Finite Group Databasebeta

← Group #13155820

Character table — Group #13155820

Order 1728.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96C97C98C99C100C101C102C103C104C105C106C107C108C109C110C111
size1111222222222222224444444444444444444444666666888888888888121212121212121212121212121212121212121212242424242424242424242424242424363636363636363636363636727272108108
order12223334466666666633366666666612121212121212121212441212121236661212121212121212244666666661212121212121212121241212121212121212121212121212226666882424242426688
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-111-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-1-1
χ311111111111111111111111111111111111111111111111111111111111-1-11111111111-1-1-1-1111111111-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111-1-1
χ411111111111111111111111111111111111111111111111111111111111-1-11111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-111
χ51111111111111111111111111111111111111111-1-1-1-1-1-1111111111111-111-1-1-1-1-1-1-1-1-1-11111-1-1-1-1111111111111111-1-1-1-1-1-1111111-1-1-1-1-1
χ61111111111111111111111111111111111111111-1-1-1-1-1-1111111111111-111-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-111111
χ71111111111111111111111111111111111111111-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111-1-11111-1-1-1-1111111-1-1-1-1-1-1-1-1-111
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
χ92222222-2-2222222222222222222222-2-2-2-2-2-2-2-2-2-22222222222-2-2-2-2-2-2-2-2-200-2-2-2-2-2-2-2-2220000222200000000000000000000000000000000
χ102222222-2-2222222222222222222222-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-22222-2-2-2-2-2-2-2-220022222222-2-20000-2-2-2-200000000000000000000000000000000
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χ12222222-122222-1-12-1222-1-122-1-1-1-1-1-12-1-1222-1-1-1-12222222-1-1-1-1-1-122-1-1-1-120022-1-1-1-1-1-1-1-10000-1-1-1-1-2-2-2110011110000000000000000-21100
χ13222222-122222-1-12-1222-1-122-1-1-1-1-1-12-1-1222-1-1-1-12-2-2-2-2-2-2-1-1-1-1-1-122-1-1-1-1-200-2-21111111100001111222-1-100-1-1-1-10000000000000000-21100
χ14222222-122222-1-12-1222-1-122-1-1-1-1-1-12-1-1222-1-1-1-12-2-2-2-2-2-2-1-1-1-1-1-122-1-1-1-1-200-2-21111111100001111-2-2-21100111100000000000000002-1-100
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χ884-4-444-2-24-4-4222-2-424-2-2-21222-1-1-212-2-22-4-2211-1-14002i3−2i32i3−2i31-1-11-22-2211-1-10002i3−2i300−i3−i3i3i3000000−i3i3−i3i300000000000000000000000000000000
χ894-4-444-2-2-44-4222-2-424-2-2-21222-1-1-212-22-242-2-1-111-400−2i32i3−2i32i31-1-112-22-2-1-1110002i3−2i300−i3−i3i3i3000000i3−i3i3−i300000000000000000000000000000000
χ904-4-444-2-2-44-4222-2-424-2-2-21222-1-1-212-22-242-2-1-111-4002i3−2i32i3−2i31-1-112-22-2-1-111000−2i32i300i3i3−i3−i3000000−i3i3−i3i300000000000000000000000000000000
χ914-4-44-2444-42-4-4-442-4-24-2-24222-4-4-242-24-424-444-4-4-2000000-222-2-22-22-2-22200000000000000000000000000000000000000000000000000000
χ924-4-44-24-24-42-4-42-222-24-21-222-1221-2-1-2-2224-4-2-222-20000001-1-111-1-2211-1-100000000000000000000000000003i−3i−3i3i000000000000000000000
χ934-4-44-24-24-42-4-42-222-24-21-222-1221-2-1-2-2224-4-2-222-20000001-1-111-1-2211-1-10000000000000000000000000000−3i3i3i−3i000000000000000000000
χ944-4-44-24-2-442-4-42-222-24-21-222-1221-2-1-22-2-2-4422-2-220000001-1-11-112-2-1-111000000000000000000000023−230000−33−33000000000000000000000
χ954-4-44-24-2-442-4-42-222-24-21-222-1221-2-1-22-2-2-4422-2-220000001-1-11-112-2-1-1110000000000000000000000−232300003−33−3000000000000000000000
χ964-4-44-2-244-4222-442-4-2-21-2-2-1-1222-2-2214-42-22-2-222-20000001-1-11-221-111-1-10000000000000−2i32i32i3−2i3000000000000000i3−i3−i3i300000000000000000
χ974-4-44-2-244-4222-442-4-2-21-2-2-1-1222-2-2214-42-22-2-222-20000001-1-11-221-111-1-100000000000002i3−2i3−2i32i3000000000000000−i3i3i3−i300000000000000000
χ984-4-44-2-24-44222-442-4-2-21-2-2-1-1222-2-221-44-22-222-2-220000001-1-112-2-11-1-11104-40000000000-22-22000000000-2200001-11-100000000000000000
χ994-4-44-2-24-44222-442-4-2-21-2-2-1-1222-2-221-44-22-222-2-220000001-1-112-2-11-1-1110-4400000000002-22-20000000002-20000-11-1100000000000000000
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
χ10288-8-8-48-400-48-8-44444-8-42-4-442-44-24-24000000000000000022-2-20000000000000000000000000000000000000000000000000000000000000
χ10388-8-8-4-4800-4-448-84-8442-4-42-2-4-44444-2000000000000000022-2-20000000000000000000000000000000000000000000000000000000000000
χ10488-8-8-4-4-400-4-44-4444442222-222-2-2-2-2-2000006i−6i6i−6i0000000-1-1110000−3i3i−3i3i00000000000000000000000000000000000000000000000000000
χ10588-8-8-4-4-400-4-44-4444442222-222-2-2-2-2-200000−6i6i−6i6i0000000-1-11100003i−3i3i−3i00000000000000000000000000000000000000000000000000000
χ1068-88-8-48-4004-8844-4-44-8-42-44-4-24-4-242400000000000000002-22-20000000000000000000000000000000000000000000000000000000000000
χ1078-88-8-4-480044-4-8-8-48442-4-4-2244-444-4-200000000000000002-22-20000000000000000000000000000000000000000000000000000000000000
χ1088-88-8-4-4-40044-444-4-444222-22-2-22-2-22-2000006i−6i−6i6i0000000-11-110000−3i3i3i−3i00000000000000000000000000000000000000000000000000000
χ1098-88-8-4-4-40044-444-4-444222-22-2-22-2-22-200000−6i6i6i−6i0000000-11-1100003i−3i−3i3i00000000000000000000000000000000000000000000000000000
χ1108-8-88-4-4-48-84444-444-4-4222-2-2-2-2-222-22-444-4422-2-2-4000000-111-12-22-2-1-11100000000000000000000000000000000000000000000000000000
χ1118-8-88-4-4-4-884444-444-4-4222-2-2-2-2-222-224-4-44-4-2-2224000000-111-1-22-2211-1-100000000000000000000000000000000000000000000000000000

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