Finite Group Databasebeta

← Group #10695325

Character table — Group #10695325

Order 768.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96
size111111112222222222222222444444444444444444666666668888888888888888888888121212121212121212121212161616161616242424244848
order122222223444444446666666448888888812121212121212124444444488881212242424242424242424242424242424244444888888884412121212888844
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111111111111111-1-1-1-11111111111-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-1
χ3111111111111111111111111111111111111111111-1-1-1-1-1-1-1-11111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1
χ4111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111
χ511111111111111111111111111-1-1-1-1-1-1-1-11111111111111111111111-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1
χ611111111111111111111111111-1-1-1-1-1-1-1-11111111111111111-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1111111-1-1-1-111
χ711111111111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-111111111-1-1-1-111111111-1-1-1-1-1-1-1-1-1-111
χ811111111111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111111111-1-1
χ9111111111-1-1-1-1-1-1-1-1111111111iiii−i−i−i−i-1-1-1-1-1-1-1-11111-1-1-1-1ii−i−i11iiii−i−i−i−iiiii−i−i−i−i11-1-1iiii−i−i−i−i1-111-1-1ii−i−i1-1
χ10111111111-1-1-1-1-1-1-1-1111111111iiii−i−i−i−i-1-1-1-1-1-1-1-11111-1-1-1-1−i−iii11iiii−i−i−i−i−i−i−i−iiiii11-1-1iiii−i−i−i−i-11-1-111−i−iii-11
χ11111111111-1-1-1-1-1-1-1-1111111111iiii−i−i−i−i-1-1-1-1-1-1-1-1-1-1-1-11111ii−i−i11iiii−i−i−i−iiiii−i−i−i−i-1-111−i−i−i−iiiii1-111-1-1−i−iii-11
χ12111111111-1-1-1-1-1-1-1-1111111111iiii−i−i−i−i-1-1-1-1-1-1-1-1-1-1-1-11111−i−iii11iiii−i−i−i−i−i−i−i−iiiii-1-111−i−i−i−iiiii-11-1-111ii−i−i1-1
χ13111111111-1-1-1-1-1-1-1-1111111111−i−i−i−iiiii-1-1-1-1-1-1-1-11111-1-1-1-1ii−i−i11−i−i−i−iiiiiiiii−i−i−i−i11-1-1−i−i−i−iiiii-11-1-111ii−i−i-11
χ14111111111-1-1-1-1-1-1-1-1111111111−i−i−i−iiiii-1-1-1-1-1-1-1-11111-1-1-1-1−i−iii11−i−i−i−iiiii−i−i−i−iiiii11-1-1−i−i−i−iiiii1-111-1-1−i−iii1-1
χ15111111111-1-1-1-1-1-1-1-1111111111−i−i−i−iiiii-1-1-1-1-1-1-1-1-1-1-1-11111ii−i−i11−i−i−i−iiiiiiiii−i−i−i−i-1-111iiii−i−i−i−i-11-1-111−i−iii1-1
χ16111111111-1-1-1-1-1-1-1-1111111111−i−i−i−iiiii-1-1-1-1-1-1-1-1-1-1-1-11111−i−iii11−i−i−i−iiiii−i−i−i−iiiii-1-111iiii−i−i−i−i1-111-1-1ii−i−i-11
χ1722222222222-2-22-22-22222222-2-200000000222-2-2-22-2222222220000-2-20000000000000000-2-2-2-200000000000000000000
χ1822222222222-2-22-22-22222222-2-200000000222-2-2-22-2-2-2-2-2-2-2-2-20000-2-20000000000000000222200000000000000000000
χ19222222222-2-222-22-222222222-2-200000000-2-2-2222-222222-2-2-2-20000-2-20000000000000000-2-22200000000000000000000
χ20222222222-2-222-22-222222222-2-200000000-2-2-2222-22-2-2-2-222220000-2-2000000000000000022-2-200000000000000000000
χ2122222222-122222222-1-1-1-1-1-1-12222222222-1-1-1-1-1-1-1-1000000002222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-100000000000022-1-1-1-1000000
χ2222222222-122222222-1-1-1-1-1-1-12222222222-1-1-1-1-1-1-1-100000000-2-2-2-2-1-1-1-1-1-1-1-1-1-111111111000000000000-2-21111000000
χ2322222222-122222222-1-1-1-1-1-1-122-2-2-2-2-2-2-2-2-1-1-1-1-1-1-1-1000000002222-1-111111111-1-1-1-1-1-1-1-1000000000000-2-21111000000
χ2422222222-122222222-1-1-1-1-1-1-122-2-2-2-2-2-2-2-2-1-1-1-1-1-1-1-100000000-2-2-2-2-1-1111111111111111100000000000022-1-1-1-1000000
χ2522222222-1-2-2-2-2-2-2-2-2-1-1-1-1-1-1-1222i2i2i2i−2i−2i−2i−2i11111111000000002i2i−2i−2i-1-1−i−i−i−iiiii−i−i−i−iiiii0000000000002-2-1-111000000
χ2622222222-1-2-2-2-2-2-2-2-2-1-1-1-1-1-1-1222i2i2i2i−2i−2i−2i−2i1111111100000000−2i−2i2i2i-1-1−i−i−i−iiiiiiiii−i−i−i−i000000000000-2211-1-1000000
χ2722222222-1-2-2-2-2-2-2-2-2-1-1-1-1-1-1-122−2i−2i−2i−2i2i2i2i2i11111111000000002i2i−2i−2i-1-1iiii−i−i−i−i−i−i−i−iiiii000000000000-2211-1-1000000
χ2822222222-1-2-2-2-2-2-2-2-2-1-1-1-1-1-1-122−2i−2i−2i−2i2i2i2i2i1111111100000000−2i−2i2i2i-1-1iiii−i−i−i−iiiii−i−i−i−i0000000000002-2-1-111000000
χ292222-2-2-2-222-2222-2-2-2-2-2-2222-22-222-2-222-2-22-2-222-22-20000000000002-222-2-222-2-200000000000000000000000000000000
χ302222-2-2-2-222-2222-2-2-2-2-2-2222-22-2-2-222-2-2222-2-222-22-20000000000002-2-2-222-2-22200000000000000000000000000000000
χ312222-2-2-2-222-2-2-222-22-2-2-2222-2-22000000002-2-2-2-2222000000000000-22000000000000000000002i2i−2i−2i2i2i−2i−2i000000000000
χ322222-2-2-2-222-2-2-222-22-2-2-2222-2-22000000002-2-2-2-2222000000000000-2200000000000000000000−2i−2i2i2i−2i−2i2i2i000000000000
χ332222-2-2-2-22-2222-2-22-2-2-2-2222-2-2200000000-22222-2-2-2000000000000-220000000000000000000022-2-2-2-222000000000000
χ342222-2-2-2-22-2222-2-22-2-2-2-2222-2-2200000000-22222-2-2-2000000000000-2200000000000000000000-2-22222-2-2000000000000
χ352222-2-2-2-22-22-2-2-2222-2-2-2222-22-22i2i−2i−2i−2i−2i2i2i-222-2-22-220000000000002-22i2i−2i−2i−2i−2i2i2i00000000000000000000000000000000
χ362222-2-2-2-22-22-2-2-2222-2-2-2222-22-2−2i−2i2i2i2i2i−2i−2i-222-2-22-220000000000002-2−2i−2i2i2i2i2i−2i−2i00000000000000000000000000000000
χ372222-2-2-2-2-12-2222-2-2-2111-1-1-112-222-2-222-2-2-111-1-11-11000000000000-11-1-111-1-11133−3−333−3−3000000000000003−33−3000000
χ382222-2-2-2-2-12-2222-2-2-2111-1-1-112-222-2-222-2-2-111-1-11-11000000000000-11-1-111-1-111−3−333−3−33300000000000000−33−33000000
χ392222-2-2-2-2-12-2222-2-2-2111-1-1-112-2-2-222-2-222-111-1-11-11000000000000-1111-1-111-1-133−3−333−3−300000000000000−33−33000000
χ402222-2-2-2-2-12-2222-2-2-2111-1-1-112-2-2-222-2-222-111-1-11-11000000000000-1111-1-111-1-1−3−333−3−333000000000000003−33−3000000
χ412222-2-2-2-2-1-22-2-2-2222111-1-1-112-22i2i−2i−2i−2i−2i2i2i1-1-111-11-1000000000000-11−i−iiiii−i−i−i3−i3i3i3i3i3−i3−i300000000000000−333−3000000
χ422222-2-2-2-2-1-22-2-2-2222111-1-1-112-22i2i−2i−2i−2i−2i2i2i1-1-111-11-1000000000000-11−i−iiiii−i−ii3i3−i3−i3−i3−i3i3i3000000000000003−3−33000000
χ432222-2-2-2-2-1-22-2-2-2222111-1-1-112-2−2i−2i2i2i2i2i−2i−2i1-1-111-11-1000000000000-11ii−i−i−i−iii−i3−i3i3i3i3i3−i3−i3000000000000003−3−33000000
χ442222-2-2-2-2-1-22-2-2-2222111-1-1-112-2−2i−2i2i2i2i2i−2i−2i1-1-111-11-1000000000000-11ii−i−i−i−iiii3i3−i3−i3−i3−i3i3i300000000000000−333−3000000
χ4522-2-22-22-22002-2020-22-2-22-2-22002−22−22−22−20002-2-20200002i2i−2i−2i0000002−22−22−22−2000000002i−2i00−i2i2−i2i2−i2i2−i2i2000000000000
χ4622-2-22-22-22002-2020-22-2-22-2-22002−22−22−22−20002-2-2020000−2i−2i2i2i0000002−22−22−22−200000000−2i2i00i2−i2i2−i2i2−i2i2−i2000000000000
χ4722-2-22-22-22002-2020-22-2-22-2-2200−22−22−22−220002-2-20200002i2i−2i−2i000000−22−22−22−22000000002i−2i00i2−i2i2−i2i2−i2i2−i2000000000000
χ4822-2-22-22-22002-2020-22-2-22-2-2200−22−22−22−220002-2-2020000−2i−2i2i2i000000−22−22−22−2200000000−2i2i00−i2i2−i2i2−i2i2−i2i2000000000000
χ4922-2-22-22-2200-220-2022-2-22-2-2200−i2i2−i2i2i2−i2i2−i2000-2220-200002i2i−2i−2i000000−i2i2−i2i2i2−i2i2−i200000000−2i2i002−22−2−22−22000000000000
χ5022-2-22-22-2200-220-2022-2-22-2-2200−i2i2−i2i2i2−i2i2−i2000-2220-20000−2i−2i2i2i000000−i2i2−i2i2i2−i2i2−i2000000002i−2i00−22−222−22−2000000000000
χ5122-2-22-22-2200-220-2022-2-22-2-2200i2−i2i2−i2−i2i2−i2i2000-2220-200002i2i−2i−2i000000i2−i2i2−i2−i2i2−i2i200000000−2i2i00−22−222−22−2000000000000
χ5222-2-22-22-2200-220-2022-2-22-2-2200i2−i2i2−i2−i2i2−i2i2000-2220-20000−2i−2i2i2i000000i2−i2i2−i2−i2i2−i2i2000000002i−2i002−22−2−22−22000000000000
χ5322-2-2-22-222002-20-202-2222-2-2-2002−2−222−2−220002-220-22i2i−2i−2i00000000002−2−222−2−2200000000002i−2i−i2i2i2−i2i2−i2−i2i2000000000000
χ5422-2-2-22-222002-20-202-2222-2-2-2002−2−222−2−220002-220-2−2i−2i2i2i00000000002−2−222−2−220000000000−2i2ii2−i2−i2i2−i2i2i2−i2000000000000
χ5522-2-2-22-222002-20-202-2222-2-2-200−222−2−222−20002-220-22i2i−2i−2i0000000000−222−2−222−200000000002i−2ii2−i2−i2i2−i2i2i2−i2000000000000
χ5622-2-2-22-222002-20-202-2222-2-2-200−222−2−222−20002-220-2−2i−2i2i2i0000000000−222−2−222−20000000000−2i2i−i2i2i2−i2i2−i2−i2i2000000000000
χ5722-2-2-22-22200-22020-2-2222-2-2-200−i2i2i2−i2i2−i2−i2i2000-22-2022i2i−2i−2i0000000000−i2i2i2−i2i2−i2−i2i20000000000−2i2i−222−2−222−2000000000000
χ5822-2-2-22-22200-22020-2-2222-2-2-200−i2i2i2−i2i2−i2−i2i2000-22-202−2i−2i2i2i0000000000−i2i2i2−i2i2−i2−i2i200000000002i−2i2−2−222−2−22000000000000
χ5922-2-2-22-22200-22020-2-2222-2-2-200i2−i2−i2i2−i2i2i2−i2000-22-2022i2i−2i−2i0000000000i2−i2−i2i2−i2i2i2−i20000000000−2i2i2−2−222−2−22000000000000
χ6022-2-2-22-22200-22020-2-2222-2-2-200i2−i2−i2i2−i2i2i2−i2000-22-202−2i−2i2i2i0000000000i2−i2−i2i2−i2i2i2−i200000000002i−2i−222−2−222−2000000000000
χ612-22-2-222-222-200-2020-22-2-22-22000000000022-2000-202i−2i2i−2i2i−2i2i−2i−i2i2−i2i20000000000−i2i2−i2i2−i2i2−i2i20000000000000000002−22−200
χ622-22-2-222-222-200-2020-22-2-22-22000000000022-2000-202i−2i2i−2i2i−2i2i−2ii2−i2i2−i20000000000i2−i2i2−i2i2−i2i2−i2000000000000000000−22−2200
χ632-22-2-222-222-200-2020-22-2-22-22000000000022-2000-20−2i2i−2i2i−2i2i−2i2i−i2i2−i2i20000000000−i2i2−i2i2−i2i2−i2i2000000000000000000−22−2200
χ642-22-2-222-222-200-2020-22-2-22-22000000000022-2000-20−2i2i−2i2i−2i2i−2i2ii2−i2i2−i20000000000i2−i2i2−i2i2−i2i2−i20000000000000000002−22−200
χ652-22-2-222-22-220020-20-22-2-22-220000000000-2-22000202i−2i2i−2i−2i2i−2i2i2−2−2200000000002−22−2−22−22000000000000000000i2−i2−i2i200
χ662-22-2-222-22-220020-20-22-2-22-220000000000-2-22000202i−2i2i−2i−2i2i−2i2i−222−20000000000−22−222−22−2000000000000000000−i2i2i2−i200
χ672-22-2-222-22-220020-20-22-2-22-220000000000-2-2200020−2i2i−2i2i2i−2i2i−2i2−2−2200000000002−22−2−22−22000000000000000000−i2i2i2−i200
χ682-22-2-222-22-220020-20-22-2-22-220000000000-2-2200020−2i2i−2i2i2i−2i2i−2i−222−20000000000−22−222−22−2000000000000000000i2−i2−i2i200
χ6944444444-244-4-44-44-4-2-2-2-2-2-2-2-4-400000000-2-2-2222-22000000000000220000000000000000000000000000000000000000
χ7044444444-2-4-444-44-44-2-2-2-2-2-2-2-4-400000000222-2-2-22-2000000000000220000000000000000000000000000000000000000
χ714444-4-4-4-4-24-4-4-444-44222-2-2-22-4400000000-22222-2-2-20000000000002-20000000000000000000000000000000000000000
χ724444-4-4-4-4-2-4444-4-44-4222-2-2-22-44000000002-2-2-2-22220000000000002-20000000000000000000000000000000000000000
χ7344-4-44-44-4-2004-4040-4-222-222-20022−2222−2222−2222−22000-2220-200000000000000−22−22−22−2200000000000000000000000000000000
χ7444-4-44-44-4-2004-4040-4-222-222-200−2222−2222−2222−2222000-2220-2000000000000002−22−22−22−200000000000000000000000000000000
χ7544-4-44-44-4-200-440-404-222-222-200−2i22i2−2i22i22i2−2i22i2−2i20002-2-20200000000000000i2−i2i2−i2−i2i2−i2i200000000000000000000000000000000
χ7644-4-44-44-4-200-440-404-222-222-2002i2−2i22i2−2i2−2i22i2−2i22i20002-2-20200000000000000−i2i2−i2i2i2−i2i2−i200000000000000000000000000000000
χ7744-4-4-44-44-2004-40-4042-2-2-22220022−22−222222−22−2222000-22-20200000000000000−222−2−222−200000000000000000000000000000000
χ7844-4-4-44-44-2004-40-4042-2-2-222200−222222−22−222222−22000-22-202000000000000002−2−222−2−2200000000000000000000000000000000
χ7944-4-4-44-44-200-44040-42-2-2-222200−2i22i22i2−2i22i2−2i2−2i22i20002-220-200000000000000i2−i2−i2i2−i2i2i2−i200000000000000000000000000000000
χ8044-4-4-44-44-200-44040-42-2-2-2222002i2−2i2−2i22i2−2i22i22i2−2i20002-220-200000000000000−i2i2i2−i2i2−i2−i2i200000000000000000000000000000000
χ814-44-44-4-4444400-40-404-44-44-4-400000000004-44000-40000000000000000000000000000000000000000000000000000000
χ824-44-44-4-444-4-40040404-44-44-4-40000000000-44-400040000000000000000000000000000000000000000000000000000000
χ834-44-44-4-44-24400-40-40-22-22-2220000000000-22-2000200000000000000000000000i6−i6−i6i6i6−i6−i6i6000000000000000000000000
χ844-44-44-4-44-24400-40-40-22-22-2220000000000-22-2000200000000000000000000000−i6i6i6−i6−i6i6i6−i6000000000000000000000000
χ854-44-44-4-44-2-4-4004040-22-22-22200000000002-22000-2000000000000000000000006−6−66−666−6000000000000000000000000
χ864-44-44-4-44-2-4-4004040-22-22-22200000000002-22000-200000000000000000000000−666−66−6−66000000000000000000000000
χ874-44-4-444-4-24-400-40402-222-22-20000000000-2-220002000000000−2i22i2−2i22i20000000000i2−i2i2−i2i2−i2i2−i2000000000000000000000000
χ884-44-4-444-4-24-400-40402-222-22-20000000000-2-2200020000000002i2−2i22i2−2i20000000000−i2i2−i2i2−i2i2−i2i2000000000000000000000000
χ894-44-4-444-4-2-440040-402-222-22-2000000000022-2000-200000000022−22−22220000000000−22−222−22−2000000000000000000000000
χ904-44-4-444-4-2-440040-402-222-22-2000000000022-2000-2000000000−222222−2200000000002−22−2−22−22000000000000000000000000
χ914-4-4444-4-440000000044-4-4-44-40000000000000000004-4-4400000000000000000000000000000000000000000000000000
χ924-4-4444-4-440000000044-4-4-44-4000000000000000000-444-400000000000000000000000000000000000000000000000000
χ934-4-44-4-444400000000-4-44-4-44400000000000000000000004-4-440000000000000000000000000000000000000000000000
χ944-4-44-4-444400000000-4-44-4-4440000000000000000000000-444-40000000000000000000000000000000000000000000000
χ958-8-8888-8-8-400000000-4-4444-44000000000000000000000000000000000000000000000000000000000000000000000000
χ968-8-88-8-888-40000000044-444-4-4000000000000000000000000000000000000000000000000000000000000000000000000

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