Finite Group Databasebeta

← Group #10697818

Character table — Group #10697818

Order 768.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96
size11112222222222222222222222222244444444444444444444444444444444448888888888888888888888884848484848484848
order12222234444444466612121212121212121212121244444444446612121212121212121212121212121212121212121212888888882424242424242424242424242424242422222488
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1
χ31111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1
χ41111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111
χ511111111111111111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-111111111-1-1-1-1-1-1-1-111-1-111-1-1
χ611111111111111111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-111111111-1-1-1-1-1-1-1-1-1-111-1-111
χ711111111111111111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-11111111111-1-1-1-111
χ811111111111111111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-111111111-1-11111-1-1
χ92222222222-2-2-2-222222222-2-2-2-2-2-2-2-2-2-22222-2-2-2-22222-2-2-2-222222222-2-2-2-2-2-2-2-200000000000000000000000000000000
χ102222222222-2-2-2-222222222-2-2-2-2-2-2-2-2-2-2-2-2-2-222222222-2-2-2-2-2-2-2-2-2-2-2-22222222200000000000000000000000000000000
χ112222222-2-2-222-2-2-2222-2-2-2-22222-2-2-2-22-20000000022-2-222-2-200000000000000000000000000000000000000002-2000000
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χ132222222-2-2-2-2-222-2222-2-2-2-2-2-2-2-22222-220000000022-2-2-2-2220000000000000000000000000000000000000000002-20000
χ142222222-2-2-2-2-222-2222-2-2-2-2-2-2-2-22222-220000000022-2-2-2-222000000000000000000000000000000000000000000-220000
χ15222222-122222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-12222222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-122222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-100000000
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χ17222222-122222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-122-2-2-2-2-2-2-2-2-1-1-1-1-1-1-1-111111111111111112222-2-2-2-2-1-1-1-1-1-1-1-11111111100000000
χ18222222-122222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-122-2-2-2-2-2-2-2-2-1-1-1-1-1-1-1-11111111111111111-2-2-2-2222211111111-1-1-1-1-1-1-1-100000000
χ19222222-1222-2-2-2-22-1-1-1-1-1-1-111111111-2-22222-2-2-2-2-1-1-1-11111-1-1-1-1-1-1-1-111111111000000003333−3−3−3−33333−3−3−3−300000000
χ20222222-1222-2-2-2-22-1-1-1-1-1-1-111111111-2-22222-2-2-2-2-1-1-1-11111-1-1-1-1-1-1-1-11111111100000000−3−3−3−33333−3−3−3−3333300000000
χ21222222-1222-2-2-2-22-1-1-1-1-1-1-111111111-2-2-2-2-2-22222-1-1-1-1111111111111-1-1-1-1-1-1-1-1000000003333−3−3−3−3−3−3−3−3333300000000
χ22222222-1222-2-2-2-22-1-1-1-1-1-1-111111111-2-2-2-2-2-22222-1-1-1-1111111111111-1-1-1-1-1-1-1-100000000−3−3−3−333333333−3−3−3−300000000
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χ342222-2-2-1-2-2222-2-22-1-1-11111-1-1-1-11111-220000000011-1-111-1-1−3−3−3−33333−3−3−3−33333-2-222000011-1-111-1-133−3−3−3−33300000000
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χ382222-2-2-1-2-22-2-2222-1-1-111111111-1-1-1-12-20000000011-1-1-1-111−3−3−3−333333333−3−3−3−30000-2-222−3−33333−3−311-1-111-1-100000000
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χ472-2-222-2-12-2-200002-111-1-111−3−333−3−33300000022-2-2-11-11−33−33−3−333−3−333-1-111-1-1112−22−22−22−2ζ13−ζ23−ζ13+ζ23ζ13−ζ23−ζ13+ζ23ζ5−ζ7−ζ5+ζ7ζ5−ζ7−ζ5+ζ7ζ5−ζ7−ζ5+ζ7ζ5−ζ7−ζ5+ζ7ζ13−ζ23−ζ13+ζ23ζ13−ζ23−ζ13+ζ2300000000
χ482-2-222-2-12-2-200002-111-1-111−3−333−3−33300000022-2-2-11-11−33−33−3−333−3−333-1-111-1-111−22−22−22−22−ζ13+ζ23ζ13−ζ23−ζ13+ζ23ζ13−ζ23−ζ5+ζ7ζ5−ζ7−ζ5+ζ7ζ5−ζ7−ζ5+ζ7ζ5−ζ7−ζ5+ζ7ζ5−ζ7−ζ13+ζ23ζ13−ζ23−ζ13+ζ23ζ13−ζ2300000000
χ492-2-222-2-12-2-200002-111-1-111−3−333−3−333000000-2-222-11-11−33−3333−3−333−3−311-1-111-1-12−22−2−22−22ζ13−ζ23−ζ13+ζ23ζ13−ζ23−ζ13+ζ23ζ5−ζ7−ζ5+ζ7ζ5−ζ7−ζ5+ζ7−ζ5+ζ7ζ5−ζ7−ζ5+ζ7ζ5−ζ7−ζ13+ζ23ζ13−ζ23−ζ13+ζ23ζ13−ζ2300000000
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χ512-2-22-222-22-2000022-2-2-2-222000000000022-2-20000-222-2000022-2-2-2-222000000002−2−22−222−22−2−222−2−22−222−2−222−200000000
χ522-2-22-222-22-2000022-2-2-2-222000000000022-2-20000-222-2000022-2-2-2-22200000000−222−22−2−22−222−2−222−22−2−222−2−2200000000
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χ542-2-22-222-22-2000022-2-2-2-2220000000000-2-2220000-222-20000-2-22222-2-200000000−222−2−222−2−222−2−222−2−222−2−222−200000000
χ552-2-22-22-1-22-200002-11111-1-133−3−3−3−3330022-2-200001-1-11−333−3-1-11111-1-1−3−33333−3−32−2−22−222−2ζ5−ζ7−ζ5+ζ7−ζ5+ζ7ζ5−ζ7ζ13−ζ23−ζ13+ζ23−ζ13+ζ23ζ13−ζ23−ζ5+ζ7ζ5−ζ7ζ5−ζ7−ζ5+ζ7−ζ13+ζ23ζ13−ζ23ζ13−ζ23−ζ13+ζ2300000000
χ562-2-22-22-1-22-200002-11111-1-133−3−3−3−3330022-2-200001-1-11−333−3-1-11111-1-1−3−33333−3−3−222−22−2−22−ζ5+ζ7ζ5−ζ7ζ5−ζ7−ζ5+ζ7−ζ13+ζ23ζ13−ζ23ζ13−ζ23−ζ13+ζ23ζ5−ζ7−ζ5+ζ7−ζ5+ζ7ζ5−ζ7ζ13−ζ23−ζ13+ζ23−ζ13+ζ23ζ13−ζ2300000000
χ572-2-22-22-1-22-200002-11111-1-133−3−3−3−33300-2-22200001-1-11−333−311-1-1-1-11133−3−3−3−3332−2−222−2−22ζ5−ζ7−ζ5+ζ7−ζ5+ζ7ζ5−ζ7ζ13−ζ23−ζ13+ζ23−ζ13+ζ23ζ13−ζ23ζ5−ζ7−ζ5+ζ7−ζ5+ζ7ζ5−ζ7ζ13−ζ23−ζ13+ζ23−ζ13+ζ23ζ13−ζ2300000000
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χ622-2-22-22-1-22-200002-11111-1-1−3−33333−3−300-2-22200001-1-113−3−3311-1-1-1-111−3−33333−3−3−222−2−222−2−ζ13+ζ23ζ13−ζ23ζ13−ζ23−ζ13+ζ23−ζ5+ζ7ζ5−ζ7ζ5−ζ7−ζ5+ζ7−ζ13+ζ23ζ13−ζ23ζ13−ζ23−ζ13+ζ23−ζ5+ζ7ζ5−ζ7ζ5−ζ7−ζ5+ζ700000000
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χ7444-4-400-2000004-402-22−2323−2323−2323−2323-22-2200-22-22-22-22000000001+3−1−31+3−1−31−3−1+31−3−1+31−3−1+31−3−1+31+3−1−31+3−1−300000000000000000000000000000000
χ7544-4-400-200000-4402-2223−2323−23−2323−23232-22-2002-22-2-22-2200000000−1+31−3−1+31−3−1−31+3−1−31+31+3−1−31+3−1−31−3−1+31−3−1+300000000000000000000000000000000
χ7644-4-400-200000-4402-2223−2323−23−2323−23232-22-200-22-222-22-2000000001−3−1+31−3−1+31+3−1−31+3−1−3−1−31+3−1−31+3−1+31−3−1+31−300000000000000000000000000000000
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χ864-44-400-20004-400022-2−232323−23-222-223−23−232300-222-2-222-2000000001−3−1+3−1+31−3−1−31+31+3−1−31−3−1+3−1+31−31+3−1−3−1−31+300000000000000000000000000000000
χ874-44-400-2000-4400022-223−23−23232-2-2223−23−2323002-2-22-222-200000000−1−31+31+3−1−31−3−1+3−1+31−31+3−1−3−1−31+31−3−1+3−1+31−300000000000000000000000000000000
χ884-44-400-2000-4400022-223−23−23232-2-2223−23−232300-222-22-2-22000000001+3−1−3−1−31+3−1+31−31−3−1+3−1−31+31+3−1−3−1+31−31−3−1+300000000000000000000000000000000
χ894-44-400-2000-4400022-2−232323−232-2-22−232323−23002-2-22-222-200000000−1+31−31−3−1+31+3−1−3−1−31+31−3−1+3−1+31−31+3−1−3−1−31+300000000000000000000000000000000
χ904-44-400-2000-4400022-2−232323−232-2-22−232323−2300-222-22-2-22000000001−3−1+3−1+31−3−1−31+31+3−1−3−1+31−31−3−1+3−1−31+31+3−1−300000000000000000000000000000000
χ914-4-444-44-4440000-44-4-4-4-4440000000000000000004-4-440000000000000000000000000000000000000000000000000000
χ924-4-444-4-2-4440000-4-22222-2-22323−23−23−23−2323230000000000-222-223−23−2323000000000000000000000000000000000000000000000000
χ934-4-444-4-2-4440000-4-22222-2-2−23−2323232323−23−230000000000-222-2−232323−23000000000000000000000000000000000000000000000000
χ944-4-44-4444-440000-44-4-444-4-4000000000000000000-44-440000000000000000000000000000000000000000000000000000
χ954-4-44-44-24-440000-4-222-2-2222323−23−232323−23−2300000000002-22-2−2323−2323000000000000000000000000000000000000000000000000
χ964-4-44-44-24-440000-4-222-2-222−23−232323−23−23232300000000002-22-223−2323−23000000000000000000000000000000000000000000000000

Here ζ is a primitive root of unity of order 24 (ζ24 = 1); i = ζ6.