Finite Group Databasebeta

← Group #10828768

Character table — Group #10828768

Order 768.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96C97C98C99C100C101C102
size111111112222222222222222444444444444444444444444444444444488888888888888888888888888121212121212121224242424242424244848
order12222222344444444666666622224444446666121212121212121212121212121212121212121222444444666666121212121212121212121212888888884444888844
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ3111111111111111111111111111111-1-1-1-11111111111111111-1-1-1-1-1-1-1-1-1-111-1-1-1-111-1-1-1-11111-1-1-1-1-1-1-1-111111111-1-1-1-11111-1-1
χ4111111111111111111111111111111-1-1-1-11111111111111111-1-1-1-1-1-1-1-1-1-111-1-1-1-111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-111
χ511111111111111111111111111-1-1-1-11111-1-1-1-111111111-1-1-1-111111111-1-1-1-111-1-111-1-1-1-1-1-1-1-11111-1-1-1-1111111111111-1-1-1-1-1-1
χ611111111111111111111111111-1-1-1-11111-1-1-1-111111111-1-1-1-111111111-1-1-1-111-1-111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111
χ711111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-111111111-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-111
χ811111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-111111111-1-1
χ91111111111-1-1-1-11111111111-1-111-1-1111111111111-1-1-1-1-1-1-1-111111111-1-11-1-1-111-1-1-1-1-1-111-1-1-1-1-1-111111111-1-1-1-111-1-111-1-11-1
χ101111111111-1-1-1-11111111111-1-111-1-1111111111111-1-1-1-1-1-1-1-111111111-1-11-1-1-111-1-1-1-1-1-111-1-1-1-1-1-11111-1-1-1-11111-1-111-1-111-11
χ111111111111-1-1-1-11111111111-1-111-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111-111-1-1-1-1111111-1-11111-1-1-1-11111-1-1-1-1-1-11111-1-1-11
χ121111111111-1-1-1-11111111111-1-111-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111-111-1-1-1-1111111-1-11111-1-1-1-1-1-1-1-1111111-1-1-1-1111-1
χ131111111111-1-1-1-11111111111-1-1-1-1111111-1-1-1-11111-1-1-1-111111111111111-11-1-1-1-1-1-11111-1-111-1-1-1-1-1-1-1-11111-1-1-1-111-1-1-1-111-11
χ141111111111-1-1-1-11111111111-1-1-1-1111111-1-1-1-11111-1-1-1-111111111111111-11-1-1-1-1-1-11111-1-111-1-1-1-1-1-1-1-1-1-1-1-11111-1-11111-1-11-1
χ151111111111-1-1-1-11111111111-1-1-1-111-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-111111-1-1-1-1-1-1-1-111111111111111-1-1-1-1-1-111-1-1111-1
χ161111111111-1-1-1-11111111111-1-1-1-111-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-111111-1-1-1-1-1-1-1-11111111111-1-1-1-1111111-1-111-1-1-11
χ17222222222-22222-2-2-22222222-2-2222200002222-2-2-2-2222222220000000000-2-20000-2-20000-2-2-2-200000000000000000000000000
χ18222222222-22222-2-2-22222222-2-2-2-2-2-20000-2-2-2-2-2-2-2-22222-2-2-2-20000000000220000-2-20000222200000000000000000000000000
χ19222222222-2-2-2-2-2-2-2-222222222222-2-200002222-2-2-2-2-2-2-2-2-2-2-2-20000000000-220000220000-2-22200000000000000000000000000
χ20222222222-2-2-2-2-2-2-2-2222222222-2-2220000-2-2-2-2-2-2-2-2-2-2-2-2222200000000002-2000022000022-2-200000000000000000000000000
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
χ2222222222-122222222-1-1-1-1-1-1-1222222-2-2-2-2-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-2-222-2-2-2-2-1-11111-1-1-1-111111111000000000000000000
χ2322222222-122222222-1-1-1-1-1-1-122-2-2-2-222221111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-2-2-2-222-2-2-1-111111111-1-1-1-11111000000000000000000
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χ2522222222-12-2-2-2-2222-1-1-1-1-1-1-1-2-222-2-22222-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-2-22-2-2-222111111-1-1111111-1-1-1-1000000000000000000
χ2622222222-12-2-2-2-2222-1-1-1-1-1-1-1-2-222-2-2-2-2-2-2-1-1-1-1-1-1-1-11111111111111111222-222-2-211-1-1-1-1-1-111-1-1-1-11111000000000000000000
χ2722222222-12-2-2-2-2222-1-1-1-1-1-1-1-2-2-2-22222221111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-122-22-2-2-2-211-1-1-1-111-1-111111111000000000000000000
χ2822222222-12-2-2-2-2222-1-1-1-1-1-1-1-2-2-2-222-2-2-2-21111-1-1-1-11111-1-1-1-111111111-2-2-22222211111111-1-1-1-1-1-1-1-1-1-1000000000000000000
χ2922222222-1-22222-2-2-2-1-1-1-1-1-1-1-2-222220000-1-1-1-11111-1-1-1-1-1-1-1-1−i3−i3−i3−i3i3i3i3i300-2-2000011−i3−i3i3i31111−i3−i3i3i3−i3−i3i3i3000000000000000000
χ3022222222-1-22222-2-2-2-1-1-1-1-1-1-1-2-222220000-1-1-1-11111-1-1-1-1-1-1-1-1i3i3i3i3−i3−i3−i3−i300-2-2000011i3i3−i3−i31111i3i3−i3−i3i3i3−i3−i3000000000000000000
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χ3522222222-1-2-2-2-2-2-2-2-2-1-1-1-1-1-1-122-2-2220000111111111111-1-1-1-1−i3−i3−i3−i3i3i3i3i3002-20000-1-1−i3−i3i3i3-1-111i3i3−i3−i3i3i3−i3−i3000000000000000000
χ3622222222-1-2-2-2-2-2-2-2-2-1-1-1-1-1-1-122-2-2220000111111111111-1-1-1-1i3i3i3i3−i3−i3−i3−i3002-20000-1-1i3i3−i3−i3-1-111−i3−i3i3i3−i3−i3i3i3000000000000000000
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χ532-2-22-2-222222-22-2-2-22-2-2-2-22222-200002-2-2200002-2-222-22-200002-2-222-2-2200002-2002-2000000002-22-20000000000000000000000
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χ8744-4-4-444-4-204i−4i−4i4i0002-22-22-2200000000002i3−2i3−2i32i30000−2i2i2i−2i−232323−230000000000000000000000000000000000000000000000000000
χ8844-4-4-444-4-20−4i4i4i−4i0002-22-22-220000000000−2i32i32i3−2i300002i−2i−2i2i−232323−230000000000000000000000000000000000000000000000000000
χ8944-4-4-444-4-20−4i4i4i−4i0002-22-22-2200000000002i3−2i3−2i32i300002i−2i−2i2i23−23−23230000000000000000000000000000000000000000000000000000
χ904-444-44-4-44400004-4-4-4-4444-4-400000000000000-44-44000000000000000000000000000000000000000000000000000000000000
χ914-444-44-4-4-2400004-4-422-2-2-222000000000000002-22-20000000023−2323−23−2323−232300000000000000000000000000000000000000000000
χ924-444-44-4-4-2400004-4-422-2-2-222000000000000002-22-200000000−2323−232323−2323−2300000000000000000000000000000000000000000000
χ934-444-44-4-4-2-40000-44422-2-2-2220000004i−4i4i−4i0000-22-2200000000−2i2i−2i2i−2i2i−2i2i00000000000000000000000000000000000000000000
χ944-444-44-4-4-2-40000-44422-2-2-222000000−4i4i−4i4i0000-22-22000000002i−2i2i−2i2i−2i2i−2i00000000000000000000000000000000000000000000
χ954-44-44-44-4-204i4i−4i−4i000-22-222-22004-44i−4i0000-2-2220000−2i−2i2i2i−2i−2i2i2i0000000000000000000000000000000000000000000000000000
χ964-44-44-44-4-204i4i−4i−4i000-22-222-2200-44−4i4i000022-2-20000−2i−2i2i2i2i2i−2i−2i0000000000000000000000000000000000000000000000000000
χ974-44-44-44-4-20−4i−4i4i4i000-22-222-22004-4−4i4i0000-2-22200002i2i−2i−2i2i2i−2i−2i0000000000000000000000000000000000000000000000000000
χ984-44-44-44-4-20−4i−4i4i4i000-22-222-2200-444i−4i000022-2-200002i2i−2i−2i−2i−2i2i2i0000000000000000000000000000000000000000000000000000
χ994-4-4-444-444000000004-4-44-4-44000000000000000000000000000000000000000000000000000000000000000022−22−22220000000000
χ1004-4-4-444-444000000004-4-44-4-440000000000000000000000000000000000000000000000000000000000000000−222222−220000000000
χ101888-8-8-8-88-4000000004-4-4444-4000000000000000000000000000000000000000000000000000000000000000000000000000000
χ1028-8-8-888-88-400000000-444-444-4000000000000000000000000000000000000000000000000000000000000000000000000000000

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