Finite Group Databasebeta

← Group #10729198

Character table — Group #10729198

Order 768.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96C97C98C99C100C101C102C103C104C105C106C107C108C109C110C111C112C113C114C115C116C117C118C119C120
size111111111111111122222222222222222222222244444444444444444444444444444444888888888888888888888888121212121212121212121212121212122424242424242424
order12222222222222222222222236666666666666664444444466666666121212121212121212121212121212124444444412121212121212121212121212121212444444444444444422224444
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
χ51111111111111111111111111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-111-1-111-1-1
χ61111111111111111111111111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-111-1-111
χ71111111111111111111111111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-11111111111111111-1-1-1-1-1-1-1-1-1-111-1-111
χ81111111111111111111111111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-11111111111-1-111-1-1
χ91111111111111111-1-1-1-1-1-1-1-111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-111-1-111-1-11111-1-1-1-11111-1-1-1-11111-1-1-1-11111-1-1-1-11111-1-1-1-1
χ101111111111111111-1-1-1-1-1-1-1-111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-111-1-111-1-11111-1-1-1-11111-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1-1-11111
χ111111111111111111-1-1-1-1-1-1-1-111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-111-1-111-1-1-1-11111-1-1-1-111111111-1-1-1-11111-1-1-1-1-1-1-1-11111
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χ131111111111111111-1-1-1-1-1-1-1-11111111111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111-1-1-1-1111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1111111-1-1-1-111
χ141111111111111111-1-1-1-1-1-1-1-11111111111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111-1-1-1-1111111-1-1-1-1-1-1-1-11111-1-1-1-111111111-1-1-1-1-1-11111-1-1
χ151111111111111111-1-1-1-1-1-1-1-11111111111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-11111-1-1-1-1-1-111111111-1-1-1-11111-1-1-1-1-1-1-1-11111-1-11111-1-1
χ161111111111111111-1-1-1-1-1-1-1-11111111111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-11111-1-1-1-1-1-111111111-1-1-1-1-1-1-1-111111111-1-1-1-111-1-1-1-111
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χ872-2-22-22-22-2-22-22-222-222-2-222-2-111-11-1-11-1-111-11-11000000001-1-111-1-11−333−33−3−333−3−33−333−32-2-220000-111-11-1-113−3−33−333−3000000000000000000000000
χ882-2-22-22-22-2-22-22-222-222-2-222-2-111-11-1-11-1-111-11-11000000001-1-111-1-11−333−33−3−333−3−33−333−3-222-200001-1-11-111-1−333−33−3−33000000000000000000000000
χ892-2-22-22-2-222-22-22-222-2-22-222-22-2-22-222-2-2-222-22-22000000002-2-22-222-2000000000000000000000000000000000000000000000000000000002-2002-200
χ902-2-22-22-2-222-22-22-222-2-22-222-22-2-22-222-2-2-222-22-22000000002-2-22-222-200000000000000000000000000000000000000000000000000000000-2200-2200
χ912-2-22-22-2-222-22-22-22-222-22-2-222-2-22-222-2-2-222-22-2200000000-222-22-2-22000000000000000000000000000000000000000000000000000000002-200-2200
χ922-2-22-22-2-222-22-22-22-222-22-2-222-2-22-222-2-2-222-22-2200000000-222-22-2-2200000000000000000000000000000000000000000000000000000000-22002-200
χ934444444-4-4-4-4-4-4-4-444444-4-4-4-4-2-2-2-2-2-2-2-22222222200000000-2-2-2-222220000000000000000000000000000000000000000000000000000000000000000
χ944444444-4-4-4-4-4-4-4-44-4-4-4-44444-2-2-2-2-2-2-2-222222222000000002222-2-2-2-20000000000000000000000000000000000000000000000000000000000000000
χ954444-4-4-44-444-4-44-4-400000000-2-2-2-22222-222-2-222-244-4-4000000000000-2-2-2-2222200000000000000000000000000000000000000000000000000000000
χ964444-4-4-44-444-4-44-4-400000000-2-2-2-22222-222-2-222-2-4-4440000000000002222-2-2-2-200000000000000000000000000000000000000000000000000000000
χ974444-4-4-4-44-4-444-44-400000000-2-2-2-222222-2-222-2-2200004i4i−4i−4i0000000000000000−2i−2i−2i−2i2i2i2i2i000000000000000000000000000000000000000000000000
χ984444-4-4-4-44-4-444-44-400000000-2-2-2-222222-2-222-2-220000−4i−4i4i4i00000000000000002i2i2i2i−2i−2i−2i−2i000000000000000000000000000000000000000000000000
χ9944-4-444-44-4-4-4444-4-400000000-2-222-2-222-22222-2-2-24-44-4000000000000-2-222-2-22200000000000000000000000000000000000000000000000000000000
χ10044-4-444-44-4-4-4444-4-400000000-2-222-2-222-22222-2-2-2-44-4400000000000022-2-222-2-200000000000000000000000000000000000000000000000000000000
χ10144-4-444-4-4444-4-4-44-400000000-2-222-2-2222-2-2-2-222200004i−4i4i−4i0000000000000000−2i−2i2i2i−2i−2i2i2i000000000000000000000000000000000000000000000000
χ10244-4-444-4-4444-4-4-44-400000000-2-222-2-2222-2-2-2-22220000−4i4i−4i4i00000000000000002i2i−2i−2i2i2i−2i−2i000000000000000000000000000000000000000000000000
χ10344-4-4-4-44-4-44444-4-4444-4-4-4-444-2-22222-2-2222-2-2-2-2200000000-2-22222-2-20000000000000000000000000000000000000000000000000000000000000000
χ10444-4-4-4-44-4-44444-4-44-4-44444-4-4-2-22222-2-2222-2-2-2-220000000022-2-2-2-2220000000000000000000000000000000000000000000000000000000000000000
χ1054-44-44-4-4-44-44-444-444-44-4-44-44-22-22-22-2222-22-22-2-200000000-22-222-22-20000000000000000000000000000000000000000000000000000000000000000
χ1064-44-44-4-4-44-44-444-44-44-444-44-4-22-22-22-2222-22-22-2-2000000002-22-2-22-220000000000000000000000000000000000000000000000000000000000000000
χ1074-44-4-444444-4-44-4-4-4000000004-44-4-44-444-444-4-44-400000000000000000000000000000000000000000000000000000000000000000000000000000000
χ1084-44-4-444444-4-44-4-4-400000000-22-222-22-2-22-2-222-22000000000000000023−2323−23−2323−232300000000000000000000000000000000000000000000000000000000
χ1094-44-4-444444-4-44-4-4-400000000-22-222-22-2-22-2-222-220000000000000000−2323−232323−2323−2300000000000000000000000000000000000000000000000000000000
χ1104-44-4-444-4-4-444-444-4000000004-44-4-44-44-44-4-444-4400000000000000000000000000000000000000000000000000000000000000000000000000000000
χ1114-44-4-444-4-4-444-444-400000000-22-222-22-22-222-2-22-2000000000000000000000000−2i32i3−2i32i32i3−2i32i3−2i3000000000000000000000000000000000000000000000000
χ1124-44-4-444-4-4-444-444-400000000-22-222-22-22-222-2-22-20000000000000000000000002i3−2i32i3−2i3−2i32i3−2i32i3000000000000000000000000000000000000000000000000
χ1134-4-444-4444-444-4-4-4-4000000004-4-444-4-444-44-444-4-400000000000000000000000000000000000000000000000000000000000000000000000000000000
χ1144-4-444-4444-444-4-4-4-400000000-222-2-222-2-22-22-2-222000000000000000023−23−232323−23−232300000000000000000000000000000000000000000000000000000000
χ1154-4-444-4444-444-4-4-4-400000000-222-2-222-2-22-22-2-2220000000000000000−232323−23−232323−2300000000000000000000000000000000000000000000000000000000
χ1164-4-444-44-4-44-4-4444-4000000004-4-444-4-44-44-44-4-44400000000000000000000000000000000000000000000000000000000000000000000000000000000
χ1174-4-444-44-4-44-4-4444-400000000-222-2-222-22-22-222-2-2000000000000000000000000−2i32i32i3−2i3−2i32i32i3−2i3000000000000000000000000000000000000000000000000
χ1184-4-444-44-4-44-4-4444-400000000-222-2-222-22-22-222-2-20000000000000000000000002i3−2i3−2i32i32i3−2i3−2i32i3000000000000000000000000000000000000000000000000
χ1194-4-44-44-4-444-44-44-444-4-44-444-4-222-22-2-2222-2-22-22-200000000-222-22-2-220000000000000000000000000000000000000000000000000000000000000000
χ1204-4-44-44-4-444-44-44-44-444-44-4-44-222-22-2-2222-2-22-22-2000000002-2-22-222-20000000000000000000000000000000000000000000000000000000000000000

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