Finite Group Databasebeta

← Group #72340815

Character table — Group #72340815

Order 3072.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80
size11113333444466661212121212121212121212121212242424242424242424242424242424242424242424242424484848484848484848489696969696969696128128128128128128128128
order124422442244444422224444444444224444448888888888888888448888888844444444366612121212
χ111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111
χ311111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-111111111iiiiiiii−i−i−i−i−i−i−i−i-1-1iiii−i−i−i−iiiii−i−i−i−i1-1-1111-1-1
χ411111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-111111111−i−i−i−i−i−i−i−iiiiiiiii-1-1−i−i−i−iiiii−i−i−i−iiiii1-1-1111-1-1
χ511-1-111-1-111-1-111-1-1-1-1-1-1111111-1-11-111-1-111-1-1iiii−i−i−i−iiiii−i−i−i−i1-1ii−i−iii−i−iii−i−iii−i−i1111-1-1-1-1
χ611-1-111-1-111-1-111-1-1-1-1-1-1111111-1-11-111-1-111-1-1−i−i−i−iiiii−i−i−i−iiiii1-1−i−iii−i−iii−i−iii−i−iii1111-1-1-1-1
χ711-1-111-1-1-1-111-1-1111111-1-1-1-111-1-1-1111-1-111-1-11111-1-1-1-1-1-1-1-11111-1111-1-1-1-11111-1-1-1-1111-1-11-1-111
χ811-1-111-1-1-1-111-1-1111111-1-1-1-111-1-1-1111-1-111-1-1-1-1-1-111111111-1-1-1-1-11-1-11111-1-1-1-11111-1-11-1-11-1-111
χ9222222222222222222222222222222222222220000000000000000220000000000000000-1-1-1-1-1-1-1-1
χ1022222222-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-22222-2-2222222220000000000000000-2-20000000000000000-111-1-1-111
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χ1222-2-222-2-2-2-222-2-2222222-2-2-2-222-2-2-2222-2-222-2-20000000000000000-220000000000000000-111-111-1-1
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χ18333333333333-1-1-1-1-1-133-1-133-1-1-1-1-1-1-1-1-1-1-13-13-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111-11-11-11-100000000
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χ2133333333-3-3-3-31111-3-311-3-311-1-1-1-111-1-1-1-13-13-1iiiiiiii−i−i−i−i−i−i−i−i11−i−i−i−iiiiii−ii−i−ii−ii00000000
χ2233333333-3-3-3-31111-3-311-3-311-1-1-1-111-1-1-1-13-13-1−i−i−i−i−i−i−i−iiiiiiiii11iiii−i−i−i−i−ii−iii−ii−i00000000
χ2333333333-3-3-3-3-3-3-3-3111111113333-3-3-1-1-1-1-1-1-1-1iiiiiiii−i−i−i−i−i−i−i−i11iiii−i−i−i−i−i−i−i−iiiii00000000
χ2433333333-3-3-3-3-3-3-3-3111111113333-3-3-1-1-1-1-1-1-1-1−i−i−i−i−i−i−i−iiiiiiiii11−i−i−i−iiiiiiiii−i−i−i−i00000000
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χ2733-3-333-3-333-3-3-1-11111-3-3-1-133-1-111-11-1-111-131-3iiii−i−i−i−iiiii−i−i−i−i-11−i−iii−i−iii−iii−i−iii−i00000000
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χ3033-3-333-3-333-3-3-1-111-3-31133-1-1-1-111-11-1-1113-1-31−i−i−i−iiiii−i−i−i−iiiii-11ii−i−iii−i−i−iii−i−iii−i00000000
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χ3333-3-333-3-3-3-33311-1-1-1-13311-3-3-1-1111-1-1-111-131-31111-1-1-1-1-1-1-1-111111-1-1-11111-1-1-111-11-1-1100000000
χ3433-3-333-3-3-3-33311-1-1-1-13311-3-3-1-1111-1-1-111-131-3-1-1-1-111111111-1-1-1-11-111-1-1-1-1111-1-11-111-100000000
χ3533-3-333-3-3-3-333-3-333-1-1-1-1111133-3-3-33-1-111-1-1111111-1-1-1-1-1-1-1-111111-111-1-1-1-111-1-11111-1-100000000
χ3633-3-333-3-3-3-333-3-333-1-1-1-1111133-3-3-33-1-111-1-111-1-1-1-111111111-1-1-1-11-1-1-11111-1-111-1-1-1-11100000000
χ374-44i−4i4-44i−4i4-44i−4i000000000000000000000000002ζ2ζ−2ζ−2ζ2ζ32ζ3−2ζ3−2ζ32ζ2ζ−2ζ−2ζ2ζ32ζ3−2ζ3−2ζ300000000000000000011-1-1i−ii−i
χ384-44i−4i4-44i−4i4-44i−4i00000000000000000000000000−2ζ−2ζ2ζ2ζ−2ζ3−2ζ32ζ32ζ3−2ζ−2ζ2ζ2ζ−2ζ3−2ζ32ζ32ζ300000000000000000011-1-1i−ii−i
χ394-44i−4i4-44i−4i-44−4i4i000000000000000000000000002ζ32ζ3−2ζ3−2ζ3−2ζ−2ζ2ζ2ζ−2ζ3−2ζ32ζ32ζ32ζ2ζ−2ζ−2ζ0000000000000000001-11-1i−i−ii
χ404-44i−4i4-44i−4i-44−4i4i00000000000000000000000000−2ζ3−2ζ32ζ32ζ32ζ2ζ−2ζ−2ζ2ζ32ζ3−2ζ3−2ζ3−2ζ−2ζ2ζ2ζ0000000000000000001-11-1i−i−ii
χ414-4−4i4i4-4−4i4i4-4−4i4i000000000000000000000000002ζ32ζ3−2ζ3−2ζ32ζ2ζ−2ζ−2ζ2ζ32ζ3−2ζ3−2ζ32ζ2ζ−2ζ−2ζ00000000000000000011-1-1−ii−ii
χ424-4−4i4i4-4−4i4i4-4−4i4i00000000000000000000000000−2ζ3−2ζ32ζ32ζ3−2ζ−2ζ2ζ2ζ−2ζ3−2ζ32ζ32ζ3−2ζ−2ζ2ζ2ζ00000000000000000011-1-1−ii−ii
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χ516-66i−6i-22−2i2i00004i−4i4-4-22-22−2i2i−2i2i2-22i−2i00-22−2i2i00002−22−2−i2i2−i2i2i2−i2i2−i2−22−2200−22i2−i2−i2i22−20000000000000000
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χ7812-1212i−12i-44−4i4i00000000-444-4−4i4i4i−4i-44−4i4i0000000000000000000000000000000000000000000000000000
χ7912-12−12i12i-444i−4i000000004-4-44−4i4i4i−4i-444i−4i0000000000000000000000000000000000000000000000000000
χ8012-12−12i12i-444i−4i00000000-444-44i−4i−4i4i-444i−4i0000000000000000000000000000000000000000000000000000

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