Finite Group Databasebeta

← Group #72226444

Character table — Group #72226444

Order 3200.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96C97C98C99C100C101C102C103C104C105C106C107C108C109C110C111C112C113
size11222444444444444444444444444448888888888888888888888888888888888888816161616161616161616161616161616161616161616161650505050100100100100100100100100100100200200200200200200
order12222245555551010101010101010101010101010101010102410101010101010101010101010101010101010101010101010101010101010101010101010101010101020202020202020202020202020202020202044442488888888248888
χ111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-111-1-1-1-1
χ3111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1iiii−i−i−i−i-1-1ii−i−i
χ4111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1−i−i−i−iiiii-1-1−i−iii
χ51111111111111111111111111111111-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-111111111111111-1-1-1-1-1-1
χ61111111111111111111111111111111-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1-1-11111
χ71111111111111111111111111111111-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1iiii−i−i−i−i11−i−iii
χ81111111111111111111111111111111-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1−i−i−i−iiiii11ii−i−i
χ911111-1-11111111111111111111111111-1111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-111-1-111-1-11-11-11-1
χ1011111-1-11111111111111111111111111-1111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-111-1-1111-1-11-11
χ1111111-1-11111111111111111111111111-1111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111ii−i−i−i−iii-11i−i−ii
χ1211111-1-11111111111111111111111111-1111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111−i−iiiii−i−i-11−iii−i
χ1311111-1-1111111111111111111111111-11111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111111111-1-111-1-111-1-1-11-11-11
χ1411111-1-1111111111111111111111111-11111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111111111-1-1-1-111-1-111-111-11-1
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χ19222-2-200222222222222-2-2-2-2-2-2-2-2-2-2-2-200222222-2-2-2-2-2-2000000000000000000000000000000000000000000000000-2-22200002-200-22000000
χ20222-2-200222222222222-2-2-2-2-2-2-2-2-2-2-2-200222222-2-2-2-2-2-2000000000000000000000000000000000000000000000000-2-2220000-22002-2000000
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χ1108-800000-2-2−2−253+53−5−2+25222+25−3−5−3+52−2525−25−252500−5+55−55+5−5−500000000000000002ζ6−2ζ14−2ζ6+2ζ14−2ζ2+2ζ182ζ2−2ζ182ζ2−2ζ18−2ζ2+2ζ182ζ6−2ζ14−2ζ6+2ζ14−2ζ2+2ζ182ζ2−2ζ18−2ζ2+2ζ182ζ2−2ζ18−2ζ6+2ζ142ζ6−2ζ1400002ζ2−2ζ18−2ζ2+2ζ182ζ6−2ζ14−2ζ6+2ζ14−2ζ6+2ζ142ζ6−2ζ1400000000000000000000000000000000000000000000
χ1118-800000-2-2−2−253+53−5−2+25222+25−3−5−3+52−2525−25−252500−5+55−55+5−5−50000000000000000−2ζ6+2ζ142ζ6−2ζ142ζ2−2ζ18−2ζ2+2ζ18−2ζ2+2ζ182ζ2−2ζ18−2ζ6+2ζ142ζ6−2ζ142ζ2−2ζ18−2ζ2+2ζ182ζ2−2ζ18−2ζ2+2ζ182ζ6−2ζ14−2ζ6+2ζ140000−2ζ2+2ζ182ζ2−2ζ18−2ζ6+2ζ142ζ6−2ζ142ζ6−2ζ14−2ζ6+2ζ1400000000000000000000000000000000000000000000
χ1128-800000-2-2−2−253+53−5−2+25222+25−3−5−3+52−25−252525−25005−5−5+5−5−55+50000000000000000−2ζ2+2ζ182ζ2−2ζ18−2ζ6+2ζ142ζ6−2ζ14−2ζ6+2ζ142ζ6−2ζ142ζ2−2ζ18−2ζ2+2ζ182ζ2−2ζ18−2ζ2+2ζ18−2ζ2+2ζ182ζ2−2ζ1800−2ζ6+2ζ142ζ6−2ζ14−2ζ2+2ζ182ζ2−2ζ18002ζ6−2ζ14−2ζ6+2ζ142ζ6−2ζ14−2ζ6+2ζ1400000000000000000000000000000000000000000000
χ1138-800000-2-2−2−253+53−5−2+25222+25−3−5−3+52−25−252525−25005−5−5+5−5−55+500000000000000002ζ2−2ζ18−2ζ2+2ζ182ζ6−2ζ14−2ζ6+2ζ142ζ6−2ζ14−2ζ6+2ζ14−2ζ2+2ζ182ζ2−2ζ18−2ζ2+2ζ182ζ2−2ζ182ζ2−2ζ18−2ζ2+2ζ18002ζ6−2ζ14−2ζ6+2ζ142ζ2−2ζ18−2ζ2+2ζ1800−2ζ6+2ζ142ζ6−2ζ14−2ζ6+2ζ142ζ6−2ζ1400000000000000000000000000000000000000000000

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