Finite Group Databasebeta

← Group #13155879

Character table — Group #13155879

Order 1728.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96C97C98C99C100C101C102C103C104C105C106C107C108C109C110C111
size1111222222222222224444444444444444444444666666888888888888121212121212121212121212121212121212121212242424242424242424242424242424363636363636363636363636727272108108
order1222333446666666663336666666661212121212121212121244121212123666121212121212121222266666666666612121212121246666661212121212121212448812121212242424244121288
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111111111111111111111111111111111111111111-1111111-1-1-1-1-1-1-1-111-1-11111-1-1-1-1-1-1-1-1-1
χ311111111111111111111111111111111111111111111111111111111111-1-11111-1-1-1-111111111111-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1111-1-1
χ411111111111111111111111111111111111111111111111111111111111-1-11111-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-11111-1-1-111
χ51111111111111111111111111111111111111111-1-1-1-1-1-1111111111111-111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1111111111111111-1-111-1-1-1-11111-1-1-1-1-1
χ61111111111111111111111111111111111111111-1-1-1-1-1-1111111111111-111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111
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
χ92222222-2-2222222222222222222222-2-2-2-2-2-2-2-2-2-22222222222-2-2-2-2-2-2-2-2-200-2-2-2-20000-2-2-2-222222200000000000000000000000000000000
χ102222222-2-2222222222222222222222-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-22222-2-2-2-2-2-2-2-2200222200002222-2-2-2-2-2-200000000000000000000000000000000
χ11222222-12222-1-12222-12-1-12-1-1-1-12-1-12222-1-1-1-1-1-1222-1-1-1-1-1-1-1-122-1-1-1-1-1-122222-1-1-1-1-1-1-1-1-1-122-1-1-1-1022-1-1-1-1000000002200-1-1-1-1000000000
χ12222222-12222-1-12222-12-1-12-1-1-1-12-1-12222-1-1-1-1-1-1222-1-1-1-1-1-1-1-122-1-1-1-1-1-12-2-222-1-11111-1-1-1-122-1-1-1-10-2-2111100000000-2-2001111000000000
χ13222222-12222-1-12222-12-1-12-1-1-1-12-1-12222-1-1-1-1-1-12-2-21111-1-1-1-122-1-1-1-1-1-1-222-2-211-1-1-1-11111-2-21111022-1-1-1-100000000-2-2001111000000000
χ14222222-12222-1-12222-12-1-12-1-1-1-12-1-12222-1-1-1-1-1-12-2-21111-1-1-1-122-1-1-1-1-1-1-2-2-2-2-21111111111-2-211110-2-21111000000002200-1-1-1-1000000000
χ15222222-1-2-222-1-12222-12-1-12-1-1-1-12-1-12-2-2-2111111-222-1-1-1-1-1-1-1-1-2-2111111-200-2-211−i3−i3i3i3111122-1-1-1-1000−i3−i3i3i3000000000000−i3−i3i3i3000000000
χ16222222-1-2-222-1-12222-12-1-12-1-1-1-12-1-12-2-2-2111111-222-1-1-1-1-1-1-1-1-2-2111111-200-2-211i3i3−i3−i3111122-1-1-1-1000i3i3−i3−i3000000000000i3i3−i3−i3000000000
χ17222222-1-2-222-1-12222-12-1-12-1-1-1-12-1-12-2-2-2111111-2-2-21111-1-1-1-1-2-211111120022-1-1−i3−i3i3i3-1-1-1-1-2-21111000−i3−i3i3i3000000000000i3i3−i3−i3000000000
χ18222222-1-2-222-1-12222-12-1-12-1-1-1-12-1-12-2-2-2111111-2-2-21111-1-1-1-1-2-211111120022-1-1i3i3−i3−i3-1-1-1-1-2-21111000i3i3−i3−i3000000000000−i3−i3i3i3000000000
χ1922222-12222-122-12-122-12-1-122-1-1-1-12-1-122222222-1000000-1-1-1-1-1-1-1-1-1-1-1-10220000222200000000002-1-1-1-1-1-122-1-1-1-1-1-100220000-1-1-1-100000
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χ262222-12222-12222-12-12-1-12-1-1-122-12-1-12-1-122-1-1-1-12-2-2-2-2-2-2-1-1-1-1-1-122-1-1-1-1-20011-2-200001111111111-200000011-2-211110000000000002-1-100
χ272222-122-2-2-12222-12-12-1-12-1-1-122-12-1-1-211-2-21111-2222222-1-1-1-111-2-21111-20011-2-200001111-1-1-1-1-1-10000000−i3i300−i3−i3i3i30000000000000−i3i300
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χ302222-122-2-2-12222-12-12-1-12-1-1-122-12-1-1-211-2-21111-2-2-2-2-2-2-2-1-1-1-111-2-21111200-1-1220000-1-1-1-11111110000000i3−i300i3i3−i3−i30000000000000−i3i300
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χ884-4-444-2-2-44-4222-2-424-2-2-21222-1-1-21-22-2-442-222-2-220000001-1-112-2-11-1-11104-40000-22-2200000000000-221-11-10000000000000000000000000
χ894-4-444-2-2-44-4222-2-424-2-2-21222-1-1-21-22-2-442-222-2-220000001-1-112-2-11-1-1110-4400002-22-2000000000002-2-11-110000000000000000000000000
χ904-4-44-2444-42-4-4-442-4-24-2-24222-4-4-24-22-4-224-4-2-2224000000-222-2-224-4-2-22200000000000000000000000000000000000000000000000000000
χ914-4-44-244-442-4-4-442-4-24-2-24222-4-4-24-2242-2-4422-2-2-4000000-222-22-2-4422-2-200000000000000000000000000000000000000000000000000000
χ924-4-44-24-24-42-42242-4-2-2-21-22-1-122-2-212-4-22-2211-1-1400−2i32i3−2i32i31-1-11-22-2211-1-100000−2i32i30000i3i3−i3−i300i3−i3i3−i300000000000000000000000000000000
χ934-4-44-24-24-42-42242-4-2-2-21-22-1-122-2-212-4-22-2211-1-14002i3−2i32i3−2i31-1-11-22-2211-1-1000002i3−2i30000−i3−i3i3i300−i3i3−i3i300000000000000000000000000000000
χ944-4-44-24-2-442-42242-4-2-2-21-22-1-122-2-21242-22-2-1-111-400−2i32i3−2i32i31-1-112-22-2-1-111000002i3−2i30000−i3−i3i3i300i3−i3i3−i300000000000000000000000000000000
χ954-4-44-24-2-442-42242-4-2-2-21-22-1-122-2-21242-22-2-1-111-4002i3−2i32i3−2i31-1-112-22-2-1-11100000−2i32i30000i3i3−i3−i300−i3i3−i3i300000000000000000000000000000000
χ964-4-44-2-244-422-4-4-222-241-2-2-122221-2-2-12-224-4-2-222-20000001-1-111-1-2211-1-1000000000000000000000000000000003i−3i−3i3i00000000000000000
χ974-4-44-2-244-422-4-4-222-241-2-2-122221-2-2-12-224-4-2-222-20000001-1-111-1-2211-1-100000000000000000000000000000000−3i3i3i−3i00000000000000000
χ984-4-44-2-24-4422-4-4-222-241-2-2-122221-2-2-1-22-2-4422-2-220000001-1-11-112-2-1-11100000000000000000000000000000023−23−33−3300000000000000000
χ994-4-44-2-24-4422-4-4-222-241-2-2-122221-2-2-1-22-2-4422-2-220000001-1-11-112-2-1-111000000000000000000000000000000−23233−33−300000000000000000
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
χ10288-8-88-4-4008-44-44-84-84-4-42-44-4-224-24400000000000000002-22-20000000000000000000000000000000000000000000000000000000000000
χ10388-8-8-4-4800-4-4-884444-82-4-424-44-4-244-200000000000000002-22-20000000000000000000000000000000000000000000000000000000000000
χ10488-8-8-4-4-400-4-44-4444442222-22-22-2-2-2-2000006i−6i6i−6i0000000-11-110000−3i3i−3i3i00000000000000000000000000000000000000000000000000000
χ10588-8-8-4-4-400-4-44-4444442222-22-22-2-2-2-200000−6i6i−6i6i0000000-11-1100003i−3i3i−3i00000000000000000000000000000000000000000000000000000
χ1068-88-88-4-400-84-4448-4-84-4-424-442-24-24-4000000000000000022-2-20000000000000000000000000000000000000000000000000000000000000
χ1078-88-8-4-4800448-84-4-44-82-4-4-2-44-44-2442000000000000000022-2-20000000000000000000000000000000000000000000000000000000000000
χ1088-88-8-4-4-40044-444-4-444222-22-22-2-2-2-22000006i−6i−6i6i0000000-1-1110000−3i3i3i−3i00000000000000000000000000000000000000000000000000000
χ1098-88-8-4-4-40044-444-4-444222-22-22-2-2-2-2200000−6i6i6i−6i0000000-1-11100003i−3i−3i3i00000000000000000000000000000000000000000000000000000
χ1108-8-88-4-4-48-84444-444-4-4222-2-2-2-2-2222-24-44-4422-2-2-4000000-111-12-22-2-1-11100000000000000000000000000000000000000000000000000000
χ1118-8-88-4-4-4-884444-444-4-4222-2-2-2-2-2222-2-44-44-4-2-2224000000-111-1-22-2211-1-100000000000000000000000000000000000000000000000000000

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