Finite Group Databasebeta

← Group #10742710

Character table — Group #10742710

Order 768.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96C97C98C99C100C101C102C103C104C105C106C107C108C109C110C111C112C113C114
size11111111111111112222222222222222444444444444444444444444444444444444444488888888888888888888881212121212121212242424242424242424242424
order1222222222222222366666666666666622222222444444446666666612121212121212121212121212121212444444666612121212121212121212121244444444444444444444
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ31111111111111111111111111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-11111111111111111-1-1-1-1-1-1-1-1
χ41111111111111111111111111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-111111111
χ5111111111111111111111111111111111111-1-1-1-111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-111-1-11111-1-1-1-1
χ6111111111111111111111111111111111111-1-1-1-111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-111-1-1-1-11111
χ7111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-111111111-1-1-1-11111-1-1-1-111-1-1-1-1-1-11111
χ8111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-111111111-1-1-1-1-1-1-1-11111-1-1111111-1-1-1-1
χ911111111111111111111111111111111-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-111-1-1-1-111111111-1-1-1-1-1-1-1-111111111-1-1-1-111-1-111-1-1
χ1011111111111111111111111111111111-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-111-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-111-1-111
χ1111111111111111111111111111111111-1-1-1-11111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-111-1-11111-1-1-1-11111-1-1-1-111111111-1-1-1-1-1-111-1-111
χ1211111111111111111111111111111111-1-1-1-11111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-111-1-11111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1111111-1-111-1-1
χ1311111111111111111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-11111-1-1-1-111
χ1411111111111111111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-111111111-1-1-1-1111111-1-1-1-11111-1-1
χ1511111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111-1-111-1-1-1-11111-1-1-1-111111111-1-1-1-1-1-111-1-11111-1-1
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χ222222222222222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-2-2-2-22222-2-2-2-222221111111111111111-1-1-1-1-1-1-1-1-2-222-2-2-1-1-1-11111-1-1-1-1111100000000000000000000
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χ812-2-2-22-2222-2-22-22-22-11111-11-111-11-1-1-1-10000-222-22-2-220000−i3i3i3−i3i3−i3−i3i3-111-1-111-1−i3−i3i3i3i3i3−i3−i3-2200001-1-111-1-11i3−i3−i3i3i3−i3−i3i300000000000000000000
χ822-2-2-22-2222-2-22-22-22-11111-11-111-11-1-1-1-10000-222-22-2-220000i3−i3−i3i3−i3i3i3−i3-111-1-111-1i3i3−i3−i3−i3−i3i3i3-2200001-1-111-1-11−i3i3i3−i3−i3i3i3−i300000000000000000000
χ832-2-2-22-2222-2-22-22-22-11111-11-111-11-1-1-1-10000-222-2-222-20000−i3i3i3−i3i3−i3−i3i31-1-111-1-11i3i3−i3−i3−i3−i3i3i32-200001-1-11-111-1−i3i3i3−i3i3−i3−i3i300000000000000000000
χ842-2-2-22-2222-2-22-22-22-11111-11-111-11-1-1-1-10000-222-2-222-20000i3−i3−i3i3−i3i3i3−i31-1-111-1-11−i3−i3i3i3i3i3−i3−i32-200001-1-11-111-1i3−i3−i3i3−i3i3i3−i300000000000000000000
χ8544444-4-4-44-4-4-4-444-444-4-44-4-44444-4-4-44-40000000000000000000000000000000000000000000000000000000000000000000000000000000000
χ8644444-4-4-44-4-4-4-444-4-2-222-222-2-2-2-2222-220000000000000000000000000000000023−23−232323−23−2323000000000000000000000000000000000000000000
χ8744444-4-4-44-4-4-4-444-4-2-222-222-2-2-2-2222-2200000000000000000000000000000000−232323−23−232323−23000000000000000000000000000000000000000000
χ88444-4-444-44-4-444-4-4-444-4-4444-4-4-4-444-44-40000000000000000000000000000000000000000000000000000000000000000000000000000000000
χ89444-4-444-44-4-444-4-4-4-2-222-2-2-22222-2-22-220000000000000000000000000000000023−23−2323−232323−23000000000000000000000000000000000000000000
χ90444-4-444-44-4-444-4-4-4-2-222-2-2-22222-2-22-2200000000000000000000000000000000−232323−2323−23−2323000000000000000000000000000000000000000000
χ9144-44-444-4-4-44-4-44-4444-44-4-4-444-4-444-4-440000000000000000000000000000000000000000000000000000000000000000000000000000000000
χ9244-44-444-4-4-44-4-44-44-2-22-2222-2-222-2-222-20000000000000000−2i3−2i32i32i32i32i3−2i3−2i30000000000000000000000000000000000000000000000000000000000
χ9344-44-444-4-4-44-4-44-44-2-22-2222-2-222-2-222-200000000000000002i32i3−2i3−2i3−2i3−2i32i32i30000000000000000000000000000000000000000000000000000000000
χ9444-44-4-4-44-44-4444-4-4-2-2-222-2-2-2-22222-222000000004i4i−4i−4i000000000000−2i−2i2i2i−2i−2i2i2i00000000000000000000000000000000000000000000000000
χ9544-44-4-4-44-44-4444-4-4-2-2-222-2-2-2-22222-22200000000−4i−4i4i4i0000000000002i2i−2i−2i2i2i−2i−2i00000000000000000000000000000000000000000000000000
χ9644-4-44444-44-4-4-4-44-4444-4-4-4-4-4-444444-4-40000000000000000000000000000000000000000000000000000000000000000000000000000000000
χ9744-4-44444-44-4-4-4-44-4-2-2-2222222-2-2-2-2-2220000000000000000000000002323−23−23−23−23232300000000000000000000000000000000000000000000000000
χ9844-4-44444-44-4-4-4-44-4-2-2-2222222-2-2-2-2-222000000000000000000000000−23−2323232323−23−2300000000000000000000000000000000000000000000000000
χ9944-4-44-4-4-4-4-4444-444-2-22-22-2-222-2-22222-244-4-4000000000000-2-222-2-2220000000000000000000000000000000000000000000000000000000000
χ10044-4-44-4-4-4-4-4444-444-2-22-22-2-222-2-22222-2-4-44400000000000022-2-222-2-20000000000000000000000000000000000000000000000000000000000
χ1014-44444-4-4-44-44-4-4-444-44-444-4-44-444-4-4-440000000000000000000000000000000000000000000000000000000000000000000000000000000000
χ1024-44444-4-4-44-44-4-4-44-22-22-2-222-22-2-2222-20000000000000000−2i32i3−2i32i32i3−2i32i3−2i30000000000000000000000000000000000000000000000000000000000
χ1034-44444-4-4-44-44-4-4-44-22-22-2-222-22-2-2222-200000000000000002i3−2i32i3−2i3−2i32i3−2i32i30000000000000000000000000000000000000000000000000000000000
χ1044-4444-444-4-44-44-4-4-44-4-444-44-44-44-444-4-40000000000000000000000000000000000000000000000000000000000000000000000000000000000
χ1054-4444-444-4-44-44-4-4-4-222-2-22-22-22-22-2-22200000000000000000000000023−2323−23−2323−232300000000000000000000000000000000000000000000000000
χ1064-4444-444-4-44-44-4-4-4-222-2-22-22-22-22-2-222000000000000000000000000−2323−232323−2323−2300000000000000000000000000000000000000000000000000
χ1074-44-4-44-44-4-444-444-4-222-2-2-22-22-22-22-222000000004i−4i4i−4i000000000000−2i2i−2i2i−2i2i−2i2i00000000000000000000000000000000000000000000000000
χ1084-44-4-44-44-4-444-444-4-222-2-2-22-22-22-22-22200000000−4i4i−4i4i0000000000002i−2i2i−2i2i−2i2i−2i00000000000000000000000000000000000000000000000000
χ1094-44-4-4-44-4-44-4-44444-22-22-22-2-22-222-222-24-44-4000000000000-22-22-22-220000000000000000000000000000000000000000000000000000000000
χ1104-44-4-4-44-4-44-4-44444-22-22-22-2-22-222-222-2-44-440000000000002-22-22-22-20000000000000000000000000000000000000000000000000000000000
χ1114-4-44-4-44-44444-4-44-4-22-2-22-222-2-222-22-220000000000004i−4i4i−4i0000000000000000−2i2i−2i2i−2i2i−2i2i000000000000000000000000000000000000000000
χ1124-4-44-4-44-44444-4-44-4-22-2-22-222-2-222-22-22000000000000−4i4i−4i4i00000000000000002i−2i2i−2i2i−2i2i−2i000000000000000000000000000000000000000000
χ1134-4-4-444-4-4444-444-4-4-22-2-222-2-222-2-222-220000000000004i−4i−4i4i0000000000000000−2i2i−2i2i2i−2i2i−2i000000000000000000000000000000000000000000
χ1144-4-4-444-4-4444-444-4-4-22-2-222-2-222-2-222-22000000000000−4i4i4i−4i00000000000000002i−2i2i−2i−2i2i−2i2i000000000000000000000000000000000000000000

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