Finite Group Databasebeta

← Group #11792583

Character table — Group #11792583

Order 1152.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96C97C98C99C100C101C102C103C104C105C106C107C108C109C110C111C112C113C114C115C116C117C118C119C120C121C122C123C124C125C126C127C128C129C130C131C132C133C134C135C136C137C138C139C140C141C142C143C144C145C146C147C148C149C150C151C152C153C154C155C156C157C158C159C160C161C162C163C164C165C166C167C168C169C170C171C172C173C174C175C176C177C178C179C180
size111111112222222222224444444444444444888888888888121212121212121224242424111111112222222222224444444444444444888888888888121212121212121224242424111111112222222222224444444444444444888888888888121212121212121224242424
order12222222344446666666444412121212121212121212121222446666121212128888888844443666666631212121266666661212121212121212121212121212121266121266661212121224242424242424241212121236666666312121212666666612121212121212121212121212121212661212666612121212242424242424242412121212
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1
χ3111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1
χ4111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111
χ511111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1111111-1-11111-1-1-1-11111-1-1-1-111-1-111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1111111-1-11111-1-1-1-11111-1-1-1-111-1-111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1111111-1-11111-1-1-1-11111-1-1-1-111-1-1
χ611111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1111111-1-11111-1-1-1-1-1-1-1-11111-1-11111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1111111-1-11111-1-1-1-1-1-1-1-11111-1-11111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1111111-1-11111-1-1-1-1-1-1-1-11111-1-111
χ711111111111111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-111-1-1-1-111111111-1-1-1-1-1-11111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-111-1-1-1-111111111-1-1-1-1-1-11111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-111-1-1-1-111111111-1-1-1-1-1-111
χ811111111111111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-111-1-1-1-11111-1-1-1-1111111-1-111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-111-1-1-1-11111-1-1-1-1111111-1-111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-111-1-1-1-11111-1-1-1-1111111-1-1
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χ1592-2-2-222-22-12-2-221111-1-1-10000−i3i3−i3i3−i3i3−i3i3-111-1002-2−i3i3i3−i3-11-11000000000000−1−i31+i31+i31+i3−1−i3−1−i31+i3−1−i31+i32−1−i31+i31+i3−1−i3−1−i32−1−i32−1−i32−1−i321+i321+i321+i320000−3+i323−i32−3+i323−i32−3+i323−i32−3+i323−i321+i32−1−i32−1−i321+i3200−1−i31+i3−3+i323−i323−i32−3+i321+i32−1−i321+i32−1−i32000000000000−1+i31−i31−i31−i3−1+i3−1+i31−i3−1+i31−i32−1+i31−i31−i3−1+i3−1+i32−1+i32−1+i32−1+i321−i321−i321−i3200003+i32−3−i323+i32−3−i323+i32−3−i323+i32−3−i321−i32−1+i32−1+i321−i3200−1+i31−i33+i32−3−i32−3−i323+i321−i32−1+i321−i32−1+i32000000000000
χ1602-2-2-222-22-12-2-221111-1-1-10000−i3i3−i3i3−i3i3−i3i3-111-100-22i3−i3−i3i31-11-1000000000000−1−i31+i31+i31+i3−1−i3−1−i31+i3−1−i31+i32−1−i31+i31+i3−1−i3−1−i32−1−i32−1−i32−1−i321+i321+i321+i320000−3+i323−i32−3+i323−i32−3+i323−i32−3+i323−i321+i32−1−i32−1−i321+i32001+i3−1−i33−i32−3+i32−3+i323−i32−1−i321+i32−1−i321+i32000000000000−1+i31−i31−i31−i3−1+i3−1+i31−i3−1+i31−i32−1+i31−i31−i3−1+i3−1+i32−1+i32−1+i32−1+i321−i321−i321−i3200003+i32−3−i323+i32−3−i323+i32−3−i323+i32−3−i321−i32−1+i32−1+i321−i32001−i3−1+i3−3−i323+i323+i32−3−i32−1+i321−i32−1+i321−i32000000000000
χ1612-2-2-222-22-12-2-221111-1-1-10000i3−i3i3−i3i3−i3i3−i3-111-1002-2i3−i3−i3i3-11-11000000000000−1−i31+i31+i31+i3−1−i3−1−i31+i3−1−i31+i32−1−i31+i31+i3−1−i3−1−i32−1−i32−1−i32−1−i321+i321+i321+i3200003−i32−3+i323−i32−3+i323−i32−3+i323−i32−3+i321+i32−1−i32−1−i321+i3200−1−i31+i33−i32−3+i32−3+i323−i321+i32−1−i321+i32−1−i32000000000000−1+i31−i31−i31−i3−1+i3−1+i31−i3−1+i31−i32−1+i31−i31−i3−1+i3−1+i32−1+i32−1+i32−1+i321−i321−i321−i320000−3−i323+i32−3−i323+i32−3−i323+i32−3−i323+i321−i32−1+i32−1+i321−i3200−1+i31−i3−3−i323+i323+i32−3−i321−i32−1+i321−i32−1+i32000000000000
χ1622-2-2-222-22-12-2-221111-1-1-10000i3−i3i3−i3i3−i3i3−i3-111-100-22−i3i3i3−i31-11-1000000000000−1−i31+i31+i31+i3−1−i3−1−i31+i3−1−i31+i32−1−i31+i31+i3−1−i3−1−i32−1−i32−1−i32−1−i321+i321+i321+i3200003−i32−3+i323−i32−3+i323−i32−3+i323−i32−3+i321+i32−1−i32−1−i321+i32001+i3−1−i3−3+i323−i323−i32−3+i32−1−i321+i32−1−i321+i32000000000000−1+i31−i31−i31−i3−1+i3−1+i31−i3−1+i31−i32−1+i31−i31−i3−1+i3−1+i32−1+i32−1+i32−1+i321−i321−i321−i320000−3−i323+i32−3−i323+i32−3−i323+i32−3−i323+i321−i32−1+i32−1+i321−i32001−i3−1+i33+i32−3−i32−3−i323+i32−1+i321−i32−1+i321−i32000000000000
χ1632-2-2-222-22-1-222-21111-1-1-10000−i3i3−i3i3i3−i3i3−i31-1-112-200-11-11−i3i3i3−i3000000000000−1−i31+i31+i31+i3−1−i3−1−i31+i3−1−i31+i321+i3−1−i3−1−i31+i3−1−i32−1−i32−1−i32−1−i321+i321+i321+i320000−3+i323−i32−3+i323−i323−i32−3+i323−i32−3+i32−1−i321+i321+i32−1−i32−1−i31+i3001+i32−1−i321+i32−1−i32−3+i323−i323−i32−3+i32000000000000−1+i31−i31−i31−i3−1+i3−1+i31−i3−1+i31−i321−i3−1+i3−1+i31−i3−1+i32−1+i32−1+i32−1+i321−i321−i321−i3200003+i32−3−i323+i32−3−i32−3−i323+i32−3−i323+i32−1+i321−i321−i32−1+i32−1+i31−i3001−i32−1+i321−i32−1+i323+i32−3−i32−3−i323+i32000000000000
χ1642-2-2-222-22-1-222-21111-1-1-10000−i3i3−i3i3i3−i3i3−i31-1-11-22001-11-1i3−i3−i3i3000000000000−1−i31+i31+i31+i3−1−i3−1−i31+i3−1−i31+i321+i3−1−i3−1−i31+i3−1−i32−1−i32−1−i32−1−i321+i321+i321+i320000−3+i323−i32−3+i323−i323−i32−3+i323−i32−3+i32−1−i321+i321+i32−1−i321+i3−1−i300−1−i321+i32−1−i321+i323−i32−3+i32−3+i323−i32000000000000−1+i31−i31−i31−i3−1+i3−1+i31−i3−1+i31−i321−i3−1+i3−1+i31−i3−1+i32−1+i32−1+i32−1+i321−i321−i321−i3200003+i32−3−i323+i32−3−i32−3−i323+i32−3−i323+i32−1+i321−i321−i32−1+i321−i3−1+i300−1+i321−i32−1+i321−i32−3−i323+i323+i32−3−i32000000000000
χ1652-2-2-222-22-1-222-21111-1-1-10000i3−i3i3−i3−i3i3−i3i31-1-112-200-11-11i3−i3−i3i3000000000000−1−i31+i31+i31+i3−1−i3−1−i31+i3−1−i31+i321+i3−1−i3−1−i31+i3−1−i32−1−i32−1−i32−1−i321+i321+i321+i3200003−i32−3+i323−i32−3+i32−3+i323−i32−3+i323−i32−1−i321+i321+i32−1−i32−1−i31+i3001+i32−1−i321+i32−1−i323−i32−3+i32−3+i323−i32000000000000−1+i31−i31−i31−i3−1+i3−1+i31−i3−1+i31−i321−i3−1+i3−1+i31−i3−1+i32−1+i32−1+i32−1+i321−i321−i321−i320000−3−i323+i32−3−i323+i323+i32−3−i323+i32−3−i32−1+i321−i321−i32−1+i32−1+i31−i3001−i32−1+i321−i32−1+i32−3−i323+i323+i32−3−i32000000000000
χ1662-2-2-222-22-1-222-21111-1-1-10000i3−i3i3−i3−i3i3−i3i31-1-11-22001-11-1−i3i3i3−i3000000000000−1−i31+i31+i31+i3−1−i3−1−i31+i3−1−i31+i321+i3−1−i3−1−i31+i3−1−i32−1−i32−1−i32−1−i321+i321+i321+i3200003−i32−3+i323−i32−3+i32−3+i323−i32−3+i323−i32−1−i321+i321+i32−1−i321+i3−1−i300−1−i321+i32−1−i321+i32−3+i323−i323−i32−3+i32000000000000−1+i31−i31−i31−i3−1+i3−1+i31−i3−1+i31−i321−i3−1+i3−1+i31−i3−1+i32−1+i32−1+i32−1+i321−i321−i321−i320000−3−i323+i32−3−i323+i323+i32−3−i323+i32−3−i32−1+i321−i321−i32−1+i321−i3−1+i300−1+i321−i32−1+i321−i323+i32−3−i32−3−i323+i32000000000000
χ167444-4-4-4-44-244-4-4-2-22222-2000000000000-2-222000000000000000000000000−2−2i3−2−2i3−2−2i32+2i32+2i32+2i32+2i3−2−2i31+i3−2−2i3−2−2i32+2i32+2i31+i31+i3−1−i3−1−i3−1−i3−1−i31+i30000000000001+i31+i3−1−i3−1−i3000000000000000000000000−2+2i3−2+2i3−2+2i32−2i32−2i32−2i32−2i3−2+2i31−i3−2+2i3−2+2i32−2i32−2i31−i31−i3−1+i3−1+i3−1+i3−1+i31−i30000000000001−i31−i3−1+i3−1+i3000000000000000000000000
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χ17144-44-44-4-4-20000-222-22-220000−232323−2300000000000000000000000000000000−2−2i3−2−2i32+2i3−2−2i32+2i3−2−2i32+2i32+2i31+i300001+i3−1−i3−1−i31+i3−1−i31+i3−1−i30000−4ζ14−2ζ224ζ14+2ζ224ζ14+2ζ22−4ζ14−2ζ2200000000000000000000000000000000−2+2i3−2+2i32−2i3−2+2i32−2i3−2+2i32−2i32−2i31−i300001−i3−1+i3−1+i31−i3−1+i31−i3−1+i300002ζ14+4ζ22−2ζ14−4ζ22−2ζ14−4ζ222ζ14+4ζ2200000000000000000000000000000000
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χ1744-4444-4-4-440000-44-444-4-40000000000000000000000000000000000000000−2−2i32+2i3−2−2i3−2−2i3−2−2i32+2i32+2i32+2i3−2−2i300002+2i3−2−2i32+2i3−2−2i3−2−2i32+2i32+2i30000000000000000000000000000000000000000−2+2i32−2i3−2+2i3−2+2i3−2+2i32−2i32−2i32−2i3−2+2i300002−2i3−2+2i32−2i3−2+2i3−2+2i32−2i32−2i30000000000000000000000000000000000000000
χ1754-4444-4-4-4-200002-22-2-2220000000023−23−23230000000000000000000000000000−2−2i32+2i3−2−2i3−2−2i3−2−2i32+2i32+2i32+2i31+i30000−1−i31+i3−1−i31+i31+i3−1−i3−1−i3000000004ζ14+2ζ22−4ζ14−2ζ22−4ζ14−2ζ224ζ14+2ζ220000000000000000000000000000−2+2i32−2i3−2+2i3−2+2i3−2+2i32−2i32−2i32−2i31−i30000−1+i31−i3−1+i31−i31−i3−1+i3−1+i300000000−2ζ14−4ζ222ζ14+4ζ222ζ14+4ζ22−2ζ14−4ζ220000000000000000000000000000
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χ1774-44-4-444-4-200002-2-222-224i−4i00−2i−2i2i2i00000000000000000000000000000000−2−2i32+2i3−2−2i32+2i32+2i3−2−2i3−2−2i32+2i31+i30000−1−i31+i31+i3−1−i3−1−i31+i3−1−i34ζ22−4ζ2200−2ζ22−2ζ222ζ222ζ2200000000000000000000000000000000−2+2i32−2i3−2+2i32−2i32−2i3−2+2i3−2+2i32−2i31−i30000−1+i31−i31−i3−1+i3−1+i31−i3−1+i34ζ14−4ζ1400−2ζ14−2ζ142ζ142ζ1400000000000000000000000000000000
χ1784-44-4-444-4-200002-2-222-22−4i4i002i2i−2i−2i00000000000000000000000000000000−2−2i32+2i3−2−2i32+2i32+2i3−2−2i3−2−2i32+2i31+i30000−1−i31+i31+i3−1−i3−1−i31+i3−1−i3−4ζ224ζ22002ζ222ζ22−2ζ22−2ζ2200000000000000000000000000000000−2+2i32−2i3−2+2i32−2i32−2i3−2+2i3−2+2i32−2i31−i30000−1+i31−i31−i3−1+i3−1+i31−i3−1+i3−4ζ144ζ14002ζ142ζ14−2ζ14−2ζ1400000000000000000000000000000000
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χ1804-4-44-4-444-2-44-4422-2-222-20000000000002-22-2000000000000000000000000−2−2i32+2i32+2i3−2−2i32+2i32+2i3−2−2i3−2−2i31+i32+2i3−2−2i32+2i3−2−2i3−1−i3−1−i31+i31+i3−1−i3−1−i31+i3000000000000−1−i31+i3−1−i31+i3000000000000000000000000−2+2i32−2i32−2i3−2+2i32−2i32−2i3−2+2i3−2+2i31−i32−2i3−2+2i32−2i3−2+2i3−1+i3−1+i31−i31−i3−1+i3−1+i31−i3000000000000−1+i31−i3−1+i31−i3000000000000000000000000

Here ζ is a primitive root of unity of order 24 (ζ24 = 1); i = ζ6.