
χ21222222-1-12222-12-122-1-1-2-1-1-12-1-122-1-2-2-2-2-2-2-2-200-1-1-1-11111111112-220-2-1-1000000001100000000-2-222-21-1-1-1-1-111-2110000211000-10000
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χ24222222-1-12222-12-122-1-1-2-1-1-12-1-122-1-2-2-2-2-2-2-2-200-1-1-1-1111111111-22-2021100000000-1-100000000-2-2-2-22-111111-1-12-1-10000211000-10000
χ2522222-122-1-122222-1-12-122-1-1-12-1-1-1222-1-1-1-1-1-122-1-1-1-1222-1-1-1-1-1-12202022-1-1-1-1222200-1-1-1-1-1-1-1-1000-1-12000-1-1-1-1000022000000000-1-10
χ2622222-122-1-122222-1-12-122-1-1-12-1-1-1222-1-1-1-1-1-122-1-1-1-1222-1-1-1-1-1-1-2-2020-2-2-1-1-1-1222200-1-1-1-1-1-1-1-100011-200011110000-2-2000000000110
χ2722222-122-1-122222-1-12-122-1-1-12-1-1-1222-1-1-1-1-1-1-2-2-1-1-1-1222-1-1-1-1-1-1220-20221111-2-2-2-20011111111000-1-12000-1-1-1-10000-2-2000000000110
χ2822222-122-1-122222-1-12-122-1-1-12-1-1-1222-1-1-1-1-1-1-2-2-1-1-1-1222-1-1-1-1-1-1-2-20-20-2-21111-2-2-2-2001111111100011-20001111000022000000000-1-10
χ2922222-122-1-122222-1-12-1-22-1-1-12-1-1-12-2-211111122-1-1-1-1-2-2-21111112-20-2022-1-111-2-22200-1-1-1-11111000-11-2000-1-11100002-2000000000-110
χ3022222-122-1-122222-1-12-1-22-1-1-12-1-1-12-2-211111122-1-1-1-1-2-2-2111111-220-20-2-2-1-111-2-22200-1-1-1-111110001-1200011-1-10000-220000000001-10
χ3122222-122-1-122222-1-12-1-22-1-1-12-1-1-12-2-2111111-2-2-1-1-1-1-2-2-21111112-20202211-1-122-2-2001111-1-1-1-1000-11-2000-1-1110000-220000000001-10
χ3222222-122-1-122222-1-12-1-22-1-1-12-1-1-12-2-2111111-2-2-1-1-1-1-2-2-2111111-22020-2-211-1-122-2-2001111-1-1-1-10001-1200011-1-100002-2000000000-110
χ332222-122222-1-12-122-1-122-122-1-12-1-1-1-1-122-1-1-1-122-1-1-1-12-1-122-1-1-1-100222002222-1-1-1-122-1-1-1-1-1-1-1-100-10002-1-10000-1-1-1200200000-10-1000
χ342222-122222-1-12-122-1-122-122-1-12-1-1-1-1-122-1-1-1-122-1-1-1-12-1-122-1-1-1-100-22-2002222-1-1-1-1-2-2-1-1-1-1-1-1-1-1001000-2110000111-200-200000101000
χ352222-122222-1-12-122-1-122-122-1-12-1-1-1-1-122-1-1-1-1-2-2-1-1-1-12-1-122-1-1-1-1002-2200-2-2-2-21111221111111100-10002-1-10000-1-1-1-200-200000101000
χ362222-122222-1-12-122-1-122-122-1-12-1-1-1-1-122-1-1-1-1-2-2-1-1-1-12-1-122-1-1-1-100-2-2-200-2-2-2-21111-2-211111111001000-2110000111200200000-10-1000
χ372222-122222-1-12-122-1-12-2-122-1-12-1-1-111-2-2111122-1-1-1-1-211-2-21111002-2-20022-2-211-1-1-2-2-1-1-1-1111100-10002-1-10000111-200200000-101000
χ382222-122222-1-12-122-1-12-2-122-1-12-1-1-111-2-2111122-1-1-1-1-211-2-2111100-2-220022-2-211-1-122-1-1-1-11111001000-2110000-1-1-1200-20000010-1000
χ392222-122222-1-12-122-1-12-2-122-1-12-1-1-111-2-21111-2-2-1-1-1-1-211-2-211110022-200-2-222-1-111-2-21111-1-1-1-100-10002-1-10000111200-20000010-1000
χ402222-122222-1-12-122-1-12-2-122-1-12-1-1-111-2-21111-2-2-1-1-1-1-211-2-2111100-22200-2-222-1-111221111-1-1-1-1001000-2110000-1-1-1-200200000-101000
χ412-22-2222-22-22-2-2-22-22220-22-2-2-2-22-22000000002i−2i22-2-200000000000000002i−2i00002i−2i002i2i−2i−2i00002-200000000000000000002-22i−2i000000
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χ934-4-44-2-24-4222-242-4-21-2-202221-2-2-1-1200−2i32i3i3−i3−i3i3001-1-11000−2i32i3i3−i3−i3i30000000000023−230000−3i3i3i−3i−333−30000000000000000000000000000000
χ944-4-44-2-24-4222-242-4-21-2-202221-2-2-1-1200−2i32i3i3−i3−i3i3001-1-11000−2i32i3i3−i3−i3i300000000000−232300003i−3i−3i3i3−3−330000000000000000000000000000000
χ954-4-44-2-24-4222-242-4-21-2-202221-2-2-1-12002i3−2i3−i3i3i3−i3001-1-110002i3−2i3−i3i3i3−i30000000000023−2300003i−3i−3i3i−333−30000000000000000000000000000000
χ964-4-44-2-24-4222-242-4-21-2-202221-2-2-1-12002i3−2i3−i3i3i3−i3001-1-110002i3−2i3−i3i3i3−i300000000000−23230000−3i3i3i−3i3−3−330000000000000000000000000000000
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
χ9988-8-88-4-4-44-4-8-84844-4-420-4-2244-24-4400000000002-22-200000000000000000000000000000000000000000000000000000000000000000
χ10088-8-8-4-4-4-44-4444-44422202-22-2-2-2-22-243−4300−23−23232300-11-110−23230033−3−300000000000000000000000000000000000000000000000000000000
χ10188-8-8-4-4-4-44-4444-44422202-22-2-2-2-22-2−4343002323−23−2300-11-11023−2300−3−33300000000000000000000000000000000000000000000000000000000
χ1028-88-88-4-44-448-84-8-44-4-42042-244-2-44-4000000000022-2-200000000000000000000000000000000000000000000000000000000000000000
χ1038-88-8-48-448-8-4444-4-8-42-40-2-444-24-442000000000022-2-200000000000000000000000000000000000000000000000000000000000000000
χ1048-88-8-4-4-44-44-4444-442220-22-2-2-2-22-2200006i−6i6i−6i00-1-11100000−3i3i−3i3i00000000000000000000000000000000000000000000000000000000
χ1058-88-8-4-4-44-44-4444-442220-22-2-2-2-22-220000−6i6i−6i6i00-1-111000003i−3i3i−3i00000000000000000000000000000000000000000000000000000000
χ1068-8-88-48-44-8-84-4-4448-42-40-244-42-444-200000000002-2-2200000000000000000000000000000000000000000000000000000000000000000
χ1078-8-88-4-4-44444-4-444-42220-2-2-2222-2-2-200−4i34i32i3−2i3−2i32i300-111-10002i3−2i3−i3i3i3−i300000000000000000000000000000000000000000000000000000000
χ1088-8-88-4-4-44444-4-444-42220-2-2-2222-2-2-2004i3−4i3−2i32i32i3−2i300-111-1000−2i32i3i3−i3−i3i300000000000000000000000000000000000000000000000000000000

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