Finite Group Databasebeta

← Group #10703019

Character table — Group #10703019

Order 768.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96C97C98C99C100C101C102C103C104C105C106C107C108
size1111111122222222222222222222222222224444444444444444444444444444444488888888888888888888888824242424242424242424242424242424
order1222222222223444444446666666666666668888888812121212121212122424242424242424242424242424242444444444121212121212121212121212121212122244888888888888
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ311111111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1
χ411111111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111
χ5111111111111111111111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-111111111-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1-1-1
χ6111111111111111111111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-11111
χ7111111111111111111111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-11111
χ8111111111111111111111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-111111111-1-1-1-111111111-1-1-1-1
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χ1011-1-1-11-1111-1-11111-1-11-1-111111-1-1-1-1-1-1-111-1iiii−i−i−i−i1111-1-1-1-1iiiiiiii−i−i−i−i−i−i−i−i11-1-1ii−i−i1111-1-1-1-1iiii−i−i−i−i-11-11−i−iii-1-111−i−iii
χ1111-1-1-11-1111-1-11111-1-11-1-111111-1-1-1-1-1-1-111-1iiii−i−i−i−i1111-1-1-1-1iiiiiiii−i−i−i−i−i−i−i−i-1-111−i−iii-1-1-1-11111−i−i−i−iiiii1-11-1ii−i−i-1-111−i−iii
χ1211-1-1-11-1111-1-11111-1-11-1-111111-1-1-1-1-1-1-111-1iiii−i−i−i−i1111-1-1-1-1iiiiiiii−i−i−i−i−i−i−i−i-1-111−i−iii-1-1-1-11111−i−i−i−iiiii-11-11−i−iii11-1-1ii−i−i
χ1311-1-1-11-1111-1-11111-1-11-1-111111-1-1-1-1-1-1-111-1−i−i−i−iiiii1111-1-1-1-1−i−i−i−i−i−i−i−iiiiiiiii11-1-1−i−iii1111-1-1-1-1−i−i−i−iiiii1-11-1−i−iii11-1-1−i−iii
χ1411-1-1-11-1111-1-11111-1-11-1-111111-1-1-1-1-1-1-111-1−i−i−i−iiiii1111-1-1-1-1−i−i−i−i−i−i−i−iiiiiiiii11-1-1−i−iii1111-1-1-1-1−i−i−i−iiiii-11-11ii−i−i-1-111ii−i−i
χ1511-1-1-11-1111-1-11111-1-11-1-111111-1-1-1-1-1-1-111-1−i−i−i−iiiii1111-1-1-1-1−i−i−i−i−i−i−i−iiiiiiiii-1-111ii−i−i-1-1-1-11111iiii−i−i−i−i1-11-1−i−iii-1-111ii−i−i
χ1611-1-1-11-1111-1-11111-1-11-1-111111-1-1-1-1-1-1-111-1−i−i−i−iiiii1111-1-1-1-1−i−i−i−i−i−i−i−iiiiiiiii-1-111ii−i−i-1-1-1-11111iiii−i−i−i−i-11-11ii−i−i11-1-1−i−iii
χ172222222222222-2-2-2-2-2-2-2-222222222222222200000000-2-2-2-2-2-2-2-2000000000000000000000000000000000000000000002i−2i2i−2i00000000
χ182222222222222-2-2-2-2-2-2-2-222222222222222200000000-2-2-2-2-2-2-2-200000000000000000000000000000000000000000000−2i2i−2i2i00000000
χ19222222222222-122222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-122222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-122222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-10000000000000000
χ20222222222222-122222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-122222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-2-2-2-2-2-2-2-211111111111111110000000000000000
χ21222222222222-122222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-2-2-2-2-2-2-2-2-1-1-1-1-1-1-1-111111111111111112222-2-2-2-2-1-1-1-1-1-1-1-1111111110000000000000000
χ22222222222222-122222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-2-2-2-2-2-2-2-2-1-1-1-1-1-1-1-11111111111111111-2-2-2-2222211111111-1-1-1-1-1-1-1-10000000000000000
χ2322222222-2-2-2-2222-2-22-22-22-2-2-2-2222-2-2-2-222222-2-222-2-222-2-22-2-222222-2-2-2-22222-2-2-2-20000000000000000000000000000000000000000
χ2422222222-2-2-2-2222-2-22-22-22-2-2-2-2222-2-2-2-2222-2-222-2-22222-2-22-2-22-2-2-2-22222-2-2-2-222220000000000000000000000000000000000000000
χ2522222222-2-2-2-22-2-222-22-222-2-2-2-2222-2-2-2-222200000000-2-222-222-2000000000000000000000000000000000000000022-2-2000000000000
χ2622222222-2-2-2-22-2-222-22-222-2-2-2-2222-2-2-2-222200000000-2-222-222-20000000000000000000000000000000000000000-2-222000000000000
χ2722222222-2-2-2-2-122-2-22-22-2-11111-1-1-11111-1-1-122-2-222-2-2-1-111-111-1-1-1-1-11111-1-1-1-1111100000000−i3−i3i3i3−i3−i3i3i3−i3−i3i3i3−i3−i3i3i30000000000000000
χ2822222222-2-2-2-2-122-2-22-22-2-11111-1-1-11111-1-1-122-2-222-2-2-1-111-111-1-1-1-1-11111-1-1-1-1111100000000i3i3−i3−i3i3i3−i3−i3i3i3−i3−i3i3i3−i3−i30000000000000000
χ2922222222-2-2-2-2-122-2-22-22-2-11111-1-1-11111-1-1-1-2-222-2-222-1-111-111-11111-1-1-1-11111-1-1-1-100000000−i3−i3i3i3−i3−i3i3i3i3i3−i3−i3i3i3−i3−i30000000000000000
χ3022222222-2-2-2-2-122-2-22-22-2-11111-1-1-11111-1-1-1-2-222-2-222-1-111-111-11111-1-1-1-11111-1-1-1-100000000i3i3−i3−i3i3i3−i3−i3−i3−i3i3i3−i3−i3i3i30000000000000000
χ3122-2-2-22-2222-2-22-2-2-222-22222222-2-2-2-2-2-2-222-200000000-2-2-2-22222000000000000000000000000000000000000000000002-2-2200000000
χ3222-2-2-22-2222-2-22-2-2-222-22222222-2-2-2-2-2-2-222-200000000-2-2-2-2222200000000000000000000000000000000000000000000-222-200000000
χ3322-2-2-22-2222-2-2-1222-2-22-2-2-1-1-1-1-11111111-1-112i2i2i2i−2i−2i−2i−2i-1-1-1-11111−i−i−i−i−i−i−i−iiiiiiiii22-2-22i2i−2i−2i-1-1-1-11111−i−i−i−iiiii0000000000000000
χ3422-2-2-22-2222-2-2-1222-2-22-2-2-1-1-1-1-11111111-1-112i2i2i2i−2i−2i−2i−2i-1-1-1-11111−i−i−i−i−i−i−i−iiiiiiiii-2-222−2i−2i2i2i1111-1-1-1-1iiii−i−i−i−i0000000000000000
χ3522-2-2-22-2222-2-2-1222-2-22-2-2-1-1-1-1-11111111-1-11−2i−2i−2i−2i2i2i2i2i-1-1-1-11111iiiiiiii−i−i−i−i−i−i−i−i22-2-2−2i−2i2i2i-1-1-1-11111iiii−i−i−i−i0000000000000000
χ3622-2-2-22-2222-2-2-1222-2-22-2-2-1-1-1-1-11111111-1-11−2i−2i−2i−2i2i2i2i2i-1-1-1-11111iiiiiiii−i−i−i−i−i−i−i−i-2-2222i2i−2i−2i1111-1-1-1-1−i−i−i−iiiii0000000000000000
χ3722-2-2-22-22-2-222222-22-2-2-222-2-2-2-2-2-2-2222222-22i2i−2i−2i−2i−2i2i2i22-2-2-222-22i2i2i2i−2i−2i−2i−2i−2i−2i−2i−2i2i2i2i2i0000000000000000000000000000000000000000
χ3822-2-2-22-22-2-222222-22-2-2-222-2-2-2-2-2-2-2222222-2−2i−2i2i2i2i2i−2i−2i22-2-2-222-2−2i−2i−2i−2i2i2i2i2i2i2i2i2i−2i−2i−2i−2i0000000000000000000000000000000000000000
χ3922-2-2-22-22-2-2222-2-22-2222-22-2-2-2-2-2-2-2222222-200000000-2-2222-2-2200000000000000000000000000000000000000002-2-22000000000000
χ4022-2-2-22-22-2-2222-2-22-2222-22-2-2-2-2-2-2-2222222-200000000-2-2222-2-220000000000000000000000000000000000000000-222-2000000000000
χ4122-2-2-22-22-2-222-122-22-2-2-22-11111111-1-1-1-1-1-112i2i−2i−2i−2i−2i2i2i-1-1111-1-11−i−i−i−iiiiiiiii−i−i−i−i00000000−i3−i3i3i3i3i3−i3−i333−3−3−3−3330000000000000000
χ4222-2-2-22-22-2-222-122-22-2-2-22-11111111-1-1-1-1-1-112i2i−2i−2i−2i−2i2i2i-1-1111-1-11−i−i−i−iiiiiiiii−i−i−i−i00000000i3i3−i3−i3−i3−i3i3i3−3−33333−3−30000000000000000
χ4322-2-2-22-22-2-222-122-22-2-2-22-11111111-1-1-1-1-1-11−2i−2i2i2i2i2i−2i−2i-1-1111-1-11iiii−i−i−i−i−i−i−i−iiiii00000000−i3−i3i3i3i3i3−i3−i3−3−33333−3−30000000000000000
χ4422-2-2-22-22-2-222-122-22-2-2-22-11111111-1-1-1-1-1-11−2i−2i2i2i2i2i−2i−2i-1-1111-1-11iiii−i−i−i−i−i−i−i−iiiii00000000i3i3−i3−i3−i3−i3i3i333−3−3−3−3330000000000000000
χ452-222-2-2-222-22-222-22-22-2-22-222-2-222-222-2-22-2-2000000002-22-2-22-2200000000000000002i−2i2i−2i00002i−2i2i−2i2i−2i2i−2i000000000000000000000000
χ462-222-2-2-222-22-222-22-22-2-22-222-2-222-222-2-22-2-2000000002-22-2-22-220000000000000000−2i2i−2i2i0000−2i2i−2i2i−2i2i−2i2i000000000000000000000000
χ472-222-2-2-222-22-22-22-22-222-2-222-2-222-222-2-22-2-200000000-22-222-22-200000000000000000000000000000000000000000000000000002i−2i2i−2i
χ482-222-2-2-222-22-22-22-22-222-2-222-2-222-222-2-22-2-200000000-22-222-22-20000000000000000000000000000000000000000000000000000−2i2i−2i2i
χ492-222-2-2-222-22-2-12-22-22-2-221-1-111-1-11-1-111-11100000000-11-111-11-1−i3−i3i3i3−i3−i3i3i3−i3−i3i3i3−i3−i3i3i32i−2i2i−2i0000−ii−ii−ii−ii3−33−33−33−30000000000000000
χ502-222-2-2-222-22-2-12-22-22-2-221-1-111-1-11-1-111-11100000000-11-111-11-1−i3−i3i3i3−i3−i3i3i3−i3−i3i3i3−i3−i3i3i3−2i2i−2i2i0000i−ii−ii−ii−i−33−33−33−330000000000000000
χ512-222-2-2-222-22-2-12-22-22-2-221-1-111-1-11-1-111-11100000000-11-111-11-1i3i3−i3−i3i3i3−i3−i3i3i3−i3−i3i3i3−i3−i32i−2i2i−2i0000−ii−ii−ii−ii−33−33−33−330000000000000000
χ522-222-2-2-222-22-2-12-22-22-2-221-1-111-1-11-1-111-11100000000-11-111-11-1i3i3−i3−i3i3i3−i3−i3i3i3−i3−i3i3i3−i3−i3−2i2i−2i2i0000i−ii−ii−ii−i3−33−33−33−30000000000000000
χ532-222-2-2-22-22-2222-2-2222-2-2-2-2-22222-2-2-2222-2-2000000002-2-22-2-222000000000000000000002i−2i2i−2i000000002i−2i−2i2i2i−2i−2i2i0000000000000000
χ542-222-2-2-22-22-2222-2-2222-2-2-2-2-22222-2-2-2222-2-2000000002-2-22-2-22200000000000000000000−2i2i−2i2i00000000−2i2i2i−2i−2i2i2i−2i0000000000000000
χ552-222-2-2-22-22-222-222-2-2-222-2-2-22222-2-2-2222-2-200000000-222-222-2-20000000000000000000000000000000000000000000000002i−2i2i−2i0000
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χ622-2-2-22-2222-2-2222-222-2-22-2-222-2-2-2-22-2-2222-22000000002-22-22-22-20000000000000000−2i2i2i−2i0000−2i2i−2i2i2i−2i2i−2i000000000000000000000000
χ632-2-2-22-2222-2-222-22-2-222-22-222-2-2-2-22-2-2222-2200000000-22-22-22-2200000000000000000000000000000000000000000000000000002-2-22
χ642-2-2-22-2222-2-222-22-2-222-22-222-2-2-2-22-2-2222-2200000000-22-22-22-220000000000000000000000000000000000000000000000000000-222-2
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χ702-2-2-22-222-222-222-2-2-2-2222-2-2-222-2-2222-2-22-22000000002-2-2222-2-200000000000000000000-222-200000000-222-22-2-220000000000000000
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χ77444444444444-2-4-4-4-4-4-4-4-4-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2000000002222222200000000000000000000000000000000000000000000000000000000
χ7844444444-4-4-4-4-2-4-444-44-44-22222-2-2-22222-2-2-20000000022-2-22-2-2200000000000000000000000000000000000000000000000000000000
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χ83444-44-4-4-40000-200000000-22i3−2i32i3−2i3-22-22i3−2i32i3−2i32220022−220022−2200000000−i6i6−i6i6−22−22−i6i6−i6i6−22−220000000000000000000000000000000000000000
χ84444-44-4-4-40000-200000000-22i3−2i32i3−2i3-22-22i3−2i32i3−2i322200−222200−222200000000i6−i6i6−i62−22−2i6−i6i6−i62−22−20000000000000000000000000000000000000000
χ8544-44-4-44-4000040000000040000-44-40000-4-4400−2i22i2002i2−2i2000000000000−2i22i2−2i22i200002i2−2i22i2−2i20000000000000000000000000000000000000000
χ8644-44-4-44-4000040000000040000-44-40000-4-44002i2−2i200−2i22i20000000000002i2−2i22i2−2i20000−2i22i2−2i22i20000000000000000000000000000000000000000
χ8744-44-4-44-40000-200000000-2−2i32i3−2i32i32-222i3−2i32i3−2i322-200−2i22i2002i2−2i2000000006−66−6i2−i2i2−i2−66−66−i2i2−i2i20000000000000000000000000000000000000000
χ8844-44-4-44-40000-200000000-2−2i32i3−2i32i32-222i3−2i32i3−2i322-2002i2−2i200−2i22i200000000−66−66−i2i2−i2i26−66−6i2−i2i2−i20000000000000000000000000000000000000000
χ8944-44-4-44-40000-200000000-22i3−2i32i3−2i32-22−2i32i3−2i32i322-200−2i22i2002i2−2i200000000−66−66i2−i2i2−i26−66−6−i2i2−i2i20000000000000000000000000000000000000000
χ9044-44-4-44-40000-200000000-22i3−2i32i3−2i32-22−2i32i3−2i32i322-2002i2−2i200−2i22i2000000006−66−6−i2i2−i2i2−66−66i2−i2i2−i20000000000000000000000000000000000000000
χ9144-4-4-44-4444-4-4-2-4-4-444-444-2-2-2-2-22222222-2-22000000002222-2-2-2-200000000000000000000000000000000000000000000000000000000
χ9244-4-4-44-44-4-444-2-4-44-4444-4-22222222-2-2-2-2-2-220000000022-2-2-222-200000000000000000000000000000000000000000000000000000000
χ934-444-4-4-444-44-4-2-44-44-444-42-2-222-2-22-2-222-222000000002-22-2-22-2200000000000000000000000000000000000000000000000000000000
χ944-444-4-4-44-44-44-2-444-4-4-444222-2-2-2-2222-2-2-222000000002-2-22-2-22200000000000000000000000000000000000000000000000000000000
χ954-44-4-444-40000400000000-400004-4-40000-44422−220022−22000000000022−22−2222000022−22−222200000000000000000000000000000000000000000000
χ964-44-4-444-40000400000000-400004-4-40000-444−222200−22220000000000−222222−220000−222222−2200000000000000000000000000000000000000000000
χ974-44-4-444-40000-2000000002−2i32i32i3−2i3-222−2i32i32i3−2i32-2-222−220022−220000000000−222−2i6−i6−i6i6−222−2i6−i6−i6i60000000000000000000000000000000000000000
χ984-44-4-444-40000-2000000002−2i32i32i3−2i3-222−2i32i32i3−2i32-2-2−222200−222200000000002−2−22−i6i6i6−i62−2−22−i6i6i6−i60000000000000000000000000000000000000000
χ994-44-4-444-40000-20000000022i3−2i3−2i32i3-2222i3−2i3−2i32i32-2-222−220022−220000000000−222−2−i6i6i6−i6−222−2−i6i6i6−i60000000000000000000000000000000000000000
χ1004-44-4-444-40000-20000000022i3−2i3−2i32i3-2222i3−2i3−2i32i32-2-2−222200−222200000000002−2−22i6−i6−i6i62−2−22i6−i6−i6i60000000000000000000000000000000000000000
χ1014-4-4444-4-40000400000000-40000-4440000-44-4−2i22i2002i2−2i20000000000−2i22i22i2−2i200002i2−2i2−2i22i200000000000000000000000000000000000000000000
χ1024-4-4444-4-40000400000000-40000-4440000-44-42i2−2i200−2i22i200000000002i2−2i2−2i22i20000−2i22i22i2−2i200000000000000000000000000000000000000000000
χ1034-4-4444-4-40000-2000000002−2i32i32i3−2i32-2-22i3−2i3−2i32i32-22−2i22i2002i2−2i20000000000i2−i2−i2i26−6−66−i2i2i2−i2−666−60000000000000000000000000000000000000000
χ1044-4-4444-4-40000-2000000002−2i32i32i3−2i32-2-22i3−2i3−2i32i32-222i2−2i200−2i22i20000000000−i2i2i2−i2−666−6i2−i2−i2i26−6−660000000000000000000000000000000000000000
χ1054-4-4444-4-40000-20000000022i3−2i3−2i32i32-2-2−2i32i32i3−2i32-22−2i22i2002i2−2i20000000000i2−i2−i2i2−666−6−i2i2i2−i26−6−660000000000000000000000000000000000000000
χ1064-4-4444-4-40000-20000000022i3−2i3−2i32i32-2-2−2i32i32i3−2i32-222i2−2i200−2i22i20000000000−i2i2i2−i26−6−66i2−i2−i2i2−666−60000000000000000000000000000000000000000
χ1074-4-4-44-4444-4-44-2-44-4-444-442-2-22222-222-2-2-22-2000000002-22-22-22-200000000000000000000000000000000000000000000000000000000
χ1084-4-4-44-444-444-4-2-44444-4-4-4222-2-222-2-2-222-22-2000000002-2-2222-2-200000000000000000000000000000000000000000000000000000000

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