Finite Group Databasebeta

← Group #10858798

Character table — Group #10858798

Order 768.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96C97C98C99C100C101C102C103C104C105C106C107C108
size1111111122222222222222222222222244444444444444444444444444444444444444888888888888888888888812121212242424242424242424244848
order1222222222223444466666666666666644444488888888121212121212121224242424242424242424242424242424444444121212121212121212121212121212124444444444888844
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ311111111111111111111111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-111111111-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-1
χ411111111111111111111111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111
χ511111111111111111111111111111111-1-1-1-11111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111-1-11-1-11111-1-1
χ611111111111111111111111111111111-1-1-1-11111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-111-1-1-1-111
χ711111111111111111111111111111111-1-1-1-111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-11111111111111-1-11-1-1-1-1-1-111
χ811111111111111111111111111111111-1-1-1-111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-111111111-1-1-1-1-111-1111111-1-1
χ911111111-1-1-1-1111111111-1-1-1-1-1-1-1-11111111-1-11111-1-1-1-1111-1-1-1-1111111111-1-1-1-1-1-1-1-1-1-111-1-11111-1-1-1-11111-1-1-1-111-1-1-1-1-111111-1-11-1
χ1011111111-1-1-1-1111111111-1-1-1-1-1-1-1-11111111-1-11111-1-1-1-1111-1-1-1-1111111111-1-1-1-1-1-1-1-1-1-111-1-11111-1-1-1-11111-1-1-1-1-1-111111-1-1-1-1-111-11
χ1111111111-1-1-1-1111111111-1-1-1-1-1-1-1-11111111-1-1-1-1-1-11111111-1-1-1-11-1-1-1-1-1-1-1-111111111-1-1-1-1111111-1-1-1-1-1-1-1-1111111-1-1-1-1-1111-1-111-11
χ1211111111-1-1-1-1111111111-1-1-1-1-1-1-1-11111111-1-1-1-1-1-11111111-1-1-1-11-1-1-1-1-1-1-1-111111111-1-1-1-1111111-1-1-1-1-1-1-1-11111-1-111111-1-1-111-1-11-1
χ1311111111-1-1-1-1111111111-1-1-1-1-1-1-1-1111-1-1-1-1-1-11111-1-1-1-1111-1-1-1-1111111111-1-1-1-1-1-1-1-111-1-111-1-1-1-11111-1-1-1-1111111-1-1-1111-1-111-1-1-11
χ1411111111-1-1-1-1111111111-1-1-1-1-1-1-1-1111-1-1-1-1-1-11111-1-1-1-1111-1-1-1-1111111111-1-1-1-1-1-1-1-111-1-111-1-1-1-11111-1-1-1-11111-1-1111-1-1-111-1-1111-1
χ1511111111-1-1-1-1111111111-1-1-1-1-1-1-1-1111-1-1-1-1-1-1-1-1-1-11111111-1-1-1-11-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-111111111-1-1-1-111-1-1-1111-1-1-1-1111-1
χ1611111111-1-1-1-1111111111-1-1-1-1-1-1-1-1111-1-1-1-1-1-1-1-1-1-11111111-1-1-1-11-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-111111111-1-1-1-1-1-1111-1-1-11111-1-1-11
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χ182222222222222-2-2-2-22222222222222220000-2-200000000-2-2-2-2-2-2-2-200000000000000000000000000000000000000-2-2-2-2200200000000
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χ20222222222222-12222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1222222-2-2-2-2-2-2-2-2-1-1-1-1-1-1-1-1111111111111111122-2-2-2-2-1-1-1-1-1-1-1-1111111110000000000000000
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χ22222222222222-12222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-2-2-2-222-2-2-2-2-2-2-2-2-1-1-1-1-1-1-1-11111111111111111-2-2222211111111-1-1-1-1-1-1-1-10000000000000000
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χ762-2-2-2222-20000-1-222-211-11i3−i3i3−i3−i3i3−i3i3-11-1-222-2000000−2i2i−2i2i1-1-1−i3i3i3−i313−33−3−33−33i−ii−i−ii−ii00002i−2i1-1-11−i3i3i3−i33−3−33i−i−ii0000000000000000
χ77444444444444-2-4-4-4-4-2-2-2-2-2-2-2-2-2-2-2-2-2-2-20000-4-40000000022222222000000000000000000000000000000000000000000000000000000
χ7844444444-4-4-4-4-2-4-4-4-4-2-2-2-222222222-2-2-200004400000000222-2-2-2-22000000000000000000000000000000000000000000000000000000
χ79444-44-4-4-44-4-44400004-4-4444-4-4-4-444-4-440000000000000000000000000000000000000000000000000000000000000000000000000000
χ80444-44-4-4-44-4-44-20000-222-2-2-22222-2-222-2000000000000000000000066−6−6−6−66666−6−6−6−66600000000000000000000000000000000000000
χ81444-44-4-4-44-4-44-20000-222-2-2-22222-2-222-20000000000000000000000−6−66666−6−6−6−66666−6−600000000000000000000000000000000000000
χ82444-44-4-4-4-444-4400004-4-44-4-44444-4-4-4-440000000000000000000000000000000000000000000000000000000000000000000000000000
χ83444-44-4-4-4-444-4-20000-222-222-2-2-2-22222-2000000000000000000000066−6−6−6−666−6−66666−6−600000000000000000000000000000000000000
χ84444-44-4-4-4-444-4-20000-222-222-2-2-2-22222-20000000000000000000000−6−66666−6−666−6−6−6−66600000000000000000000000000000000000000
χ8544-44-44-4-444-4-4-244-4-4-2-222-2-2-2-22222-22200004-400000000-2-22-2-2222000000000000000000000000000000000000000000000000000000
χ8644-44-44-4-4-4-444-244-4-4-2-2222222-2-2-2-2-2220000-4400000000-2-2222-2-22000000000000000000000000000000000000000000000000000000
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χ8844-4-4-4-4444-44-4-20000-22-22-2-222-2-2222-220000002i22i2−2i2−2i22i22i2−2i2−2i200000000−i2−i2i2i2−i2−i2i2i2−i2−i2i2i2−i2−i2i2i200000000000000000000000000000000000000
χ8944-4-4-4-444-44-44-20000-22-2222-2-222-2-22-22000000−2i2−2i22i22i22i22i2−2i2−2i200000000i2i2−i2−i2i2i2−i2−i2−i2−i2i2i2−i2−i2i2i200000000000000000000000000000000000000
χ9044-4-4-4-444-44-44-20000-22-2222-2-222-2-22-220000002i22i2−2i2−2i2−2i2−2i22i22i200000000−i2−i2i2i2−i2−i2i2i2i2i2−i2−i2i2i2−i2−i200000000000000000000000000000000000000
χ914-444-4-44-4000040000-444400000000-4-4-4000000000022−22−2222000000000000000022−22−2222−222222−2200000000000000000000000000000000000000
χ924-444-4-44-4000040000-444400000000-4-4-40000000000−222222−220000000000000000−222222−2222−22−222200000000000000000000000000000000000000
χ934-444-4-44-40000-200002-2-2-2−2i32i32i3−2i32i3−2i3−2i32i3222000000000022−22−222200000000−i6i6i6−i6i6−i6−i6i6−222−22−2−2200000000000000000000000000000000000000
χ944-444-4-44-40000-200002-2-2-2−2i32i32i3−2i32i3−2i3−2i32i32220000000000−222222−2200000000i6−i6−i6i6−i6i6i6−i62−2−22−222−200000000000000000000000000000000000000
χ954-444-4-44-40000-200002-2-2-22i3−2i3−2i32i3−2i32i32i3−2i3222000000000022−22−222200000000i6−i6−i6i6−i6i6i6−i6−222−22−2−2200000000000000000000000000000000000000
χ964-444-4-44-40000-200002-2-2-22i3−2i3−2i32i3−2i32i32i3−2i32220000000000−222222−2200000000−i6i6i6−i6i6−i6−i6i62−2−22−222−200000000000000000000000000000000000000
χ974-44-4-44-4400004-44-44-4-4-440000000044-400000000000000-44-400004000000000000000000000000000000000000000000000000000000
χ984-44-4-44-440000-2-44-44222-2−2i32i3−2i32i3−2i32i3−2i32i3-2-22000000000000002-222i3−2i32i3−2i3-2000000000000000000000000000000000000000000000000000000
χ994-44-4-44-440000-2-44-44222-22i3−2i32i3−2i32i3−2i32i3−2i3-2-22000000000000002-22−2i32i3−2i32i3-2000000000000000000000000000000000000000000000000000000
χ1004-4-444-4-44000040000-44-4-400000000-44400000022−22−222200000000000022−22−222222−22−22220000000000000000000000000000000000000000000000
χ1014-4-444-4-44000040000-44-4-400000000-444000000−222222−22000000000000−222222−22−222222−220000000000000000000000000000000000000000000000
χ1024-4-444-4-440000-200002-222−2i32i32i3−2i3−2i32i32i3−2i32-2-200000022−22−2222000000000000−222−2−222−2−i6i6i6−i6−i6i6i6−i600000000000000000000000000000000000000
χ1034-4-444-4-440000-200002-222−2i32i32i3−2i3−2i32i32i3−2i32-2-2000000−222222−220000000000002−2−222−2−22i6−i6−i6i6i6−i6−i6i600000000000000000000000000000000000000
χ1044-4-444-4-440000-200002-2222i3−2i3−2i32i32i3−2i3−2i32i32-2-200000022−22−2222000000000000−222−2−222−2i6−i6−i6i6i6−i6−i6i600000000000000000000000000000000000000
χ1054-4-444-4-440000-200002-2222i3−2i3−2i32i32i3−2i3−2i32i32-2-2000000−222222−220000000000002−2−222−2−22−i6i6i6−i6−i6i6i6−i600000000000000000000000000000000000000
χ1064-4-4-4444-4000044-4-44-4-44-4000000004-44000000000000004-4-400004000000000000000000000000000000000000000000000000000000
χ1074-4-4-4444-40000-24-4-4422-22−2i32i3−2i32i32i3−2i32i3−2i3-22-200000000000000-222−2i32i32i3−2i3-2000000000000000000000000000000000000000000000000000000
χ1084-4-4-4444-40000-24-4-4422-222i3−2i32i3−2i3−2i32i3−2i32i3-22-200000000000000-2222i3−2i3−2i32i3-2000000000000000000000000000000000000000000000000000000

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