Finite Group Databasebeta

← Group #10858822

Character table — Group #10858822

Order 768.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96C97C98C99C100C101C102
size111111112222222222222222444444444444444444444444444444444488888888888888888888888888121212121212121224242424242424244848
order12222222222234444666666644444444446666121212121212121212121212121212121212121244444444121212121212121212121212121212121212888888884444888844
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ3111111111111111111111111111111-1-1-1-11111111111111111-1-1-1-1-1-1-1-1-1-1-1-11-1-1111-1-1-1-111-1-1-1-111-1-1-1-111111111-1-1-1-11111-1-1
χ4111111111111111111111111111111-1-1-1-11111111111111111-1-1-1-1-1-1-1-1-1-1-1-11-1-1111-1-1-1-111-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-111
χ5111111111111111111111111-1-1-1-11111111111-1-1-1-1-1-1-1-1111111111111-1-1-1-1-111-1-1-1-1-1-1-111-1-1-1-1-1-11111111111111111-1-1-1-1-1-1
χ6111111111111111111111111-1-1-1-11111111111-1-1-1-1-1-1-1-1111111111111-1-1-1-1-111-1-1-1-1-1-1-111-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1111111
χ7111111111111111111111111-1-1-1-111-1-1-1-11111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-11111-1-1-1-1-1-11111111111-1-1-1-1-1-111111111-1-1-1-1-1-1-1-111
χ8111111111111111111111111-1-1-1-111-1-1-1-11111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-11111-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1
χ911111111-1-1-1-111111111111111-1-1-1-11111-1-1-1-11111-1-1-1-111111111111111-1-1-1-1-11111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-111-1-111-1-11-1
χ1011111111-1-1-1-111111111111111-1-1-1-11111-1-1-1-11111-1-1-1-111111111111111-1-1-1-1-11111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-111-1-111-11
χ1111111111-1-1-1-111111111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1-1-1-1-1-1-1-1-111-111111-1-1-1-1-1-11111-1-111111111-1-1-1-1-1-11111-1-1-11
χ1211111111-1-1-1-111111111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1-1-1-1-1-1-1-1-111-111111-1-1-1-1-1-11111-1-11111-1-1-1-1111111-1-1-1-1111-1
χ1311111111-1-1-1-1111111111111-1-111-1-11111-1-1-1-1-1-1-1-11111111111111111-1-1111-1-1-1-1-1-1-1-1-1-1-1111111-1-1-1-11111-1-1-1-111-1-1-1-111-11
χ1411111111-1-1-1-1111111111111-1-111-1-11111-1-1-1-1-1-1-1-11111111111111111-1-1111-1-1-1-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-11111-1-11111-1-11-1
χ1511111111-1-1-1-1111111111111-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-111-1-1111-1-1-11111-1-1-1-1-1-11111111111-1-1-1-1-1-111-1-1111-1
χ1611111111-1-1-1-1111111111111-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-111-1-1111-1-1-11111-1-1-1-1-1-1111111-1-1-1-1111111-1-111-1-1-11
χ172222222222222-2-2-2-222222222222-2-20000222222222222-2-2-2-2000000000000-200-2-2-20000-2-20000-2-20000000000000000000000
χ182222222222222-2-2-2-22222222-2-2-2-2-2-200002222-2-2-2-2-2-2-2-2-2-2-2-20000000000002002220000-2-20000220000000000000000000000
χ19222222222222-12222-1-1-1-1-1-1-12222222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-122222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1000000000000000000
χ20222222222222-12222-1-1-1-1-1-1-1222222-2-2-2-2-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-2-2-2-22-2-22-1-11111-1-11111-1-11111000000000000000000
χ21222222222222-12222-1-1-1-1-1-1-1-2-2-2-2222222-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-2-2-2-2-222-2111111-1-1111111-1-1-1-1000000000000000000
χ22222222222222-12222-1-1-1-1-1-1-1-2-2-2-222-2-2-2-2-1-1-1-111111111-1-1-1-1111111112222-2-2-2-211-1-1-1-1-1-1-1-1-1-1111111000000000000000000
χ23222222222222-1-2-2-2-2-1-1-1-1-1-1-12222-2-20000-1-1-1-1-1-1-1-1-1-1-1-11111−i3−i3−i3−i3i3i3i3i30000-200-211−i3−i3i3i311−i3−i3i3i311−i3−i3i3i3000000000000000000
χ24222222222222-1-2-2-2-2-1-1-1-1-1-1-12222-2-20000-1-1-1-1-1-1-1-1-1-1-1-11111i3i3i3i3−i3−i3−i3−i30000-200-211i3i3−i3−i311i3i3−i3−i311i3i3−i3−i3000000000000000000
χ25222222222222-1-2-2-2-2-1-1-1-1-1-1-1-2-2-2-2-2-20000-1-1-1-1111111111111−i3−i3−i3−i3i3i3i3i300002002-1-1i3i3−i3−i311i3i3−i3−i3-1-1−i3−i3i3i3000000000000000000
χ26222222222222-1-2-2-2-2-1-1-1-1-1-1-1-2-2-2-2-2-20000-1-1-1-1111111111111i3i3i3i3−i3−i3−i3−i300002002-1-1−i3−i3i3i311−i3−i3i3i3-1-1i3i3−i3−i3000000000000000000
χ2722222222-2-2-2-22-2-2-2-2222222222-2-2220000-2-2-2-22222-2-2-2-2-2-2-2-2000000000000200-2-2-20000220000220000000000000000000000
χ2822222222-2-2-2-22-2-2-2-22222222-2-222220000-2-2-2-2-2-2-2-22222-2-2-2-2000000000000-2002220000220000-2-20000000000000000000000
χ2922222222-2-2-2-2-12222-1-1-1-1-1-1-122-2-2-2-222221111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-122-2-2-2-2-22-1-1-1-1-1-1111111111111000000000000000000
χ3022222222-2-2-2-2-12222-1-1-1-1-1-1-122-2-2-2-2-2-2-2-21111-1-1-1-11111-1-1-1-111111111-2-222-2222-1-1111111-1-1-1-111-1-1-1-1000000000000000000
χ3122222222-2-2-2-2-12222-1-1-1-1-1-1-1-2-222-2-2222211111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-2-2222-2-2-211111111-1-1-1-1-1-11111000000000000000000
χ3222222222-2-2-2-2-12222-1-1-1-1-1-1-1-2-222-2-2-2-2-2-211111111-1-1-1-1-1-1-1-11111111122-2-2222-211-1-1-1-1111111-1-1-1-1-1-1000000000000000000
χ3322222222-2-2-2-2-1-2-2-2-2-1-1-1-1-1-1-122-2-22200001111-1-1-1-111111111−i3−i3−i3−i3i3i3i3i30000200-211−i3−i3i3i3-1-1i3i3−i3−i3-1-1i3i3−i3−i3000000000000000000
χ3422222222-2-2-2-2-1-2-2-2-2-1-1-1-1-1-1-122-2-22200001111-1-1-1-111111111i3i3i3i3−i3−i3−i3−i30000200-211i3i3−i3−i3-1-1−i3−i3i3i3-1-1−i3−i3i3i3000000000000000000
χ3522222222-2-2-2-2-1-2-2-2-2-1-1-1-1-1-1-1-2-22222000011111111-1-1-1-11111−i3−i3−i3−i3i3i3i3i30000-2002-1-1i3i3−i3−i3-1-1−i3−i3i3i311i3i3−i3−i3000000000000000000
χ3622222222-2-2-2-2-1-2-2-2-2-1-1-1-1-1-1-1-2-22222000011111111-1-1-1-11111i3i3i3i3−i3−i3−i3−i30000-2002-1-1−i3−i3i3i3-1-1i3i3−i3−i311−i3−i3i3i3000000000000000000
χ372222-2-2-2-222-2-220000222-2-2-2-22-22-200000022-2-222-2-222-2-20000000000000000000000000000000000000022−2−222−2−200002−22−200
χ382222-2-2-2-222-2-220000222-2-2-2-22-22-200000022-2-222-2-222-2-200000000000000000000000000000000000000−2−222−2−2220000−22−2200
χ392222-2-2-2-222-2-220000222-2-2-2-2-22-2200000022-2-2-2-222-2-2220000000000000000000000000000000000000022−2−222−2−20000−22−2200
χ402222-2-2-2-222-2-220000222-2-2-2-2-22-2200000022-2-2-2-222-2-22200000000000000000000000000000000000000−2−222−2−22200002−22−200
χ412222-2-2-2-2-2-22220000222-2-2-2-22-2-22000000-2-22222-2-2-2-2220000000000000000000000000000000000000022−2−2−2−22200002−2−2200
χ422222-2-2-2-2-2-22220000222-2-2-2-22-2-22000000-2-22222-2-2-2-22200000000000000000000000000000000000000−2−22222−2−20000−222−200
χ432222-2-2-2-2-2-22220000222-2-2-2-2-222-2000000-2-222-2-22222-2-20000000000000000000000000000000000000022−2−2−2−2220000−222−200
χ442222-2-2-2-2-2-22220000222-2-2-2-2-222-2000000-2-222-2-22222-2-200000000000000000000000000000000000000−2−22222−2−200002−2−2200
χ4522-2-222-2-22-22-2222-2-22-2-2-222-200002-200002-22-20000000022-2-2000000002-22-20000002-22-22-22-22-2000000000000000000000000
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χ4922-2-222-2-22-22-2-122-2-2-1111-1-1100002-20000-11-113−33−33−33−3-1-11133−3−3−3−3332-22-200003−3-11-11-11-11-113−33−3−33000000000000000000
χ5022-2-222-2-22-22-2-122-2-2-1111-1-1100002-20000-11-113−33−33−33−3-1-111−3−33333−3−3-22-2200003−31-11-1-111-11-13−3−333−3000000000000000000
χ5122-2-222-2-22-22-2-122-2-2-1111-1-1100002-20000-11-11−33−33−33−33-1-11133−3−3−3−333-22-220000−331-11-1-111-11-1−333−3−33000000000000000000
χ5222-2-222-2-22-22-2-122-2-2-1111-1-1100002-20000-11-11−33−33−33−33-1-111−3−33333−3−32-22-20000−33-11-11-11-11-11−33−333−3000000000000000000
χ5322-2-222-2-22-22-2-1-2-222-1111-1-110000-222i2i−2i−2i-11-113−33−33−33−311-1-1−i−iii−i−iii000002i−2i0−33−i3i3i3−i31-1−i3i3i3−i3−33−ii−ii000000000000000000
χ5422-2-222-2-22-22-2-1-2-222-1111-1-110000-222i2i−2i−2i-11-11−33−33−33−3311-1-1−i−iii−i−iii000002i−2i03−3i3−i3−i3i31-1i3−i3−i3i33−3−ii−ii000000000000000000
χ5522-2-222-2-22-22-2-1-2-222-1111-1-110000-22−2i−2i2i2i-11-113−33−33−33−311-1-1ii−i−iii−i−i00000−2i2i0−33i3−i3−i3i31-1i3−i3−i3i3−33i−ii−i000000000000000000
χ5622-2-222-2-22-22-2-1-2-222-1111-1-110000-22−2i−2i2i2i-11-11−33−33−33−3311-1-1ii−i−iii−i−i00000−2i2i03−3−i3i3i3−i31-1−i3i3i3−i33−3i−ii−i000000000000000000
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χ6122-2-222-2-2-22-22-122-2-2-1111-1-110000-2200001-11-13−33−3−33−33-1-11133−3−3−3−3332-2-2200003−3-11-111-11-11-1−33−333−3000000000000000000
χ6222-2-222-2-2-22-22-122-2-2-1111-1-110000-2200001-11-13−33−3−33−33-1-111−3−33333−3−3-222-200003−31-11-11-1-11-11−333−3−33000000000000000000
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χ6422-2-222-2-2-22-22-122-2-2-1111-1-110000-2200001-11-1−33−333−33−3-1-111−3−33333−3−32-2-220000−33-11-111-11-11-13−33−3−33000000000000000000
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χ994-4-44-44-440000-2-444-422-2-22-220000004i−4i−4i4i0000000000002-2-22−2i2i2i−2i−2i2i2i−2i00000000000000000000000000000000000000000000
χ1004-4-44-44-440000-2-444-422-2-22-22000000−4i4i4i−4i0000000000002-2-222i−2i−2i2i2i−2i−2i2i00000000000000000000000000000000000000000000
χ1018-88-88-8-880000-400004-44-4-444000000000000000000000000000000000000000000000000000000000000000000000000000000
χ1028-8-888-88-80000-4000044-44-44-4000000000000000000000000000000000000000000000000000000000000000000000000000000

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