Finite Group Databasebeta

← Group #110978

Character table — Group #110978

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92
size111122222222222222222244444444444444444444444444444444444444444444444444444416161616161616161616161616161616
order12222244444444444444442244448888888888888888888888888888888888888888888888884444888888888888
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
χ51111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1-1-1
χ61111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-11111
χ71111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111111111111111-1-1-1-1-1-1-1-11111
χ81111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111111111-1-1-1-111111111-1-1-1-1
χ911111111-1-111-1-111-1-1-1-1-1-1-1-1-111111111111-1-1-1-1-1-1-1-1iiiiiiii−i−i−i−i−i−i−i−iiiiiiiii−i−i−i−i−i−i−i−i11-1-111-1-1ii−i−iii−i−i
χ1011111111-1-111-1-111-1-1-1-1-1-1-1-1-111111111111-1-1-1-1-1-1-1-1iiiiiiii−i−i−i−i−i−i−i−iiiiiiiii−i−i−i−i−i−i−i−i-1-111-1-111−i−iii−i−iii
χ1111111111-1-111-1-111-1-1-1-1-1-1-1-1-111111111111-1-1-1-1-1-1-1-1−i−i−i−i−i−i−i−iiiiiiiii−i−i−i−i−i−i−i−iiiiiiiii11-1-111-1-1−i−iii−i−iii
χ1211111111-1-111-1-111-1-1-1-1-1-1-1-1-111111111111-1-1-1-1-1-1-1-1−i−i−i−i−i−i−i−iiiiiiiii−i−i−i−i−i−i−i−iiiiiiiii-1-111-1-111ii−i−iii−i−i
χ1311111111-1-111-1-111-1-1-1-1-1-1-1-1-1111-1-1-1-1-1-1-1-111111111iiiiiiii−i−i−i−i−i−i−i−i−i−i−i−i−i−i−i−iiiiiiiii11-1-1-1-111ii−i−i−i−iii
χ1411111111-1-111-1-111-1-1-1-1-1-1-1-1-1111-1-1-1-1-1-1-1-111111111iiiiiiii−i−i−i−i−i−i−i−i−i−i−i−i−i−i−i−iiiiiiiii-1-11111-1-1−i−iiiii−i−i
χ1511111111-1-111-1-111-1-1-1-1-1-1-1-1-1111-1-1-1-1-1-1-1-111111111−i−i−i−i−i−i−i−iiiiiiiiiiiiiiiii−i−i−i−i−i−i−i−i11-1-1-1-111−i−iiiii−i−i
χ1611111111-1-111-1-111-1-1-1-1-1-1-1-1-1111-1-1-1-1-1-1-1-111111111−i−i−i−i−i−i−i−iiiiiiiiiiiiiiiii−i−i−i−i−i−i−i−i-1-11111-1-1ii−i−i−i−iii
χ17111111-1-111-1-111-1-111-1-1-1-1-1-1111-1iiii−i−i−i−iiiii−i−i−i−i1111-1-1-1-11111-1-1-1-1iiii−i−i−i−iiiii−i−i−i−i1-11-1i−ii−i1-11-1i−ii−i
χ18111111-1-111-1-111-1-111-1-1-1-1-1-1111-1iiii−i−i−i−iiiii−i−i−i−i1111-1-1-1-11111-1-1-1-1iiii−i−i−i−iiiii−i−i−i−i-11-11−ii−ii-11-11−ii−ii
χ19111111-1-111-1-111-1-111-1-1-1-1-1-1111-1iiii−i−i−i−iiiii−i−i−i−i-1-1-1-11111-1-1-1-11111−i−i−i−iiiii−i−i−i−iiiii1-11-1i−ii−i-11-11−ii−ii
χ20111111-1-111-1-111-1-111-1-1-1-1-1-1111-1iiii−i−i−i−iiiii−i−i−i−i-1-1-1-11111-1-1-1-11111−i−i−i−iiiii−i−i−i−iiiii-11-11−ii−ii1-11-1i−ii−i
χ21111111-1-111-1-111-1-111-1-1-1-1-1-1111-1−i−i−i−iiiii−i−i−i−iiiii1111-1-1-1-11111-1-1-1-1−i−i−i−iiiii−i−i−i−iiiii1-11-1−ii−ii1-11-1−ii−ii
χ22111111-1-111-1-111-1-111-1-1-1-1-1-1111-1−i−i−i−iiiii−i−i−i−iiiii1111-1-1-1-11111-1-1-1-1−i−i−i−iiiii−i−i−i−iiiii-11-11i−ii−i-11-11i−ii−i
χ23111111-1-111-1-111-1-111-1-1-1-1-1-1111-1−i−i−i−iiiii−i−i−i−iiiii-1-1-1-11111-1-1-1-11111iiii−i−i−i−iiiii−i−i−i−i1-11-1−ii−ii-11-11i−ii−i
χ24111111-1-111-1-111-1-111-1-1-1-1-1-1111-1−i−i−i−iiiii−i−i−i−iiiii-1-1-1-11111-1-1-1-11111iiii−i−i−i−iiiii−i−i−i−i-11-11i−ii−i1-11-1−ii−ii
χ25111111-1-1-1-1-1-1-1-1-1-1-1-1111111-111-1iiii−i−i−i−i−i−i−i−iiiiiiiii−i−i−i−i−i−i−i−iiiii-1-1-1-111111111-1-1-1-11-1-11i−i−iii−i−ii-111-1
χ26111111-1-1-1-1-1-1-1-1-1-1-1-1111111-111-1iiii−i−i−i−i−i−i−i−iiiiiiiii−i−i−i−i−i−i−i−iiiii-1-1-1-111111111-1-1-1-1-111-1−iii−i−iii−i1-1-11
χ27111111-1-1-1-1-1-1-1-1-1-1-1-1111111-111-1iiii−i−i−i−i−i−i−i−iiiii−i−i−i−iiiiiiiii−i−i−i−i1111-1-1-1-1-1-1-1-111111-1-11i−i−ii−iii−i1-1-11
χ28111111-1-1-1-1-1-1-1-1-1-1-1-1111111-111-1iiii−i−i−i−i−i−i−i−iiiii−i−i−i−iiiiiiiii−i−i−i−i1111-1-1-1-1-1-1-1-11111-111-1−iii−ii−i−ii-111-1
χ29111111-1-1-1-1-1-1-1-1-1-1-1-1111111-111-1−i−i−i−iiiiiiiii−i−i−i−iiiii−i−i−i−i−i−i−i−iiiii1111-1-1-1-1-1-1-1-111111-1-11−iii−ii−i−ii1-1-11
χ30111111-1-1-1-1-1-1-1-1-1-1-1-1111111-111-1−i−i−i−iiiiiiiii−i−i−i−iiiii−i−i−i−i−i−i−i−iiiii1111-1-1-1-1-1-1-1-11111-111-1i−i−ii−iii−i-111-1
χ31111111-1-1-1-1-1-1-1-1-1-1-1-1111111-111-1−i−i−i−iiiiiiiii−i−i−i−i−i−i−i−iiiiiiiii−i−i−i−i-1-1-1-111111111-1-1-1-11-1-11−iii−i−iii−i-111-1
χ32111111-1-1-1-1-1-1-1-1-1-1-1-1111111-111-1−i−i−i−iiiiiiiii−i−i−i−i−i−i−i−iiiiiiiii−i−i−i−i-1-1-1-111111111-1-1-1-1-111-1i−i−iii−i−ii1-1-11
χ33222222222222-2-2-2-2222222-2-2-2-2-2-20000000000000000000000000000000022-2-222-2-222-2-222-2-20000000000000000
χ34222222222222-2-2-2-2222222-2-2-2-2-2-200000000000000000000000000000000-2-222-2-222-2-222-2-2220000000000000000
χ3522222222-2-22222-2-2-2-2-2-2-2-2222-2-2-2000000000000000000000000000000002i2i−2i−2i2i2i−2i−2i−2i−2i2i2i−2i−2i2i2i0000000000000000
χ3622222222-2-22222-2-2-2-2-2-2-2-2222-2-2-200000000000000000000000000000000−2i−2i2i2i−2i−2i2i2i2i2i−2i−2i2i2i−2i−2i0000000000000000
χ37222222-2-222-2-2-2-22222-2-2-2-222-2-2-22000000000000000000000000000000002i2i−2i−2i−2i−2i2i2i2i2i−2i−2i−2i−2i2i2i0000000000000000
χ38222222-2-222-2-2-2-22222-2-2-2-222-2-2-2200000000000000000000000000000000−2i−2i2i2i2i2i−2i−2i−2i−2i2i2i2i2i−2i−2i0000000000000000
χ39222222-2-2-2-2-2-22222-2-22222-2-22-2-220000000000000000000000000000000022-2-2-2-222-2-22222-2-20000000000000000
χ40222222-2-2-2-2-2-22222-2-22222-2-22-2-2200000000000000000000000000000000-2-22222-2-222-2-2-2-2220000000000000000
χ412222-2-22222-2-222-2-2-2-222-2-22-2-22-222i2i−2i−2i2i2i−2i−2i2i2i−2i−2i2i2i−2i−2i000000000000000000000000000000000000000000000000
χ422222-2-22222-2-222-2-2-2-222-2-22-2-22-22−2i−2i2i2i−2i−2i2i2i−2i−2i2i2i−2i−2i2i2i000000000000000000000000000000000000000000000000
χ432222-2-22222-2-2-2-222-2-222-2-2-222-22-200000000000000002i2i−2i−2i2i2i−2i−2i2i2i−2i−2i2i2i−2i−2i00000000000000000000000000000000
χ442222-2-22222-2-2-2-222-2-222-2-2-222-22-20000000000000000−2i−2i2i2i−2i−2i2i2i−2i−2i2i2i−2i−2i2i2i00000000000000000000000000000000
χ452222-2-222-2-2-2-2222222-2-2222-2-2-22-2000000000000000022-2-222-2-2-2-222-2-22200000000000000000000000000000000
χ462222-2-222-2-2-2-2222222-2-2222-2-2-22-20000000000000000-2-222-2-22222-2-222-2-200000000000000000000000000000000
χ472222-2-222-2-2-2-2-2-2-2-222-2-222-2222-222i2i−2i−2i2i2i−2i−2i−2i−2i2i2i−2i−2i2i2i000000000000000000000000000000000000000000000000
χ482222-2-222-2-2-2-2-2-2-2-222-2-222-2222-22−2i−2i2i2i−2i−2i2i2i2i2i−2i−2i2i2i−2i−2i000000000000000000000000000000000000000000000000
χ492222-2-2-2-222222222-2-2-2-222-22-22-2-222-2-2-2-22222-2-2-2-222000000000000000000000000000000000000000000000000
χ502222-2-2-2-222222222-2-2-2-222-22-22-2-2-2-22222-2-2-2-22222-2-2000000000000000000000000000000000000000000000000
χ512222-2-2-2-22222-2-2-2-2-2-2-2-2222-22-22200000000000000002i2i−2i−2i−2i−2i2i2i2i2i−2i−2i−2i−2i2i2i00000000000000000000000000000000
χ522222-2-2-2-22222-2-2-2-2-2-2-2-2222-22-2220000000000000000−2i−2i2i2i2i2i−2i−2i−2i−2i2i2i2i2i−2i−2i00000000000000000000000000000000
χ532222-2-2-2-2-2-22222-2-22222-2-2-22-2-222000000000000000022-2-2-2-222-2-22222-2-200000000000000000000000000000000
χ542222-2-2-2-2-2-22222-2-22222-2-2-22-2-2220000000000000000-2-22222-2-222-2-2-2-22200000000000000000000000000000000
χ552222-2-2-2-2-2-222-2-2222222-2-22-222-2-222-2-2-2-222-2-22222-2-2000000000000000000000000000000000000000000000000
χ562222-2-2-2-2-2-222-2-2222222-2-22-222-2-2-2-22222-2-222-2-2-2-222000000000000000000000000000000000000000000000000
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χ582-22-22-22i−2i2-22i−2i00002-22i−2i2i−2i0000001+i−1−i1+i−1−i1−i−1+i1−i−1+i1+i−1−i1+i−1−i1−i−1+i1−i−1+i−i2i2−i2i2−22−22−i2i2−i2i2−22−2200−2ζ32ζ300−2ζ2ζ00−2ζ32ζ300−2ζ2ζ0000000000000000
χ592-22-22-22i−2i2-22i−2i00002-22i−2i2i−2i000000−1−i1+i−1−i1+i−1+i1−i−1+i1−i−1−i1+i−1−i1+i−1+i1−i−1+i1−ii2−i2i2−i22−22−2i2−i2i2−i22−22−200−2ζ32ζ300−2ζ2ζ00−2ζ32ζ300−2ζ2ζ0000000000000000
χ602-22-22-22i−2i2-22i−2i00002-22i−2i2i−2i000000−1−i1+i−1−i1+i−1+i1−i−1+i1−i−1−i1+i−1−i1+i−1+i1−i−1+i1−i−i2i2−i2i2−22−22−i2i2−i2i2−22−22002ζ3−2ζ3002ζ−2ζ002ζ3−2ζ3002ζ−2ζ0000000000000000
χ612-22-22-22i−2i-222i−2i0000-22−2i2i−2i2i0000001+i−1−i1+i−1−i1−i−1+i1−i−1+i−1−i1+i−1−i1+i−1+i1−i−1+i1−i2−22−2−i2i2−i2i2−22−22i2−i2i2−i2002ζ−2ζ00−2ζ32ζ300−2ζ2ζ002ζ3−2ζ30000000000000000
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χ632-22-22-22i−2i-222i−2i0000-22−2i2i−2i2i000000−1−i1+i−1−i1+i−1+i1−i−1+i1−i1+i−1−i1+i−1−i1−i−1+i1−i−1+i2−22−2−i2i2−i2i2−22−22i2−i2i2−i200−2ζ2ζ002ζ3−2ζ3002ζ−2ζ00−2ζ32ζ30000000000000000
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χ692-22-22-2−2i2i-22−2i2i0000-222i−2i2i−2i0000001−i−1+i1−i−1+i1+i−1−i1+i−1−i−1+i1−i−1+i1−i−1−i1+i−1−i1+i2−22−2i2−i2i2−i2−22−22−i2i2−i2i200−2ζ32ζ3002ζ−2ζ002ζ3−2ζ300−2ζ2ζ0000000000000000
χ702-22-22-2−2i2i-22−2i2i0000-222i−2i2i−2i0000001−i−1+i1−i−1+i1+i−1−i1+i−1−i−1+i1−i−1+i1−i−1−i1+i−1−i1+i−22−22−i2i2−i2i22−22−2i2−i2i2−i2002ζ3−2ζ300−2ζ2ζ00−2ζ32ζ3002ζ−2ζ0000000000000000
χ712-22-22-2−2i2i-22−2i2i0000-222i−2i2i−2i000000−1+i1−i−1+i1−i−1−i1+i−1−i1+i1−i−1+i1−i−1+i1+i−1−i1+i−1−i2−22−2i2−i2i2−i2−22−22−i2i2−i2i2002ζ3−2ζ300−2ζ2ζ00−2ζ32ζ3002ζ−2ζ0000000000000000
χ722-22-22-2−2i2i-22−2i2i0000-222i−2i2i−2i000000−1+i1−i−1+i1−i−1−i1+i−1−i1+i1−i−1+i1−i−1+i1+i−1−i1+i−1−i−22−22−i2i2−i2i22−22−2i2−i2i2−i200−2ζ32ζ3002ζ−2ζ002ζ3−2ζ300−2ζ2ζ0000000000000000
χ732-22-2-222i−2i2-2−2i2i0000-222i−2i−2i2i0000001−i−1+i−1+i1−i−1−i1+i1+i−1−i1−i−1+i−1+i1−i−1−i1+i1+i−1−i2−2−22−i2i2i2−i22−2−22−i2i2i2−i22ζ3−2ζ3002ζ−2ζ002ζ3−2ζ3002ζ−2ζ000000000000000000
χ742-22-2-222i−2i2-2−2i2i0000-222i−2i−2i2i0000001−i−1+i−1+i1−i−1−i1+i1+i−1−i1−i−1+i−1+i1−i−1−i1+i1+i−1−i−222−2i2−i2−i2i2−222−2i2−i2−i2i2−2ζ32ζ300−2ζ2ζ00−2ζ32ζ300−2ζ2ζ000000000000000000
χ752-22-2-222i−2i2-2−2i2i0000-222i−2i−2i2i000000−1+i1−i1−i−1+i1+i−1−i−1−i1+i−1+i1−i1−i−1+i1+i−1−i−1−i1+i2−2−22−i2i2i2−i22−2−22−i2i2i2−i2−2ζ32ζ300−2ζ2ζ00−2ζ32ζ300−2ζ2ζ000000000000000000
χ762-22-2-222i−2i2-2−2i2i0000-222i−2i−2i2i000000−1+i1−i1−i−1+i1+i−1−i−1−i1+i−1+i1−i1−i−1+i1+i−1−i−1−i1+i−222−2i2−i2−i2i2−222−2i2−i2−i2i22ζ3−2ζ3002ζ−2ζ002ζ3−2ζ3002ζ−2ζ000000000000000000
χ772-22-2-222i−2i-22−2i2i00002-2−2i2i2i−2i0000001−i−1+i−1+i1−i−1−i1+i1+i−1−i−1+i1−i1−i−1+i1+i−1−i−1−i1+ii2−i2−i2i22−2−22−i2i2i2−i2−222−2−2ζ2ζ002ζ3−2ζ3002ζ−2ζ00−2ζ32ζ3000000000000000000
χ782-22-2-222i−2i-22−2i2i00002-2−2i2i2i−2i0000001−i−1+i−1+i1−i−1−i1+i1+i−1−i−1+i1−i1−i−1+i1+i−1−i−1−i1+i−i2i2i2−i2−222−2i2−i2−i2i22−2−222ζ−2ζ00−2ζ32ζ300−2ζ2ζ002ζ3−2ζ3000000000000000000
χ792-22-2-222i−2i-22−2i2i00002-2−2i2i2i−2i000000−1+i1−i1−i−1+i1+i−1−i−1−i1+i1−i−1+i−1+i1−i−1−i1+i1+i−1−ii2−i2−i2i22−2−22−i2i2i2−i2−222−22ζ−2ζ00−2ζ32ζ300−2ζ2ζ002ζ3−2ζ3000000000000000000
χ802-22-2-222i−2i-22−2i2i00002-2−2i2i2i−2i000000−1+i1−i1−i−1+i1+i−1−i−1−i1+i1−i−1+i−1+i1−i−1−i1+i1+i−1−i−i2i2i2−i2−222−2i2−i2−i2i22−2−22−2ζ2ζ002ζ3−2ζ3002ζ−2ζ00−2ζ32ζ3000000000000000000
χ812-22-2-22−2i2i2-22i−2i0000-22−2i2i2i−2i0000001+i−1−i−1−i1+i−1+i1−i1−i−1+i1+i−1−i−1−i1+i−1+i1−i1−i−1+i2−2−22i2−i2−i2i22−2−22i2−i2−i2i2−2ζ2ζ00−2ζ32ζ300−2ζ2ζ00−2ζ32ζ3000000000000000000
χ822-22-2-22−2i2i2-22i−2i0000-22−2i2i2i−2i0000001+i−1−i−1−i1+i−1+i1−i1−i−1+i1+i−1−i−1−i1+i−1+i1−i1−i−1+i−222−2−i2i2i2−i2−222−2−i2i2i2−i22ζ−2ζ002ζ3−2ζ3002ζ−2ζ002ζ3−2ζ3000000000000000000
χ832-22-2-22−2i2i2-22i−2i0000-22−2i2i2i−2i000000−1−i1+i1+i−1−i1−i−1+i−1+i1−i−1−i1+i1+i−1−i1−i−1+i−1+i1−i2−2−22i2−i2−i2i22−2−22i2−i2−i2i22ζ−2ζ002ζ3−2ζ3002ζ−2ζ002ζ3−2ζ3000000000000000000
χ842-22-2-22−2i2i2-22i−2i0000-22−2i2i2i−2i000000−1−i1+i1+i−1−i1−i−1+i−1+i1−i−1−i1+i1+i−1−i1−i−1+i−1+i1−i−222−2−i2i2i2−i2−222−2−i2i2i2−i2−2ζ2ζ00−2ζ32ζ300−2ζ2ζ00−2ζ32ζ3000000000000000000
χ852-22-2-22−2i2i-222i−2i00002-22i−2i−2i2i0000001+i−1−i−1−i1+i−1+i1−i1−i−1+i−1−i1+i1+i−1−i1−i−1+i−1+i1−ii2−i2−i2i2−222−2−i2i2i2−i22−2−22−2ζ32ζ3002ζ−2ζ002ζ3−2ζ300−2ζ2ζ000000000000000000
χ862-22-2-22−2i2i-222i−2i00002-22i−2i−2i2i0000001+i−1−i−1−i1+i−1+i1−i1−i−1+i−1−i1+i1+i−1−i1−i−1+i−1+i1−i−i2i2i2−i22−2−22i2−i2−i2i2−222−22ζ3−2ζ300−2ζ2ζ00−2ζ32ζ3002ζ−2ζ000000000000000000
χ872-22-2-22−2i2i-222i−2i00002-22i−2i−2i2i000000−1−i1+i1+i−1−i1−i−1+i−1+i1−i1+i−1−i−1−i1+i−1+i1−i1−i−1+ii2−i2−i2i2−222−2−i2i2i2−i22−2−222ζ3−2ζ300−2ζ2ζ00−2ζ32ζ3002ζ−2ζ000000000000000000
χ882-22-2-22−2i2i-222i−2i00002-22i−2i−2i2i000000−1−i1+i1+i−1−i1−i−1+i−1+i1−i1+i−1−i−1−i1+i−1+i1−i1−i−1+i−i2i2i2−i22−2−22i2−i2−i2i2−222−2−2ζ32ζ3002ζ−2ζ002ζ3−2ζ300−2ζ2ζ000000000000000000
χ8988-8-8000000008-8000000000000000000000000000000000000000000000000000000000000000000000000000000
χ9088-8-800000000-88000000000000000000000000000000000000000000000000000000000000000000000000000000
χ918-8-8800000000008i−8i0000000000000000000000000000000000000000000000000000000000000000000000000000
χ928-8-880000000000−8i8i0000000000000000000000000000000000000000000000000000000000000000000000000000

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