Finite Group Databasebeta

← Group #10896504

Character table — Group #10896504

Order 768.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96C97C98C99C100C101C102C103C104C105C106C107C108
size1111111122222222222222222222222222224444444444444444444444444444444488888888888888888888888824242424242424242424242424242424
order122222223444444444444666666612121212121212124444444412121212121212121212121212121212121212121212121244444444121212121212121212121212121212124444444488888888
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ311111111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1
χ411111111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111
χ5111111111111111-1-1-1-1111111111-1-1-1-1-1-1-1-1-1-111-1-1-1-111111111-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1-1-111111111-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1-1-1
χ6111111111111111-1-1-1-1111111111-1-1-1-1-1-1-1-1-1-111-1-1-1-111111111-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-11111
χ7111111111111111-1-1-1-1111111111-1-1-1-1-1-1-1-1-1-111-1-1-1-111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-11111
χ8111111111111111-1-1-1-1111111111-1-1-1-1-1-1-1-1-1-111-1-1-1-111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-111111111-1-1-1-111111111-1-1-1-1
χ911111111111-1-1-1-111111111111111111111111-1-1-1-1-1-11111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-111-1-111-1-11111-1-1-1-11111-1-1-1-111-1-111-1-111-1-111-1-1
χ1011111111111-1-1-1-111111111111111111111111-1-1-1-1-1-11111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-111-1-111-1-11111-1-1-1-11111-1-1-1-1-1-111-1-111-1-111-1-111
χ1111111111111-1-1-1-111111111111111111111111-1-1-1-1-1-11111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-111-1-1-1-11111-1-1-1-1111111-1-111-1-1-1-111-1-111
χ1211111111111-1-1-1-111111111111111111111111-1-1-1-1-1-11111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-111-1-1-1-11111-1-1-1-11111-1-111-1-11111-1-111-1-1
χ1311111111111-1-1-1-1-1-1-1-1111111111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-11111-1-1-1-1111111-1-1-1-1111111-1-1-1-1-1-1-1-1111111-1-1-1-11111-1-1-1-111
χ1411111111111-1-1-1-1-1-1-1-1111111111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-11111-1-1-1-1111111-1-1-1-1111111-1-1-1-1-1-1-1-11111-1-11111-1-1-1-11111-1-1
χ1511111111111-1-1-1-1-1-1-1-1111111111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-11111-1-1-1-11111-1-11111-1-1-1-1-1-111111111-1-1-1-111-1-1-1-111-1-11111-1-1
χ1611111111111-1-1-1-1-1-1-1-1111111111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-11111-1-1-1-11111-1-11111-1-1-1-1-1-111111111-1-1-1-1-1-11111-1-111-1-1-1-111
χ17222222222-2-222222222-2-2222222222222222-2-2-2-2-2-222-2-2-2-22222-2-2-2-22222-2-2-2-2-2-2-2-20000000000000000000000000000000000000000
χ18222222222-2-22222-2-2-2-2-2-22222222-2-2-2-2-2-2-2-222-2-222-2-2-2-2-2-222222222-2-2-2-2-2-2-2-222220000000000000000000000000000000000000000
χ19222222222-2-2-2-2-2-22222-2-2222222222222222-2-22222-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2222222220000000000000000000000000000000000000000
χ20222222222-2-2-2-2-2-2-2-2-2-2-2-22222222-2-2-2-2-2-2-2-22222-2-222-2-2-2-2-2-2-2-2222222222222-2-2-2-20000000000000000000000000000000000000000
χ2122222222-1222222222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-122222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-122222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-10000000000000000
χ2222222222-1222222222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-122222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-2-2-2-2-2-2-2-211111111111111110000000000000000
χ2322222222-1222222-2-2-2-222-1-1-1-1-1-1-111111111-2-222-2-2-2-2-1-1-1-1-1-1-1-111111111-1-1-1-111112222-2-2-2-2-1-1-1-1-1-1-1-1111111110000000000000000
χ2422222222-1222222-2-2-2-222-1-1-1-1-1-1-111111111-2-222-2-2-2-2-1-1-1-1-1-1-1-111111111-1-1-1-11111-2-2-2-2222211111111-1-1-1-1-1-1-1-10000000000000000
χ2522222222-122-2-2-2-2222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-122-2-2-2-2-2-2-1-1-1-11111-1-1-1-111111111111122-2-222-2-2-1-1-1-11111-1-1-1-111110000000000000000
χ2622222222-122-2-2-2-2222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-122-2-2-2-2-2-2-1-1-1-11111-1-1-1-1111111111111-2-222-2-2221111-1-1-1-11111-1-1-1-10000000000000000
χ2722222222-122-2-2-2-2-2-2-2-222-1-1-1-1-1-1-111111111-2-2-2-22222-1-1-1-111111111-1-1-1-11111-1-1-1-122-2-2-2-222-1-1-1-111111111-1-1-1-10000000000000000
χ2822222222-122-2-2-2-2-2-2-2-222-1-1-1-1-1-1-111111111-2-2-2-22222-1-1-1-111111111-1-1-1-11111-1-1-1-1-2-22222-2-21111-1-1-1-1-1-1-1-111110000000000000000
χ2922222222-1-2-222222222-2-2-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-2-2-2-2-2-2221111-1-1-1-11111-1-1-1-11111111100000000−i3−i3i3i3−i3−i3i3i3−i3−i3i3i3−i3−i3i3i30000000000000000
χ3022222222-1-2-222222222-2-2-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-2-2-2-2-2-2221111-1-1-1-11111-1-1-1-11111111100000000i3i3−i3−i3i3i3−i3−i3i3i3−i3−i3i3i3−i3−i30000000000000000
χ3122222222-1-2-22222-2-2-2-2-2-2-1-1-1-1-1-1-11111111122-2-222-2-21111-1-1-1-1-1-1-1-111111111-1-1-1-100000000−i3−i3i3i3−i3−i3i3i3i3i3−i3−i3i3i3−i3−i30000000000000000
χ3222222222-1-2-22222-2-2-2-2-2-2-1-1-1-1-1-1-11111111122-2-222-2-21111-1-1-1-1-1-1-1-111111111-1-1-1-100000000i3i3−i3−i3i3i3−i3−i3−i3−i3i3i3−i3−i3i3i30000000000000000
χ3322222222-1-2-2-2-2-2-22222-2-2-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-2-22222-2-21111111111111111-1-1-1-1-1-1-1-100000000−i3−i3i3i3i3i3−i3−i3−i3−i3i3i3i3i3−i3−i30000000000000000
χ3422222222-1-2-2-2-2-2-22222-2-2-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-2-22222-2-21111111111111111-1-1-1-1-1-1-1-100000000i3i3−i3−i3−i3−i3i3i3i3i3−i3−i3−i3−i3i3i30000000000000000
χ3522222222-1-2-2-2-2-2-2-2-2-2-2-2-2-1-1-1-1-1-1-1111111112222-2-22211111111-1-1-1-1-1-1-1-1-1-1-1-1111100000000−i3−i3i3i3i3i3−i3−i3i3i3−i3−i3−i3−i3i3i30000000000000000
χ3622222222-1-2-2-2-2-2-2-2-2-2-2-2-2-1-1-1-1-1-1-1111111112222-2-22211111111-1-1-1-1-1-1-1-1-1-1-1-1111100000000i3i3−i3−i3−i3−i3i3i3−i3−i3i3i3i3i3−i3−i30000000000000000
χ37222-2-2-22-2222000022-2-2-2-2222-2-2-2-22222-2-2-2-22-200000022-2-2000022-2-2000000000000000000000000000000000000002-2002-200000000
χ38222-2-2-22-2222000022-2-2-2-2222-2-2-2-22222-2-2-2-22-200000022-2-2000022-2-200000000000000000000000000000000000000-2200-2200000000
χ39222-2-2-22-22220000-2-222-2-2222-2-2-2-2-2-2-2-22222-2200000022-2-20000-2-222000000000000000000000000000000000000002-200-2200000000
χ40222-2-2-22-22220000-2-222-2-2222-2-2-2-2-2-2-2-22222-2200000022-2-20000-2-22200000000000000000000000000000000000000-22002-200000000
χ41222-2-2-22-22-2-2000022-2-222222-2-2-2-22222-2-2-2-2-22000000-2-2220000-2-2220000000000000000000000000000000000002i−2i002i−2i0000000000
χ42222-2-2-22-22-2-2000022-2-222222-2-2-2-22222-2-2-2-2-22000000-2-2220000-2-222000000000000000000000000000000000000−2i2i00−2i2i0000000000
χ43222-2-2-22-22-2-20000-2-22222222-2-2-2-2-2-2-2-222222-2000000-2-222000022-2-20000000000000000000000000000000000002i−2i00−2i2i0000000000
χ44222-2-2-22-22-2-20000-2-22222222-2-2-2-2-2-2-2-222222-2000000-2-222000022-2-2000000000000000000000000000000000000−2i2i002i−2i0000000000
χ4522-2-22-2-2222-22i2i−2i−2i00002-22-2-22-22-200000000002i−2i00002-22-22i2i−2i−2i000000002i2i−2i−2i000000002i−2i2-2000000002i−2i2i−2i2-22-20000000000000000
χ4622-2-22-2-2222-22i2i−2i−2i00002-22-2-22-22-200000000002i−2i00002-22-22i2i−2i−2i000000002i2i−2i−2i00000000−2i2i-2200000000−2i2i−2i2i-22-220000000000000000
χ4722-2-22-2-2222-2−2i−2i2i2i00002-22-2-22-22-20000000000−2i2i00002-22-2−2i−2i2i2i00000000−2i−2i2i2i000000002i−2i-22000000002i−2i2i−2i-22-220000000000000000
χ4822-2-22-2-2222-2−2i−2i2i2i00002-22-2-22-22-20000000000−2i2i00002-22-2−2i−2i2i2i00000000−2i−2i2i2i00000000−2i2i2-200000000−2i2i−2i2i2-22-20000000000000000
χ4922-2-22-2-222-222i2i−2i−2i0000-222-2-22-22-20000000000−2i2i0000-22-222i2i−2i−2i00000000−2i−2i2i2i00002-22i−2i00002-22-22i−2i2i−2i000000000000000000000000
χ5022-2-22-2-222-222i2i−2i−2i0000-222-2-22-22-20000000000−2i2i0000-22-222i2i−2i−2i00000000−2i−2i2i2i0000-22−2i2i0000-22-22−2i2i−2i2i000000000000000000000000
χ5122-2-22-2-222-22−2i−2i2i2i0000-222-2-22-22-200000000002i−2i0000-22-22−2i−2i2i2i000000002i2i−2i−2i00002-2−2i2i00002-22-2−2i2i−2i2i000000000000000000000000
χ5222-2-22-2-222-22−2i−2i2i2i0000-222-2-22-22-200000000002i−2i0000-22-22−2i−2i2i2i000000002i2i−2i−2i0000-222i−2i0000-22-222i−2i2i−2i000000000000000000000000
χ5322-2-22-2-22-12-22i2i−2i−2i00002-2-111-11-1133−3−333−3−3002i−2i0000-11-11−i−iii3−33−3−i3−i3i3i3−i−iii−i3−i3i3i300002i−2i2-2−i3i3i3−i33−3−33−ii−ii-11-110000000000000000
χ5422-2-22-2-22-12-22i2i−2i−2i00002-2-111-11-1133−3−333−3−3002i−2i0000-11-11−i−iii3−33−3−i3−i3i3i3−i−iii−i3−i3i3i30000−2i2i-22i3−i3−i3i3−333−3i−ii−i1-11-10000000000000000
χ5522-2-22-2-22-12-22i2i−2i−2i00002-2-111-11-11−3−333−3−333002i−2i0000-11-11−i−iii−33−33i3i3−i3−i3−i−iiii3i3−i3−i300002i−2i2-2i3−i3−i3i3−333−3−ii−ii-11-110000000000000000
χ5622-2-22-2-22-12-22i2i−2i−2i00002-2-111-11-11−3−333−3−333002i−2i0000-11-11−i−iii−33−33i3i3−i3−i3−i−iiii3i3−i3−i30000−2i2i-22−i3i3i3−i33−3−33i−ii−i1-11-10000000000000000
χ5722-2-22-2-22-12-2−2i−2i2i2i00002-2-111-11-1133−3−333−3−300−2i2i0000-11-11ii−i−i3−33−3i3i3−i3−i3ii−i−ii3i3−i3−i300002i−2i-22−i3i3i3−i3−333−3−ii−ii1-11-10000000000000000
χ5822-2-22-2-22-12-2−2i−2i2i2i00002-2-111-11-1133−3−333−3−300−2i2i0000-11-11ii−i−i3−33−3i3i3−i3−i3ii−i−ii3i3−i3−i30000−2i2i2-2i3−i3−i3i33−3−33i−ii−i-11-110000000000000000
χ5922-2-22-2-22-12-2−2i−2i2i2i00002-2-111-11-11−3−333−3−33300−2i2i0000-11-11ii−i−i−33−33−i3−i3i3i3ii−i−i−i3−i3i3i300002i−2i-22i3−i3−i3i33−3−33−ii−ii1-11-10000000000000000
χ6022-2-22-2-22-12-2−2i−2i2i2i00002-2-111-11-11−3−333−3−33300−2i2i0000-11-11ii−i−i−33−33−i3−i3i3i3ii−i−i−i3−i3i3i30000−2i2i2-2−i3i3i3−i3−333−3i−ii−i-11-110000000000000000
χ6122-2-22-2-22-1-222i2i−2i−2i0000-22-111-11-1133−3−333−3−300−2i2i00001-11-1−i−iii−33−33−i3−i3i3i3ii−i−ii3i3−i3−i32-22i−2i0000-11-11−ii−ii3−3−33−i3i3i3−i30000000000000000
χ6222-2-22-2-22-1-222i2i−2i−2i0000-22-111-11-1133−3−333−3−300−2i2i00001-11-1−i−iii−33−33−i3−i3i3i3ii−i−ii3i3−i3−i3-22−2i2i00001-11-1i−ii−i−333−3i3−i3−i3i30000000000000000
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χ6522-2-22-2-22-1-22−2i−2i2i2i0000-22-111-11-1133−3−333−3−3002i−2i00001-11-1ii−i−i−33−33i3i3−i3−i3−i−iii−i3−i3i3i32-2−2i2i0000-11-11i−ii−i3−3−33i3−i3−i3i30000000000000000
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χ6722-2-22-2-22-1-22−2i−2i2i2i0000-22-111-11-11−3−333−3−333002i−2i00001-11-1ii−i−i3−33−3−i3−i3i3i3−i−iiii3i3−i3−i32-2−2i2i0000-11-11i−ii−i−333−3−i3i3i3−i30000000000000000
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χ702-2-22-2-2222002-22-22-22-200-22-222-2-22-22-22-22-20000002-200002-22-200002-22-20000000000000000000000000000000000000000i2−i2i2−i2i2−i2i2−i2
χ712-2-22-2-2222002-22-2-22-2200-22-222-2-2-22-22-22-22000000-2200002-22-20000-22-220000000000000000000000000000000000000000−i2i2−i2i2i2−i2i2−i2
χ722-2-22-2-2222002-22-2-22-2200-22-222-2-2-22-22-22-22000000-2200002-22-20000-22-220000000000000000000000000000000000000000i2−i2i2−i2−i2i2−i2i2
χ732-2-22-2-222200-22-222-22-200-22-222-2-22-22-22-22-2000000-220000-22-220000-22-220000000000000000000000000000000000000000−i2i2i2−i2−i2i2i2−i2
χ742-2-22-2-222200-22-222-22-200-22-222-2-22-22-22-22-2000000-220000-22-220000-22-220000000000000000000000000000000000000000i2−i2−i2i2i2−i2−i2i2
χ752-2-22-2-222200-22-22-22-2200-22-222-2-2-22-22-22-220000002-20000-22-2200002-22-20000000000000000000000000000000000000000−i2i2i2−i2i2−i2−i2i2
χ762-2-22-2-222200-22-22-22-2200-22-222-2-2-22-22-22-220000002-20000-22-2200002-22-20000000000000000000000000000000000000000i2−i2−i2i2−i2i2i2−i2
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χ80444-4-4-44-4-2-4-40000-4-44444-2-2-222222222-2-2-2-24-400000022-2-20000-2-2220000000000000000000000000000000000000000000000000000
χ8144-44-44-4-444-400000000-444-4-4-44-4400000000000000004-4-44000000000000000000000000000000000000000000000000000000000000
χ8244-44-44-4-44-44000000004-44-4-4-44-440000000000000000-444-4000000000000000000000000000000000000000000000000000000000000
χ8344-44-44-4-4-24-400000000-44-2222-22-22323−23−23−23−23232300000000-222-2000023−23−23230000000000000000000000000000000000000000000000000000
χ8444-44-44-4-4-24-400000000-44-2222-22-2−23−2323232323−23−2300000000-222-20000−232323−230000000000000000000000000000000000000000000000000000
χ8544-44-44-4-4-2-44000000004-4-2222-22-22323−23−23−23−232323000000002-2-220000−232323−230000000000000000000000000000000000000000000000000000
χ8644-44-44-4-4-2-44000000004-4-2222-22-2−23−2323232323−23−23000000002-2-22000023−23−23230000000000000000000000000000000000000000000000000000
χ874-4444-4-4-44000000000000-4-44-444-40000000000004-400000000000000000000004-44-40000000000000000000000000000000000000000
χ884-4444-4-4-44000000000000-4-44-444-4000000000000-440000000000000000000000-44-440000000000000000000000000000000000000000
χ894-4444-4-4-4-200000000000022-22-2-2223−23−2323−232323−2300004-400000000000000000023−2323−23-22-220000000000000000000000000000000000000000
χ904-4444-4-4-4-200000000000022-22-2-2223−23−2323−232323−230000-44000000000000000000−2323−23232-22-20000000000000000000000000000000000000000
χ914-4444-4-4-4-200000000000022-22-2-22−232323−2323−23−232300004-4000000000000000000−2323−2323-22-220000000000000000000000000000000000000000
χ924-4444-4-4-4-200000000000022-22-2-22−232323−2323−23−23230000-4400000000000000000023−2323−232-22-20000000000000000000000000000000000000000
χ934-44-4-44-444004i−4i−4i4i000000-4-444-4-44000000000000000000004i−4i−4i4i00000000000000000000000000000000000000000000000000000000
χ944-44-4-44-44400−4i4i4i−4i000000-4-444-4-4400000000000000000000−4i4i4i−4i00000000000000000000000000000000000000000000000000000000
χ954-44-4-44-44-2004i−4i−4i4i00000022-2-222-223−23−232323−23−2323000000000000−2i2i2i−2i0000−2i32i32i3−2i3000000000000000000000000000000000000000000000000
χ964-44-4-44-44-2004i−4i−4i4i00000022-2-222-2−232323−23−232323−23000000000000−2i2i2i−2i00002i3−2i3−2i32i3000000000000000000000000000000000000000000000000
χ974-44-4-44-44-200−4i4i4i−4i00000022-2-222-223−23−232323−23−23230000000000002i−2i−2i2i00002i3−2i3−2i32i3000000000000000000000000000000000000000000000000
χ984-44-4-44-44-200−4i4i4i−4i00000022-2-222-2−232323−23−232323−230000000000002i−2i−2i2i0000−2i32i32i3−2i3000000000000000000000000000000000000000000000000
χ994-4-44-4-444-2004-44-44-44-4002-22-2-222-22-22-22-220000004-40000-22-220000-22-22000000000000000000000000000000000000000000000000
χ1004-4-44-4-444-2004-44-4-44-44002-22-2-2222-22-22-22-2000000-440000-22-2200002-22-2000000000000000000000000000000000000000000000000
χ1014-4-44-4-444-200-44-444-44-4002-22-2-222-22-22-22-22000000-4400002-22-200002-22-2000000000000000000000000000000000000000000000000
χ1024-4-44-4-444-200-44-44-44-44002-22-2-2222-22-22-22-20000004-400002-22-20000-22-22000000000000000000000000000000000000000000000000
χ1034-4-4-4444-440000004-4-4400-44-4-4-4444-44-4-44-44000000000000000000000000000000000000000000000000000000000000000000000000
χ1044-4-4-4444-44000000-444-400-44-4-4-444-44-444-44-4000000000000000000000000000000000000000000000000000000000000000000000000
χ1054-4-4-4444-4-20000004-4-44002-2222-2-2-22-222-22-2000000000000000000000000−2i32i32i3−2i3−2i32i32i3−2i30000000000000000000000000000000000000000
χ1064-4-4-4444-4-20000004-4-44002-2222-2-2-22-222-22-20000000000000000000000002i3−2i3−2i32i32i3−2i3−2i32i30000000000000000000000000000000000000000
χ1074-4-4-4444-4-2000000-444-4002-2222-2-22-22-2-22-22000000000000000000000000−2i32i32i3−2i32i3−2i3−2i32i30000000000000000000000000000000000000000
χ1084-4-4-4444-4-2000000-444-4002-2222-2-22-22-2-22-220000000000000000000000002i3−2i3−2i32i3−2i32i32i3−2i30000000000000000000000000000000000000000

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