Finite Group Databasebeta

← Group #10733605

Character table — Group #10733605

Order 768.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96C97C98C99C100C101C102C103C104C105C106C107C108C109C110C111C112C113C114
size11111111111111112222222222222222444444444444444444444444444444444444444488888888888888888888881212121212121212242424242424242424242424
order1222222222222222366666666666666644444444444444441212121212121212121212121212121212121212121212124444441212121212121212121212121212121222224444224444444444
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ31111111111111111111111111111111111111111-1-1-1-11111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-111-1-1-1-1-1-11111
χ41111111111111111111111111111111111111111-1-1-1-11111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1111111-1-1-1-1
χ5111111111111111111111111111111111111-1-1-1-11111-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-111111111-1-1-1-1-1-1-1-111111111-1-111-1-1-1-111-1-1
χ6111111111111111111111111111111111111-1-1-1-11111-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-11111-1-111
χ7111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-1111111-1-1
χ8111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-111111111-1-1-1-111111111-1-1-1-1-1-111
χ911111111111111111111111111111111-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-111-1-111
χ1011111111111111111111111111111111-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1111111-1-111-1-1
χ1111111111111111111111111111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-111111111-1-1-1-11111-1-1-1-1-1-11111-1-1-1-111
χ1211111111111111111111111111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1111111-1-1-1-11111-1-1
χ1311111111111111111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-111-1-11111-1-1-1-11111-1-1-1-11111111111-1-111-1-1-1-1-1-1
χ1411111111111111111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-111-1-11111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1111111
χ1511111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111-1-111-1-1-1-11111-1-1-1-111111111-1-1-1-11111-1-111-1-1-1-1
χ1611111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111-1-111-1-1-1-11111-1-1-1-11111-1-1-1-11111-1-1-1-111-1-11111
χ172222222222222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-12222222222222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-100000000000000000000
χ182222222222222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-122222222-2-2-2-22222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-2-2-2-2-2-2111111111111111100000000000000000000
χ192222222222222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-12222-2-2-2-22222-2-2-2-2-1-1-1-1-1-1-1-1111111111111111122-2-2-2-2-1-1-1-1-1-1-1-11111111100000000000000000000
χ202222222222222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-12222-2-2-2-2-2-2-2-2-2-2-2-2-1-1-1-1-1-1-1-11111111111111111-2-2222211111111-1-1-1-1-1-1-1-100000000000000000000
χ212222222222222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-2-2-2-222222222-2-2-2-211111111-1-1-1-1-1-1-1-111111111-2-2-2-222-1-1-1-111111111-1-1-1-100000000000000000000
χ222222222222222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-2-2-2-22222-2-2-2-2-2-2-2-211111111-1-1-1-1-1-1-1-1111111112222-2-21111-1-1-1-1-1-1-1-1111100000000000000000000
χ232222222222222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-2-2-2-2-2-2-2-2222222221111111111111111-1-1-1-1-1-1-1-1-2-222-2-2-1-1-1-11111-1-1-1-1111100000000000000000000
χ242222222222222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-2-2-2-2-2-2-2-2-2-2-2-222221111111111111111-1-1-1-1-1-1-1-122-2-2221111-1-1-1-11111-1-1-1-100000000000000000000
χ25222222-2-22-2-2-2-2-2-22222222-2-2-2-22-2-2-2-22000000002i2i−2i−2i22-2-200000000000000002222-2-2-2-2002i−2i002i2i−2i−2i00002i2i−2i−2i000000000000000000000000
χ26222222-2-22-2-2-2-2-2-22222222-2-2-2-22-2-2-2-22000000002i2i−2i−2i-2-2220000000000000000-2-2-2-2222200−2i2i002i2i−2i−2i0000−2i−2i2i2i000000000000000000000000
χ27222222-2-22-2-2-2-2-2-22222222-2-2-2-22-2-2-2-2200000000−2i−2i2i2i22-2-200000000000000002222-2-2-2-200−2i2i00−2i−2i2i2i0000−2i−2i2i2i000000000000000000000000
χ28222222-2-22-2-2-2-2-2-22222222-2-2-2-22-2-2-2-2200000000−2i−2i2i2i-2-2220000000000000000-2-2-2-22222002i−2i00−2i−2i2i2i00002i2i−2i−2i000000000000000000000000
χ29222222-2-22-2-2-2-2-2-22-1-1-1-1-1-11111-11111-1000000002i2i−2i−2i22-2-23333−3−3−3−33333−3−3−3−3-1-1-1-11111002i−2i00−i−iii−i3−i3i3i3−i−iii−i3−i3i3i300000000000000000000
χ30222222-2-22-2-2-2-2-2-22-1-1-1-1-1-11111-11111-1000000002i2i−2i−2i22-2-2−3−3−3−33333−3−3−3−33333-1-1-1-11111002i−2i00−i−iiii3i3−i3−i3−i−iiii3i3−i3−i300000000000000000000
χ31222222-2-22-2-2-2-2-2-22-1-1-1-1-1-11111-11111-1000000002i2i−2i−2i-2-2223333−3−3−3−3−3−3−3−333331111-1-1-1-100−2i2i00−i−iii−i3−i3i3i3ii−i−ii3i3−i3−i300000000000000000000
χ32222222-2-22-2-2-2-2-2-22-1-1-1-1-1-11111-11111-1000000002i2i−2i−2i-2-222−3−3−3−333333333−3−3−3−31111-1-1-1-100−2i2i00−i−iiii3i3−i3−i3ii−i−i−i3−i3i3i300000000000000000000
χ33222222-2-22-2-2-2-2-2-22-1-1-1-1-1-11111-11111-100000000−2i−2i2i2i22-2-23333−3−3−3−33333−3−3−3−3-1-1-1-1111100−2i2i00ii−i−ii3i3−i3−i3ii−i−ii3i3−i3−i300000000000000000000
χ34222222-2-22-2-2-2-2-2-22-1-1-1-1-1-11111-11111-100000000−2i−2i2i2i22-2-2−3−3−3−33333−3−3−3−33333-1-1-1-1111100−2i2i00ii−i−i−i3−i3i3i3ii−i−i−i3−i3i3i300000000000000000000
χ35222222-2-22-2-2-2-2-2-22-1-1-1-1-1-11111-11111-100000000−2i−2i2i2i-2-2223333−3−3−3−3−3−3−3−333331111-1-1-1-1002i−2i00ii−i−ii3i3−i3−i3−i−iii−i3−i3i3i300000000000000000000
χ36222222-2-22-2-2-2-2-2-22-1-1-1-1-1-11111-11111-100000000−2i−2i2i2i-2-222−3−3−3−333333333−3−3−3−31111-1-1-1-1002i−2i00ii−i−i−i3−i3i3i3−i−iiii3i3−i3−i300000000000000000000
χ372222-2-22-2-22-2-2-222-22222-2-22-2-2-2-2222-2-22i2i−2i−2i0000000000002i2i−2i−2i2i2i−2i−2i00000000000000000000000000000000000000000022-2-2002i−2i00000000
χ382222-2-22-2-22-2-2-222-22222-2-22-2-2-2-2222-2-22i2i−2i−2i0000000000002i2i−2i−2i2i2i−2i−2i000000000000000000000000000000000000000000-2-22200−2i2i00000000
χ392222-2-22-2-22-2-2-222-22222-2-22-2-2-2-2222-2-2−2i−2i2i2i000000000000−2i−2i2i2i−2i−2i2i2i00000000000000000000000000000000000000000022-2-200−2i2i00000000
χ402222-2-22-2-22-2-2-222-22222-2-22-2-2-2-2222-2-2−2i−2i2i2i000000000000−2i−2i2i2i−2i−2i2i2i000000000000000000000000000000000000000000-2-222002i−2i00000000
χ4122-2-222-2-2-2222-22-2-222-2-222-22-2-2-222-22-200002i2i−2i−2i00000000000000002i2i−2i−2i2i2i−2i−2i00000000000000000000000000000000002-22-20000002i−2i0000
χ4222-2-222-2-2-2222-22-2-222-2-222-22-2-2-222-22-200002i2i−2i−2i00000000000000002i2i−2i−2i2i2i−2i−2i0000000000000000000000000000000000-22-22000000−2i2i0000
χ4322-2-222-2-2-2222-22-2-222-2-222-22-2-2-222-22-20000−2i−2i2i2i0000000000000000−2i−2i2i2i−2i−2i2i2i00000000000000000000000000000000002-22-2000000−2i2i0000
χ4422-2-222-2-2-2222-22-2-222-2-222-22-2-2-222-22-20000−2i−2i2i2i0000000000000000−2i−2i2i2i−2i−2i2i2i0000000000000000000000000000000000-22-220000002i−2i0000
χ4522-2-2-2-22-22-222-2-22222-2-2-2-222-2-22-2-22220000000000002-22-2000000000000000022-2-222-2-2000000000000000000000022-2-200002-20000000000
χ4622-2-2-2-22-22-222-2-22222-2-2-2-222-2-22-2-22220000000000002-22-2000000000000000022-2-222-2-20000000000000000000000-2-2220000-220000000000
χ4722-2-2-2-22-22-222-2-22222-2-2-2-222-2-22-2-2222000000000000-22-220000000000000000-2-222-2-222000000000000000000000022-2-20000-220000000000
χ4822-2-2-2-22-22-222-2-22222-2-2-2-222-2-22-2-2222000000000000-22-220000000000000000-2-222-2-2220000000000000000000000-2-22200002-20000000000
χ4922-2-2-2-2-2222-2-222-2222-2-2-2-2-2-222222-2-220000000000002-2-22000000000000000022-2-2-2-222000000000000000000000000002-2-2200002-2000000
χ5022-2-2-2-2-2222-2-222-2222-2-2-2-2-2-222222-2-220000000000002-2-22000000000000000022-2-2-2-22200000000000000000000000000-222-20000-22000000
χ5122-2-2-2-2-2222-2-222-2222-2-2-2-2-2-222222-2-22000000000000-222-20000000000000000-2-22222-2-2000000000000000000000000002-2-220000-22000000
χ5222-2-2-2-2-2222-2-222-2222-2-2-2-2-2-222222-2-22000000000000-222-20000000000000000-2-22222-2-200000000000000000000000000-222-200002-2000000
χ532-22-22-22-22-22-222-2-22-22-22-22-22-222-2-22-200002i−2i2i−2i2-22-20000000000002i−2i2i−2i2i−2i2i−2i0000000000002i−2i2-22-2000000002i−2i2i−2i00000000000000000000
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χ552-22-22-22-22-22-222-2-22-22-22-22-22-222-2-22-20000−2i2i−2i2i2-22-2000000000000−2i2i−2i2i−2i2i−2i2i000000000000−2i2i2-22-200000000−2i2i−2i2i00000000000000000000
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χ582-22-22-22-22-22-222-2-2-11-11-11-11-11-1-111-1100002i−2i2i−2i2-22-20000i3−i3i3−i3i3−i3i3−i3−ii−ii−ii−ii−33−33−33−3300002i−2i-11-11i3−i3i3−i3−33−33−ii−ii00000000000000000000
χ592-22-22-22-22-22-222-2-2-11-11-11-11-11-1-111-1100002i−2i2i−2i-22-220000−i3i3−i3i3−i3i3−i3i3−ii−ii−ii−ii3−33−33−33−30000−2i2i1-11-1i3−i3i3−i3−33−33i−ii−i00000000000000000000
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χ732-22-22-2-2222-22-2-22-2-11-11-111-11-1-11-1-111−2i2i−2i2i00002i−2i−2i2i0000i−ii−i−ii−ii−i3i3−i3i3i3−i3i3−i33−33−3−33−33-220000−iii−i1-1-11i3−i3−i3i3−333−300000000000000000000
χ742-22-22-2-2222-22-2-22-2-11-11-111-11-1-11-1-111−2i2i−2i2i00002i−2i−2i2i0000i−ii−i−ii−iii3−i3i3−i3−i3i3−i3i3−33−333−33−3-220000−iii−i1-1-11−i3i3i3−i33−3−3300000000000000000000
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χ772-22-2-22-2-2-222-22-2222-22-2-22-2-22-2-2-222222-2-220000000000002-2-22-222-2000000000000000000000000000000000000002-22-20000000000002-200
χ782-22-2-22-2-2-222-22-2222-22-2-22-2-22-2-2-222222-2-220000000000002-2-22-222-200000000000000000000000000000000000000-22-22000000000000-2200
χ792-22-2-22-2-2-222-22-2222-22-2-22-2-22-2-2-22222-222-2000000000000-222-22-2-22000000000000000000000000000000000000002-22-2000000000000-2200
χ802-22-2-22-2-2-222-22-2222-22-2-22-2-22-2-2-22222-222-2000000000000-222-22-2-2200000000000000000000000000000000000000-22-220000000000002-200
χ812-2-222-2-22-2-22-2-22222-2-222-2-2-2-22-22-222200002-2-2200000000000000002-2-222-2-220000000000000000000000000000002-2-22000000000000002-2
χ822-2-222-2-22-2-22-2-22222-2-222-2-2-2-22-22-222200002-2-2200000000000000002-2-222-2-22000000000000000000000000000000-222-200000000000000-22
χ832-2-222-2-22-2-22-2-22222-2-222-2-2-2-22-22-22220000-222-20000000000000000-222-2-222-20000000000000000000000000000002-2-2200000000000000-22
χ842-2-222-2-22-2-22-2-22222-2-222-2-2-2-22-22-22220000-222-20000000000000000-222-2-222-2000000000000000000000000000000-222-2000000000000002-2
χ854444-4-44-4-44-4-4-444-4-2-2-2-222-22222-2-2-2224i4i−4i−4i000000000000−2i−2i2i2i−2i−2i2i2i0000000000000000000000000000000000000000000000000000000000
χ864444-4-44-4-44-4-4-444-4-2-2-2-222-22222-2-2-222−4i−4i4i4i0000000000002i2i−2i−2i2i2i−2i−2i0000000000000000000000000000000000000000000000000000000000
χ874444-4-4-44-4-4444-4-4-44444-4-4-4444-4-4-4-44-40000000000000000000000000000000000000000000000000000000000000000000000000000000000
χ884444-4-4-44-4-4444-4-4-4-2-2-2-2222-2-2-22222-220000000000000000−2i3−2i32i32i32i32i3−2i3−2i30000000000000000000000000000000000000000000000000000000000
χ894444-4-4-44-4-4444-4-4-4-2-2-2-2222-2-2-22222-2200000000000000002i32i3−2i3−2i3−2i3−2i32i32i30000000000000000000000000000000000000000000000000000000000
χ9044-4-44444-4-4-4-44-44-444-4-4444-444-4-4-44-4-40000000000000000000000000000000000000000000000000000000000000000000000000000000000
χ9144-4-44444-4-4-4-44-44-4-2-222-2-2-22-2-2222-222000000000000000000000000−2i3−2i32i32i32i32i3−2i3−2i300000000000000000000000000000000000000000000000000
χ9244-4-44444-4-4-4-44-44-4-2-222-2-2-22-2-2222-2220000000000000000000000002i32i3−2i3−2i3−2i3−2i32i32i300000000000000000000000000000000000000000000000000
χ9344-4-444-4-4-4444-44-4-4-2-222-2-22-2222-2-22-2200004i4i−4i−4i0000000000000000−2i−2i2i2i−2i−2i2i2i00000000000000000000000000000000000000000000000000
χ9444-4-444-4-4-4444-44-4-4-2-222-2-22-2222-2-22-220000−4i−4i4i4i00000000000000002i2i−2i−2i2i2i−2i−2i00000000000000000000000000000000000000000000000000
χ9544-4-4-4-44-44-444-4-444-2-22222-2-222-222-2-2-20000000000004-44-40000000000000000-2-222-2-222000000000000000000000000000000000000000000
χ9644-4-4-4-44-44-444-4-444-2-22222-2-222-222-2-2-2000000000000-44-44000000000000000022-2-222-2-2000000000000000000000000000000000000000000
χ9744-4-4-4-4-4444-4-444-44-2-2222222-2-2-2-2-222-20000000000004-4-440000000000000000-2-22222-2-2000000000000000000000000000000000000000000
χ9844-4-4-4-4-4444-4-444-44-2-2222222-2-2-2-2-222-2000000000000-444-4000000000000000022-2-2-2-222000000000000000000000000000000000000000000
χ994-44-4-4444-4-4-44-44-444-44-4-4444-44-44-4-4-440000000000000000000000000000000000000000000000000000000000000000000000000000000000
χ1004-44-4-4444-4-4-44-44-44-22-222-2-2-22-22-2222-2000000000000000023−23−232323−23−23230000000000000000000000000000000000000000000000000000000000
χ1014-44-4-4444-4-4-44-44-44-22-222-2-2-22-22-2222-20000000000000000−232323−23−232323−230000000000000000000000000000000000000000000000000000000000
χ1024-44-4-44-4-4-444-44-444-22-222-222-2222-2-2-2-24-4-44000000000000-222-22-2-220000000000000000000000000000000000000000000000000000000000
χ1034-44-4-44-4-4-444-44-444-22-222-222-2222-2-2-2-2-444-40000000000002-2-22-222-20000000000000000000000000000000000000000000000000000000000
χ1044-4-444-44-4-44-444-4-444-4-444-4444-4-4-44-4-440000000000000000000000000000000000000000000000000000000000000000000000000000000000
χ1054-4-444-44-4-44-444-4-44-222-2-22-2-2-2222-222-200000000000000000000000023−23−2323−232323−2300000000000000000000000000000000000000000000000000
χ1064-4-444-44-4-44-444-4-44-222-2-22-2-2-2222-222-2000000000000000000000000−232323−2323−23−232300000000000000000000000000000000000000000000000000
χ1074-4-444-4-44-4-44-4-4444-222-2-22222-22-22-2-2-200004-4-440000000000000000-222-2-222-200000000000000000000000000000000000000000000000000
χ1084-4-444-4-44-4-44-4-4444-222-2-22222-22-22-2-2-20000-444-400000000000000002-2-222-2-2200000000000000000000000000000000000000000000000000
χ1094-4-44-4444444-4-4-4-4-44-4-44-444-4-444-44-44-40000000000000000000000000000000000000000000000000000000000000000000000000000000000
χ1104-4-44-4444444-4-4-4-4-4-222-22-2-222-2-22-22-220000000000000000000000000000000023−23−232323−23−2323000000000000000000000000000000000000000000
χ1114-4-44-4444444-4-4-4-4-4-222-22-2-222-2-22-22-2200000000000000000000000000000000−232323−23−232323−23000000000000000000000000000000000000000000
χ1124-4-44-44-4-44-4-44444-44-4-44-44-444-444-44-4-40000000000000000000000000000000000000000000000000000000000000000000000000000000000
χ1134-4-44-44-4-44-4-44444-4-222-22-22-2-22-2-22-2220000000000000000000000000000000023−23−2323−232323−23000000000000000000000000000000000000000000
χ1144-4-44-44-4-44-4-44444-4-222-22-22-2-22-2-22-22200000000000000000000000000000000−232323−2323−23−2323000000000000000000000000000000000000000000

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