Finite Group Databasebeta

← Group #10713677

Character table — Group #10713677

Order 768.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78
size11112222222222222244444444444466668888888888888888881212121212121616161616161616161624242424242424244848
order1222223444466688886688121212122424242444448888161616162424484848484848484844888844121212122424242488881616161622
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111-1-1-1-111-1-1-1-1-1-1-1-1111111-1-1-1-1-1-111111111-1-1-1-1-1-1
χ31111111111111111111111111111111111-1-1-1-111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1
χ41111111111111111111111111111111111-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-111
χ5111111111111111111111111111111-1-1-1-1111111111111111111-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-1
χ6111111111111111111111111111111-1-1-1-11111-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1111111
χ7111111111111111111111111111111-1-1-1-1-1-1-1-111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-111
χ8111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-1-111111111-1-1
χ91111-1-111-11-1111-1-1-1-1-1-1111-11-1-1-1-1-111-1-1ii−i−iii−i−i11iiii−i−i−i−i1-111-1-11-111-1-1ii−i−iii−i−iii−i−i1-1
χ101111-1-111-11-1111-1-1-1-1-1-1111-11-1-1-1-1-111-1-1ii−i−i−i−iii11−i−i−i−iiiii1-111-1-1-11-1-111ii−i−iii−i−i−i−iii-11
χ111111-1-111-11-1111-1-1-1-1-1-1111-11-1-1-1-1-111-1-1−i−iiiii−i−i11iiii−i−i−i−i1-111-1-1-11-1-111−i−iii−i−iiiii−i−i-11
χ121111-1-111-11-1111-1-1-1-1-1-1111-11-1-1-1-1-111-1-1−i−iii−i−iii11−i−i−i−iiiii1-111-1-11-111-1-1−i−iii−i−iii−i−iii1-1
χ131111-1-111-11-1111-1-1-1-1-1-1111-11-1-1-1-1-1-1-111ii−i−iii−i−i11iiii−i−i−i−i-11-1-1111-111-1-1ii−i−i−i−iii−i−iii-11
χ141111-1-111-11-1111-1-1-1-1-1-1111-11-1-1-1-1-1-1-111ii−i−i−i−iii11−i−i−i−iiiii-11-1-111-11-1-111ii−i−i−i−iiiii−i−i1-1
χ151111-1-111-11-1111-1-1-1-1-1-1111-11-1-1-1-1-1-1-111−i−iiiii−i−i11iiii−i−i−i−i-11-1-111-11-1-111−i−iiiii−i−i−i−iii1-1
χ161111-1-111-11-1111-1-1-1-1-1-1111-11-1-1-1-1-1-1-111−i−iii−i−iii11−i−i−i−iiiii-11-1-1111-111-1-1−i−iiiii−i−iii−i−i-11
χ1722222222222222-2-2-2-222-2-22222-2-2-2-2222200000000-2-20000000022-2-2-2-200000000000000000000
χ1822222222222222-2-2-2-222-2-22222-2-2-2-2-2-2-2-200000000-2-200000000-2-2222200000000000000000000
χ192222222-2-2-2-222200002200-2-2-2-2000022-2-20000−i2i2−i2i200−i2−i2i2i2−i2−i2i2i2-22000000000000000000−i2i2−i2i200
χ202222222-2-2-2-222200002200-2-2-2-2000022-2-20000i2−i2i2−i200i2i2−i2−i2i2i2−i2−i2-22000000000000000000i2−i2i2−i200
χ212222222-2-2-2-222200002200-2-2-2-20000-2-2220000−i2i2−i2i200−i2−i2i2i2−i2−i2i2i22-2000000000000000000i2−i2i2−i200
χ222222222-2-2-2-222200002200-2-2-2-20000-2-2220000i2−i2i2−i200i2i2−i2−i2i2i2−i2−i22-2000000000000000000−i2i2−i2i200
χ23222222-12222-1-1-12222-1-122-1-1-1-1-1-1-1-1000022222222-1-1-1-1-1-1-1-1-1-100000022-1-1-1-1-1-1-1-10000000000
χ24222222-12222-1-1-12222-1-122-1-1-1-1-1-1-1-100002222-2-2-2-2-1-111111111000000-2-21111-1-1-1-10000000000
χ25222222-12222-1-1-12222-1-122-1-1-1-1-1-1-1-10000-2-2-2-22222-1-1-1-1-1-1-1-1-1-1000000-2-2111111110000000000
χ26222222-12222-1-1-12222-1-122-1-1-1-1-1-1-1-10000-2-2-2-2-2-2-2-2-1-11111111100000022-1-1-1-111110000000000
χ272222-2-222-22-22222222-2-2-2-22-22-2222222-2-200000000-2-2000000002-2-2-22200000000000000000000
χ282222-2-222-22-22222222-2-2-2-22-22-22222-2-22200000000-2-200000000-2222-2-200000000000000000000
χ292222-2-22-22-222220000-2-200-22-220000222200002−2−220022−2−2−2−222-2-20000000000000000002−2−2200
χ302222-2-22-22-222220000-2-200-22-22000022220000−222−200−2−22222−2−2-2-2000000000000000000−222−200
χ312222-2-22-22-222220000-2-200-22-220000-2-2-2-200002−2−220022−2−2−2−22222000000000000000000−222−200
χ322222-2-22-22-222220000-2-200-22-220000-2-2-2-20000−222−200−2−22222−2−2220000000000000000002−2−2200
χ332222-2-2-12-22-2-1-1-1-2-2-2-21122-11-11111100002i2i−2i−2i2i2i−2i−2i-1-1−i−i−i−iiiii0000002-2-1-111−i−iii0000000000
χ342222-2-2-12-22-2-1-1-1-2-2-2-21122-11-11111100002i2i−2i−2i−2i−2i2i2i-1-1iiii−i−i−i−i000000-2211-1-1−i−iii0000000000
χ352222-2-2-12-22-2-1-1-1-2-2-2-21122-11-1111110000−2i−2i2i2i2i2i−2i−2i-1-1−i−i−i−iiiii000000-2211-1-1ii−i−i0000000000
χ362222-2-2-12-22-2-1-1-1-2-2-2-21122-11-1111110000−2i−2i2i2i−2i−2i2i2i-1-1iiii−i−i−i−i0000002-2-1-111ii−i−i0000000000
χ372-2-222-2222-2-2-2-2222-2-22-22-2-2-22222-2-20000000000002-20000000000000000000000002i−2i2i−2i000000
χ382-2-222-2222-2-2-2-2222-2-22-22-2-2-22222-2-20000000000002-2000000000000000000000000−2i2i−2i2i000000
χ392-2-222-2222-2-2-2-22-2-2222-2-22-2-222-2-22200002-22-20000-22000000000000000000002-22-20000000000
χ402-2-222-2222-2-2-2-22-2-2222-2-22-2-222-2-2220000-22-220000-2200000000000000000000-22-220000000000
χ412-2-222-2-122-2-211-1-2-222-11-2211-1-111-1-100002-22-200001-1−i3i3−i3i3−i3i3−i3i300000000−i3i3−i3i3-11-110000000000
χ422-2-222-2-122-2-211-1-2-222-11-2211-1-111-1-100002-22-200001-1i3−i3i3−i3i3−i3i3−i300000000i3−i3i3−i3-11-110000000000
χ432-2-222-2-122-2-211-1-2-222-11-2211-1-111-1-10000-22-2200001-1−i3i3−i3i3−i3i3−i3i300000000i3−i3i3−i31-11-10000000000
χ442-2-222-2-122-2-211-1-2-222-11-2211-1-111-1-10000-22-2200001-1i3−i3i3−i3i3−i3i3−i300000000−i3i3−i3i31-11-10000000000
χ452-2-22-2222-2-22-2-2222-2-2-22-22-222-222-2-200002i−2i−2i2i0000-22000000000000000000002i−2i−2i2i0000000000
χ462-2-22-2222-2-22-2-2222-2-2-22-22-222-222-2-20000−2i2i2i−2i0000-2200000000000000000000−2i2i2i−2i0000000000
χ472-2-22-2222-2-22-2-22-2-222-222-2-222-2-2-2220000000000002-20000000000000000000000002-2-22000000
χ482-2-22-2222-2-22-2-22-2-222-222-2-222-2-2-2220000000000002-2000000000000000000000000-222-2000000
χ492-2-22-22-12-2-2211-122-2-21-1-221-1-11-1-11100002i−2i−2i2i00001-13−33−3−33−3300000000−i3i3i3−i3−iii−i0000000000
χ502-2-22-22-12-2-2211-122-2-21-1-221-1-11-1-11100002i−2i−2i2i00001-1−33−333−33−300000000i3−i3−i3i3−iii−i0000000000
χ512-2-22-22-12-2-2211-122-2-21-1-221-1-11-1-1110000−2i2i2i−2i00001-13−33−3−33−3300000000i3−i3−i3i3i−i−ii0000000000
χ522-2-22-22-12-2-2211-122-2-21-1-221-1-11-1-1110000−2i2i2i−2i00001-1−33−333−33−300000000−i3i3i3−i3i−i−ii0000000000
χ53444444-24444-2-2-2-4-4-4-4-2-2-4-4-2-2-2-22222000000000000220000000000000000000000000000000000
χ54444444-2-4-4-4-4-2-2-20000-2-2002222000000000000−2i22i2−2i22i200i2i2−i2−i2i2i2−i2−i200000000000000000000000000
χ55444444-2-4-4-4-4-2-2-20000-2-20022220000000000002i2−2i22i2−2i200−i2−i2i2i2−i2−i2i2i200000000000000000000000000
χ564444-4-4-24-44-4-2-2-2444422-4-4-22-22-2-2-2-2000000000000220000000000000000000000000000000000
χ574444-4-4-2-44-44-2-2-2000022002-22-200000000000022−22−222200−2−22222−2−200000000000000000000000000
χ584444-4-4-2-44-44-2-2-2000022002-22-2000000000000−222222−220022−2−2−2−22200000000000000000000000000
χ5944-4-400400004-4-422−2222−220000000022−2222−22004i−4i00000000000000000000−2i22i20000000000000000000000
χ6044-4-400400004-4-422−2222−220000000022−2222−2200−4i4i000000000000000000002i2−2i20000000000000000000000
χ6144-4-400400004-4-4−2222−222200000000−2222−2222004i−4i000000000000000000002i2−2i20000000000000000000000
χ6244-4-400400004-4-4−2222−222200000000−2222−222200−4i4i00000000000000000000−2i22i20000000000000000000000
χ634-44-40040000-44-422−22−22220000000022−22−22224i−4i000000000000000000000000−2i22i200000000000000000000
χ644-44-40040000-44-422−22−22220000000022−22−2222−4i4i0000000000000000000000002i2−2i200000000000000000000
χ654-44-40040000-44-4−222222−2200000000−222222−224i−4i0000000000000000000000002i2−2i200000000000000000000
χ664-44-40040000-44-4−222222−2200000000−222222−22−4i4i000000000000000000000000−2i22i200000000000000000000
χ674-4-444-44-4-444-4-4400004-40044-4-40000000000000000000000000000000000000000000000000000
χ684-4-444-4-244-4-422-244-4-4-224-422-2-2-2-222000000000000-220000000000000000000000000000000000
χ694-4-444-4-2-4-44422-20000-2200-2-2220000000000000000006−6−666−6−6600000000000000000000000000
χ704-4-444-4-2-4-44422-20000-2200-2-222000000000000000000−666−6−666−600000000000000000000000000
χ714-4-44-444-444-4-4-440000-44004-4-440000000000000000000000000000000000000000000000000000
χ724-4-44-44-24-4-4422-2-4-4442-24-42-2-2222-2-2000000000000-220000000000000000000000000000000000
χ734-4-44-44-2-444-422-200002-200-222-2000000000000000000i6−i6−i6i6−i6i6i6−i600000000000000000000000000
χ744-4-44-44-2-444-422-200002-200-222-2000000000000000000−i6i6i6−i6i6−i6−i6i600000000000000000000000000
χ7588-8-800-40000-44442−4242−4200000000−2222−2222000000000000000000000000000000000000000000000000
χ7688-8-800-40000-444−4242−42420000000022−2222−22000000000000000000000000000000000000000000000000
χ778-88-800-400004-4442−42−424200000000−222222−22000000000000000000000000000000000000000000000000
χ788-88-800-400004-44−424242−420000000022−22−2222000000000000000000000000000000000000000000000000

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