Finite Group Databasebeta

← Group #162452

Character table — Group #162452

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86
size1111111122222222222222224444444444444444444444888888888888888888888888888888881616161616161616
order12222222444444444444444444444444444444888888884444888888888888888888888888888822444444
χ111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111111111111111-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ311111111111111111111111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-1
χ411111111111111111111111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111
χ51111111111111111111111111111-1-1-1-1-1-111-1-111111111-1-1-1-111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-11-11-11-11-1
χ61111111111111111111111111111-1-1-1-1-1-111-1-111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-111111111-11-11-11-11
χ71111111111111111111111111111-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1111111111111-1-1-1-1-1-1-1-1-11-11-11-11
χ81111111111111111111111111111-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1111111111-11-11-11-1
χ9111111111111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1iiii−i−i−i−i11-1-1ii−i−iii−i−iiiii−i−i−i−iii−i−iiiii−i−i−i−i1-111-1-1-11
χ10111111111111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1iiii−i−i−i−i11-1-1−i−iiiii−i−iiiii−i−i−i−i−i−iii−i−i−i−iiiii-11-1-1111-1
χ11111111111111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1−i−i−i−iiiii11-1-1ii−i−i−i−iii−i−i−i−iiiiiii−i−iiiii−i−i−i−i-11-1-1111-1
χ12111111111111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1−i−i−i−iiiii11-1-1−i−iii−i−iii−i−i−i−iiiii−i−iii−i−i−i−iiiii1-111-1-1-11
χ13111111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-111-1-111iiii−i−i−i−i-1-111ii−i−iii−i−i−i−i−i−iiiiiii−i−i−i−i−i−iiiii111-1-11-1-1
χ14111111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-111-1-111iiii−i−i−i−i-1-111−i−iiiii−i−i−i−i−i−iiiii−i−iiiiiii−i−i−i−i-1-1-111-111
χ15111111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-111-1-111−i−i−i−iiiii-1-111ii−i−i−i−iiiiiii−i−i−i−iii−i−i−i−i−i−iiiii-1-1-111-111
χ16111111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-111-1-111−i−i−i−iiiii-1-111−i−iii−i−iiiiiii−i−i−i−i−i−iiiiiii−i−i−i−i111-1-11-1-1
χ1711111111-1-1-1-11111-1-1-1-1-1-1-1-111-1-111-1-11111-1-1iiii−i−i−i−i-11-11ii−i−i−i−iiiii−i−iii−i−i−i−iiiii−i−iii−i−i-1-11-1-1111
χ1811111111-1-1-1-11111-1-1-1-1-1-1-1-111-1-111-1-11111-1-1iiii−i−i−i−i-11-11−i−iii−i−iiiii−i−iii−i−iii−i−i−i−iii−i−iii11-111-1-1-1
χ1911111111-1-1-1-11111-1-1-1-1-1-1-1-111-1-111-1-11111-1-1−i−i−i−iiiii-11-11ii−i−iii−i−i−i−iii−i−iii−i−iiiii−i−iii−i−i11-111-1-1-1
χ2011111111-1-1-1-11111-1-1-1-1-1-1-1-111-1-111-1-11111-1-1−i−i−i−iiiii-11-11−i−iiiii−i−i−i−iii−i−iiiii−i−i−i−iii−i−iii-1-11-1-1111
χ2111111111-1-1-1-11111-1-1-1-1-1-1-1-111-1-1-1-111-1-11111iiii−i−i−i−i1-11-1ii−i−i−i−iii−i−iii−i−iii−i−iii−i−iii−i−iii-1111-1-11-1
χ2211111111-1-1-1-11111-1-1-1-1-1-1-1-111-1-1-1-111-1-11111iiii−i−i−i−i1-11-1−i−iii−i−iii−i−iii−i−iiiii−i−iii−i−iii−i−i1-1-1-111-11
χ2311111111-1-1-1-11111-1-1-1-1-1-1-1-111-1-1-1-111-1-11111−i−i−i−iiiii1-11-1ii−i−iii−i−iii−i−iii−i−i−i−iii−i−iii−i−iii1-1-1-111-11
χ2411111111-1-1-1-11111-1-1-1-1-1-1-1-111-1-1-1-111-1-11111−i−i−i−iiiii1-11-1−i−iiiii−i−iii−i−iii−i−iii−i−iii−i−iii−i−i-1111-1-11-1
χ2511111111-1-1-1-1-1-1-1-11111111111-1-111-1-1-1-1-1-11111111111-111-11111-1-1-1-111-1-1-1-111-1-1-1-111-1-1-1-111-111-11-1-11
χ2611111111-1-1-1-1-1-1-1-11111111111-1-111-1-1-1-1-1-11111111111-111-1-1-1-1-1-1-1-1-111-1-1-1-1111111-1-11111-1-11-1-11-111-1
χ2711111111-1-1-1-1-1-1-1-11111111111-1-111-1-1-1-1-1-111-1-1-1-1-1-1-1-1-111-111111111-1-11111-1-1-1-1-1-111-1-1-1-1111-1-11-111-1
χ2811111111-1-1-1-1-1-1-1-11111111111-1-111-1-1-1-1-1-111-1-1-1-1-1-1-1-1-111-1-1-1-1-11111-1-11111-1-11111-1-11111-1-1-111-11-1-11
χ2911111111-1-1-1-1-1-1-1-11111111111-1-1-1-11111-1-1-1-1111111111-1-111111-1-1-1-1-1-11111-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1
χ3011111111-1-1-1-1-1-1-1-11111111111-1-1-1-11111-1-1-1-1111111111-1-11-1-1-1-1-1-1-1-1-1-11111-1-1111111-1-1-1-11111-1-1-1-111
χ3111111111-1-1-1-1-1-1-1-11111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-11-1-111111111111-1-1-1-111-1-1-1-1-1-11111-1-111-1-1-1-111
χ3211111111-1-1-1-1-1-1-1-11111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-11-1-11-1-1-1-1111111-1-1-1-111111111-1-1-1-111-1-11111-1-1
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χ342222222222222222-2-22222-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2000000002222000000000000000000000000000000000000
χ35222222222222-2-2-2-222-2-2-2-222-2-2-2-22222-2-222-2-200000000-2-222000000000000000000000000000000000000
χ36222222222222-2-2-2-222-2-2-2-222-2-2-2-2-2-2-2-22222220000000022-2-2000000000000000000000000000000000000
χ3722222222-2-2-2-2222222-2-2-2-222-2-22222-2-222-2-2-2-2000000002-22-2000000000000000000000000000000000000
χ3822222222-2-2-2-2222222-2-2-2-222-2-222-2-222-2-2-2-22200000000-22-22000000000000000000000000000000000000
χ3922222222-2-2-2-2-2-2-2-2-2-22222-2-2-2-22222-2-2-2-22222000000002-2-22000000000000000000000000000000000000
χ4022222222-2-2-2-2-2-2-2-2-2-22222-2-2-2-222-2-2222222-2-200000000-222-2000000000000000000000000000000000000
χ412-222-22-2-222-2-22i2i−2i−2i2i−2i2i2i−2i−2i2i−2i2-22-20000002i−2i00000000000000000000002ζ−2ζ2ζ−2ζ2ζ3−2ζ32ζ3−2ζ300000000000000000000
χ422-222-22-2-222-2-22i2i−2i−2i2i−2i2i2i−2i−2i2i−2i2-22-20000002i−2i0000000000000000000000−2ζ2ζ−2ζ2ζ−2ζ32ζ3−2ζ32ζ300000000000000000000
χ432-222-22-2-222-2-22i2i−2i−2i−2i2i2i2i−2i−2i−2i2i-22-22000000−2i2i002ζ2ζ−2ζ−2ζ2ζ32ζ3−2ζ3−2ζ3000000002ζ−2ζ2ζ3−2ζ30000000000000000000000000000
χ442-222-22-2-222-2-22i2i−2i−2i−2i2i2i2i−2i−2i−2i2i-22-22000000−2i2i00−2ζ−2ζ2ζ2ζ−2ζ3−2ζ32ζ32ζ300000000−2ζ2ζ−2ζ32ζ30000000000000000000000000000
χ452-222-22-2-222-2-2−2i−2i2i2i2i−2i−2i−2i2i2i2i−2i-22-220000002i−2i002ζ32ζ3−2ζ3−2ζ32ζ2ζ−2ζ−2ζ000000002ζ3−2ζ32ζ−2ζ0000000000000000000000000000
χ462-222-22-2-222-2-2−2i−2i2i2i2i−2i−2i−2i2i2i2i−2i-22-220000002i−2i00−2ζ3−2ζ32ζ32ζ3−2ζ−2ζ2ζ2ζ00000000−2ζ32ζ3−2ζ2ζ0000000000000000000000000000
χ472-222-22-2-222-2-2−2i−2i2i2i−2i2i−2i−2i2i2i−2i2i2-22-2000000−2i2i00000000000000000000002ζ3−2ζ32ζ3−2ζ32ζ−2ζ2ζ−2ζ00000000000000000000
χ482-222-22-2-222-2-2−2i−2i2i2i−2i2i−2i−2i2i2i−2i2i2-22-2000000−2i2i0000000000000000000000−2ζ32ζ3−2ζ32ζ3−2ζ2ζ−2ζ2ζ00000000000000000000
χ492-222-22-2-2-2-2222i2i−2i−2i2i−2i−2i−2i2i2i2i−2i-222-2000000−2i2i002ζ32ζ3−2ζ3−2ζ32ζ2ζ−2ζ−2ζ00000000−2ζ32ζ3−2ζ2ζ0000000000000000000000000000
χ502-222-22-2-2-2-2222i2i−2i−2i2i−2i−2i−2i2i2i2i−2i-222-2000000−2i2i00−2ζ3−2ζ32ζ32ζ3−2ζ−2ζ2ζ2ζ000000002ζ3−2ζ32ζ−2ζ0000000000000000000000000000
χ512-222-22-2-2-2-2222i2i−2i−2i−2i2i−2i−2i2i2i−2i2i2-2-220000002i−2i00000000000000000000002ζ3−2ζ3−2ζ32ζ3−2ζ2ζ2ζ−2ζ00000000000000000000
χ522-222-22-2-2-2-2222i2i−2i−2i−2i2i−2i−2i2i2i−2i2i2-2-220000002i−2i0000000000000000000000−2ζ32ζ32ζ3−2ζ32ζ−2ζ−2ζ2ζ00000000000000000000
χ532-222-22-2-2-2-222−2i−2i2i2i2i−2i2i2i−2i−2i2i−2i2-2-22000000−2i2i00000000000000000000002ζ−2ζ−2ζ2ζ−2ζ32ζ32ζ3−2ζ300000000000000000000
χ542-222-22-2-2-2-222−2i−2i2i2i2i−2i2i2i−2i−2i2i−2i2-2-22000000−2i2i0000000000000000000000−2ζ2ζ2ζ−2ζ2ζ3−2ζ3−2ζ32ζ300000000000000000000
χ552-222-22-2-2-2-222−2i−2i2i2i−2i2i2i2i−2i−2i−2i2i-222-20000002i−2i002ζ2ζ−2ζ−2ζ2ζ32ζ3−2ζ3−2ζ300000000−2ζ2ζ−2ζ32ζ30000000000000000000000000000
χ562-222-22-2-2-2-222−2i−2i2i2i−2i2i2i2i−2i−2i−2i2i-222-20000002i−2i00−2ζ−2ζ2ζ2ζ−2ζ3−2ζ32ζ32ζ3000000002ζ−2ζ2ζ3−2ζ30000000000000000000000000000
χ572-22-22-22-22i−2i2i−2i2-22-2002i−2i2i−2i0000002-22i−2i2-2002i−2i0000000000001−i−1+i1+i−1−i0000000000001+i−1−i1−i−1+i1−i−1+i1+i−1−i1−i−1+i1+i−1−i00000000
χ582-22-22-22-22i−2i2i−2i2-22-2002i−2i2i−2i0000002-22i−2i2-2002i−2i000000000000−1+i1−i−1−i1+i000000000000−1−i1+i−1+i1−i−1+i1−i−1−i1+i−1+i1−i−1−i1+i00000000
χ592-22-22-22-22i−2i2i−2i2-22-2002i−2i2i−2i000000-22−2i2i-2200−2i2i0000000000001−i−1+i1+i−1−i0000000000001+i−1−i1−i−1+i−1+i1−i−1−i1+i−1+i1−i−1−i1+i00000000
χ602-22-22-22-22i−2i2i−2i2-22-2002i−2i2i−2i000000-22−2i2i-2200−2i2i000000000000−1+i1−i−1−i1+i000000000000−1−i1+i−1+i1−i1−i−1+i1+i−1−i1−i−1+i1+i−1−i00000000
χ612-22-22-22-22i−2i2i−2i-22-2200−2i2i−2i2i0000002-22i−2i-2200−2i2i0000000000001+i−1−i1−i−1+i000000000000−1+i1−i−1−i1+i1+i−1−i−1+i1−i−1−i1+i1−i−1+i00000000
χ622-22-22-22-22i−2i2i−2i-22-2200−2i2i−2i2i0000002-22i−2i-2200−2i2i000000000000−1−i1+i−1+i1−i0000000000001−i−1+i1+i−1−i−1−i1+i1−i−1+i1+i−1−i−1+i1−i00000000
χ632-22-22-22-22i−2i2i−2i-22-2200−2i2i−2i2i000000-22−2i2i2-2002i−2i0000000000001+i−1−i1−i−1+i000000000000−1+i1−i−1−i1+i−1−i1+i1−i−1+i1+i−1−i−1+i1−i00000000
χ642-22-22-22-22i−2i2i−2i-22-2200−2i2i−2i2i000000-22−2i2i2-2002i−2i000000000000−1−i1+i−1+i1−i0000000000001−i−1+i1+i−1−i1+i−1−i−1+i1−i−1−i1+i1−i−1+i00000000
χ652-22-22-22-2−2i2i−2i2i2-22-200−2i2i−2i2i0000002-2−2i2i2-200−2i2i0000000000001+i−1−i1−i−1+i0000000000001−i−1+i1+i−1−i1+i−1−i1−i−1+i1+i−1−i1−i−1+i00000000
χ662-22-22-22-2−2i2i−2i2i2-22-200−2i2i−2i2i0000002-2−2i2i2-200−2i2i000000000000−1−i1+i−1+i1−i000000000000−1+i1−i−1−i1+i−1−i1+i−1+i1−i−1−i1+i−1+i1−i00000000
χ672-22-22-22-2−2i2i−2i2i2-22-200−2i2i−2i2i000000-222i−2i-22002i−2i0000000000001+i−1−i1−i−1+i0000000000001−i−1+i1+i−1−i−1−i1+i−1+i1−i−1−i1+i−1+i1−i00000000
χ682-22-22-22-2−2i2i−2i2i2-22-200−2i2i−2i2i000000-222i−2i-22002i−2i000000000000−1−i1+i−1+i1−i000000000000−1+i1−i−1−i1+i1+i−1−i1−i−1+i1+i−1−i1−i−1+i00000000
χ692-22-22-22-2−2i2i−2i2i-22-22002i−2i2i−2i0000002-2−2i2i-22002i−2i0000000000001−i−1+i1+i−1−i000000000000−1−i1+i−1+i1−i1−i−1+i−1−i1+i−1+i1−i1+i−1−i00000000
χ702-22-22-22-2−2i2i−2i2i-22-22002i−2i2i−2i0000002-2−2i2i-22002i−2i000000000000−1+i1−i−1−i1+i0000000000001+i−1−i1−i−1+i−1+i1−i1+i−1−i1−i−1+i−1−i1+i00000000
χ712-22-22-22-2−2i2i−2i2i-22-22002i−2i2i−2i000000-222i−2i2-200−2i2i0000000000001−i−1+i1+i−1−i000000000000−1−i1+i−1+i1−i−1+i1−i1+i−1−i1−i−1+i−1−i1+i00000000
χ722-22-22-22-2−2i2i−2i2i-22-22002i−2i2i−2i000000-222i−2i2-200−2i2i000000000000−1+i1−i−1−i1+i0000000000001+i−1−i1−i−1+i1−i−1+i−1−i1+i−1+i1−i1+i−1−i00000000
χ73444-4-4-4-444i−4i−4i4i4i−4i−4i4i00-444-40000000000000000000000000000000000000000000000000000000000000000
χ74444-4-4-4-444i−4i−4i4i−4i4i4i−4i004-4-440000000000000000000000000000000000000000000000000000000000000000
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χ76444-4-4-4-44−4i4i4i−4i−4i4i4i−4i00-444-40000000000000000000000000000000000000000000000000000000000000000
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χ7944-4-4-444-400000000−4i4i00004i−4i000000000000002−2i−2+2i2−2i−2+2i2+2i−2−2i2+2i−2−2i0000000000000000000000000000000000000000
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χ814-4-4-444-4400000000440000-4-4000000000000002i2−2i2−2i22i22i2−2i2−2i22i20000000000000000000000000000000000000000
χ824-4-4-444-4400000000440000-4-400000000000000−2i22i22i2−2i2−2i22i22i2−2i20000000000000000000000000000000000000000
χ834-4-4-444-4400000000-4-40000440000000000000022−22−2222−222222−220000000000000000000000000000000000000000
χ844-4-4-444-4400000000-4-400004400000000000000−222222−2222−22−22220000000000000000000000000000000000000000
χ8588-888-8-8-8000000000000000000000000000000000000000000000000000000000000000000000000000000
χ868-8-88-8-888000000000000000000000000000000000000000000000000000000000000000000000000000000

Here ζ is a primitive root of unity of order 8 (ζ8 = 1); i = ζ2.