Finite Group Databasebeta

← Group #481349

Character table — Group #481349

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92
size111122222222222222222244444444444444444444444444444444444444444444444444444416161616161616161616161616161616
order1222224444444444448888224444448888888888888816161616161616161616161616161616161616161616161616161616161616162224444488888888
χ111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ311111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1
χ411111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111
χ51111111111111111111111-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-11111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-111-11111-1-1-1-1
χ61111111111111111111111-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-11111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111-1-11-1-1-1-11111
χ71111111111111111111111-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111111111-1-1-111-1-1-1-1-11111
χ81111111111111111111111-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111111111-1-1111-1-111111-1-1-1-1
χ911111111-1-1-1-1-1-111-1-1-1-1-1-11111-1-1-1-11111-1-11111-1-1-1-1iiiiiiii−i−i−i−i−i−i−i−iiiiiiiii−i−i−i−i−i−i−i−i11-11-1-1-11ii−i−iii−i−i
χ1011111111-1-1-1-1-1-111-1-1-1-1-1-11111-1-1-1-11111-1-11111-1-1-1-1iiiiiiii−i−i−i−i−i−i−i−iiiiiiiii−i−i−i−i−i−i−i−i-1-11-1111-1−i−iii−i−iii
χ1111111111-1-1-1-1-1-111-1-1-1-1-1-11111-1-1-1-11111-1-11111-1-1-1-1−i−i−i−i−i−i−i−iiiiiiiii−i−i−i−i−i−i−i−iiiiiiiii11-11-1-1-11−i−iii−i−iii
χ1211111111-1-1-1-1-1-111-1-1-1-1-1-11111-1-1-1-11111-1-11111-1-1-1-1−i−i−i−i−i−i−i−iiiiiiiii−i−i−i−i−i−i−i−iiiiiiiii-1-11-1111-1ii−i−iii−i−i
χ1311111111-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-11111iiiiiiii−i−i−i−i−i−i−i−i−i−i−i−i−i−i−i−iiiiiiiii111-11-1-1-1ii−i−i−i−iii
χ1411111111-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-11111iiiiiiii−i−i−i−i−i−i−i−i−i−i−i−i−i−i−i−iiiiiiiii-1-1-11-1111−i−iiiii−i−i
χ1511111111-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-11111−i−i−i−i−i−i−i−iiiiiiiiiiiiiiiii−i−i−i−i−i−i−i−i111-11-1-1-1−i−iiiii−i−i
χ1611111111-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-11111−i−i−i−i−i−i−i−iiiiiiiiiiiiiiiii−i−i−i−i−i−i−i−i-1-1-11-1111ii−i−i−i−iii
χ171111-1-1-1-11111-1-111-1-1-1-1-1-11-11-11-11-111-1-11111-1-111-1-1iiii−i−i−i−iiiii−i−i−i−iiiii−i−i−i−iiiii−i−i−i−i1-111-11-1-1i−ii−ii−ii−i
χ181111-1-1-1-11111-1-111-1-1-1-1-1-11-11-11-11-111-1-11111-1-111-1-1iiii−i−i−i−iiiii−i−i−i−iiiii−i−i−i−iiiii−i−i−i−i-11-1-11-111−ii−ii−ii−ii
χ191111-1-1-1-11111-1-111-1-1-1-1-1-11-11-11-11-111-1-11111-1-111-1-1−i−i−i−iiiii−i−i−i−iiiii−i−i−i−iiiii−i−i−i−iiiii1-111-11-1-1−ii−ii−ii−ii
χ201111-1-1-1-11111-1-111-1-1-1-1-1-11-11-11-11-111-1-11111-1-111-1-1−i−i−i−iiiii−i−i−i−iiiii−i−i−i−iiiii−i−i−i−iiiii-11-1-11-111i−ii−ii−ii−i
χ211111-1-1-1-11111-1-111-1-1-1-1-1-1-11-11-11-1111-1-111-1-111-1-111iiii−i−i−i−iiiii−i−i−i−i−i−i−i−iiiii−i−i−i−iiiii1-1-1-111-11i−ii−i−ii−ii
χ221111-1-1-1-11111-1-111-1-1-1-1-1-1-11-11-11-1111-1-111-1-111-1-111iiii−i−i−i−iiiii−i−i−i−i−i−i−i−iiiii−i−i−i−iiiii-1111-1-11-1−ii−iii−ii−i
χ231111-1-1-1-11111-1-111-1-1-1-1-1-1-11-11-11-1111-1-111-1-111-1-111−i−i−i−iiiii−i−i−i−iiiiiiiii−i−i−i−iiiii−i−i−i−i1-1-1-111-11−ii−iii−ii−i
χ241111-1-1-1-11111-1-111-1-1-1-1-1-1-11-11-11-1111-1-111-1-111-1-111−i−i−i−iiiii−i−i−i−iiiiiiiii−i−i−i−iiiii−i−i−i−i-1111-1-11-1i−ii−i−ii−ii
χ251111-1-1-1-1-1-1-1-111111111111-11-1-11-1111-1-1-1-111-1-1-1-1111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-111111-1-111-11-11-1-111-1-11
χ261111-1-1-1-1-1-1-1-111111111111-11-1-11-1111-1-1-1-111-1-1-1-1111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-11111-111-1-11-11-111-1-111-1
χ271111-1-1-1-1-1-1-1-111111111111-11-1-11-1111-1-1-1-111-1-1-1-111-1-1-1-111111111-1-1-1-1-1-1-1-111111111-1-1-1-11-1-111-11-1-111-1-111-1
χ281111-1-1-1-1-1-1-1-111111111111-11-1-11-1111-1-1-1-111-1-1-1-111-1-1-1-111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-111-1-11-111-1-111-1-11
χ291111-1-1-1-1-1-1-1-11111111111-11-111-11-111-1-1-1-1-1-11111-1-11111-1-1-1-1-1-1-1-11111-1-1-1-111111111-1-1-1-11-11-1-1-1111-1-11-111-1
χ301111-1-1-1-1-1-1-1-11111111111-11-111-11-111-1-1-1-1-1-11111-1-11111-1-1-1-1-1-1-1-11111-1-1-1-111111111-1-1-1-1-11-1111-1-1-111-11-1-11
χ311111-1-1-1-1-1-1-1-11111111111-11-111-11-111-1-1-1-1-1-11111-1-1-1-1-1-111111111-1-1-1-11111-1-1-1-1-1-1-1-111111-11-1-1-111-111-11-1-11
χ321111-1-1-1-1-1-1-1-11111111111-11-111-11-111-1-1-1-1-1-11111-1-1-1-1-1-111111111-1-1-1-11111-1-1-1-1-1-1-1-11111-11-1111-1-11-1-11-111-1
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χ3522222222-2-2-2-2-2-222-2-222222222-2-2-2-2-2-2-2-222-2-2-2-22222000000000000000000000000000000000000000000000000
χ3622222222-2-2-2-2-2-222-2-22222-2-2-2-22222-2-2-2-2222222-2-2-2-2000000000000000000000000000000000000000000000000
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χ38222222-2-222-2-2-2-2-2-22200002-2-22-222-200000000000000−2−222−2−222−2−222−2−222−2−222−2−222−2−222−2−2220000000000000000
χ39222222-2-222-2-2-2-2-2-2220000-222-22-2-220000000000000022−2−222−2−222−2−222−2−2−2−222−2−222−2−222−2−2220000000000000000
χ40222222-2-222-2-2-2-2-2-2220000-222-22-2-2200000000000000−2−222−2−222−2−222−2−22222−2−222−2−222−2−222−2−20000000000000000
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χ42222222-2-2-2-22222-2-2-2-200002-2-222-2-2200000000000000−i2−i2i2i2−i2−i2i2i2i2i2−i2−i2i2i2−i2−i2−i2−i2i2i2−i2−i2i2i2i2i2−i2−i2i2i2−i2−i20000000000000000
χ43222222-2-2-2-22222-2-2-2-20000-222-2-222-200000000000000i2i2−i2−i2i2i2−i2−i2−i2−i2i2i2−i2−i2i2i2−i2−i2i2i2−i2−i2i2i2i2i2−i2−i2i2i2−i2−i20000000000000000
χ44222222-2-2-2-22222-2-2-2-20000-222-2-222-200000000000000−i2−i2i2i2−i2−i2i2i2i2i2−i2−i2i2i2−i2−i2i2i2−i2−i2i2i2−i2−i2−i2−i2i2i2−i2−i2i2i20000000000000000
χ452222-2-22222-2-222-2-2-2-2000022-2-2-2-22200000000000000i2i2−i2−i2−i2−i2i2i2i2i2−i2−i2−i2−i2i2i2i2i2−i2−i2−i2−i2i2i2i2i2−i2−i2−i2−i2i2i20000000000000000
χ462222-2-22222-2-222-2-2-2-2000022-2-2-2-22200000000000000−i2−i2i2i2i2i2−i2−i2−i2−i2i2i2i2i2−i2−i2−i2−i2i2i2i2i2−i2−i2−i2−i2i2i2i2i2−i2−i20000000000000000
χ472222-2-22222-2-222-2-2-2-20000-2-22222-2-200000000000000i2i2−i2−i2−i2−i2i2i2i2i2−i2−i2−i2−i2i2i2−i2−i2i2i2i2i2−i2−i2−i2−i2i2i2i2i2−i2−i20000000000000000
χ482222-2-22222-2-222-2-2-2-20000-2-22222-2-200000000000000−i2−i2i2i2i2i2−i2−i2−i2−i2i2i2i2i2−i2−i2i2i2−i2−i2−i2−i2i2i2i2i2−i2−i2−i2−i2i2i20000000000000000
χ492222-2-222-2-222-2-2-2-222000022-2-222-2-20000000000000022−2−2−2−222−2−22222−2−222−2−2−2−222−2−22222−2−20000000000000000
χ502222-2-222-2-222-2-2-2-222000022-2-222-2-200000000000000−2−22222−2−222−2−2−2−222−2−22222−2−222−2−2−2−2220000000000000000
χ512222-2-222-2-222-2-2-2-2220000-2-222-2-2220000000000000022−2−2−2−222−2−22222−2−2−2−22222−2−222−2−2−2−2220000000000000000
χ522222-2-222-2-222-2-2-2-2220000-2-222-2-22200000000000000−2−22222−2−222−2−2−2−22222−2−2−2−222−2−22222−2−20000000000000000
χ532222-2-2-2-22222-2-222-2-222222-22-22-22-2-2-222-2-2-2-222-2-222000000000000000000000000000000000000000000000000
χ542222-2-2-2-22222-2-222-2-22222-22-22-22-22-2-222-2-222-2-222-2-2000000000000000000000000000000000000000000000000
χ552222-2-2-2-2-2-2-2-2222222-2-2-2-22-22-2-22-22-2-22222-2-22222-2-2000000000000000000000000000000000000000000000000
χ562222-2-2-2-2-2-2-2-2222222-2-2-2-2-22-222-22-2-2-2222222-2-2-2-222000000000000000000000000000000000000000000000000
χ5722-2-22-22-22i−2i2i−2i2i−2i2-22i−2i0000000000000000002i−2i2i−2i2-22-21+i−1−i1+i−1−i1+i−1−i1+i−1−i1−i−1+i1−i−1+i1−i−1+i1−i−1+i1−i−1+i1−i−1+i1−i−1+i1−i−1+i1+i−1−i1+i−1−i1+i−1−i1+i−1−i0000000000000000
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χ6622-2-22-2-222i−2i−2i2i−2i2i-222i−2i2i2i−2i−2i000000002-22-22i−2i000000000000000000000000−2ζ32ζ32ζ3−2ζ3−2ζ32ζ32ζ3−2ζ32ζ−2ζ−2ζ2ζ2ζ−2ζ−2ζ2ζ0000000000000000
χ6722-2-22-2-222i−2i−2i2i−2i2i-222i−2i−2i−2i2i2i00000000-22-22−2i2i000000002ζ−2ζ−2ζ2ζ2ζ−2ζ−2ζ2ζ−2ζ32ζ32ζ3−2ζ3−2ζ32ζ32ζ3−2ζ300000000000000000000000000000000
χ6822-2-22-2-222i−2i−2i2i−2i2i-222i−2i−2i−2i2i2i00000000-22-22−2i2i00000000−2ζ2ζ2ζ−2ζ−2ζ2ζ2ζ−2ζ2ζ3−2ζ3−2ζ32ζ32ζ3−2ζ3−2ζ32ζ300000000000000000000000000000000
χ6922-2-22-2-22−2i2i2i−2i2i−2i-22−2i2i2i2i−2i−2i00000000-22-222i−2i000000002ζ3−2ζ3−2ζ32ζ32ζ3−2ζ3−2ζ32ζ3−2ζ2ζ2ζ−2ζ−2ζ2ζ2ζ−2ζ00000000000000000000000000000000
χ7022-2-22-2-22−2i2i2i−2i2i−2i-22−2i2i2i2i−2i−2i00000000-22-222i−2i00000000−2ζ32ζ32ζ3−2ζ3−2ζ32ζ32ζ3−2ζ32ζ−2ζ−2ζ2ζ2ζ−2ζ−2ζ2ζ00000000000000000000000000000000
χ7122-2-22-2-22−2i2i2i−2i2i−2i-22−2i2i−2i−2i2i2i000000002-22-2−2i2i0000000000000000000000002ζ−2ζ−2ζ2ζ2ζ−2ζ−2ζ2ζ−2ζ32ζ32ζ3−2ζ3−2ζ32ζ32ζ3−2ζ30000000000000000
χ7222-2-22-2-22−2i2i2i−2i2i−2i-22−2i2i−2i−2i2i2i000000002-22-2−2i2i000000000000000000000000−2ζ2ζ2ζ−2ζ−2ζ2ζ2ζ−2ζ2ζ3−2ζ3−2ζ32ζ32ζ3−2ζ3−2ζ32ζ30000000000000000
χ7322-2-2-222-22i−2i−2i2i2i−2i-22−2i2i2i2i−2i−2i00000000-222-2−2i2i000000002ζ3−2ζ3−2ζ32ζ3−2ζ32ζ32ζ3−2ζ32ζ−2ζ−2ζ2ζ−2ζ2ζ2ζ−2ζ00000000000000000000000000000000
χ7422-2-2-222-22i−2i−2i2i2i−2i-22−2i2i2i2i−2i−2i00000000-222-2−2i2i00000000−2ζ32ζ32ζ3−2ζ32ζ3−2ζ3−2ζ32ζ3−2ζ2ζ2ζ−2ζ2ζ−2ζ−2ζ2ζ00000000000000000000000000000000
χ7522-2-2-222-22i−2i−2i2i2i−2i-22−2i2i−2i−2i2i2i000000002-2-222i−2i0000000000000000000000002ζ−2ζ−2ζ2ζ−2ζ2ζ2ζ−2ζ2ζ3−2ζ3−2ζ32ζ3−2ζ32ζ32ζ3−2ζ30000000000000000
χ7622-2-2-222-22i−2i−2i2i2i−2i-22−2i2i−2i−2i2i2i000000002-2-222i−2i000000000000000000000000−2ζ2ζ2ζ−2ζ2ζ−2ζ−2ζ2ζ−2ζ32ζ32ζ3−2ζ32ζ3−2ζ3−2ζ32ζ30000000000000000
χ7722-2-2-222-2−2i2i2i−2i−2i2i-222i−2i2i2i−2i−2i000000002-2-22−2i2i0000000000000000000000002ζ3−2ζ3−2ζ32ζ3−2ζ32ζ32ζ3−2ζ32ζ−2ζ−2ζ2ζ−2ζ2ζ2ζ−2ζ0000000000000000
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χ898-88-8000000000000004i2−4i24i2−4i20000000000000000000000000000000000000000000000000000000000000000000000
χ908-88-800000000000000−4i24i2−4i24i20000000000000000000000000000000000000000000000000000000000000000000000
χ918-8-880000000000000042−42−42420000000000000000000000000000000000000000000000000000000000000000000000
χ928-8-8800000000000000−424242−420000000000000000000000000000000000000000000000000000000000000000000000

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