Finite Group Databasebeta

← Group #72226539

Character table — Group #72226539

Order 3200.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96C97C98C99C100C101C102C103C104C105C106C107C108C109C110C111C112C113C114C115C116
size11222444444444444444444444444444488888888888888888888888888888888888881616161616161616161616161616161616161616161616162525505050100100100100100100100100100100100100200200200200200
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χ111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-11-1-1-1-1
χ31111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1iiii−i−i−i−i-1ii−i−i
χ41111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1−i−i−i−iiiii-1−i−iii
χ51111111-1-1111111111111111111111111-1111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-11111111111111-1-111111111-1-1-1-1-1
χ61111111-1-1111111111111111111111111-1111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-11111111111111-1-1-1-1-1-1-1-1-1-1-11111
χ71111111-1-1111111111111111111111111-1111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-111iiii−i−i−i−i1−i−iii
χ81111111-1-1111111111111111111111111-1111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-111−i−i−i−iiiii1ii−i−i
χ911111-1-111111111111111111111111111-1111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111-1-11111-1-111-1-1-11-11-1
χ1011111-1-111111111111111111111111111-1111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111-1-111-1-111-1-111-1-11-11
χ1111111-1-111111111111111111111111111-1111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1ii−i−i−i−iii1i−i−ii
χ1211111-1-111111111111111111111111111-1111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1−i−iiiii−i−i1−iii−i
χ1311111-1-1-1-11111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-111111-1-1-1-111-1-111-1-11-11-11
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χ20222-2-20000222222-2-2-2-2-2-2-2-2-2-2-2-22222220222222-2-2-2-2-2-2000000000000000000000000000000000000000000000000-2-22-22000000−2i2i002i−2i00000
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χ2522-2-222-2002222222222222222222222220-2-2-2-2-2-2-2-2-2-2-2-2000000000000000000000000222222000000000000-2-2-2-2-2-2222-2-22-2000000000000000
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χ1098-800000−4i4i-2-2−2+253−53+5−2−2525−25−2525005+5−5−5−5+55−500222−25−3+5−3−52+2500000000000002ζ3+2ζ7−2ζ3−2ζ72ζ11+2ζ19−2ζ11−2ζ192ζ11+2ζ19−2ζ11−2ζ192ζ3+2ζ7−2ζ3−2ζ72ζ11+2ζ19−2ζ11−2ζ192ζ11+2ζ19−2ζ11−2ζ192ζ3+2ζ7−2ζ3−2ζ7−4i4i−4i4i2ζ11+2ζ19−2ζ11−2ζ192ζ3+2ζ7−2ζ3−2ζ72ζ3+2ζ7−2ζ3−2ζ70000000000000000000000000000000000000000000000
χ1108-800000−4i4i-2-2−2+253−53+5−2−25−252525−2500−5−55+55−5−5+500222−25−3+5−3−52+2500000000000002ζ11+2ζ19−2ζ11−2ζ192ζ3+2ζ7−2ζ3−2ζ72ζ3+2ζ7−2ζ3−2ζ72ζ11+2ζ19−2ζ11−2ζ192ζ11+2ζ19−2ζ11−2ζ192ζ11+2ζ19−2ζ11−2ζ19−4i4i2ζ3+2ζ7−2ζ3−2ζ72ζ11+2ζ19−2ζ11−2ζ19−4i4i2ζ3+2ζ7−2ζ3−2ζ72ζ3+2ζ7−2ζ3−2ζ70000000000000000000000000000000000000000000000
χ1118-800000−4i4i-2-23−5−2−25−2+253+525−2525−25−5−55+500005−5−5+522−3+52+252−25−3−500000000000002ζ3+2ζ7−2ζ3−2ζ72ζ11+2ζ19−2ζ11−2ζ192ζ3+2ζ7−2ζ3−2ζ72ζ11+2ζ19−2ζ11−2ζ19−4i4i2ζ3+2ζ7−2ζ3−2ζ72ζ3+2ζ7−2ζ3−2ζ72ζ3+2ζ7−2ζ3−2ζ72ζ11+2ζ19−2ζ11−2ζ192ζ11+2ζ19−2ζ11−2ζ192ζ11+2ζ19−2ζ11−2ζ19−4i4i0000000000000000000000000000000000000000000000
χ1128-800000−4i4i-2-23−5−2−25−2+253+5−2525−25255+5−5−50000−5+55−522−3+52+252−25−3−500000000000002ζ11+2ζ19−2ζ11−2ζ192ζ3+2ζ7−2ζ3−2ζ72ζ11+2ζ19−2ζ11−2ζ192ζ3+2ζ7−2ζ3−2ζ72ζ3+2ζ7−2ζ3−2ζ7−4i4i2ζ3+2ζ7−2ζ3−2ζ72ζ3+2ζ7−2ζ3−2ζ72ζ11+2ζ19−2ζ11−2ζ192ζ11+2ζ19−2ζ11−2ζ19−4i4i2ζ11+2ζ19−2ζ11−2ζ190000000000000000000000000000000000000000000000
χ1138-800000−4i4i-2-23+5−2+25−2−253−525−2525−255−5−5+50000−5−55+522−3−52−252+25−3+500000000000002ζ3+2ζ7−2ζ3−2ζ72ζ11+2ζ19−2ζ11−2ζ192ζ3+2ζ7−2ζ3−2ζ72ζ11+2ζ19−2ζ11−2ζ192ζ11+2ζ19−2ζ11−2ζ19−4i4i2ζ11+2ζ19−2ζ11−2ζ192ζ11+2ζ19−2ζ11−2ζ192ζ3+2ζ7−2ζ3−2ζ72ζ3+2ζ7−2ζ3−2ζ7−4i4i2ζ3+2ζ7−2ζ3−2ζ70000000000000000000000000000000000000000000000
χ1148-800000−4i4i-2-23+5−2+25−2−253−5−2525−2525−5+55−500005+5−5−522−3−52−252+25−3+500000000000002ζ11+2ζ19−2ζ11−2ζ192ζ3+2ζ7−2ζ3−2ζ72ζ11+2ζ19−2ζ11−2ζ192ζ3+2ζ7−2ζ3−2ζ7−4i4i2ζ11+2ζ19−2ζ11−2ζ192ζ11+2ζ19−2ζ11−2ζ192ζ11+2ζ19−2ζ11−2ζ192ζ3+2ζ7−2ζ3−2ζ72ζ3+2ζ7−2ζ3−2ζ72ζ3+2ζ7−2ζ3−2ζ7−4i4i0000000000000000000000000000000000000000000000
χ1158-800000−4i4i-2-2−2−253+53−5−2+2525−25−252500−5+55−55+5−5−500222+25−3−5−3+52−2500000000000002ζ3+2ζ7−2ζ3−2ζ72ζ11+2ζ19−2ζ11−2ζ192ζ11+2ζ19−2ζ11−2ζ192ζ3+2ζ7−2ζ3−2ζ72ζ3+2ζ7−2ζ3−2ζ72ζ3+2ζ7−2ζ3−2ζ7−4i4i2ζ11+2ζ19−2ζ11−2ζ192ζ3+2ζ7−2ζ3−2ζ7−4i4i2ζ11+2ζ19−2ζ11−2ζ192ζ11+2ζ19−2ζ11−2ζ190000000000000000000000000000000000000000000000
χ1168-800000−4i4i-2-2−2−253+53−5−2+25−252525−25005−5−5+5−5−55+500222+25−3−5−3+52−2500000000000002ζ11+2ζ19−2ζ11−2ζ192ζ3+2ζ7−2ζ3−2ζ72ζ3+2ζ7−2ζ3−2ζ72ζ11+2ζ19−2ζ11−2ζ192ζ3+2ζ7−2ζ3−2ζ72ζ3+2ζ7−2ζ3−2ζ72ζ11+2ζ19−2ζ11−2ζ19−4i4i−4i4i2ζ3+2ζ7−2ζ3−2ζ72ζ11+2ζ19−2ζ11−2ζ192ζ11+2ζ19−2ζ11−2ζ190000000000000000000000000000000000000000000000

Here ζ is a primitive root of unity of order 20 (ζ20 = 1); i = ζ5.