Finite Group Databasebeta

← Group #10867913

Character table — Group #10867913

Order 768.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96C97C98C99C100C101C102
size111111112222222222222222444444444444444444444444444444444488888888888888888888888888121212121212121224242424242424244848
order12222222344444444666666622444444446666121212121212121212121212121212121212121244444444121212121212121212121212121212121212888888884444888844
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ3111111111111111111111111111111-1-1-1-11111111111111111-1-1-1-1-1-1-1-111-1-1-1-1-1-111-1-1-1-111-1-1-1-111-1-1-1-111111111-1-1-1-11111-1-1
χ4111111111111111111111111111111-1-1-1-11111111111111111-1-1-1-1-1-1-1-111-1-1-1-1-1-111-1-1-1-111-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-111
χ5111111111111111111111111-1-1-1-1111111-1-1-1-11111-1-1-1-1111111111111-1-111-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-1-1111111111111-1-1-1-1-1-1
χ6111111111111111111111111-1-1-1-1111111-1-1-1-11111-1-1-1-1111111111111-1-111-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111
χ7111111111111111111111111-1-1-1-111-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-11111-1-11111-1-1-1-1-1-111111111111111-1-1-1-1-1-1-1-111
χ8111111111111111111111111-1-1-1-111-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-11111-1-11111-1-1-1-1-1-1111111-1-1-1-1-1-1-1-111111111-1-1
χ9111111111-1-1-1-11111111111111-1-1-1-111111111-1-1-1-1-1-1-1-1111111111111-11-1-1-1-111-1-1-1-1-1-111-1-1-1-1-1-111111111-1-1-1-1-1-111-1-1111-1
χ10111111111-1-1-1-11111111111111-1-1-1-111111111-1-1-1-1-1-1-1-1111111111111-11-1-1-1-111-1-1-1-1-1-111-1-1-1-1-1-11111-1-1-1-1111111-1-111-1-1-11
χ11111111111-1-1-1-11111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-111111-1-1-1-11111111111-1-1-1-1-1-11111-1-1-1-111-1-1-1-111-11
χ12111111111-1-1-1-11111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-111111-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-11111-1-11111-1-11-1
χ13111111111-1-1-1-111111111111-1-111-1-11111-1-1-1-1-1-1-1-111111111111111111-1-1-111-1-1111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-11111-1-1-11
χ14111111111-1-1-1-111111111111-1-111-1-11111-1-1-1-1-1-1-1-111111111111111111-1-1-111-1-1111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-1-1111-1
χ15111111111-1-1-1-111111111111-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-11-111-1-11111-1-1-1-1-1-11111-1-111111111-1-1-1-111-1-111-1-11-1
χ16111111111-1-1-1-111111111111-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-11-111-1-11111-1-1-1-1-1-11111-1-11111-1-1-1-11111-1-111-1-111-11
χ172222222222222-2-2-2-222222222222-2-20000222222222222-2-2-2-200000000-2-2000000-2-20000-2-20000-2-20000000000000000000000
χ182222222222222-2-2-2-22222222-2-2-2-2-2-20000-2-2-2-22222-2-2-2-2-2-2-2-20000000022000000220000220000-2-20000000000000000000000
χ19222222222-2-2-2-2-2-2-2-2222222222-2-22200002222-2-2-2-2-2-2-2-2-2-2-2-2000000002-2000000220000-2-20000220000000000000000000000
χ20222222222-2-2-2-2-2-2-2-22222222-2-222220000-2-2-2-2-2-2-2-22222-2-2-2-200000000-22000000-2-20000220000220000000000000000000000
χ2122222222-122222222-1-1-1-1-1-1-12222222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-122222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1000000000000000000
χ2222222222-122222222-1-1-1-1-1-1-1222222-2-2-2-2-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111122-2-2-2-2-2-2-1-11111-1-11111-1-11111000000000000000000
χ2322222222-122222222-1-1-1-1-1-1-1-2-2-2-22222221111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-2-222-2-2-2-211111111-1-1-1-1-1-11111000000000000000000
χ2422222222-122222222-1-1-1-1-1-1-1-2-2-2-222-2-2-2-21111-1-1-1-11111-1-1-1-111111111-2-2-2-2222211-1-1-1-1111111-1-1-1-1-1-1000000000000000000
χ2522222222-12222-2-2-2-2-1-1-1-1-1-1-12222-2-20000-1-1-1-1-1-1-1-1-1-1-1-11111−i3−i3−i3−i3i3i3i3i3-2-200000011−i3−i3i3i311−i3−i3i3i311−i3−i3i3i3000000000000000000
χ2622222222-12222-2-2-2-2-1-1-1-1-1-1-12222-2-20000-1-1-1-1-1-1-1-1-1-1-1-11111i3i3i3i3−i3−i3−i3−i3-2-200000011i3i3−i3−i311i3i3−i3−i311i3i3−i3−i3000000000000000000
χ2722222222-12222-2-2-2-2-1-1-1-1-1-1-1-2-2-2-2-2-200001111-1-1-1-111111111−i3−i3−i3−i3i3i3i3i322000000-1-1i3i3−i3−i3-1-1−i3−i3i3i311i3i3−i3−i3000000000000000000
χ2822222222-12222-2-2-2-2-1-1-1-1-1-1-1-2-2-2-2-2-200001111-1-1-1-111111111i3i3i3i3−i3−i3−i3−i322000000-1-1−i3−i3i3i3-1-1i3i3−i3−i311−i3−i3i3i3000000000000000000
χ2922222222-1-2-2-2-22222-1-1-1-1-1-1-122-2-2-2-22222-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-22-2-2-2-222111111-1-1111111-1-1-1-1000000000000000000
χ3022222222-1-2-2-2-22222-1-1-1-1-1-1-122-2-2-2-2-2-2-2-2-1-1-1-111111111-1-1-1-111111111-222222-2-211-1-1-1-1-1-1-1-1-1-1111111000000000000000000
χ3122222222-1-2-2-2-22222-1-1-1-1-1-1-1-2-222-2-2222211111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-12-2-2-222-2-2-1-1-1-1-1-1111111111111000000000000000000
χ3222222222-1-2-2-2-22222-1-1-1-1-1-1-1-2-222-2-2-2-2-2-211111111-1-1-1-1-1-1-1-1111111112-222-2-222-1-1111111-1-1-1-111-1-1-1-1000000000000000000
χ3322222222-1-2-2-2-2-2-2-2-2-1-1-1-1-1-1-122-2-2220000-1-1-1-1111111111111−i3−i3−i3−i3i3i3i3i32-2000000-1-1i3i3−i3−i311i3i3−i3−i3-1-1−i3−i3i3i3000000000000000000
χ3422222222-1-2-2-2-2-2-2-2-2-1-1-1-1-1-1-122-2-2220000-1-1-1-1111111111111i3i3i3i3−i3−i3−i3−i32-2000000-1-1−i3−i3i3i311−i3−i3i3i3-1-1i3i3−i3−i3000000000000000000
χ3522222222-1-2-2-2-2-2-2-2-2-1-1-1-1-1-1-1-2-22222000011111111-1-1-1-11111−i3−i3−i3−i3i3i3i3i3-2200000011−i3−i3i3i3-1-1i3i3−i3−i3-1-1i3i3−i3−i3000000000000000000
χ3622222222-1-2-2-2-2-2-2-2-2-1-1-1-1-1-1-1-2-22222000011111111-1-1-1-11111i3i3i3i3−i3−i3−i3−i3-2200000011i3i3−i3−i3-1-1−i3−i3i3i3-1-1−i3−i3i3i3000000000000000000
χ3722-22-22-2-220000-22-22-222-2-22-20000002i2i−2i−2i00000000000022-2-22i2i−2i−2i2i2i−2i−2i00000000000000000000000000000022-2-22i−2i00000000
χ3822-22-22-2-220000-22-22-222-2-22-20000002i2i−2i−2i00000000000022-2-22i2i−2i−2i2i2i−2i−2i000000000000000000000000000000-2-222−2i2i00000000
χ3922-22-22-2-220000-22-22-222-2-22-2000000−2i−2i2i2i00000000000022-2-2−2i−2i2i2i−2i−2i2i2i00000000000000000000000000000022-2-2−2i2i00000000
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χ4122-2-22-2-2222i2i−2i−2i000022-2-2-2-222-22i−2i00000022-2-22i2i−2i−2i2i2i−2i−2i00000000000000000000000000000000000000−i2−i2i2i22−22−200002−2−i2i200
χ4222-2-22-2-2222i2i−2i−2i000022-2-2-2-222-22i−2i00000022-2-22i2i−2i−2i2i2i−2i−2i00000000000000000000000000000000000000i2i2−i2−i2−22−220000−22i2−i200
χ4322-2-22-2-2222i2i−2i−2i000022-2-2-2-22-22−2i2i000000-2-2222i2i−2i−2i−2i−2i2i2i00000000000000000000000000000000000000−i2−i2i2i22−22−20000−22i2−i200
χ4422-2-22-2-2222i2i−2i−2i000022-2-2-2-22-22−2i2i000000-2-2222i2i−2i−2i−2i−2i2i2i00000000000000000000000000000000000000i2i2−i2−i2−22−2200002−2−i2i200
χ4522-2-22-2-222−2i−2i2i2i000022-2-2-2-222-2−2i2i00000022-2-2−2i−2i2i2i−2i−2i2i2i00000000000000000000000000000000000000−i2−i2i2i2−22−220000−22−i2i200
χ4622-2-22-2-222−2i−2i2i2i000022-2-2-2-222-2−2i2i00000022-2-2−2i−2i2i2i−2i−2i2i2i00000000000000000000000000000000000000i2i2−i2−i22−22−200002−2i2−i200
χ4722-2-22-2-222−2i−2i2i2i000022-2-2-2-22-222i−2i000000-2-222−2i−2i2i2i2i2i−2i−2i00000000000000000000000000000000000000−i2−i2i2i2−22−2200002−2i2−i200
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χ492-222-2-2-222000022-2-2-2-2-22-2220000002-22-20000000000002-22-22-22-22-22-2000000000000000000000000002i−2i2i−2i0000002i−2i000000
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χ512-222-2-2-222000022-2-2-2-2-22-222000000-22-220000000000002-22-2-22-22-22-22000000000000000000000000002i−2i2i−2i000000−2i2i000000
χ522-222-2-2-222000022-2-2-2-2-22-222000000-22-220000000000002-22-2-22-22-22-2200000000000000000000000000−2i2i−2i2i0000002i−2i000000
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χ542-2-222-22-222i−2i2i−2i2-2-222-2-2-222-200002i−2i000000002i−2i2i−2i0000-222-2000000000000-22−2i2i00-22-220000002i−2i−2i2i−2i2i000000000000000000
χ552-2-222-22-222i−2i2i−2i-222-22-2-2-222-20000−2i2i2i−2i−2i2i00002i−2i2i−2i00002-2-222i−2i−2i2i2i−2i−2i2i002-20000000000002-22-2−2i2i0000000000000000000000
χ562-2-222-22-222i−2i2i−2i-222-22-2-2-222-20000−2i2i−2i2i2i−2i00002i−2i2i−2i00002-2-22−2i2i2i−2i−2i2i2i−2i00-22000000000000-22-22−2i2i0000000000000000000000
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χ582-2-222-22-22−2i2i−2i2i2-2-222-2-2-222-20000−2i2i00000000−2i2i−2i2i0000-222-2000000000000-222i−2i00-22-22000000−2i2i2i−2i2i−2i000000000000000000
χ592-2-222-22-22−2i2i−2i2i-222-22-2-2-222-200002i−2i2i−2i−2i2i0000−2i2i−2i2i00002-2-222i−2i−2i2i2i−2i−2i2i00-22000000000000-22-222i−2i0000000000000000000000
χ602-2-222-22-22−2i2i−2i2i-222-22-2-2-222-200002i−2i−2i2i2i−2i0000−2i2i−2i2i00002-2-22−2i2i2i−2i−2i2i2i−2i002-20000000000002-22-22i−2i0000000000000000000000
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χ622-2-222-22-2-12i−2i2i−2i2-2-22-1111-1-1100002i−2i0000−i3i3−i3i3−ii−ii3−33−31-1-11−333−33−3−330000-22−2i2i3−31-11-1−i3i3i3−i3−i3i3−iii−ii−i000000000000000000
χ632-2-222-22-2-12i−2i2i−2i2-2-22-1111-1-1100002i−2i0000i3−i3i3−i3−ii−ii−33−331-1-113−3−33−333−30000-22−2i2i−331-11-1i3−i3−i3i3i3−i3−iii−ii−i000000000000000000
χ642-2-222-22-2-12i−2i2i−2i2-2-22-1111-1-1100002i−2i0000i3−i3i3−i3−ii−ii−33−331-1-11−333−33−3−3300002-22i−2i−33-11-11i3−i3i3−i3−i3i3−ii−ii−ii000000000000000000
χ652-2-222-22-2-12i−2i2i−2i-222-2-1111-1-110000−2i2i2i−2i−2i2i−i3i3−i3i3−ii−ii3−33−3-111-1−iii−i−iii−i002-20000−33−i3i3i3−i3i3−i3-11-11i−i3−3−33000000000000000000
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χ702-2-222-22-2-1−2i2i−2i2i2-2-22-1111-1-110000−2i2i0000−i3i3−i3i3i−ii−i−33−331-1-11−333−33−3−3300002-2−2i2i−33-11-11−i3i3−i3i3i3−i3i−ii−ii−i000000000000000000
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χ722-2-222-22-2-1−2i2i−2i2i2-2-22-1111-1-110000−2i2i0000i3−i3i3−i3i−ii−i3−33−31-1-11−333−33−3−330000-222i−2i3−31-11-1i3−i3−i3i3i3−i3i−i−ii−ii000000000000000000
χ732-2-222-22-2-1−2i2i−2i2i-222-2-1111-1-1100002i−2i2i−2i−2i2i−i3i3−i3i3i−ii−i−33−33-111-1−iii−i−iii−i00-2200003−3i3−i3−i3i3i3−i31-11-1−ii3−3−33000000000000000000
χ742-2-222-22-2-1−2i2i−2i2i-222-2-1111-1-1100002i−2i2i−2i−2i2ii3−i3i3−i3i−ii−i3−33−3-111-1−iii−i−iii−i00-220000−33−i3i3i3−i3−i3i31-11-1−ii−333−3000000000000000000
χ752-2-222-22-2-1−2i2i−2i2i-222-2-1111-1-1100002i−2i−2i2i2i−2i−i3i3−i3i3i−ii−i−33−33-111-1i−i−iii−i−ii002-200003−3−i3i3i3−i3i3−i3-11-11−ii−333−3000000000000000000
χ762-2-222-22-2-1−2i2i−2i2i-222-2-1111-1-1100002i−2i−2i2i2i−2ii3−i3i3−i3i−ii−i3−33−3-111-1i−i−iii−i−ii002-20000−33i3−i3−i3i3−i3i3-11-11−ii3−3−33000000000000000000
χ77444-4-4-44-4400000000-44-444-4-4000000000000000000000000000000000000000000000000000000000000000022−22−22220000000000
χ78444-4-4-44-4400000000-44-444-4-40000000000000000000000000000000000000000000000000000000000000000−222222−220000000000
χ7944-44-44-4-4400004-44-4-444-4-44-40000000000000000000000-4-4440000000000000000000000000000000000000000000000000000
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χ8444-4-44-4-44-24i4i−4i−4i0000-2-22222-24-44i−4i000000-2-222−2i−2i2i2i−2i−2i2i2i00000000000000000000000000000000000000000000000000000000
χ8544-4-44-4-44-24i4i−4i−4i0000-2-22222-2-44−4i4i00000022-2-2−2i−2i2i2i2i2i−2i−2i00000000000000000000000000000000000000000000000000000000
χ8644-4-44-4-44-2−4i−4i4i4i0000-2-22222-24-4−4i4i000000-2-2222i2i−2i−2i2i2i−2i−2i00000000000000000000000000000000000000000000000000000000
χ8744-4-44-4-44-2−4i−4i4i4i0000-2-22222-2-444i−4i00000022-2-22i2i−2i−2i−2i−2i2i2i00000000000000000000000000000000000000000000000000000000
χ884-444-4-4-4440000-4-444-4-4-44-4440000000000000000000000-44-440000000000000000000000000000000000000000000000000000
χ894-444-4-4-44-2000044-4-4222-22-2-20000004-44-4000000000000-22-22-22-22-22-2200000000000000000000000000000000000000000000
χ904-444-4-4-44-2000044-4-4222-22-2-2000000-44-44000000000000-22-222-22-22-22-200000000000000000000000000000000000000000000
χ914-444-4-4-44-20000-4-444222-22-2-200000000000000000000002-22-2−2i32i3−2i32i32i3−2i32i3−2i300000000000000000000000000000000000000000000
χ924-444-4-4-44-20000-4-444222-22-2-200000000000000000000002-22-22i3−2i32i3−2i3−2i32i3−2i32i300000000000000000000000000000000000000000000
χ934-44-444-4-444-4-4400004-444-4-4-4000000000000004-4-44000000000000000000000000000000000000000000000000000000000000
χ944-44-444-4-44-444-400004-444-4-4-400000000000000-444-4000000000000000000000000000000000000000000000000000000000000
χ954-44-444-4-4-24-4-440000-22-2-22220000000000−2i32i32i3−2i3-222-2−2i32i32i3−2i300000000000000000000000000000000000000000000000000000000
χ964-44-444-4-4-24-4-440000-22-2-222200000000002i3−2i3−2i32i3-222-22i3−2i3−2i32i300000000000000000000000000000000000000000000000000000000
χ974-44-444-4-4-2-444-40000-22-2-22220000000000−2i32i32i3−2i32-2-222i3−2i3−2i32i300000000000000000000000000000000000000000000000000000000
χ984-44-444-4-4-2-444-40000-22-2-222200000000002i3−2i3−2i32i32-2-22−2i32i32i3−2i300000000000000000000000000000000000000000000000000000000
χ994-4-4-4-4444400000000-4-44-44-4400000000000000000000000000000000000000000000000000000000000022−22−222200000000000000
χ1004-4-4-4-4444400000000-4-44-44-44000000000000000000000000000000000000000000000000000000000000−222222−2200000000000000
χ101888-8-8-88-8-4000000004-44-4-444000000000000000000000000000000000000000000000000000000000000000000000000000000
χ1028-8-8-8-8888-40000000044-44-44-4000000000000000000000000000000000000000000000000000000000000000000000000000000

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