Finite Group Databasebeta

← Group #13155817

Character table — Group #13155817

Order 1728.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96C97C98C99C100C101C102C103C104C105C106C107C108C109C110C111
size1111222222222222224444444444444444444444666666888888888888121212121212121212121212121212121212121212242424242424242424242424242424363636363636363636363636727272108108
order12223334466666666633366666666612121212121212121212441212121236661212121212121212222666666666666121212121212466666612121212121212124488121212122424242426688
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111111111111111111111111111111111111111111-1111111-1-1-1-1-1-1-1-111-1-11111-1-1-1-1-1-1-1-1-1
χ311111111111111111111111111111111111111111111111111111111111-1-111-1-1-1-11111111111111-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1111-1-1
χ411111111111111111111111111111111111111111111111111111111111-1-111-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-11111-1-1-111
χ51111111111111111111111111111111111111111-1-1-1-1-1-1111111111111-111-1-11111-1-1-1-1-1-1-1-1-1-1-1-1111111111111111-1-111-1-1-1-11111-1-1-1-1-1
χ61111111111111111111111111111111111111111-1-1-1-1-1-1111111111111-111-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111
χ71111111111111111111111111111111111111111-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11-1-1-1-1-1-11111111111-1-11111-1-1-1-1-1-1-111
χ81111111111111111111111111111111111111111-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111111-1-1
χ92222222-2-2222222222222222222222-2-2-2-2-2-2-2-2-2-22222222222-2-2-2-2-2-2-2-2-200-2-20000-2-2-2-2-2-222222200000000000000000000000000000000
χ102222222-2-2222222222222222222222-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-22222-2-2-2-2-2-2-2-2200220000222222-2-2-2-2-2-200000000000000000000000000000000
χ11222222-122222-12-12-12-1-12-1-1-122-12-1-12-1-122-1-1-1-12222222-1-1-1-122-1-1-1-1-1-1200220000-1-1-1-1-1-1-1-1-1-1-1-1200000022-1-1-1-1-1-10000000000002-1-100
χ12222222-122222-12-12-12-1-12-1-1-122-12-1-12-1-122-1-1-1-12222222-1-1-1-122-1-1-1-1-1-1200220000-1-1-1-1-1-1-1-1-1-1-1-1-2000000-2-2111111000000000000-21100
χ13222222-122222-12-12-12-1-12-1-1-122-12-1-12-1-122-1-1-1-12-2-2-2-2-2-2-1-1-1-122-1-1-1-1-1-1-200-2-20000111111111111200000022-1-1-1-1-1-1000000000000-21100
χ14222222-122222-12-12-12-1-12-1-1-122-12-1-12-1-122-1-1-1-12-2-2-2-2-2-2-1-1-1-122-1-1-1-1-1-1-200-2-20000111111111111-2000000-2-21111110000000000002-1-100
χ15222222-1-2-2222-12-12-12-1-12-1-1-122-12-1-1-211-2-21111-2222222-1-1-1-1-2-2111111-200-2-20000111111-1-1-1-1-1-1000000000−i3i3−i3−i3i3i30000000000000−i3i300
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χ17222222-1-2-2222-12-12-12-1-12-1-1-122-12-1-1-211-2-21111-2-2-2-2-2-2-2-1-1-1-1-2-2111111200220000-1-1-1-1-1-1111111000000000−i3i3−i3−i3i3i30000000000000i3−i300
χ18222222-1-2-2222-12-12-12-1-12-1-1-122-12-1-1-211-2-21111-2-2-2-2-2-2-2-1-1-1-1-2-2111111200220000-1-1-1-1-1-1111111000000000i3−i3i3i3−i3−i30000000000000−i3i300
χ1922222-12222-1-122222-12-1-12-1-1-1-12-1-12222-1-1-1-1-1-1222-1-1-1-1-1-1-1-1-1-122-1-1-1-1222-1-1-1-1-1-122-1-1-1-122-1-1-1-1022-1-1-1-1000000002200-1-1-1-1000000000
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χ392-2-222-122-2-211-222-2-2-12-1-1-211112-1-1-2-22-2-11-1-111200−i3i3−i3i3-111-1-112-2-1-111000−i3i3−i3i3i3−i300−i3−i3i3i300−i3i3−i3i3000−i3i3i3−i3000000002-200-11-11000000000
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χ422-2-222-122-2-211-222-2-2-12-1-1-211112-1-1-2-22-2-11-1-111200i3−i3i3−i3-111-1-112-2-1-111000i3−i3i3−i3−i3i300i3i3−i3−i300i3−i3i3−i3000i3−i3−i3i3000000002-200-11-11000000000
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χ884-4-444-2-24-4-42224-2-42-2-21-22-1-122-2-212-4-22-2211-1-14002i3−2i32i3−2i31-1-11-22-2211-1-10002i3−2i3000000−i3−i3i3i300−i3i3−i3i300000000000000000000000000000000
χ894-4-444-2-2-44-42224-2-42-2-21-22-1-122-2-21242-22-2-1-111-400−2i32i3−2i32i31-1-112-22-2-1-1110002i3−2i3000000−i3−i3i3i300i3−i3i3−i300000000000000000000000000000000
χ904-4-444-2-2-44-42224-2-42-2-21-22-1-122-2-21242-22-2-1-111-4002i3−2i32i3−2i31-1-112-22-2-1-111000−2i32i3000000i3i3−i3−i300−i3i3−i3i300000000000000000000000000000000
χ914-4-44-2444-42-4-4-4-242-44-24-22-4-422-2-24224-44-444-4-4-2000000-222-2-22-22-2-22200000000000000000000000000000000000000000000000000000
χ924-4-44-24-24-42-4-42-2-22241-2-2-122221-2-2-12-224-4-2-222-20000001-1-11-221-111-1-1000000000000000000000000000000003i−3i−3i3i00000000000000000
χ934-4-44-24-24-42-4-42-2-22241-2-2-122221-2-2-12-224-4-2-222-20000001-1-11-221-111-1-100000000000000000000000000000000−3i3i3i−3i00000000000000000
χ944-4-44-24-2-442-4-42-2-22241-2-2-122221-2-2-1-22-2-4422-2-220000001-1-112-2-11-1-111000000000000000000000000000023−2300−33−3300000000000000000
χ954-4-44-24-2-442-4-42-2-22241-2-2-122221-2-2-1-22-2-4422-2-220000001-1-112-2-11-1-1110000000000000000000000000000−2323003−33−300000000000000000
χ964-4-44-2-244-4222-4-242-4-2-2-21222-1-1-21-2224-4-22-2-222-20000001-1-111-1-2211-1-100000−2i32i32i3−2i3000000000000000i3−i3−i3i30000000000000000000000000
χ974-4-44-2-244-4222-4-242-4-2-2-21222-1-1-21-2224-4-22-2-222-20000001-1-111-1-2211-1-1000002i3−2i3−2i32i3000000000000000−i3i3i3−i30000000000000000000000000
χ984-4-44-2-24-44222-4-242-4-2-2-21222-1-1-21-22-2-442-222-2-220000001-1-11-112-2-1-11104-400-22-220000000000000-221-11-10000000000000000000000000
χ994-4-44-2-24-44222-4-242-4-2-2-21222-1-1-21-22-2-442-222-2-220000001-1-11-112-2-1-1110-44002-22-200000000000002-2-11-110000000000000000000000000
χ1008888-4-4-488-4-4-4-4-4-4-4-4-4222222222222-4-4-4-4-42222-4000000-1-1-1-12222-1-1-1-100000000000000000000000000000000000000000000000000000
χ1018888-4-4-4-8-8-4-4-4-4-4-4-4-4-422222222222244444-2-2-2-24000000-1-1-1-1-2-2-2-2111100000000000000000000000000000000000000000000000000000
χ10288-8-8-48-400-48-8-44444-82-4-42-44-44-244-2000000000000000022-2-20000000000000000000000000000000000000000000000000000000000000
χ10388-8-8-4-4800-4-4484-84-84-4-42-4-442-24-244000000000000000022-2-20000000000000000000000000000000000000000000000000000000000000
χ10488-8-8-4-4-400-4-44-44444422222-22-2-2-2-2-2000006i−6i6i−6i0000000-1-1110000−3i3i−3i3i00000000000000000000000000000000000000000000000000000
χ10588-8-8-4-4-400-4-44-44444422222-22-2-2-2-2-200000−6i6i−6i6i0000000-1-11100003i−3i3i−3i00000000000000000000000000000000000000000000000000000
χ1068-88-8-48-4004-88444-4-4-82-4-4-24-44-4-244200000000000000002-22-20000000000000000000000000000000000000000000000000000000000000
χ1078-88-8-4-480044-4-84-8-484-4-4244-4-224-24-400000000000000002-22-20000000000000000000000000000000000000000000000000000000000000
χ1088-88-8-4-4-40044-4444-4-44222-2-22-22-2-2-22000006i−6i−6i6i0000000-11-110000−3i3i3i−3i00000000000000000000000000000000000000000000000000000
χ1098-88-8-4-4-40044-4444-4-44222-2-22-22-2-2-2200000−6i6i6i−6i0000000-11-1100003i−3i−3i3i00000000000000000000000000000000000000000000000000000
χ1108-8-88-4-4-48-84444-4-444-4222-2-2-2-2-2222-24-44-4422-2-2-4000000-111-12-22-2-1-11100000000000000000000000000000000000000000000000000000
χ1118-8-88-4-4-4-884444-4-444-4222-2-2-2-2-2222-2-44-44-4-2-2224000000-111-1-22-2211-1-100000000000000000000000000000000000000000000000000000

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