Finite Group Databasebeta

← Group #10729192

Character table — Group #10729192

Order 768.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96C97C98C99C100C101C102C103C104C105C106C107C108C109C110C111C112C113C114C115C116C117C118C119C120
size111111111111111122222222222222222222222244444444444444444444444444444444888888888888888888888888121212121212121212121212121212122424242424242424
order1222222222222222222222223666666666666666444444446666666612121212121212121212121212121212224444446666121212121212121212121212444444444444444422444444
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ3111111111111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111111111-1-1-1-1-1-1-1-1
χ4111111111111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111
χ51111111111111111111111111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-1111111-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-111-1-1-1-111
χ61111111111111111111111111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-1111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-111111111-1-11111-1-1
χ71111111111111111111111111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-111111111-1-1-1-111111111-1-1-1-1-1-1-1-1-1-11111-1-1
χ81111111111111111111111111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-11111111111-1-1-1-111
χ91111111111111111-1-1-1-1-1-1-1-111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-11111-1-1-1-111111111-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1-1-11111-1-1-1-1
χ101111111111111111-1-1-1-1-1-1-1-111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-11111-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1-1-11111
χ111111111111111111-1-1-1-1-1-1-1-111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1111111111111-1-1-1-11111-1-1-1-1-1-1-1-11111
χ121111111111111111-1-1-1-1-1-1-1-111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-111111111-1-1-1-11111-1-1-1-111111111-1-1-1-1
χ131111111111111111-1-1-1-1-1-1-1-11111111111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111-1-111-1-11111-1-1-1-11111-1-1-1-11111-1-1-1-1-1-1-1-1111111-1-111-1-1
χ141111111111111111-1-1-1-1-1-1-1-11111111111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111-1-111-1-11111-1-1-1-11111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-111-1-111
χ151111111111111111-1-1-1-1-1-1-1-11111111111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-111-1-111-1-1-1-11111-1-1-1-111111111-1-1-1-1-1-1-1-11111-1-111-1-111
χ161111111111111111-1-1-1-1-1-1-1-11111111111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-111-1-111-1-1-1-11111-1-1-1-11111-1-1-1-111111111-1-1-1-111-1-111-1-1
χ17222222222222222222222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-122222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-122222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1000000000000000000000000
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χ812-2-22-22-2-2222-2-222-22-2-22-222-22-2-22-22-2-22-2-2-22222000000002-2-22-222-20000000000000000002-22-20000002-2-222-2-220000000000000000000000000000
χ822-2-22-22-2-2222-2-222-22-2-22-222-22-2-22-22-2-22-2-2-22222000000002-2-22-222-2000000000000000000-22-22000000-222-2-222-20000000000000000000000000000
χ832-2-22-22-2-2222-2-222-22-2-22-222-2-111-11-111-1111-1-1-1-100000000-111-11-1-11−i3i3i3−i3i3−i3−i3i3−i3i3i3−i3i3−i3−i3i3002-22-200−i3i3i3−i3-111-1-111-1−i3i3i3−i3000000000000000000000000
χ842-2-22-22-2-2222-2-222-22-2-22-222-2-111-11-111-1111-1-1-1-100000000-111-11-1-11−i3i3i3−i3i3−i3−i3i3−i3i3i3−i3i3−i3−i3i300-22-2200i3−i3−i3i31-1-111-1-11i3−i3−i3i3000000000000000000000000
χ852-2-22-22-2-2222-2-222-22-2-22-222-2-111-11-111-1111-1-1-1-100000000-111-11-1-11i3−i3−i3i3−i3i3i3−i3i3−i3−i3i3−i3i3i3−i3002-22-200i3−i3−i3i3-111-1-111-1i3−i3−i3i3000000000000000000000000
χ862-2-22-22-2-2222-2-222-22-2-22-222-2-111-11-111-1111-1-1-1-100000000-111-11-1-11i3−i3−i3i3−i3i3i3−i3i3−i3−i3i3−i3i3i3−i300-22-2200−i3i3i3−i31-1-111-1-11−i3i3i3−i3000000000000000000000000
χ872-2-22-22-2-2222-2-222-2-222-22-2-222-2-22-22-2-22-2-2-2222200000000-222-22-2-220000000000000000002-2-220000002-2-22-222-20000000000000000000000000000
χ882-2-22-22-2-2222-2-222-2-222-22-2-222-2-22-22-2-22-2-2-2222200000000-222-22-2-22000000000000000000-222-2000000-222-22-2-220000000000000000000000000000
χ892-2-22-22-2-2222-2-222-2-222-22-2-22-111-11-111-1111-1-1-1-1000000001-1-11-111-1−i3i3i3−i3i3−i3−i3i3i3−i3−i3i3−i3i3i3−i3002-2-2200−i3i3i3−i3-111-11-1-11i3−i3−i3i3000000000000000000000000
χ902-2-22-22-2-2222-2-222-2-222-22-2-22-111-11-111-1111-1-1-1-1000000001-1-11-111-1−i3i3i3−i3i3−i3−i3i3i3−i3−i3i3−i3i3i3−i300-222-200i3−i3−i3i31-1-11-111-1−i3i3i3−i3000000000000000000000000
χ912-2-22-22-2-2222-2-222-2-222-22-2-22-111-11-111-1111-1-1-1-1000000001-1-11-111-1i3−i3−i3i3−i3i3i3−i3−i3i3i3−i3i3−i3−i3i3002-2-2200i3−i3−i3i3-111-11-1-11−i3i3i3−i3000000000000000000000000
χ922-2-22-22-2-2222-2-222-2-222-22-2-22-111-11-111-1111-1-1-1-1000000001-1-11-111-1i3−i3−i3i3−i3i3i3−i3−i3i3i3−i3i3−i3−i3i300-222-200−i3i3i3−i31-1-11-111-1i3−i3−i3i3000000000000000000000000
χ934444444-4-4-4-4-4-44-4-44444-4-4-4-4-2-2-2-2-2-2-222222222-200000000-2-2-2-222220000000000000000000000000000000000000000000000000000000000000000
χ944444444-4-4-4-4-4-44-4-4-4-4-4-44444-2-2-2-2-2-2-222222222-2000000002222-2-2-2-20000000000000000000000000000000000000000000000000000000000000000
χ954444-4-4-44-44-44-4-44-400000000-2-2-2-2222-2-2-2222-22200004i4i−4i−4i0000000000000000−2i−2i−2i−2i2i2i2i2i000000000000000000000000000000000000000000000000
χ964444-4-4-44-44-44-4-44-400000000-2-2-2-2222-2-2-2222-2220000−4i−4i4i4i00000000000000002i2i2i2i−2i−2i−2i−2i000000000000000000000000000000000000000000000000
χ974444-4-4-4-44-44-44-4-4400000000-2-2-2-2222222-2-2-22-224i4i−4i−4i000000000000−2i−2i−2i−2i2i2i2i2i00000000000000000000000000000000000000000000000000000000
χ984444-4-4-4-44-44-44-4-4400000000-2-2-2-2222222-2-2-22-22−4i−4i4i4i0000000000002i2i2i2i−2i−2i−2i−2i00000000000000000000000000000000000000000000000000000000
χ9944-4-444-44-4-44-44-44-400000000-2-222-2-22-2-22-2222-224i−4i4i−4i000000000000−2i−2i2i2i−2i−2i2i2i00000000000000000000000000000000000000000000000000000000
χ10044-4-444-44-4-44-44-44-400000000-2-222-2-22-2-22-2222-22−4i4i−4i4i0000000000002i2i−2i−2i2i2i−2i−2i00000000000000000000000000000000000000000000000000000000
χ10144-4-444-4-444-44-4-4-4400000000-2-222-2-2222-22-2-2-22200004i−4i4i−4i0000000000000000−2i−2i2i2i−2i−2i2i2i000000000000000000000000000000000000000000000000
χ10244-4-444-4-444-44-4-4-4400000000-2-222-2-2222-22-2-2-2220000−4i4i−4i4i00000000000000002i2i−2i−2i2i2i−2i−2i000000000000000000000000000000000000000000000000
χ10344-4-4-4-4444-4-4-4-444444-4-444-4-4-2-22222-2-2-222-2-222-200000000-2-222-2-2220000000000000000000000000000000000000000000000000000000000000000
χ10444-4-4-4-4444-4-4-4-4444-4-444-4-444-2-22222-2-2-222-2-222-20000000022-2-222-2-20000000000000000000000000000000000000000000000000000000000000000
χ1054-44-44-4-4-44-4-44444-44-44-4-44-44-22-22-2222-2-2-22-222-200000000-22-222-22-20000000000000000000000000000000000000000000000000000000000000000
χ1064-44-44-4-4-44-4-44444-4-44-444-44-4-22-22-2222-2-2-22-222-2000000002-22-2-22-220000000000000000000000000000000000000000000000000000000000000000
χ1074-44-4-444444-4-44-4-4-4000000004-44-4-4444-4-44-444-4-400000000000000000000000000000000000000000000000000000000000000000000000000000000
χ1084-44-4-444444-4-44-4-4-400000000-22-222-2-2-222-22-2-22200000000000000000000000023−2323−23−2323−2323000000000000000000000000000000000000000000000000
χ1094-44-4-444444-4-44-4-4-400000000-22-222-2-2-222-22-2-222000000000000000000000000−2323−232323−2323−23000000000000000000000000000000000000000000000000
χ1104-44-4-444-4-4-444-4-444000000004-44-4-444-444-44-4-44-400000000000000000000000000000000000000000000000000000000000000000000000000000000
χ1114-44-4-444-4-4-444-4-44400000000-22-222-2-22-2-22-222-22000000000000000023−2323−23−2323−232300000000000000000000000000000000000000000000000000000000
χ1124-44-4-444-4-4-444-4-44400000000-22-222-2-22-2-22-222-220000000000000000−2323−232323−2323−2300000000000000000000000000000000000000000000000000000000
χ1134-4-444-4444-444-4-4-4-4000000004-4-444-444-44-4-44-44-400000000000000000000000000000000000000000000000000000000000000000000000000000000
χ1144-4-444-4444-444-4-4-4-400000000-222-2-22-2-22-222-22-22000000000000000023−23−232323−23−232300000000000000000000000000000000000000000000000000000000
χ1154-4-444-4444-444-4-4-4-400000000-222-2-22-2-22-222-22-220000000000000000−232323−23−232323−2300000000000000000000000000000000000000000000000000000000
χ1164-4-444-44-4-44-4-44-444000000004-4-444-44-44-444-44-4-400000000000000000000000000000000000000000000000000000000000000000000000000000000
χ1174-4-444-44-4-44-4-44-44400000000-222-2-22-22-22-2-22-22200000000000000000000000023−23−232323−23−2323000000000000000000000000000000000000000000000000
χ1184-4-444-44-4-44-4-44-44400000000-222-2-22-22-22-2-22-222000000000000000000000000−232323−23−232323−23000000000000000000000000000000000000000000000000
χ1194-4-44-44-44-4-4-4444-444-4-444-4-44-222-22-22-22-2-2-2222-200000000-222-2-222-20000000000000000000000000000000000000000000000000000000000000000
χ1204-4-44-44-44-4-4-4444-44-444-4-444-4-222-22-22-22-2-2-2222-2000000002-2-222-2-220000000000000000000000000000000000000000000000000000000000000000

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