Finite Group Databasebeta

← Group #72226528

Character table — Group #72226528

Order 3200.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92
size1122244444444448888888888888888888888888888888888888888888820202020252540405050508080808080808080100100100100100100100100100100200200200200
order1222244551010101010105510101010101010101010101010101010101020202020202020202020202020202020202020202020202022442244222101020202020202044444444444444
χ111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1
χ3111111111111111111111111111111111111111111111111111111111111-11-1-1-11-1-1-1-11-111-1-11-1-1-1iiii−i−i−i−iii−i−i
χ4111111111111111111111111111111111111111111111111111111111111-11-1-1-11-1-1-1-11-111-1-11-1-1-1−i−i−i−iiiii−i−iii
χ511111111111111111111111111111111111111111111111111111111111-11-11-1-1-11-1-1-1-11-1-111-11-1-1ii−i−iii−i−ii−ii−i
χ611111111111111111111111111111111111111111111111111111111111-11-11-1-1-11-1-1-1-11-1-111-11-1-1−i−iii−i−iii−ii−ii
χ711111111111111111111111111111111111111111111111111111111111-1-1-1-111-1-1111-1-1-1-1-1-1-1-11111-1-1-1-1111-1-11
χ811111111111111111111111111111111111111111111111111111111111-1-1-1-111-1-1111-1-1-1-1-1-1-1-111-1-11111-1-1-111-1
χ911111-1-11111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111-1-111111-1-1-1-111-1-111111111-1-1-1-1
χ1011111-1-11111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111-1-111111-1-1-1-111-1-1-1-1-1-1-1-1-1-11111
χ1111111-1-11111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11-11-1-1-1-11-1-1-11-1-1-1111-111iiii−i−i−i−i−i−iii
χ1211111-1-11111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11-11-1-1-1-11-1-1-11-1-1-1111-111−i−i−i−iiiiiii−i−i
χ1311111-1-11111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11-11-1-11-1-1-1-1-1111-1-1-1111ii−i−iii−i−i−ii−ii
χ1411111-1-11111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11-11-1-11-1-1-1-1-1111-1-1-1111−i−iii−i−iiii−ii−i
χ1511111-1-11111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111-1-11111-1-1-1-111-1-1-1-111-111-1
χ1611111-1-11111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111-1-11111-1-1-1-1-1-11111-1-11-1-11
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χ498888888-2-2-2-2-2-2-2-23-2-2-2-2-233-2-233-2-233-2-23-2-2-2-2-2-2-2-2-23333-2-2-2-2-2-2-2-23333000000000000000000000000000000000
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χ5288888-8-8-2-2-2-2-2-2-2-2-23-2-2-2-2-2-233-2-233-2-233-23222222222222-3-3-3-3-3-3-3-32222000000000000000000000000000000000
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χ828-8000−4i4i8-200−2525-82-2-2000000000000−2525−252522−4i4i−4i4i2ζ11+2ζ19−2ζ11−2ζ192ζ3+2ζ7−2ζ3−2ζ72ζ11+2ζ192ζ11+2ζ19−2ζ11−2ζ19−2ζ11−2ζ192ζ11+2ζ192ζ11+2ζ19−2ζ11−2ζ19−2ζ11−2ζ192ζ3+2ζ72ζ3+2ζ7−2ζ3−2ζ7−2ζ3−2ζ72ζ3+2ζ72ζ3+2ζ7−2ζ3−2ζ7−2ζ3−2ζ7000000000000000000000000000000000
χ838-8000−4i4i-2825−25002-8-2-200000000000025−25−2525222ζ3+2ζ7−2ζ3−2ζ72ζ11+2ζ19−2ζ11−2ζ19−4i4i−4i4i2ζ3+2ζ72ζ3+2ζ7−2ζ3−2ζ7−2ζ3−2ζ72ζ11+2ζ192ζ11+2ζ19−2ζ11−2ζ19−2ζ11−2ζ192ζ3+2ζ72ζ3+2ζ7−2ζ3−2ζ7−2ζ3−2ζ72ζ11+2ζ192ζ11+2ζ19−2ζ11−2ζ19−2ζ11−2ζ19000000000000000000000000000000000
χ848-8000−4i4i-28−2525002-8-2-2000000000000−252525−25222ζ11+2ζ19−2ζ11−2ζ192ζ3+2ζ7−2ζ3−2ζ7−4i4i−4i4i2ζ11+2ζ192ζ11+2ζ19−2ζ11−2ζ19−2ζ11−2ζ192ζ3+2ζ72ζ3+2ζ7−2ζ3−2ζ7−2ζ3−2ζ72ζ11+2ζ192ζ11+2ζ19−2ζ11−2ζ19−2ζ11−2ζ192ζ3+2ζ72ζ3+2ζ7−2ζ3−2ζ7−2ζ3−2ζ7000000000000000000000000000000000
χ858-8000−4i4i-2-225−2525−25223-200005-5005−525−25−5500-322ζ3+2ζ7−2ζ3−2ζ72ζ11+2ζ19−2ζ11−2ζ192ζ3+2ζ7−2ζ3−2ζ72ζ11+2ζ19−2ζ11−2ζ19i−5ζ3−5ζ7−3ζ11−3ζ19−i5ζ3+5ζ7+3ζ11+3ζ192ζ3+2ζ72ζ11+2ζ19−2ζ3−2ζ7−2ζ11−2ζ192ζ11+2ζ192ζ3+2ζ7−2ζ11−2ζ19−2ζ3−2ζ7i−3ζ3−3ζ7−5ζ11−5ζ19−i3ζ3+3ζ7+5ζ11+5ζ19000000000000000000000000000000000
χ868-8000−4i4i-2-225−2525−25223-20000-5500−55−2525−5500-322ζ3+2ζ7−2ζ3−2ζ72ζ11+2ζ19−2ζ11−2ζ192ζ3+2ζ7−2ζ3−2ζ72ζ11+2ζ19−2ζ11−2ζ19−5ζ3−5ζ7−3ζ11−3ζ19i5ζ3+5ζ7+3ζ11+3ζ19−i2ζ11+2ζ192ζ3+2ζ7−2ζ11−2ζ19−2ζ3−2ζ72ζ3+2ζ72ζ11+2ζ19−2ζ3−2ζ7−2ζ11−2ζ19−3ζ3−3ζ7−5ζ11−5ζ19i3ζ3+3ζ7+5ζ11+5ζ19−i000000000000000000000000000000000
χ878-8000−4i4i-2-225−25−252522-230000005-525−25−55005−52-32ζ3+2ζ7−2ζ3−2ζ72ζ11+2ζ19−2ζ11−2ζ192ζ11+2ζ19−2ζ11−2ζ192ζ3+2ζ7−2ζ3−2ζ72ζ3+2ζ72ζ11+2ζ19−2ζ3−2ζ7−2ζ11−2ζ19i−3ζ3−3ζ7−5ζ11−5ζ19−i3ζ3+3ζ7+5ζ11+5ζ19i−5ζ3−5ζ7−3ζ11−3ζ19−i5ζ3+5ζ7+3ζ11+3ζ192ζ11+2ζ192ζ3+2ζ7−2ζ11−2ζ19−2ζ3−2ζ7000000000000000000000000000000000
χ888-8000−4i4i-2-225−25−252522-23000000-55−25255−5005−52-32ζ3+2ζ7−2ζ3−2ζ72ζ11+2ζ19−2ζ11−2ζ192ζ11+2ζ19−2ζ11−2ζ192ζ3+2ζ7−2ζ3−2ζ72ζ11+2ζ192ζ3+2ζ7−2ζ11−2ζ19−2ζ3−2ζ7−3ζ3−3ζ7−5ζ11−5ζ19i3ζ3+3ζ7+5ζ11+5ζ19−i−5ζ3−5ζ7−3ζ11−3ζ19i5ζ3+5ζ7+3ζ11+3ζ19−i2ζ3+2ζ72ζ11+2ζ19−2ζ3−2ζ7−2ζ11−2ζ19000000000000000000000000000000000
χ898-8000−4i4i-2-2−252525−2522-230000005-5−25255−500−552-32ζ11+2ζ19−2ζ11−2ζ192ζ3+2ζ7−2ζ3−2ζ72ζ3+2ζ7−2ζ3−2ζ72ζ11+2ζ19−2ζ11−2ζ192ζ11+2ζ192ζ3+2ζ7−2ζ11−2ζ19−2ζ3−2ζ7i−5ζ3−5ζ7−3ζ11−3ζ19−i5ζ3+5ζ7+3ζ11+3ζ19i−3ζ3−3ζ7−5ζ11−5ζ19−i3ζ3+3ζ7+5ζ11+5ζ192ζ3+2ζ72ζ11+2ζ19−2ζ3−2ζ7−2ζ11−2ζ19000000000000000000000000000000000
χ908-8000−4i4i-2-2−252525−2522-23000000-5525−25−5500−552-32ζ11+2ζ19−2ζ11−2ζ192ζ3+2ζ7−2ζ3−2ζ72ζ3+2ζ7−2ζ3−2ζ72ζ11+2ζ19−2ζ11−2ζ192ζ3+2ζ72ζ11+2ζ19−2ζ3−2ζ7−2ζ11−2ζ19−5ζ3−5ζ7−3ζ11−3ζ19i5ζ3+5ζ7+3ζ11+3ζ19−i−3ζ3−3ζ7−5ζ11−5ζ19i3ζ3+3ζ7+5ζ11+5ζ19−i2ζ11+2ζ192ζ3+2ζ7−2ζ11−2ζ19−2ζ3−2ζ7000000000000000000000000000000000
χ918-8000−4i4i-2-2−2525−2525223-200005-500−55−25255−500-322ζ11+2ζ19−2ζ11−2ζ192ζ3+2ζ7−2ζ3−2ζ72ζ11+2ζ19−2ζ11−2ζ192ζ3+2ζ7−2ζ3−2ζ7i−3ζ3−3ζ7−5ζ11−5ζ19−i3ζ3+3ζ7+5ζ11+5ζ192ζ11+2ζ192ζ3+2ζ7−2ζ11−2ζ19−2ζ3−2ζ72ζ3+2ζ72ζ11+2ζ19−2ζ3−2ζ7−2ζ11−2ζ19i−5ζ3−5ζ7−3ζ11−3ζ19−i5ζ3+5ζ7+3ζ11+3ζ19000000000000000000000000000000000
χ928-8000−4i4i-2-2−2525−2525223-20000-55005−525−255−500-322ζ11+2ζ19−2ζ11−2ζ192ζ3+2ζ7−2ζ3−2ζ72ζ11+2ζ19−2ζ11−2ζ192ζ3+2ζ7−2ζ3−2ζ7−3ζ3−3ζ7−5ζ11−5ζ19i3ζ3+3ζ7+5ζ11+5ζ19−i2ζ3+2ζ72ζ11+2ζ19−2ζ3−2ζ7−2ζ11−2ζ192ζ11+2ζ192ζ3+2ζ7−2ζ11−2ζ19−2ζ3−2ζ7−5ζ3−5ζ7−3ζ11−3ζ19i5ζ3+5ζ7+3ζ11+3ζ19−i000000000000000000000000000000000

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