Finite Group Databasebeta

← Group #10823170

Character table — Group #10823170

Order 768.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96C97C98C99C100C101C102C103C104C105C106C107C108
size1111111122222222222222222222222222224444444444444444444444444444444488888888888888888888888824242424242424242424242424242424
order1222222222223444444446666666121212121212121266668888888812121212242424242424242424242424242424242244444466661212121212121212121212122222444444448888
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ311111111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1-1-1
χ411111111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-11111
χ51111111111111111111111111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-1111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-11111
χ61111111111111111111111111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-1111111-1-1-1-1-1-1-1-11111-1-1-1-111111111-1-1-1-1
χ71111111111111111111111111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-111111111-1-1-1-111111111-1-1-1-1-1-1-1-1
χ81111111111111111111111111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-111111111
χ911111111-1-1-1-11111-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1111111111111-1-1-1-1-1-1-1-11111-1-1-1-111111111-1-1-1-1-1-1-1-111-1-111-1-111-1-111-1-1
χ1011111111-1-1-1-11111-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1111111111111-1-1-1-1-1-1-1-11111-1-1-1-111111111-1-1-1-1-1-1-1-1-1-111-1-111-1-111-1-111
χ1111111111-1-1-1-11111-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-11111111111-1-1-1-11111-1-1-1-111
χ1211111111-1-1-1-11111-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-111111111-1-11111-1-1-1-11111-1-1
χ1311111111-1-1-1-11111-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-11111111111-1-111-1-11111-1-1-1-11111-1-1-1-111-1-1-1-111-1-11111-1-1
χ1411111111-1-1-1-11111-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-11111111111-1-111-1-11111-1-1-1-11111-1-1-1-1-1-11111-1-111-1-1-1-111
χ1511111111-1-1-1-11111-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-111111111-1-111-1-111-1-1-1-11111-1-1-1-1111111-1-111-1-1-1-111-1-111
χ1611111111-1-1-1-11111-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-111111111-1-111-1-111-1-1-1-11111-1-1-1-11111-1-111-1-11111-1-111-1-1
χ172222222222222-2-2-2-2-2-2-2-22222222-2-2-2-2-2-2-2-2222200000000-2-2-2-2000000000000000000000000000000000000000000002-22-200000000
χ182222222222222-2-2-2-2-2-2-2-22222222-2-2-2-2-2-2-2-2222200000000-2-2-2-200000000000000000000000000000000000000000000-22-2200000000
χ19222222222222-122222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-122222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-122222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-10000000000000000
χ20222222222222-122222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-122222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-2-2-2-2-2-2-2-211111111111111110000000000000000
χ21222222222222-122222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-2-2-2-2-2-2-2-2-1-1-1-1111111111111111122-2-2-2-222-1-1-1-111111111-1-1-1-10000000000000000
χ22222222222222-122222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-2-2-2-2-2-2-2-2-1-1-1-11111111111111111-2-22222-2-21111-1-1-1-1-1-1-1-111110000000000000000
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χ2422222222-2-2-2-22-2-2-22222-2222222222222222-2-2-2-200000000-2-2-2-200000000000000000000000000000000000000000000-222-200000000
χ2522222222-2-2-2-2-1222-2-2-2-22-1-1-1-1-1-1-11111111111112222-2-2-2-2-1-1-1-1-1-1-1-1-1-1-1-1111111112222-2-2-2-2-1-1-1-1-1-1-1-1111111110000000000000000
χ2622222222-2-2-2-2-1222-2-2-2-22-1-1-1-1-1-1-11111111111112222-2-2-2-2-1-1-1-1-1-1-1-1-1-1-1-111111111-2-2-2-2222211111111-1-1-1-1-1-1-1-10000000000000000
χ2722222222-2-2-2-2-1222-2-2-2-22-1-1-1-1-1-1-1111111111111-2-2-2-22222-1-1-1-111111111-1-1-1-1-1-1-1-122-2-222-2-2-1-1-1-11111-1-1-1-111110000000000000000
χ2822222222-2-2-2-2-1222-2-2-2-22-1-1-1-1-1-1-1111111111111-2-2-2-22222-1-1-1-111111111-1-1-1-1-1-1-1-1-2-222-2-2221111-1-1-1-11111-1-1-1-10000000000000000
χ2922-2-22-2-2222-2-2222-222-2-2-222-2-2-2-222222-2-2-2-222-2-20000000022-2-20000000000000000002i−2i2i−2i0000002i2i−2i−2i2i2i−2i−2i00000000000000000000
χ3022-2-22-2-2222-2-2222-222-2-2-222-2-2-2-222222-2-2-2-222-2-20000000022-2-2000000000000000000−2i2i−2i2i000000−2i−2i2i2i−2i−2i2i2i00000000000000000000
χ3122-2-22-2-2222-2-22-2-22-2-222222-2-2-2-22-2-2-2-2222222-2-200000000-2-22200000000000000000000000000000000000000002-22-2000000000000
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χ3622-2-22-2-2222-2-2-122-222-2-2-2-1-11111-1-1-1-1-11111-1-11100000000-1-111−3−3−3−33333−3−3−3−3333300−2i2i−2i2i00−i3−i3i3i3ii−i−iii−i−i−i3−i3i3i30000000000000000
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χ3922-2-22-2-22-2-2222-2-2222-2-2222-2-2-2-222222-2-2-2-2-2-22200000000-2-22200000000000000000000000000000000000000002-2-22000000000000
χ4022-2-22-2-22-2-2222-2-2222-2-2222-2-2-2-222222-2-2-2-2-2-22200000000-2-2220000000000000000000000000000000000000000-222-2000000000000
χ4122-2-22-2-22-2-222-122-2-2-222-2-1-11111-11111-1-1-1-111-1-100000000-1-1113333−3−3−3−3−3−3−3−33333002i−2i−2i2i00−i3−i3i3i3−i−iiiii−i−ii3i3−i3−i30000000000000000
χ4222-2-22-2-22-2-222-122-2-2-222-2-1-11111-11111-1-1-1-111-1-100000000-1-1113333−3−3−3−3−3−3−3−3333300−2i2i2i−2i00i3i3−i3−i3ii−i−i−i−iii−i3−i3i3i30000000000000000
χ4322-2-22-2-22-2-222-122-2-2-222-2-1-11111-11111-1-1-1-111-1-100000000-1-111−3−3−3−333333333−3−3−3−3002i−2i−2i2i00i3i3−i3−i3−i−iiiii−i−i−i3−i3i3i30000000000000000
χ4422-2-22-2-22-2-222-122-2-2-222-2-1-11111-11111-1-1-1-111-1-100000000-1-111−3−3−3−333333333−3−3−3−300−2i2i2i−2i00−i3−i3i3i3ii−i−i−i−iiii3i3−i3−i30000000000000000
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χ462-2222-2-2-22-22-222-222-22-2-2-2-2-2-222222-2-222-2-22-22-2000000002-22-2000000000000000000000000000000000000000000000000−2i2i−2i2i0000
χ472-2222-2-2-22-22-22-22-2-22-222-2-2-2-2222-2-222-2-2222-22-200000000-22-2200000000000000002-200002-22-22-2000000002-22-20000000000000000
χ482-2222-2-2-22-22-22-22-2-22-222-2-2-2-2222-2-222-2-2222-22-200000000-22-220000000000000000-220000-22-22-2200000000-22-220000000000000000
χ492-2222-2-2-22-22-2-1-22-2-22-2221111-1-1-111-1-111-1-1-11-11000000001-11-1−i3−i3i3i3−i3−i3i3i3−i3−i3i3i3−i3−i3i3i32-200002-2-11-11−i3i3−i3i3−i3i3−i3i3-11-110000000000000000
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χ522-2222-2-2-22-22-2-1-22-2-22-2221111-1-1-111-1-111-1-1-11-11000000001-11-1i3i3−i3−i3i3i3−i3−i3i3i3−i3−i3i3i3−i3−i3-220000-221-11-1−i3i3−i3i3−i3i3−i3i31-11-10000000000000000
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χ542-2222-2-2-2-22-2222-22-22-22-2-2-2-2-2222-2-222-2-222-22-22000000002-22-2000000000000000000000000000000000000000000000000−2i2i2i−2i0000
χ552-2222-2-2-2-22-222-22-22-22-22-2-2-2-222222-2-222-2-2-22-2200000000-22-2200000000000000002-20000-222-22-200000000-22-220000000000000000
χ562-2222-2-2-2-22-222-22-22-22-22-2-2-2-222222-2-222-2-2-22-2200000000-22-220000000000000000-2200002-2-22-22000000002-22-20000000000000000
χ572-2222-2-2-2-22-22-1-22-22-22-221111-1-1-1-1-111-1-1111-11-1000000001-11-1−i3−i3i3i3−i3−i3i3i3i3i3−i3−i3i3i3−i3−i32-20000-22-11-11−i3i3−i3i3i3−i3i3−i31-11-10000000000000000
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χ632-2-2-2222-22-2-222-222-222-2-2-2-222-2-22-2-22222-2-22-2-222i2i−2i−2i2i2i−2i−2i-222-22i2i−2i−2i−2i−2i2i2i2i2i−2i−2i−2i−2i2i2i0000000000000000000000000000000000000000
χ642-2-2-2222-22-2-222-222-222-2-2-2-222-2-22-2-22222-2-22-2-22−2i−2i2i2i−2i−2i2i2i-222-2−2i−2i2i2i2i2i−2i−2i−2i−2i2i2i2i2i−2i−2i0000000000000000000000000000000000000000
χ652-2-2-2222-22-2-22-1-222-222-2-211-1-111-111-1-1-1-111-111-12i2i−2i−2i2i2i−2i−2i1-1-11−i−iiiii−i−i−i−iiiii−i−i00000000−i3i3i3−i33−3−333−3−33−i3i3i3−i30000000000000000
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χ82444-4-44-4-40000-200000000-22-22-22223−2323−2323−2323−23000000002i2−2i22i2−2i20000−i6i6−i6i6−i6i6−i6i6−i2i2−i2i2−i2i2−i2i20000000000000000000000000000000000000000
χ83444-4-44-4-40000-200000000-22-22-222−2323−2323−2323−232300000000−2i22i2−2i22i20000−i6i6−i6i6−i6i6−i6i6i2−i2i2−i2i2−i2i2−i20000000000000000000000000000000000000000
χ84444-4-44-4-40000-200000000-22-22-222−2323−2323−2323−2323000000002i2−2i22i2−2i20000i6−i6i6−i6i6−i6i6−i6−i2i2−i2i2−i2i2−i2i20000000000000000000000000000000000000000
χ8544-44-4-44-400004000000004-4-44-44-4000000000000−2i22i2−2i22i200000000−2i22i2−2i22i22i2−2i22i2−2i2000000000000000000000000000000000000000000000000
χ8644-44-4-44-400004000000004-4-44-44-40000000000002i2−2i22i2−2i2000000002i2−2i22i2−2i2−2i22i2−2i22i2000000000000000000000000000000000000000000000000
χ8744-44-4-44-40000-200000000-222-22-2223−2323−23−2323−23230000−2i22i2−2i22i200000000i2−i2i2−i2−i2i2−i2i2−i6i6−i6i6i6−i6i6−i60000000000000000000000000000000000000000
χ8844-44-4-44-40000-200000000-222-22-2223−2323−23−2323−232300002i2−2i22i2−2i200000000−i2i2−i2i2i2−i2i2−i2i6−i6i6−i6−i6i6−i6i60000000000000000000000000000000000000000
χ8944-44-4-44-40000-200000000-222-22-22−2323−232323−2323−230000−2i22i2−2i22i200000000i2−i2i2−i2−i2i2−i2i2i6−i6i6−i6−i6i6−i6i60000000000000000000000000000000000000000
χ9044-44-4-44-40000-200000000-222-22-22−2323−232323−2323−2300002i2−2i22i2−2i200000000−i2i2−i2i2i2−i2i2−i2−i6i6−i6i6i6−i6i6−i60000000000000000000000000000000000000000
χ9144-4-44-4-4444-4-4-2-4-44-4-4444-2-22222-22222-2-2-2-2-2-2220000000022-2-200000000000000000000000000000000000000000000000000000000
χ9244-4-44-4-44-4-444-2-4-4444-4-44-2-22222-2-2-2-2-2222222-2-20000000022-2-200000000000000000000000000000000000000000000000000000000
χ934-4444-4-4-44-44-4-24-444-44-4-42222-2-2-2-2-222-2-222-22-2200000000-22-2200000000000000000000000000000000000000000000000000000000
χ944-4444-4-4-4-44-44-24-44-44-44-42222-2-2-222-2-222-2-22-22-200000000-22-2200000000000000000000000000000000000000000000000000000000
χ954-44-4-4-4440000400000000-44-444-4-400000000000022−22−22220000000022−22−222222−22−2222000000000000000000000000000000000000000000000000
χ964-44-4-4-4440000400000000-44-444-4-4000000000000−222222−2200000000−222222−22−222222−22000000000000000000000000000000000000000000000000
χ974-44-4-4-4440000-2000000002-22-2-22223−23−232323−23−2323000022−22−222200000000−222−2−222−2−666−6−666−60000000000000000000000000000000000000000
χ984-44-4-4-4440000-2000000002-22-2-22223−23−232323−23−23230000−222222−22000000002−2−222−2−226−6−666−6−660000000000000000000000000000000000000000
χ994-44-4-4-4440000-2000000002-22-2-222−232323−23−232323−23000022−22−222200000000−222−2−222−26−6−666−6−660000000000000000000000000000000000000000
χ1004-44-4-4-4440000-2000000002-22-2-222−232323−23−232323−230000−222222−22000000002−2−222−2−22−666−6−666−60000000000000000000000000000000000000000
χ1014-4-44-44-440000400000000-444-4-44-4000000000000000022−22−222200000000000022−22−2222−222222−220000000000000000000000000000000000000000
χ1024-4-44-44-440000400000000-444-4-44-40000000000000000−222222−22000000000000−222222−2222−22−22220000000000000000000000000000000000000000
χ1034-4-44-44-440000-2000000002-2-222-2223−23−2323−232323−230000000022−22−222200006−6−66−666−6−222−22−2−220000000000000000000000000000000000000000
χ1044-4-44-44-440000-2000000002-2-222-2223−23−2323−232323−2300000000−222222−220000−666−66−6−662−2−22−222−20000000000000000000000000000000000000000
χ1054-4-44-44-440000-2000000002-2-222-22−232323−2323−23−23230000000022−22−22220000−666−66−6−66−222−22−2−220000000000000000000000000000000000000000
χ1064-4-44-44-440000-2000000002-2-222-22−232323−2323−23−232300000000−222222−2200006−6−66−666−62−2−22−222−20000000000000000000000000000000000000000
χ1074-4-4-4444-44-4-44-24-4-44-4-44422-2-222-2-2-22222-2-2-222-200000000-222-200000000000000000000000000000000000000000000000000000000
χ1084-4-4-4444-4-444-4-24-4-4-444-4422-2-222-222-2-2-2-2222-2-2200000000-222-200000000000000000000000000000000000000000000000000000000

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