Finite Group Databasebeta

← Group #72277325

Character table — Group #72277325

Order 9216.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96C97C98C99C100C101C102C103C104C105C106C107C108C109C110C111C112C113C114C115C116C117C118C119C120C121C122C123C124C125C126C127C128C129C130C131C132C133C134C135C136C137C138C139C140C141C142C143C144C145C146C147C148C149C150C151C152C153C154C155C156C157C158C159C160C161C162C163C164C165C166C167C168C169C170C171C172C173C174C175C176C177C178C179C180C181C182C183C184C185C186C187C188C189C190C191C192C193C194C195C196C197C198C199C200C201C202C203C204C205C206C207C208C209C210C211C212C213C214C215C216
size112668812121212121224242424242424242448484848646464641281281281281281281126688121212121212242424242424242424484848486464646412812812812812812811266881212121212122424242424242424244848484864646464128128128128128128112668812121212121224242424242424242448484848646464641281281281281281281126688121212121212242424242424242424484848486464646412812812812812812811266881212121212122424242424242424244848484864646464128128128128128128
order1222224222244222444444444433666666121236666612666612126661212121212121212121233666666121236666612666612126661212121212121212121233666666121222222242222442224444444444666666661212666666126666121266612121212121212121212666666661212666666126666121266612121212121212121212666666661212
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
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χ1431212-12-440000000000-4040000000000000000001212-12-440000000000-4040000000000000000001212-12-440000000000-404000000000000000000-12-12124-4000000000040-4000000000000000000-12-12124-4000000000040-4000000000000000000-12-12124-4000000000040-4000000000000000000
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χ14611111111111111111111111111−1+i32−1−i32−1+i32−1−i32−1+i32−1+i32−1−i32−1−i32−1+i32−1−i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1−i321−1−i321−1−i32−1−i3211−1−i321−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i321−1+i321−1+i3211−1+i32−1+i321−1+i32-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11−i321+i321−i321+i321−i321−i321+i321+i321−i321+i321−i321−i321−i321−i321−i321−i321−i321−i321−i321−i321−i321−i321−i321−i321−i321−i321−i321−i321−i321−i321−i321−i321−i321−i321−i321−i321+i32-11+i32-11+i321+i32-1-11+i32-11+i321+i321+i321+i321+i321+i321+i321+i321+i321+i321+i321+i321+i321+i321+i321+i321+i321+i321+i321+i321+i321+i321+i321+i321+i321+i32-11−i32-11−i32-1-11−i321−i32-11−i32
χ14711111111111111111111111111−1−i32−1+i32−1−i32−1+i32−1−i32−1−i32−1+i32−1+i32−1−i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i321−1−i321−1−i3211−1−i32−1−i321−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1+i321−1+i321−1+i32−1+i3211−1+i321-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11+i321−i321+i321−i321+i321+i321−i321−i321+i321−i321−i321−i321−i321−i321−i321−i321−i321−i321−i321−i321−i321−i321−i321−i321−i321−i321−i321−i321−i321−i321−i321−i321−i321−i321−i321−i32-11+i32-11+i32-1-11+i321+i32-11+i321+i321+i321+i321+i321+i321+i321+i321+i321+i321+i321+i321+i321+i321+i321+i321+i321+i321+i321+i321+i321+i321+i321+i321+i321+i321+i321−i32-11−i32-11−i321−i32-1-11−i32-1
χ14811111-1-111111111-11-11111-1-1-1-111111-11-1-1-1−1+i32−1+i32−1+i32−1+i32−1+i321−i321−i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i321−i32−1+i321−i32−1+i32−1+i32−1+i32−1+i321−i321−i321−i321−i32−1+i32−1+i32−1+i32−1+i32−1+i321−i32−1+i321−i321−i321−i32−1−i32−1−i32−1−i32−1−i32−1−i321+i321+i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i321+i32−1−i321+i32−1−i32−1−i32−1−i32−1−i321+i321+i321+i321+i32−1−i32−1−i32−1−i32−1−i32−1−i321+i32−1−i321+i321+i321+i32-1-1-1-1-111-1-1-1-1-1-1-1-11-11-1-1-1-11111-1-1-1-1-11-11111−i321−i321−i321−i321−i32−1+i32−1+i321−i321−i321−i321−i321−i321−i321−i321−i32−1+i321−i32−1+i321−i321−i321−i321−i32−1+i32−1+i32−1+i32−1+i321−i321−i321−i321−i321−i32−1+i321−i32−1+i32−1+i32−1+i321+i321+i321+i321+i321+i32−1−i32−1−i321+i321+i321+i321+i321+i321+i321+i321+i32−1−i321+i32−1−i321+i321+i321+i321+i32−1−i32−1−i32−1−i32−1−i321+i321+i321+i321+i321+i32−1−i321+i32−1−i32−1−i32−1−i32
χ14911111-1-111111111-11-11111-1-1-1-1−1+i32−1−i32−1+i32−1−i32−1+i321−i32−1−i321+i321−i321+i32−1+i32−1+i32−1+i32−1+i32−1+i321−i321−i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i321−i32−1+i321−i32−1+i32−1+i32−1+i32−1+i321−i321−i321−i321−i32−1−i321−1−i321−1−i321+i321-11+i32-1−1−i32−1−i32−1−i32−1−i32−1−i321+i321+i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i321+i32−1−i321+i32−1−i32−1−i32−1−i32−1−i321+i321+i321+i321+i321−1+i321−1+i321-1−1+i321−i32-11−i32-1-1-1-1-111-1-1-1-1-1-1-1-11-11-1-1-1-111111−i321+i321−i321+i321−i32−1+i321+i32−1−i32−1+i32−1−i321−i321−i321−i321−i321−i32−1+i32−1+i321−i321−i321−i321−i321−i321−i321−i321−i32−1+i321−i32−1+i321−i321−i321−i321−i32−1+i32−1+i32−1+i32−1+i321+i32-11+i32-11+i32−1−i32-11−1−i3211+i321+i321+i321+i321+i32−1−i32−1−i321+i321+i321+i321+i321+i321+i321+i321+i32−1−i321+i32−1−i321+i321+i321+i321+i32−1−i32−1−i32−1−i32−1−i32-11−i32-11−i32-111−i32−1+i321−1+i32
χ15011111-1-111111111-11-11111-1-1-1-1−1−i32−1+i32−1−i32−1+i32−1−i321+i32−1+i321−i321+i321−i32−1+i32−1+i32−1+i32−1+i32−1+i321−i321−i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i321−i32−1+i321−i32−1+i32−1+i32−1+i32−1+i321−i321−i321−i321−i321−1−i321−1−i321-1−1−i321+i32-11+i32−1−i32−1−i32−1−i32−1−i32−1−i321+i321+i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i321+i32−1−i321+i32−1−i32−1−i32−1−i32−1−i321+i321+i321+i321+i32−1+i321−1+i321−1+i321−i321-11−i32-1-1-1-1-1-111-1-1-1-1-1-1-1-11-11-1-1-1-111111+i321−i321+i321−i321+i32−1−i321−i32−1+i32−1−i32−1+i321−i321−i321−i321−i321−i32−1+i32−1+i321−i321−i321−i321−i321−i321−i321−i321−i32−1+i321−i32−1+i321−i321−i321−i321−i32−1+i32−1+i32−1+i32−1+i32-11+i32-11+i32-111+i32−1−i321−1−i321+i321+i321+i321+i321+i32−1−i32−1−i321+i321+i321+i321+i321+i321+i321+i321+i32−1−i321+i32−1−i321+i321+i321+i321+i32−1−i32−1−i32−1−i32−1−i321−i32-11−i32-11−i32−1+i32-11−1+i321
χ151333333333-1-133-1-13-13-1-1-1-1-1-1-1-10000000000−3+3i32−3+3i32−3+3i32−3+3i32−3+3i32−3+3i32−3+3i32−3+3i32−3+3i321−i321−i32−3+3i32−3+3i321−i321−i32−3+3i321−i32−3+3i321−i321−i321−i321−i321−i321−i321−i321−i320000000000−3−3i32−3−3i32−3−3i32−3−3i32−3−3i32−3−3i32−3−3i32−3−3i32−3−3i321+i321+i32−3−3i32−3−3i321+i321+i32−3−3i321+i32−3−3i321+i321+i321+i321+i321+i321+i321+i321+i320000000000-3-3-3-3-3-3-3-3-311-3-311-31-31111111100000000003−3i323−3i323−3i323−3i323−3i323−3i323−3i323−3i323−3i32−1+i32−1+i323−3i323−3i32−1+i32−1+i323−3i32−1+i323−3i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i3200000000003+3i323+3i323+3i323+3i323+3i323+3i323+3i323+3i323+3i32−1−i32−1−i323+3i323+3i32−1−i32−1−i323+3i32−1−i323+3i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i320000000000
χ1523333333-1-133-1-13-1-1-1-1-1-1-1-13-1-1-10000000000−3+3i32−3+3i32−3+3i32−3+3i32−3+3i32−3+3i32−3+3i321−i321−i32−3+3i32−3+3i321−i321−i32−3+3i321−i321−i321−i321−i321−i321−i321−i321−i32−3+3i321−i321−i321−i320000000000−3−3i32−3−3i32−3−3i32−3−3i32−3−3i32−3−3i32−3−3i321+i321+i32−3−3i32−3−3i321+i321+i32−3−3i321+i321+i321+i321+i321+i321+i321+i321+i32−3−3i321+i321+i321+i320000000000-3-3-3-3-3-3-311-3-311-311111111-311100000000003−3i323−3i323−3i323−3i323−3i323−3i323−3i32−1+i32−1+i323−3i323−3i32−1+i32−1+i323−3i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i323−3i32−1+i32−1+i32−1+i3200000000003+3i323+3i323+3i323+3i323+3i323+3i323+3i32−1−i32−1−i323+3i323+3i32−1−i32−1−i323+3i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i323+3i32−1−i32−1−i32−1−i320000000000
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χ205666-2-200-2622-2-2-220-20-22-2200000000000000−3−3i3−3−3i3−3−3i31+i31+i3001+i3−3−3i3−1−i3−1−i31+i31+i31+i3−1−i301+i301+i3−1−i31+i3−1−i300000000000000−3+3i3−3+3i3−3+3i31−i31−i3001−i3−3+3i3−1+i3−1+i31−i31−i31−i3−1+i301−i301−i3−1+i31−i3−1+i300000000000000-6-6-622002-6-2-2222-20202-22-2000000000000003+3i33+3i33+3i3−1−i3−1−i300−1−i33+3i31+i31+i3−1−i3−1−i3−1−i31+i30−1−i30−1−i31+i3−1−i31+i3000000000000003−3i33−3i33−3i3−1+i3−1+i300−1+i33−3i31−i31−i3−1+i3−1+i3−1+i31−i30−1+i30−1+i31−i3−1+i31−i300000000000000
χ206666-2-200-26-2-2-2-22-20202-22-200000000000000−3−3i3−3−3i3−3−3i31+i31+i3001+i3−3−3i31+i31+i31+i31+i3−1−i31+i30−1−i30−1−i31+i3−1−i31+i300000000000000−3+3i3−3+3i3−3+3i31−i31−i3001−i3−3+3i31−i31−i31−i31−i3−1+i31−i30−1+i30−1+i31−i3−1+i31−i300000000000000-6-6-622002-62222-220-20-22-22000000000000003+3i33+3i33+3i3−1−i3−1−i300−1−i33+3i3−1−i3−1−i3−1−i3−1−i31+i3−1−i301+i301+i3−1−i31+i3−1−i3000000000000003−3i33−3i33−3i3−1+i3−1+i300−1+i33−3i3−1+i3−1+i3−1+i3−1+i31−i3−1+i301−i301−i3−1+i31−i3−1+i300000000000000
χ207666-2-200-2-2226-2-2-20202-2-2200000000000000−3−3i3−3−3i3−3−3i31+i31+i3001+i31+i3−1−i3−1−i3−3−3i31+i31+i31+i30−1−i30−1−i31+i31+i3−1−i300000000000000−3+3i3−3+3i3−3+3i31−i31−i3001−i31−i3−1+i3−1+i3−3+3i31−i31−i31−i30−1+i30−1+i31−i31−i3−1+i300000000000000-6-6-6220022-2-2-62220-20-222-2000000000000003+3i33+3i33+3i3−1−i3−1−i300−1−i3−1−i31+i31+i33+3i3−1−i3−1−i3−1−i301+i301+i3−1−i3−1−i31+i3000000000000003−3i33−3i33−3i3−1+i3−1+i300−1+i3−1+i31−i31−i33−3i3−1+i3−1+i3−1+i301−i301−i3−1+i3−1+i31−i300000000000000
χ208666-2-200-2-222-26-2-2020-222-200000000000000−3−3i3−3−3i3−3−3i31+i31+i3001+i31+i3−1−i3−1−i31+i3−3−3i31+i31+i30−1−i301+i3−1−i3−1−i31+i300000000000000−3+3i3−3+3i3−3+3i31−i31−i3001−i31−i3−1+i3−1+i31−i3−3+3i31−i31−i30−1+i301−i3−1+i3−1+i31−i300000000000000-6-6-6220022-2-22-6220-202-2-22000000000000003+3i33+3i33+3i3−1−i3−1−i300−1−i3−1−i31+i31+i3−1−i33+3i3−1−i3−1−i301+i30−1−i31+i31+i3−1−i3000000000000003−3i33−3i33−3i3−1+i3−1+i300−1+i3−1+i31−i31−i3−1+i33−3i3−1+i3−1+i301−i30−1+i31−i31−i3−1+i300000000000000
χ209666-2-200-2-2-2-26-2220-20-222-200000000000000−3−3i3−3−3i3−3−3i31+i31+i3001+i31+i31+i31+i3−3−3i31+i3−1−i3−1−i301+i301+i3−1−i3−1−i31+i300000000000000−3+3i3−3+3i3−3+3i31−i31−i3001−i31−i31−i31−i3−3+3i31−i3−1+i3−1+i301−i301−i3−1+i3−1+i31−i300000000000000-6-6-622002222-62-2-20202-2-22000000000000003+3i33+3i33+3i3−1−i3−1−i300−1−i3−1−i3−1−i3−1−i33+3i3−1−i31+i31+i30−1−i30−1−i31+i31+i3−1−i3000000000000003−3i33−3i33−3i3−1+i3−1+i300−1+i3−1+i3−1+i3−1+i33−3i3−1+i31−i31−i30−1+i30−1+i31−i31−i3−1+i300000000000000
χ210666-2-200-2-2-2-2-26220-202-2-2200000000000000−3−3i3−3−3i3−3−3i31+i31+i3001+i31+i31+i31+i31+i3−3−3i3−1−i3−1−i301+i30−1−i31+i31+i3−1−i300000000000000−3+3i3−3+3i3−3+3i31−i31−i3001−i31−i31−i31−i31−i3−3+3i3−1+i3−1+i301−i30−1+i31−i31−i3−1+i300000000000000-6-6-6220022222-6-2-2020-222-2000000000000003+3i33+3i33+3i3−1−i3−1−i300−1−i3−1−i3−1−i3−1−i3−1−i33+3i31+i31+i30−1−i301+i3−1−i3−1−i31+i3000000000000003−3i33−3i33−3i3−1+i3−1+i300−1+i3−1+i3−1+i3−1+i3−1+i33−3i31−i31−i30−1+i301−i3−1+i3−1+i31−i300000000000000
χ2118-800000004-400000000000000022-2-2000000−4−4i34+4i30000000−2−2i32+2i3000000000000000−1−i3−1−i31+i31+i3000000−4+4i34−4i30000000−2+2i32−2i3000000000000000−1+i3−1+i31−i31−i3000000-880000000-44000000000000000-2-2220000004+4i3−4−4i300000002+2i3−2−2i30000000000000001+i31+i3−1−i3−1−i30000004−4i3−4+4i300000002−2i3−2+2i30000000000000001−i31−i3−1+i3−1+i3000000
χ2128-800000004-4000000000000000−1+i3−1−i31−i31+i3000000−4−4i34+4i30000000−2−2i32+2i30000000000000002−1+i3-21−i3000000−4+4i34−4i30000000−2+2i32−2i3000000000000000−1−i321+i3-2000000-880000000-440000000000000001−i31+i3−1+i3−1−i30000004+4i3−4−4i300000002+2i3−2−2i3000000000000000-21−i32−1+i30000004−4i3−4+4i300000002−2i3−2+2i30000000000000001+i3-2−1−i32000000
χ2138-800000004-4000000000000000−1−i3−1+i31+i31−i3000000−4−4i34+4i30000000−2−2i32+2i3000000000000000−1+i321−i3-2000000−4+4i34−4i30000000−2+2i32−2i30000000000000002−1−i3-21+i3000000-880000000-440000000000000001+i31−i3−1−i3−1+i30000004+4i3−4−4i300000002+2i3−2−2i30000000000000001−i3-2−1+i320000004−4i3−4+4i300000002−2i3−2+2i3000000000000000-21+i32−1−i3000000
χ2141212-12-44000000000040-4000000000000000000−6−6i3−6−6i36+6i32+2i3−2−2i30000000000−2−2i302+2i3000000000000000000−6+6i3−6+6i36−6i32−2i3−2+2i30000000000−2+2i302−2i3000000000000000000-12-12124-40000000000-4040000000000000000006+6i36+6i3−6−6i3−2−2i32+2i300000000002+2i30−2−2i30000000000000000006−6i36−6i3−6+6i3−2+2i32−2i300000000002−2i30−2+2i3000000000000000000
χ2151212-12-440000000000-404000000000000000000−6−6i3−6−6i36+6i32+2i3−2−2i300000000002+2i30−2−2i3000000000000000000−6+6i3−6+6i36−6i32−2i3−2+2i300000000002−2i30−2+2i3000000000000000000-12-12124-4000000000040-40000000000000000006+6i36+6i3−6−6i3−2−2i32+2i30000000000−2−2i302+2i30000000000000000006−6i36−6i3−6+6i3−2+2i32−2i30000000000−2+2i302−2i3000000000000000000
χ21624-240000000-440000000000000000000000000−12−12i312+12i300000002+2i3−2−2i30000000000000000000000000−12+12i312−12i300000002−2i3−2+2i30000000000000000000000000-242400000004-4000000000000000000000000012+12i3−12−12i30000000−2−2i32+2i3000000000000000000000000012−12i3−12+12i30000000−2+2i32−2i30000000000000000000000000

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