Finite Group Databasebeta

← Group #11799411

Character table — Group #11799411

Order 1152.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90
size11222222222222244444444444444444444444448888888888888888888816161616161616161616161616161616161618181818363636363636144144
order12233334466668866668121212121212121216161616242424242424242424242424484848484848484848484848484848484812121212121212122424242424242424161616162488161648
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1
χ3111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111-1-1
χ4111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111
χ51111111111111111111111111111-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11-111111111-1-1-1-1-1-1-1-11111-1-1-1-1111-1
χ61111111111111111111111111111-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11-111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-11
χ71111111111111111111111111111-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11-1-1-1-1-1-1-1-1111111111111-1-1-1-111-11
χ81111111111111111111111111111-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11-1-1-1-1-1-1-1-111111111-1-1-1-11111-1-11-1
χ92222222222222-2-22222-2222222220000-2-2-2-2-2-2-2-2-2-2-2-20000000000000000000000000000000000000022-2-20000
χ102222222222222-2-22222-2222222220000-2-2-2-2-2-2-2-2-2-2-2-200000000000000000000000000000000000000-2-2220000
χ112222222-2-222220022220-2-2-2-2-2-2-2-2−i2−i2i2i2000000000000−i2−i2−i2−i2−i2−i2−i2−i2i2i2i2i2i2i2i2i200000000000000000022−2−2002i−2i2−200
χ122222222-2-222220022220-2-2-2-2-2-2-2-2−i2−i2i2i2000000000000−i2−i2−i2−i2−i2−i2−i2−i2i2i2i2i2i2i2i2i2000000000000000000−2−22200−2i2i−2200
χ132222222-2-222220022220-2-2-2-2-2-2-2-2i2i2−i2−i2000000000000i2i2i2i2i2i2i2i2−i2−i2−i2−i2−i2−i2−i2−i200000000000000000022−2−200−2i2i2−200
χ142222222-2-222220022220-2-2-2-2-2-2-2-2i2i2−i2−i2000000000000i2i2i2i2i2i2i2i2−i2−i2−i2−i2−i2−i2−i2−i2000000000000000000−2−222002i−2i−2200
χ152222-1-1-1222-1-1-1222-1-1-122-1-1-12-1-1-1222222-1-1-1-1-1-12-1-1-122-1-1-1-1-1-122-1-1-1-1-1-12222-1-1-1-1-1-122-1-1-1-1-1-1000000000000
χ162222-1-1-1222-1-1-1222-1-1-122-1-1-12-1-1-1222222-1-1-1-1-1-12-1-1-122-1-1-1-1-1-122-1-1-1-1-1-1-2-2-2-2111111-2-2111111000000000000
χ172222-1-1-1222-1-1-1222-1-1-122-1-1-12-1-1-1-2-2-2-222-1-1-1-1-1-12-1-1-1-2-2111111-2-21111112-222-1-1-1-1-1-1-2-2111111000000000000
χ182222-1-1-1222-1-1-1222-1-1-122-1-1-12-1-1-1-2-2-2-222-1-1-1-1-1-12-1-1-1-2-2111111-2-2111111-22-2-211111122-1-1-1-1-1-1000000000000
χ19222-12-1-122-12-1-122-12-1-12-12-1-1-12-1-12222-1-122-1-1-1-1-12-1-1-1-122-1-1-1-1-1-122-1-1-1-122-1-122-1-1-1-1-1-122-1-1-1-1000000000000
χ20222-12-1-122-12-1-122-12-1-12-12-1-1-12-1-12222-1-122-1-1-1-1-12-1-1-1-122-1-1-1-1-1-122-1-1-1-1-2-211-2-2111111-2-21111000000000000
χ21222-12-1-122-12-1-122-12-1-12-12-1-1-12-1-1-2-2-2-2-1-122-1-1-1-1-12-1-111-2-2111111-2-211112-2-1-122-1-1-1-111-2-21111000000000000
χ22222-12-1-122-12-1-122-12-1-12-12-1-1-12-1-1-2-2-2-2-1-122-1-1-1-1-12-1-111-2-2111111-2-21111-2211-2-21111-1-122-1-1-1-1000000000000
χ23222-1-12-122-1-12-122-1-12-12-1-12-1-1-12-12222-1-1-1-122-1-1-1-12-1-1-1-1-122-1-1-1-1-1-122-1-122-1-1-1-122-1-1-1-1-1-122-1-1000000000000
χ24222-1-12-122-1-12-122-1-12-12-1-12-1-1-12-12222-1-1-1-122-1-1-1-12-1-1-1-1-122-1-1-1-1-1-122-1-1-2-21111-2-2111111-2-211000000000000
χ25222-1-12-122-1-12-122-1-12-12-1-12-1-1-12-1-2-2-2-2-1-1-1-122-1-1-1-12-11111-2-2111111-2-2112-2-1-1-1-122-1-11111-2-211000000000000
χ26222-1-12-122-1-12-122-1-12-12-1-12-1-1-12-1-2-2-2-2-1-1-1-122-1-1-1-12-11111-2-2111111-2-211-221111-2-211-1-1-1-122-1-1000000000000
χ27222-1-1-1222-1-1-1222-1-1-122-1-1-12-1-1-122222-1-1-1-1-1-122-1-1-12-1-1-1-1-1-122-1-1-1-1-1-12222-1-1-1-1-1-122-1-1-1-1-1-122000000000000
χ28222-1-1-1222-1-1-1222-1-1-122-1-1-12-1-1-122222-1-1-1-1-1-122-1-1-12-1-1-1-1-1-122-1-1-1-1-1-122-2-2111111-2-2111111-2-2000000000000
χ29222-1-1-1222-1-1-1222-1-1-122-1-1-12-1-1-12-2-2-2-2-1-1-1-1-1-122-1-1-12111111-2-2111111-2-22-2-1-1-1-1-1-122111111-2-2000000000000
χ30222-1-1-1222-1-1-1222-1-1-122-1-1-12-1-1-12-2-2-2-2-1-1-1-1-1-122-1-1-12111111-2-2111111-2-2-22111111-2-2-1-1-1-1-1-122000000000000
χ3122-222222-2222222-2-2-2-2-22222-2-2-2-2000022222222-2-2-2-2000000000000000000000000000000000022220000-2-200
χ3222-222222-2222222-2-2-2-2-22222-2-2-2-2000022222222-2-2-2-20000000000000000000000000000000000-2-2-2-200002200
χ3322-222222-22222-2-2-2-2-2-222222-2-2-2-22i−2i2i−2i-2-2-2-2-2-2-2-222222i−2i2i−2i2i−2i2i−2i2i−2i2i−2i2i−2i2i−2i000000000000000000000000000000
χ3422-222222-22222-2-2-2-2-2-222222-2-2-2-2−2i2i−2i2i-2-2-2-2-2-2-2-22222−2i2i−2i2i−2i2i−2i2i−2i2i−2i2i−2i2i−2i2i000000000000000000000000000000
χ3522-22222-22222200-2-2-2-20-2-2-2-222222−2−220000000000002−22−22−22−2−22−22−22−2200000000000000000022−2−22-200−2200
χ3622-22222-22222200-2-2-2-20-2-2-2-222222−2−220000000000002−22−22−22−2−22−22−22−22000000000000000000−2−222-22002−200
χ3722-22222-22222200-2-2-2-20-2-2-2-22222−222−2000000000000−22−22−22−222−22−22−22−200000000000000000022−2−2-2200−2200
χ3822-22222-22222200-2-2-2-20-2-2-2-22222−222−2000000000000−22−22−22−222−22−22−22−2000000000000000000−2−2222-2002−200
χ3922-22-1-1-12-22-1-1-1-2-2-211122-1-1-1-21112i−2i2i−2i-2-21111112-1-1-12i−2i−ii−ii−ii2i−2i−ii−ii−ii0000−i3i3−i3i3−i3i3003−33−33−3000000000000
χ4022-22-1-1-12-22-1-1-1-2-2-211122-1-1-1-21112i−2i2i−2i-2-21111112-1-1-12i−2i−ii−ii−ii2i−2i−ii−ii−ii0000i3−i3i3−i3i3−i300−33−33−33000000000000
χ4122-22-1-1-12-22-1-1-1-2-2-211122-1-1-1-2111−2i2i−2i2i-2-21111112-1-1-1−2i2ii−ii−ii−i−2i2ii−ii−ii−i0000−i3i3−i3i3−i3i300−33−33−33000000000000
χ4222-22-1-1-12-22-1-1-1-2-2-211122-1-1-1-2111−2i2i−2i2i-2-21111112-1-1-1−2i2ii−ii−ii−i−2i2ii−ii−ii−i0000i3−i3i3−i3i3−i3003−33−33−3000000000000
χ4322-2-12-1-12-2-12-1-1-2-21-2112-12-1-11-2112i−2i2i−2i11-2-21111-12-1-1−ii2i−2i−ii−ii−ii2i−2i−ii−ii00−i3i300−i3i3i3−i33−3003−3−33000000000000
χ4422-2-12-1-12-2-12-1-1-2-21-2112-12-1-11-2112i−2i2i−2i11-2-21111-12-1-1−ii2i−2i−ii−ii−ii2i−2i−ii−ii00i3−i300i3−i3−i3i3−3300−333−3000000000000
χ4522-2-12-1-12-2-12-1-1-2-21-2112-12-1-11-211−2i2i−2i2i11-2-21111-12-1-1i−i−2i2ii−ii−ii−i−2i2ii−ii−i00−i3i300−i3i3i3−i3−3300−333−3000000000000
χ4622-2-12-1-12-2-12-1-1-2-21-2112-12-1-11-211−2i2i−2i2i11-2-21111-12-1-1i−i−2i2ii−ii−ii−i−2i2ii−ii−i00i3−i300i3−i3−i3i33−3003−3−33000000000000
χ4722-2-1-12-12-2-1-12-1-2-211-212-1-12-111-212i−2i2i−2i1111-2-211-1-12-1−ii−ii2i−2i−ii−ii−ii2i−2i−ii00−i3i3i3−i300−i3i33−3−33003−3000000000000
χ4822-2-1-12-12-2-1-12-1-2-211-212-1-12-111-212i−2i2i−2i1111-2-211-1-12-1−ii−ii2i−2i−ii−ii−ii2i−2i−ii00i3−i3−i3i300i3−i3−333−300−33000000000000
χ4922-2-1-12-12-2-1-12-1-2-211-212-1-12-111-21−2i2i−2i2i1111-2-211-1-12-1i−ii−i−2i2ii−ii−ii−i−2i2ii−i00−i3i3i3−i300−i3i3−333−300−33000000000000
χ5022-2-1-12-12-2-1-12-1-2-211-212-1-12-111-21−2i2i−2i2i1111-2-211-1-12-1i−ii−i−2i2ii−ii−ii−i−2i2ii−i00i3−i3−i3i300i3−i33−3−33003−3000000000000
χ5122-2-1-1-122-2-1-1-12-2-2111-22-1-1-12111-22i−2i2i−2i111111-2-2-1-1-12−ii−ii−ii2i−2i−ii−ii−ii2i−2i00−i3i3−i3i3i3−i3003−33−3−3300000000000000
χ5222-2-1-1-122-2-1-1-12-2-2111-22-1-1-12111-22i−2i2i−2i111111-2-2-1-1-12−ii−ii−ii2i−2i−ii−ii−ii2i−2i00i3−i3i3−i3−i3i300−33−333−300000000000000
χ5322-2-1-1-122-2-1-1-12-2-2111-22-1-1-12111-2−2i2i−2i2i111111-2-2-1-1-12i−ii−ii−i−2i2ii−ii−ii−i−2i2i00−i3i3−i3i3i3−i300−33−333−300000000000000
χ5422-2-1-1-122-2-1-1-12-2-2111-22-1-1-12111-2−2i2i−2i2i111111-2-2-1-1-12i−ii−ii−i−2i2ii−ii−ii−i−2i2i00i3−i3i3−i3−i3i3003−33−3−3300000000000000
χ554444-2-2-2444-2-2-2-4-44-2-2-2-44-2-2-24-2-2-20000-4-4222222-42220000000000000000000000000000000000000000000000
χ564444-2-2-2-4-44-2-2-2004-2-2-20-4222-4222−2i2−2i22i22i2000000000000−2i2−2i2i2i2i2i2i2i22i22i2−i2−i2−i2−i2−i2−i2000000000000000000000000000000
χ574444-2-2-2-4-44-2-2-2004-2-2-20-4222-42222i22i2−2i2−2i20000000000002i22i2−i2−i2−i2−i2−i2−i2−2i2−2i2i2i2i2i2i2i2000000000000000000000000000000
χ58444-24-2-244-24-2-2-4-4-24-2-2-4-24-2-2-24-2-2000022-4-422222-4220000000000000000000000000000000000000000000000
χ59444-24-2-2-4-4-24-2-200-24-2-202-4222-422−2i2−2i22i22i2000000000000i2i2−2i2−2i2i2i2i2i2−i2−i22i22i2−i2−i2−i2−i2000000000000000000000000000000
χ60444-24-2-2-4-4-24-2-200-24-2-202-4222-4222i22i2−2i2−2i2000000000000−i2−i22i22i2−i2−i2−i2−i2i2i2−2i2−2i2i2i2i2i2000000000000000000000000000000
χ61444-2-24-244-2-24-2-4-4-2-24-2-4-2-24-2-2-24-200002222-4-42222-420000000000000000000000000000000000000000000000
χ62444-2-24-2-4-4-2-24-200-2-24-2022-4222-42−2i2−2i22i22i2000000000000i2i2i2i2−2i2−2i2i2i2−i2−i2−i2−i22i22i2−i2−i2000000000000000000000000000000
χ63444-2-24-2-4-4-2-24-200-2-24-2022-4222-422i22i2−2i2−2i2000000000000−i2−i2−i2−i22i22i2−i2−i2i2i2i2i2−2i2−2i2i2i2000000000000000000000000000000
χ64444-2-2-2444-2-2-24-4-4-2-2-24-4-2-2-24-2-2-240000222222-4-4222-40000000000000000000000000000000000000000000000
χ65444-2-2-24-4-4-2-2-2400-2-2-240222-4222-4−2i2−2i22i22i2000000000000i2i2i2i2i2i2−2i2−2i2−i2−i2−i2−i2−i2−i22i22i2000000000000000000000000000000
χ66444-2-2-24-4-4-2-2-2400-2-2-240222-4222-42i22i2−2i2−2i2000000000000−i2−i2−i2−i2−i2−i22i22i2i2i2i2i2i2i2−2i2−2i2000000000000000000000000000000
χ6744-44-2-2-24-44-2-2-244-4222-44-2-2-2-4222000044-2-2-2-2-2-2-42220000000000000000000000000000000000000000000000
χ6844-44-2-2-2-444-2-2-200-42220-42224-2-2-222−22−222200000000000022−22−22−22−22−22222−22−22−2000000000000000000000000000000
χ6944-44-2-2-2-444-2-2-200-42220-42224-2-2-2−222222−22000000000000−22222−22−22−222−22−22−22−22000000000000000000000000000000
χ7044-4-24-2-24-4-24-2-2442-422-4-24-2-22-4220000-2-244-2-2-2-22-4220000000000000000000000000000000000000000000000
χ7144-4-24-2-2-44-24-2-2002-42202-422-24-2-222−22−2222000000000000−2222−22−22−222−2−22222−22−2000000000000000000000000000000
χ7244-4-24-2-2-44-24-2-2002-42202-422-24-2-2−222222−220000000000002−2−22222−22−2−2222−22−22−22000000000000000000000000000000
χ7344-4-2-24-24-4-2-24-24422-42-4-2-24-222-420000-2-2-2-244-2-222-420000000000000000000000000000000000000000000000
χ7444-4-2-24-2-44-2-24-20022-42022-42-2-24-222−22−2222000000000000−22−2222−22−222−22−2−22222−2000000000000000000000000000000
χ7544-4-2-24-2-44-2-24-20022-42022-42-2-24-2−222222−220000000000002−22−2−22222−2−22−2222−22−22000000000000000000000000000000
χ7644-4-2-2-244-4-2-2-2444222-4-4-2-2-24222-40000-2-2-2-2-2-244222-40000000000000000000000000000000000000000000000
χ7744-4-2-2-24-44-2-2-2400222-40222-4-2-2-2422−22−2222000000000000−22−22−2222−222−22−22−2−2222000000000000000000000000000000
χ7844-4-2-2-24-44-2-2-2400222-40222-4-2-2-24−222222−220000000000002−22−22−2−2222−22−22−2222−22000000000000000000000000000000
χ794-40444400-4-4-4-422−220000000000000000022−2222−2222−2222−22000000000000000000000000000000000000002ζ11−2ζ13−2ζ29+2ζ43−2ζ11+2ζ13+2ζ29−2ζ43−2ζ25+2ζ31−2ζ41+2ζ472ζ25−2ζ31+2ζ41−2ζ4700000000
χ804-40444400-4-4-4-422−220000000000000000022−2222−2222−2222−2200000000000000000000000000000000000000−2ζ11+2ζ13+2ζ29−2ζ432ζ11−2ζ13−2ζ29+2ζ432ζ25−2ζ31+2ζ41−2ζ47−2ζ25+2ζ31−2ζ41+2ζ4700000000
χ814-40444400-4-4-4-4−222200000000000000000−2222−2222−2222−222200000000000000000000000000000000000000−2ζ25+2ζ31−2ζ41+2ζ472ζ25−2ζ31+2ζ41−2ζ47−2ζ11+2ζ13+2ζ29−2ζ432ζ11−2ζ13−2ζ29+2ζ4300000000
χ824-40444400-4-4-4-4−222200000000000000000−2222−2222−2222−2222000000000000000000000000000000000000002ζ25−2ζ31+2ζ41−2ζ47−2ζ25+2ζ31−2ζ41+2ζ472ζ11−2ζ13−2ζ29+2ζ43−2ζ11+2ζ13+2ζ29−2ζ4300000000
χ838-808-4-4-400-844442−420000000000000000042−42−2222−2222−222200000000000000000000000000000000000000000000000000
χ848-808-4-4-400-8444−424200000000000000000−424222−2222−2222−2200000000000000000000000000000000000000000000000000
χ858-80-48-4-4004-84442−4200000000000000000−222242−42−2222−222200000000000000000000000000000000000000000000000000
χ868-80-48-4-4004-844−42420000000000000000022−22−424222−2222−2200000000000000000000000000000000000000000000000000
χ878-80-4-48-40044-8442−4200000000000000000−2222−222242−42−222200000000000000000000000000000000000000000000000000
χ888-80-4-48-40044-84−42420000000000000000022−2222−22−424222−2200000000000000000000000000000000000000000000000000
χ898-80-4-4-4800444-842−4200000000000000000−2222−2222−222242−4200000000000000000000000000000000000000000000000000
χ908-80-4-4-4800444-8−42420000000000000000022−2222−2222−22−424200000000000000000000000000000000000000000000000000

Here ζ is a primitive root of unity of order 48 (ζ48 = 1); i = ζ12.