Finite Group Databasebeta

← Group #13168111

Character table — Group #13168111

Order 1728.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96C97C98C99C100C101C102C103C104C105C106C107C108C109C110C111
size11112222222222224444444444444446666888888888888888812121212121212121212121212121212121212121818181818181818181818182424242424242424242424242424242436363636363636367272108108
order1222333666666666333466666666612122244366612121212121212121212121224446666661212121212121212121222444444666666666121212121212121212121244121212121212121224
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111111111111111-11-1111111-1-1111111-1-11111-1-1-1-1111111111-1-111111-1-1-1-1-1-111-1-1-1-1-1-1-1-1
χ3111111111111111111111111111111111-1-11111111111111111-11111111-1-11111-1-1-1-111-1-1-1-111-1-1-1-1-1-1-111-1-111111-1-111111-1-1-1-1-111-11-1-1
χ4111111111111111111111111111111111-1-11111111111111111-1-11-11111-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-1-111-1-1-1-1111-1-1-1-1-1-1-11-1-111-1-11-111
χ51111111111111111111111111111111-1-111111111111111111111-11-1-1-1-11111-1-1111111-1-1-1-1-1-111-1-1-1-11-1-11111-1-1-1111111-11-1-111-1-11-1-1-1
χ61111111111111111111111111111111-1-11111111111111111111-1-1-1-1-1-1-111-1-1-1-11111-1-1-1-1-1-111-1-1-1-1-1-11-1-111-1-1-1-1-111-1-1-1-11-1-1-1-1-111-1111
χ71111111111111111111111111111111-1-1-1-11111111111111111-11-11-1-1-1-1-1-111-1-1-1-1-1-1111111-1-1-1-11111-1-1-1-1-111-1-1-1-1-11111-1-111-1-1-1-1-1-111
χ81111111111111111111111111111111-1-1-1-11111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111-1-1
χ91111111111111111111-1111111111-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-11-1-11111-1-111-1-11111-1-1-1-111-1-111-1-1-1-1-111-1-11-1-1-1-111-1-1111-11111-1-1-11-11
χ101111111111111111111-1111111111-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111-1-1-1-1-1-1111111-1-11111-1-1-1-1-1-1-111-1-1-11-1-1-11111-1-1-1111-1-1111-11-1
χ111111111111111111111-1111111111-1-111-1-11111-1-1-1-1-1-1-1-1-1-1-1-111-1-111111111-1-1-1-1-1-1-1-111-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1111-1
χ121111111111111111111-1111111111-1-111-1-11111-1-1-1-1-1-1-1-1-1-1-1-11-1-11111111-1-1-1-1-1-1-1-11111-1-11111111111111-11-1-1-1-1-111-1-1-1-1-1-11111-1-1-11
χ131111111111111111111-1111111111-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-1-111111111-1-111-1-111111111-1-1-1-1-11-111111-1-111-1-1-1-11111-1-11-1
χ141111111111111111111-1111111111-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-11111-1-1-1-1-1-111111111-1-111-1-1-1-1-1-111-11
χ151111111111111111111-1111111111-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1111-1-1-1-1-1111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-11-1-1111-1111-1-1-1-111-1111-1-1111-1-11
χ161111111111111111111-1111111111-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-11-111-1-1-1-111-1-111-1-1-1-111-1-111-1-111-1-1-1-11-1-111-11111-1-111-1-11-11111-1-1-111-1
χ17222222-12-1222-1-1222-1-122-1-1-1-12-1-12-1-12222-1-1-1-122-1-1-1-122-1-1-1-1202022-1-1-1-100-1-122-1-10022220000-1-1-1-12-1-1-1-1002-1-1-1-1000000-1-100000000
χ18222222-12-1222-1-1222-1-122-1-1-1-12-1-12-1-122-2-2-1-1-1-122-1-1-1-122-1-1-1-1-202022-1-11100-1-1-2-21100-2-2-2-200001111-2-1-111002-1-1110000001100000000
χ19222222-12-1222-1-1222-1-122-1-1-1-12-1-12-1-1-2-222-1-1-1-122-1-1-1-122-1-1-1-120-20-2-211-1-1001122-1-100-2-2-2-200001111211-1-100-211-1-10000001100000000
χ20222222-12-1222-1-1222-1-122-1-1-1-12-1-12-1-1-2-2-2-2-1-1-1-122-1-1-1-122-1-1-1-1-20-20-2-211110011-2-2110022220000-1-1-1-1-2111100-21111000000-1-100000000
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χ2522222-12222-1-122-12-12-12-12-12-1-12-1-1220022-1-1-1-12-122-1-1-1-1-1-1-1-12202000022-1-100-1-12222000000220000-100-1-12-1000-1-1-1-1-1-10200-1-100-1000
χ2622222-12222-1-122-12-12-12-12-12-1-12-1-1220022-1-1-1-12-122-1-1-1-1-1-1-1-12-20-20000221100-1-122-2-2000000-2-20000-100-1-1-21000-1-111110-20011001000
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χ2822222-12222-1-122-12-12-12-12-12-1-12-1-12200-2-2-1-1-1-12-122-1-1-1-1-1-1-1-1-2-20-20000-2-2110011-2-2-2-200000022000010011-210001111110200-1-100-1000
χ2922222-12222-1-122-12-12-1-2-12-12-1-12-1-1-2-20022-1-1-1-1-21-2-211111111-220-20000-2-2-1-100-1-122-2-20000002200001001121000-1-111-1-10-200-1-1001000
χ3022222-12222-1-122-12-12-1-2-12-12-1-12-1-1-2-20022-1-1-1-1-21-2-211111111-2-2020000-2-21100-1-12222000000-2-2000010011-2-1000-1-1-1-11102001100-1000
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χ352222-122-12-122222-1-1-122-1-12-12-1-12-122-2-200-1-1-1-1-12-1-122-1-1-1-1-1-102-2211-2-20022-2-20000-1-10000-2-200000001100-1211100-1-1-1-1-200000110100
χ362222-122-12-122222-1-1-122-1-12-12-1-12-122-2-200-1-1-1-1-12-1-122-1-1-1-1-1-10-2-2-211-2-200-2-2-2-2000011000022000000011001-2111001111200000-1-10-100
χ372222-122-12-122222-1-1-12-2-1-12-12-1-12-1-2-22200-1-1-1-11-211-2-211111102-2-2-1-1220022-2-20000110000-2-20000000-1-100-1-21110011-1-1200000110-100
χ382222-122-12-122222-1-1-12-2-1-12-12-1-12-1-2-22200-1-1-1-11-211-2-21111110-2-22-1-12200-2-2-2-20000-1-10000220000000-1-1001211100-1-111-200000-1-10100
χ392222-122-12-122222-1-1-12-2-1-12-12-1-12-1-2-2-2-200-1-1-1-11-211-2-2111111022-211-2-200222200001100002200000001100-1-2-1-1-10011-1-1-200000-1-10100
χ402222-122-12-122222-1-1-12-2-1-12-12-1-12-1-2-2-2-200-1-1-1-11-211-2-21111110-22211-2-200-2-2220000-1-10000-2-20000000110012-1-1-100-1-111200000110-100
χ4122-2-2222-2-222-2-22-2-22220-2-2-222-2-2-220000002-2-22000000000000000000000000000000002-2002i−2i2i−2i22-2-2000000000000000000002i−2i2i−2i0000
χ4222-2-2222-2-222-2-22-2-22220-2-2-222-2-2-220000002-2-22000000000000000000000000000000002-200−2i2i−2i2i22-2-200000000000000000000−2i2i−2i2i0000
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χ894-4-444-2-24-2-42222-2-4-2-210-2-212-122-1223−2300−4i4i11-1-10023−23−3300−3−333000000002i3−2i300002i−2i2i−2i00000000000000000−i3i300000−ii0000000000000000
χ904-4-444-2-24-2-42222-2-4-2-210-2-212-122-12−2323004i−4i11-1-100−23233−30033−3−3000000002i3−2i30000−2i2i−2i2i00000000000000000−i3i300000i−i0000000000000000
χ914-4-444-2-24-2-42222-2-4-2-210-2-212-122-12−232300−4i4i11-1-100−23233−30033−3−300000000−2i32i300002i−2i2i−2i00000000000000000i3−i300000−ii0000000000000000
χ924-4-44-244-242-4-4-4-442-2-240-2-242-422-42004-400-2-2220000000000000000-224-40000000000000000000000000-220000000000000000000000000
χ934-4-44-244-242-4-4-4-442-2-240-2-242-422-4200-4400-2-22200000000000000002-2-4400000000000000000000000002-20000000000000000000000000
χ944-4-44-24-2-2-22-4-42242-21-20-21-2-122-12223−234-40011-1-100−3323−2300−3−3330000-22-22000023−2300000000000000000001-100000−33000000000000000000
χ954-4-44-24-2-2-22-4-42242-21-20-21-2-122-12223−23-440011-1-100−3323−2300−3−33300002-22-20000−23230000000000000000000-11000003−3000000000000000000
χ964-4-44-24-2-2-22-4-42242-21-20-21-2-122-122−23234-40011-1-1003−3−23230033−3−30000-22-220000−232300000000000000000001-1000003−3000000000000000000
χ974-4-44-24-2-2-22-4-42242-21-20-21-2-122-122−2323-440011-1-1003−3−23230033−3−300002-22-2000023−230000000000000000000-1100000−33000000000000000000
χ988888-4-4-4-4-4-4-4-4-4-4-4-42228222222222-4-40000-1-1-1-1-4-4222222-1-1-1-1000000000000000000000000000000000000000000000000000000000000
χ998888-4-4-4-4-4-4-4-4-4-4-4-4222-8222222222440000-1-1-1-144-2-2-2-2-2-21111000000000000000000000000000000000000000000000000000000000000
χ10088-8-88-4-4-848-444-44-8-4-42044-2-4244-2-40000002-2-22000000000000000000000000000000000000000000000000000000000000000000000000
χ10188-8-8-48-444-48-84-4-84-42-404-242-44-24-40000002-2-22000000000000000000000000000000000000000000000000000000000000000000000000
χ10288-8-8-4-484-8-4-44-88442-4-40-244-4-4-24420000002-2-22000000000000000000000000000000000000000000000000000000000000000000000000
χ10388-8-8-4-4-444-4-444-4442220-2-2-222-2-2-22000000-111-100000000−3i33i33i3−3i3000000000000000000000000000000000000000000000000000000000000
χ10488-8-8-4-4-444-4-444-4442220-2-2-222-2-2-22000000-111-1000000003i3−3i3−3i33i3000000000000000000000000000000000000000000000000000000000000
χ1058-88-88-4-4-84-84-4-4448-4-42044-24-2-4-4240000002-22-2000000000000000000000000000000000000000000000000000000000000000000000000
χ1068-88-8-48-4444-88-44-8-4-42-404-24-24-42-440000002-22-2000000000000000000000000000000000000000000000000000000000000000000000000
χ1078-88-8-4-4-44444-4-444-42220-2-2-2-2-2222-2000000-11-110000006i−6i−3i3i−3i3i000000000000000000000000000000000000000000000000000000000000
χ1088-88-8-4-4-44444-4-444-42220-2-2-2-2-2222-2000000-11-11000000−6i6i3i−3i3i−3i000000000000000000000000000000000000000000000000000000000000
χ1098-8-88-4-48-48444-8-8-442-4-402-4-444-244-200000022-2-2000000000000000000000000000000000000000000000000000000000000000000000000
χ1108-8-88-4-4-4-4-444444-442220222-2-2-2-2-2-243−430000-1-11100−2323−23230033−3−3000000000000000000000000000000000000000000000000000000000000
χ1118-8-88-4-4-4-4-444444-442220222-2-2-2-2-2-2−43430000-1-1110023−2323−2300−3−333000000000000000000000000000000000000000000000000000000000000

Here i is the imaginary unit (i² = −1).