Finite Group Databasebeta

← Group #199373

Character table — Group #199373

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92
size111122222222222222222244444444444444444444444444444444444444444444444444444416161616161616161616161616161616
order12222222444444444444442222244444444444444444888888888888888888888888888888884444444488888888
χ111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ311111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1-1-1
χ411111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-11111
χ511111111111111111111111-1-1-1-111-1-1-1-1111-1-1-1-1-1-1-1-11111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-11111
χ611111111111111111111111-1-1-1-111-1-1-1-1111-1-1-1-1-1-1-1-11111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1
χ711111111111111111111111-1-1-1-111-1-1-1-1111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111111111111111-1-1-1-1-1-1-1-1
χ811111111111111111111111-1-1-1-111-1-1-1-1111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111111111-1-1-1-1-1-1-1-111111111
χ9111111-1-111-1-111-1-111-1-1-1-1-111111-1111111-1-1-1-1-1-1-1-1-1iiii−i−i−i−iiiii−i−i−i−iiiiiiiii−i−i−i−i−i−i−i−i11-1-1ii−i−i11-1-1ii−i−i
χ10111111-1-111-1-111-1-111-1-1-1-1-111111-1111111-1-1-1-1-1-1-1-1-1iiii−i−i−i−iiiii−i−i−i−iiiiiiiii−i−i−i−i−i−i−i−i-1-111−i−iii-1-111−i−iii
χ11111111-1-111-1-111-1-111-1-1-1-1-111111-1111111-1-1-1-1-1-1-1-1-1−i−i−i−iiiii−i−i−i−iiiii−i−i−i−i−i−i−i−iiiiiiiii11-1-1−i−iii11-1-1−i−iii
χ12111111-1-111-1-111-1-111-1-1-1-1-111111-1111111-1-1-1-1-1-1-1-1-1−i−i−i−iiiii−i−i−i−iiiii−i−i−i−i−i−i−i−iiiiiiiii-1-111ii−i−i-1-111ii−i−i
χ13111111-1-111-1-111-1-111-1-1-1-1-1-1-1-1-11-1-1-1-1-111-111111111iiii−i−i−i−iiiii−i−i−i−i−i−i−i−i−i−i−i−iiiiiiiii11-1-1−i−iii-1-111ii−i−i
χ14111111-1-111-1-111-1-111-1-1-1-1-1-1-1-1-11-1-1-1-1-111-111111111iiii−i−i−i−iiiii−i−i−i−i−i−i−i−i−i−i−i−iiiiiiiii-1-111ii−i−i11-1-1−i−iii
χ15111111-1-111-1-111-1-111-1-1-1-1-1-1-1-1-11-1-1-1-1-111-111111111−i−i−i−iiiii−i−i−i−iiiiiiiiiiiii−i−i−i−i−i−i−i−i11-1-1ii−i−i-1-111−i−iii
χ16111111-1-111-1-111-1-111-1-1-1-1-1-1-1-1-11-1-1-1-1-111-111111111−i−i−i−iiiii−i−i−i−iiiiiiiiiiiii−i−i−i−i−i−i−i−i-1-111−i−iii11-1-1ii−i−i
χ171111-1-111-1-1-1-1-1-1-1-1111111-111-1-11111-1-11-1-11111-1-1-1-111-1-111-1-111-1-111-1-11111-1-1-1-11111-1-1-1-11-11-11-11-11-11-11-11-1
χ181111-1-111-1-1-1-1-1-1-1-1111111-111-1-11111-1-11-1-11111-1-1-1-111-1-111-1-111-1-111-1-11111-1-1-1-11111-1-1-1-1-11-11-11-11-11-11-11-11
χ191111-1-111-1-1-1-1-1-1-1-1111111-111-1-11111-1-11-1-11111-1-1-1-1-1-111-1-111-1-111-1-111-1-1-1-11111-1-1-1-111111-11-1-11-111-11-1-11-11
χ201111-1-111-1-1-1-1-1-1-1-1111111-111-1-11111-1-11-1-11111-1-1-1-1-1-111-1-111-1-111-1-111-1-1-1-11111-1-1-1-11111-11-111-11-1-11-111-11-1
χ211111-1-111-1-1-1-1-1-1-1-1111111-1-1-11111-1-1111-1-1-1-1-1-1111111-1-111-1-111-1-111-1-1-1-1-1-11111-1-1-1-111111-11-1-11-11-11-111-11-1
χ221111-1-111-1-1-1-1-1-1-1-1111111-1-1-11111-1-1111-1-1-1-1-1-1111111-1-111-1-111-1-111-1-1-1-1-1-11111-1-1-1-11111-11-111-11-11-11-1-11-11
χ231111-1-111-1-1-1-1-1-1-1-1111111-1-1-11111-1-1111-1-1-1-1-1-11111-1-111-1-111-1-111-1-1111111-1-1-1-11111-1-1-1-11-11-11-11-1-11-11-11-11
χ241111-1-111-1-1-1-1-1-1-1-1111111-1-1-11111-1-1111-1-1-1-1-1-11111-1-111-1-111-1-111-1-1111111-1-1-1-11111-1-1-1-1-11-11-11-111-11-11-11-1
χ251111-1-1-1-1-1-111-1-11111-1-1-1-1111-1-11-111-1-11-11-1-1-1-11111ii−i−i−i−iiiii−i−i−i−iiiiiii−i−i−i−i−i−i−i−iiiii1-1-11i−i−ii1-1-11i−i−ii
χ261111-1-1-1-1-1-111-1-11111-1-1-1-1111-1-11-111-1-11-11-1-1-1-11111ii−i−i−i−iiiii−i−i−i−iiiiiii−i−i−i−i−i−i−i−iiiii-111-1−iii−i-111-1−iii−i
χ271111-1-1-1-1-1-111-1-11111-1-1-1-1111-1-11-111-1-11-11-1-1-1-11111−i−iiiii−i−i−i−iiiii−i−i−i−i−i−iiiiiiiii−i−i−i−i1-1-11−iii−i1-1-11−iii−i
χ281111-1-1-1-1-1-111-1-11111-1-1-1-1111-1-11-111-1-11-11-1-1-1-11111−i−iiiii−i−i−i−iiiii−i−i−i−i−i−iiiiiiiii−i−i−i−i-111-1i−i−ii-111-1i−i−ii
χ291111-1-1-1-1-1-111-1-11111-1-1-1-11-1-1111-1-1-1111-111111-1-1-1-1ii−i−i−i−iiiii−i−i−i−iii−i−i−i−iiiiiiiii−i−i−i−i1-1-11−iii−i-111-1i−i−ii
χ301111-1-1-1-1-1-111-1-11111-1-1-1-11-1-1111-1-1-1111-111111-1-1-1-1ii−i−i−i−iiiii−i−i−i−iii−i−i−i−iiiiiiiii−i−i−i−i-111-1i−i−ii1-1-11−iii−i
χ311111-1-1-1-1-1-111-1-11111-1-1-1-11-1-1111-1-1-1111-111111-1-1-1-1−i−iiiii−i−i−i−iiiii−i−iiiii−i−i−i−i−i−i−i−iiiii1-1-11i−i−ii-111-1−iii−i
χ321111-1-1-1-1-1-111-1-11111-1-1-1-11-1-1111-1-1-1111-111111-1-1-1-1−i−iiiii−i−i−i−iiiii−i−iiiii−i−i−i−i−i−i−i−iiiii-111-1−iii−i1-1-11i−i−ii
χ33222222222222-2-2-2-2-2-2-2-2-2-220000220000-2-2-2000000002i2i2i2i−2i−2i−2i−2i−2i−2i−2i−2i2i2i2i2i00000000000000000000000000000000
χ34222222222222-2-2-2-2-2-2-2-2-2-220000220000-2-2-200000000−2i−2i−2i−2i2i2i2i2i2i2i2i2i−2i−2i−2i−2i00000000000000000000000000000000
χ3522222222-2-2-2-22222-2-22-2-2220000-2-200002-2-200000000000000000000000022-2-222-2-222-2-222-2-20000000000000000
χ3622222222-2-2-2-22222-2-22-2-2220000-2-200002-2-2000000000000000000000000-2-222-2-222-2-222-2-2220000000000000000
χ3722222222-2-2-2-2-2-2-2-222-222-222222-2-2-2-2-2-2-22222-2-222-2-2000000000000000000000000000000000000000000000000
χ3822222222-2-2-2-2-2-2-2-222-222-22-2-2-2-2-2-22222-222-2-222-2-222000000000000000000000000000000000000000000000000
χ39222222-2-222-2-2-2-222-2-22222-200002-20000-2-220000000022222222-2-2-2-2-2-2-2-200000000000000000000000000000000
χ40222222-2-222-2-2-2-222-2-22222-200002-20000-2-2200000000-2-2-2-2-2-2-2-22222222200000000000000000000000000000000
χ41222222-2-2-2-22222-2-2-2-2-222-2-20000-2200002-220000000000000000000000002i2i−2i−2i2i2i−2i−2i−2i−2i2i2i−2i−2i2i2i0000000000000000
χ42222222-2-2-2-22222-2-2-2-2-222-2-20000-2200002-22000000000000000000000000−2i−2i2i2i−2i−2i2i2i2i2i−2i−2i2i2i−2i−2i0000000000000000
χ43222222-2-2-2-222-2-222222-2-22-22222-22-2-2-2-2-22-2-2-222-2-222000000000000000000000000000000000000000000000000
χ44222222-2-2-2-222-2-222222-2-22-2-2-2-2-2-222222-22-222-2-222-2-2000000000000000000000000000000000000000000000000
χ452222-2-2222222222222-222-2-222-2-2-2-2-2-222-2-2-222-2-2-2-222000000000000000000000000000000000000000000000000
χ462222-2-2222222222222-222-2-2-2-222-2-222-2-2-2-2-2-2-22222-2-2000000000000000000000000000000000000000000000000
χ472222-2-2222222-2-2-2-2-2-22-2-22-20000-2-2000022200000000000000000000000022-2-2-2-22222-2-2-2-2220000000000000000
χ482222-2-2222222-2-2-2-2-2-22-2-22-20000-2-20000222000000000000000000000000-2-22222-2-2-2-22222-2-20000000000000000
χ492222-2-222-2-2-2-22222-2-2-2-2-2-2-20000220000-222000000002i2i−2i−2i−2i−2i2i2i−2i−2i2i2i2i2i−2i−2i00000000000000000000000000000000
χ502222-2-222-2-2-2-22222-2-2-2-2-2-2-20000220000-22200000000−2i−2i2i2i2i2i−2i−2i2i2i−2i−2i−2i−2i2i2i00000000000000000000000000000000
χ512222-2-2-2-222-2-222-2-2222-2-22222-2-2-22-2-222-2-22-2-22222-2-2000000000000000000000000000000000000000000000000
χ522222-2-2-2-222-2-222-2-2222-2-222-2-222-2222-2-2-2-2222-2-2-2-222000000000000000000000000000000000000000000000000
χ532222-2-2-2-222-2-2-2-222-2-2-222-220000-22000022-20000000000000000000000002i2i−2i−2i−2i−2i2i2i−2i−2i2i2i2i2i−2i−2i0000000000000000
χ542222-2-2-2-222-2-2-2-222-2-2-222-220000-22000022-2000000000000000000000000−2i−2i2i2i2i2i−2i−2i2i2i−2i−2i−2i−2i2i2i0000000000000000
χ552222-2-2-2-2-2-22222-2-2-2-22222200002-20000-22-20000000022-2-222-2-2-2-222-2-22200000000000000000000000000000000
χ562222-2-2-2-2-2-22222-2-2-2-22222200002-20000-22-200000000-2-222-2-22222-2-222-2-200000000000000000000000000000000
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χ602-22-2002-22i−2i2i−2i2i−2i2i−2i2-202-20000-2200−2i2i0000000−2i2i-2200−i2i2−22−i2i2−22−i2i2−22−i2i2−222−22−2i2−i2i2−i22−22−2i2−i2i2−i20000000000000000
χ612-22-2002-22i−2i2i−2i−2i2i−2i2i-220-22002-20000002i−2i0002-200002i−2i2−2−i2i2−22i2−i2−22i2−i22−2−i2i22−2−22−i2i2i2−i22−2−22−i2i2i2−i20000000000000000
χ622-22-2002-22i−2i2i−2i−2i2i−2i2i-220-22002-20000002i−2i0002-200002i−2i−22i2−i22−2−i2i22−2−i2i2−22i2−i2−222−2i2−i2−i2i2−222−2i2−i2−i2i20000000000000000
χ632-22-2002-22i−2i2i−2i−2i2i−2i2i-220-2200-22000000−2i2i000-220000−2i2i2−2−i2i2−22i2−i2−22i2−i22−2−i2i2−222−2i2−i2−i2i2−222−2i2−i2−i2i20000000000000000
χ642-22-2002-22i−2i2i−2i−2i2i−2i2i-220-2200-22000000−2i2i000-220000−2i2i−22i2−i22−2−i2i22−2−i2i2−22i2−i22−2−22−i2i2i2−i22−2−22−i2i2i2−i20000000000000000
χ652-22-2002-2−2i2i−2i2i2i−2i2i−2i-220-22002-2000000−2i2i0002-20000−2i2i2−2i2−i2−22−i2i2−22−i2i22−2i2−i22−2−22i2−i2−i2i22−2−22i2−i2−i2i20000000000000000
χ662-22-2002-2−2i2i−2i2i2i−2i2i−2i-220-22002-2000000−2i2i0002-20000−2i2i−22−i2i22−2i2−i22−2i2−i2−22−i2i2−222−2−i2i2i2−i2−222−2−i2i2i2−i20000000000000000
χ672-22-2002-2−2i2i−2i2i2i−2i2i−2i-220-2200-220000002i−2i000-2200002i−2i2−2i2−i2−22−i2i2−22−i2i22−2i2−i2−222−2−i2i2i2−i2−222−2−i2i2i2−i20000000000000000
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χ702-22-2002-2−2i2i−2i2i−2i2i−2i2i2-202-200002-200−2i2i0000000−2i2i2-200−i2i22−2−i2i22−2−i2i22−2−i2i22−22−22−2−i2i2−i2i22−22−2−i2i2−i2i20000000000000000
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χ722-22-2002-2−2i2i−2i2i−2i2i−2i2i2-202-20000-22002i−2i00000002i−2i-2200−i2i22−2−i2i22−2−i2i22−2−i2i22−2−22−22i2−i2i2−i2−22−22i2−i2i2−i20000000000000000
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χ752-22-200-222i−2i−2i2i2i−2i−2i2i2-20-220000-2200−2i2i00000002i−2i2-2002−2−i2i2−22i2−i22−2−i2i2−22i2−i2i2−i2i2−i2−22−22−i2i2−i2i22−22−20000000000000000
χ762-22-200-222i−2i−2i2i2i−2i−2i2i2-20-220000-2200−2i2i00000002i−2i2-200−22i2−i22−2−i2i2−22i2−i22−2−i2i2−i2i2−i2i22−22−2i2−i2i2−i2−22−220000000000000000
χ772-22-200-222i−2i−2i2i−2i2i2i−2i-2202-2002-20000002i−2i000-220000−2i2ii2−i22−2i2−i22−2−i2i2−22−i2i2−22i2−i2−i2i22−2−22−i2i2i2−i2−222−20000000000000000
χ782-22-200-222i−2i−2i2i−2i2i2i−2i-2202-2002-20000002i−2i000-220000−2i2i−i2i2−22−i2i2−22i2−i22−2i2−i22−2−i2i2i2−i2−222−2i2−i2−i2i22−2−220000000000000000
χ792-22-200-222i−2i−2i2i−2i2i2i−2i-2202-200-22000000−2i2i0002-200002i−2ii2−i22−2i2−i22−2−i2i2−22−i2i2−22−i2i2i2−i2−222−2i2−i2−i2i22−2−220000000000000000
χ802-22-200-222i−2i−2i2i−2i2i2i−2i-2202-200-22000000−2i2i0002-200002i−2i−i2i2−22−i2i2−22i2−i22−2i2−i22−2i2−i2−i2i22−2−22−i2i2i2−i2−222−20000000000000000
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χ822-22-200-22−2i2i2i−2i2i−2i−2i2i-2202-2002-2000000−2i2i000-2200002i−2i−i2i22−2−i2i22−2i2−i2−22i2−i2−22−i2i2i2−i22−2−22i2−i2−i2i2−222−20000000000000000
χ832-22-200-22−2i2i2i−2i2i−2i−2i2i-2202-200-220000002i−2i0002-20000−2i2ii2−i2−22i2−i2−22−i2i22−2−i2i22−2−i2i2i2−i22−2−22i2−i2−i2i2−222−20000000000000000
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χ852-22-200-22−2i2i2i−2i−2i2i2i−2i2-20-2200002-200−2i2i00000002i−2i-22002−2i2−i2−22−i2i22−2i2−i2−22−i2i2i2−i2i2−i22−22−2−i2i2−i2i2−22−220000000000000000
χ862-22-200-22−2i2i2i−2i−2i2i2i−2i2-20-2200002-200−2i2i00000002i−2i-2200−22−i2i22−2i2−i2−22−i2i22−2i2−i2−i2i2−i2i2−22−22i2−i2i2−i22−22−20000000000000000
χ872-22-200-22−2i2i2i−2i−2i2i2i−2i2-20-220000-22002i−2i0000000−2i2i2-2002−2i2−i2−22−i2i22−2i2−i2−22−i2i2−i2i2−i2i2−22−22i2−i2i2−i22−22−20000000000000000
χ882-22-200-22−2i2i2i−2i−2i2i2i−2i2-20-220000-22002i−2i0000000−2i2i2-200−22−i2i22−2i2−i2−22−i2i22−2i2−i2i2−i2i2−i22−22−2−i2i2−i2i2−22−220000000000000000
χ8988-8-88-800000000000000000000000000000000000000000000000000000000000000000000000000000000000000
χ9088-8-8-8800000000000000000000000000000000000000000000000000000000000000000000000000000000000000
χ918-8-8800000000000000800-80000000000000000000000000000000000000000000000000000000000000000000000
χ928-8-8800000000000000-80080000000000000000000000000000000000000000000000000000000000000000000000

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