Finite Group Databasebeta

← Group #10694080

Character table — Group #10694080

Order 768.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96C97C98C99C100C101C102C103C104C105C106C107C108C109C110C111C112C113C114C115C116C117C118C119C120
size111111111111111122222222222222222222222244444444444444444444444444444444888888888888888888888888121212121212121212121212121212122424242424242424
order122222224444444434444444466666661212121212121212888888881212121212121212242424242424242424242424242424244444444412121212121212121212121212121212888888888888888888888888
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ3111111111111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111111111-1-1-1-1-1-1-1-1
χ4111111111111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111
χ51111111111111111111111111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-11111-1-1-1-1
χ61111111111111111111111111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-11111
χ71111111111111111111111111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-11111111111111111-1-1-1-1-1-1-1-1-1-1-1-11111
χ81111111111111111111111111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1111111111111-1-1-1-1
χ911111111-1-1-1-1-1-1-1-1111-1-111-1-11111111-1-1-1-1-1-1-1-11111-1-1-1-111-1-1-1-11111111111-1-1-1-1-1-1-1-111-1-111-1-11111-1-1-1-11111-1-1-1-1iiii−i−i−i−iiiii−i−i−i−iii−i−iii−i−i
χ1011111111-1-1-1-1-1-1-1-1111-1-111-1-11111111-1-1-1-1-1-1-1-11111-1-1-1-111-1-1-1-11111111111-1-1-1-1-1-1-1-111-1-111-1-11111-1-1-1-11111-1-1-1-1−i−i−i−iiiii−i−i−i−iiiii−i−iii−i−iii
χ1111111111-1-1-1-1-1-1-1-1111-1-111-1-11111111-1-1-1-1-1-1-1-11111-1-1-1-111-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-111-1-111-1-1-1-11111-1-1-1-11111iiii−i−i−i−iiiii−i−i−i−i−i−iii−i−iii
χ1211111111-1-1-1-1-1-1-1-1111-1-111-1-11111111-1-1-1-1-1-1-1-11111-1-1-1-111-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-111-1-111-1-1-1-11111-1-1-1-11111−i−i−i−iiiii−i−i−i−iiiiiii−i−iii−i−i
χ1311111111-1-1-1-1-1-1-1-1111-1-111-1-11111111-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-1-111-1-1-1-1-1-1-1-11111111111-1-1-1-1111111-1-1-1-1-1-1-1-11111iiii−i−i−i−i−i−i−i−iiiiiii−i−i−i−iii
χ1411111111-1-1-1-1-1-1-1-1111-1-111-1-11111111-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-1-111-1-1-1-1-1-1-1-11111111111-1-1-1-1111111-1-1-1-1-1-1-1-11111−i−i−i−iiiiiiiii−i−i−i−i−i−iiiii−i−i
χ1511111111-1-1-1-1-1-1-1-1111-1-111-1-11111111-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-1-111-1-1-1-1-1-1-1-111111111-1-11111-1-1-1-1-1-111111111-1-1-1-1iiii−i−i−i−i−i−i−i−iiiii−i−iiiii−i−i
χ1611111111-1-1-1-1-1-1-1-1111-1-111-1-11111111-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-1-111-1-1-1-1-1-1-1-111111111-1-11111-1-1-1-1-1-111111111-1-1-1-1−i−i−i−iiiiiiiii−i−i−i−iii−i−i−i−iii
χ1722222222222222222-2-2-2-2-2-2-2-222222222222222200000000-2-2-2-2-2-2-2-2000000000000000000000000000000000000000022-2-222-2-20000000000000000
χ1822222222222222222-2-2-2-2-2-2-2-222222222222222200000000-2-2-2-2-2-2-2-20000000000000000000000000000000000000000-2-222-2-2220000000000000000
χ192222222222222222-122222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-122222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-122222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1000000000000000000000000
χ202222222222222222-122222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-122222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-2-2-2-2-2-2-2-21111111111111111000000000000000000000000
χ212222222222222222-122222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-2-2-2-2-2-2-2-2-1-1-1-1-1-1-1-111111111111111112222-2-2-2-2-1-1-1-1-1-1-1-111111111000000000000000000000000
χ222222222222222222-122222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-2-2-2-2-2-2-2-2-1-1-1-1-1-1-1-11111111111111111-2-2-2-2222211111111-1-1-1-1-1-1-1-1000000000000000000000000
χ2322222222-2-2-2-2-2-2-2-22-2-222-2-2222222222-2-2-2-2-2-2-2-200000000-2-22222-2-200000000000000000000000000000000000000002i2i−2i−2i−2i−2i2i2i0000000000000000
χ2422222222-2-2-2-2-2-2-2-22-2-222-2-2222222222-2-2-2-2-2-2-2-200000000-2-22222-2-20000000000000000000000000000000000000000−2i−2i2i2i2i2i−2i−2i0000000000000000
χ2522222222-2-2-2-2-2-2-2-2-122-2-222-2-2-1-1-1-1-1-1-1111111112222-2-2-2-2-1-11111-1-1-1-1-1-1-1-1-1-11111111122-2-222-2-2-1-1-1-11111-1-1-1-11111000000000000000000000000
χ2622222222-2-2-2-2-2-2-2-2-122-2-222-2-2-1-1-1-1-1-1-1111111112222-2-2-2-2-1-11111-1-1-1-1-1-1-1-1-1-111111111-2-222-2-2221111-1-1-1-11111-1-1-1-1000000000000000000000000
χ2722222222-2-2-2-2-2-2-2-2-122-2-222-2-2-1-1-1-1-1-1-111111111-2-2-2-22222-1-11111-1-111111111-1-1-1-1-1-1-1-122-2-2-2-222-1-1-1-111111111-1-1-1-1000000000000000000000000
χ2822222222-2-2-2-2-2-2-2-2-122-2-222-2-2-1-1-1-1-1-1-111111111-2-2-2-22222-1-11111-1-111111111-1-1-1-1-1-1-1-1-2-22222-2-21111-1-1-1-1-1-1-1-11111000000000000000000000000
χ29222-2-22-2-22222-2-2-2-220000000022-2-22-2-22222-2-2-2-222−2−222−2−2000000002222−2−2−2−22222−2−2−2−2000000000000000000000000002-2002-222−2−222−2−200000000
χ30222-2-22-2-22222-2-2-2-220000000022-2-22-2-22222-2-2-2-222−2−222−2−2000000002222−2−2−2−22222−2−2−2−200000000000000000000000000-2200-22−2−222−2−22200000000
χ31222-2-22-2-22222-2-2-2-220000000022-2-22-2-22222-2-2-2-2−2−222−2−22200000000−2−2−2−22222−2−2−2−22222000000000000000000000000002-2002-2−2−222−2−22200000000
χ32222-2-22-2-22222-2-2-2-220000000022-2-22-2-22222-2-2-2-2−2−222−2−22200000000−2−2−2−22222−2−2−2−2222200000000000000000000000000-2200-2222−2−222−2−200000000
χ33222-2-22-2-2-2-2-2-2222220000000022-2-22-2-2-2-2-2-2222222−2−2−2−222000000002222−2−2−2−2−2−2−2−22222000000000000000000000000002i−2i00−2i2ii2i2−i2−i2−i2−i2i2i200000000
χ34222-2-22-2-2-2-2-2-2222220000000022-2-22-2-2-2-2-2-2222222−2−2−2−222000000002222−2−2−2−2−2−2−2−2222200000000000000000000000000−2i2i002i−2i−i2−i2i2i2i2i2−i2−i200000000
χ35222-2-22-2-2-2-2-2-2222220000000022-2-22-2-2-2-2-2-22222−2−22222−2−200000000−2−2−2−222222222−2−2−2−2000000000000000000000000002i−2i00−2i2i−i2−i2i2i2i2i2−i2−i200000000
χ36222-2-22-2-2-2-2-2-2222220000000022-2-22-2-2-2-2-2-22222−2−22222−2−200000000−2−2−2−222222222−2−2−2−200000000000000000000000000−2i2i002i−2ii2i2−i2−i2−i2−i2i2i200000000
χ3722-22-2-22-22i−2i2i−2i2i−2i2i−2i22-22i−2i2-22i−2i2-22-2-22-22i2i−2i−2i2i2i−2i−2i000000002-22i2i−2i−2i2-2000000000000000000000000000000000000000000000000000000000000−2ζ5−2ζ132ζ5+2ζ132ζ7+2ζ23−2ζ7−2ζ23
χ3822-22-2-22-22i−2i2i−2i2i−2i2i−2i22-22i−2i2-22i−2i2-22-2-22-22i2i−2i−2i2i2i−2i−2i000000002-22i2i−2i−2i2-20000000000000000000000000000000000000000000000000000000000002ζ5+2ζ13−2ζ5−2ζ13−2ζ7−2ζ232ζ7+2ζ23
χ3922-22-2-22-22i−2i2i−2i2i−2i2i−2i2-22−2i2i-22−2i2i2-22-2-22-22i2i−2i−2i2i2i−2i−2i00000000-22−2i−2i2i2i-22000000000000000000002i−2i2-2000000002i2i−2i−2i22-2-2000000000000000000000000
χ4022-22-2-22-22i−2i2i−2i2i−2i2i−2i2-22−2i2i-22−2i2i2-22-2-22-22i2i−2i−2i2i2i−2i−2i00000000-22−2i−2i2i2i-2200000000000000000000−2i2i-2200000000−2i−2i2i2i-2-222000000000000000000000000
χ4122-22-2-22-22i−2i2i−2i2i−2i2i−2i-1-22−2i2i-22−2i2i-11-111-11−i−iii−i−iii000000001-1ii−i−i1-133−3−333−3−3−i3−i3i3i3−i3−i3i3i300002i−2i2-2−i3−i3i3i333−3−3−i−iii-1-111000000000000000000000000
χ4222-22-2-22-22i−2i2i−2i2i−2i2i−2i-1-22−2i2i-22−2i2i-11-111-11−i−iii−i−iii000000001-1ii−i−i1-133−3−333−3−3−i3−i3i3i3−i3−i3i3i30000−2i2i-22i3i3−i3−i3−3−333ii−i−i11-1-1000000000000000000000000
χ4322-22-2-22-22i−2i2i−2i2i−2i2i−2i-1-22−2i2i-22−2i2i-11-111-11−i−iii−i−iii000000001-1ii−i−i1-1−3−333−3−333i3i3−i3−i3i3i3−i3−i300002i−2i2-2i3i3−i3−i3−3−333−i−iii-1-111000000000000000000000000
χ4422-22-2-22-22i−2i2i−2i2i−2i2i−2i-1-22−2i2i-22−2i2i-11-111-11−i−iii−i−iii000000001-1ii−i−i1-1−3−333−3−333i3i3−i3−i3i3i3−i3−i30000−2i2i-22−i3−i3i3i333−3−3ii−i−i11-1-1000000000000000000000000
χ4522-22-2-22-2−2i2i−2i2i−2i2i−2i2i22-2−2i2i2-2−2i2i2-22-2-22-2−2i−2i2i2i−2i−2i2i2i000000002-2−2i−2i2i2i2-20000000000000000000000000000000000000000000000000000000000002ζ7+2ζ23−2ζ7−2ζ23−2ζ5−2ζ132ζ5+2ζ13
χ4622-22-2-22-2−2i2i−2i2i−2i2i−2i2i22-2−2i2i2-2−2i2i2-22-2-22-2−2i−2i2i2i−2i−2i2i2i000000002-2−2i−2i2i2i2-2000000000000000000000000000000000000000000000000000000000000−2ζ7−2ζ232ζ7+2ζ232ζ5+2ζ13−2ζ5−2ζ13
χ4722-22-2-22-2−2i2i−2i2i−2i2i−2i2i2-222i−2i-222i−2i2-22-2-22-2−2i−2i2i2i−2i−2i2i2i00000000-222i2i−2i−2i-22000000000000000000002i−2i-22000000002i2i−2i−2i-2-222000000000000000000000000
χ4822-22-2-22-2−2i2i−2i2i−2i2i−2i2i2-222i−2i-222i−2i2-22-2-22-2−2i−2i2i2i−2i−2i2i2i00000000-222i2i−2i−2i-2200000000000000000000−2i2i2-200000000−2i−2i2i2i22-2-2000000000000000000000000
χ4922-22-2-22-2−2i2i−2i2i−2i2i−2i2i-1-222i−2i-222i−2i-11-111-11ii−i−iii−i−i000000001-1−i−iii1-133−3−333−3−3i3i3−i3−i3i3i3−i3−i300002i−2i-22−i3−i3i3i3−3−333−i−iii11-1-1000000000000000000000000
χ5022-22-2-22-2−2i2i−2i2i−2i2i−2i2i-1-222i−2i-222i−2i-11-111-11ii−i−iii−i−i000000001-1−i−iii1-133−3−333−3−3i3i3−i3−i3i3i3−i3−i30000−2i2i2-2i3i3−i3−i333−3−3ii−i−i-1-111000000000000000000000000
χ5122-22-2-22-2−2i2i−2i2i−2i2i−2i2i-1-222i−2i-222i−2i-11-111-11ii−i−iii−i−i000000001-1−i−iii1-1−3−333−3−333−i3−i3i3i3−i3−i3i3i300002i−2i-22i3i3−i3−i333−3−3−i−iii11-1-1000000000000000000000000
χ5222-22-2-22-2−2i2i−2i2i−2i2i−2i2i-1-222i−2i-222i−2i-11-111-11ii−i−iii−i−i000000001-1−i−iii1-1−3−333−3−333−i3−i3i3i3−i3−i3i3i30000−2i2i2-2−i3−i3i3i3−3−333ii−i−i-1-111000000000000000000000000
χ532-22-22-22-22i−2i−2i2i−2i2i2i−2i22-2−2i2i-222i−2i-22-22-22-22i−2i2i−2i2i−2i2i−2i000000002-22i−2i2i−2i-2200000000000000002-22i−2i00002-22-22i−2i2i−2i00000000000000000000000000000000
χ542-22-22-22-22i−2i−2i2i−2i2i2i−2i22-2−2i2i-222i−2i-22-22-22-22i−2i2i−2i2i−2i2i−2i000000002-22i−2i2i−2i-220000000000000000-22−2i2i0000-22-22−2i2i−2i2i00000000000000000000000000000000
χ552-22-22-22-22i−2i−2i2i−2i2i2i−2i2-222i−2i2-2−2i2i-22-22-22-22i−2i2i−2i2i−2i2i−2i00000000-22−2i2i−2i2i2-200000000000000000000000000000000000000000000000000000000−2ζ5−2ζ132ζ5+2ζ132ζ7+2ζ23−2ζ7−2ζ230000
χ562-22-22-22-22i−2i−2i2i−2i2i2i−2i2-222i−2i2-2−2i2i-22-22-22-22i−2i2i−2i2i−2i2i−2i00000000-22−2i2i−2i2i2-2000000000000000000000000000000000000000000000000000000002ζ5+2ζ13−2ζ5−2ζ13−2ζ7−2ζ232ζ7+2ζ230000
χ572-22-22-22-22i−2i−2i2i−2i2i2i−2i-12-2−2i2i-222i−2i1-11-11-11−ii−ii−ii−ii00000000-11−ii−ii1-13−33−33−33−3−i3i3−i3i3−i3i3−i3i32-22i−2i0000-11-11−ii−ii3−33−3−i3i3−i3i3000000000000000000000000
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χ632-22-22-22-2−2i2i2i−2i2i−2i−2i2i2-22−2i2i2-22i−2i-22-22-22-2−2i2i−2i2i−2i2i−2i2i00000000-222i−2i2i−2i2-2000000000000000000000000000000000000000000000000000000002ζ7+2ζ23−2ζ7−2ζ23−2ζ5−2ζ132ζ5+2ζ130000
χ642-22-22-22-2−2i2i2i−2i2i−2i−2i2i2-22−2i2i2-22i−2i-22-22-22-2−2i2i−2i2i−2i2i−2i2i00000000-222i−2i2i−2i2-200000000000000000000000000000000000000000000000000000000−2ζ7−2ζ232ζ7+2ζ232ζ5+2ζ13−2ζ5−2ζ130000
χ652-22-22-22-2−2i2i2i−2i2i−2i−2i2i-12-22i−2i-22−2i2i1-11-11-11i−ii−ii−ii−i00000000-11i−ii−i1-13−33−33−33−3i3−i3i3−i3i3−i3i3−i32-2−2i2i0000-11-11i−ii−i3−33−3i3−i3i3−i3000000000000000000000000
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Here ζ is a primitive root of unity of order 24 (ζ24 = 1); i = ζ6.