Finite Group Databasebeta

← Group #10697556

Character table — Group #10697556

Order 768.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69
size11112222222222224444444444444888888888888881616161616161616161616162424242424242424242424244848
order12222234444446664446612121212121212128888121224242424242424244488121212122424242422444444888824
χ1111111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ31111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1
χ41111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-111
χ511111111111111111111111111111-1-1-1-111-1-1-1-1-1-1-1-111-1-11111-1-1-1-111111111-1-1-1-1-1-1
χ611111111111111111111111111111-1-1-1-111-1-1-1-1-1-1-1-111-1-11111-1-1-1-1-1-1-1-1-1-1-1-1111111
χ711111111111111111111111111111-1-1-1-111-1-1-1-1-1-1-1-1-1-111-1-1-1-111111111-1-1-1-1-1-1-1-111
χ811111111111111111111111111111-1-1-1-111-1-1-1-1-1-1-1-1-1-111-1-1-1-11111-1-1-1-111111111-1-1
χ922222222222-2-2222-2-2-222-2-2222-2-220000-2-20000000000000000000022-2-20000000000
χ1022222222222-2-2222-2-2-222-2-2222-2-220000-2-200000000000000000000-2-2220000000000
χ112222222-2-2-2-222222-22-22222-2-2-2-2-2-200002-2000000002-20022-2-2000000000000000000
χ122222222-2-2-2-222222-22-22222-2-2-2-2-2-200002-200000000-2200-2-222000000000000000000
χ132222222-2-2-2-2-2-22222-2222-2-2-2-2-222-20000-2200000000000000000000000022-2-2000000
χ142222222-2-2-2-2-2-22222-2222-2-2-2-2-222-20000-22000000000000000000000000-2-222000000
χ15222222-1222222-1-1-1222-1-1-1-1-1-1-1-1-1-12222-1-1-1-1-1-1-1-1-1-12222-1-1-1-1-1-1-1-100000000000000
χ16222222-1222222-1-1-1222-1-1-1-1-1-1-1-1-1-12222-1-1-1-1-1-1-1-1-1-1-2-2-2-21111111100000000000000
χ17222222-1222222-1-1-1222-1-1-1-1-1-1-1-1-1-1-2-2-2-2-1-11111111122-2-2-1-1-1-1111100000000000000
χ18222222-1222222-1-1-1222-1-1-1-1-1-1-1-1-1-1-2-2-2-2-1-111111111-2-2221111-1-1-1-100000000000000
χ19222222-1-2-2-2-222-1-1-1-22-2-1-1-1-11111110000-113333−3−3−3−32-200-1-11133−3−300000000000000
χ20222222-1-2-2-2-222-1-1-1-22-2-1-1-1-11111110000-113333−3−3−3−3-220011-1-1−3−33300000000000000
χ21222222-1-2-2-2-222-1-1-1-22-2-1-1-1-11111110000-11−3−3−3−333332-200-1-111−3−33300000000000000
χ22222222-1-2-2-2-222-1-1-1-22-2-1-1-1-11111110000-11−3−3−3−33333-220011-1-133−3−300000000000000
χ232222-2-2222-2-222222-2-22-2-22222-222-20000-2-2000000000000000000000000000022-2-200
χ242222-2-2222-2-222222-2-22-2-22222-222-20000-2-20000000000000000000000000000-2-22200
χ252222-2-2222-2-2-2-222222-2-2-2-2-222-2-2-2-22i2i−2i−2i222i2i−2i−2i2i2i−2i−2i00000000000000000000000000
χ262222-2-2222-2-2-2-222222-2-2-2-2-222-2-2-2-2−2i−2i2i2i22−2i−2i2i2i−2i−2i2i2i00000000000000000000000000
χ272222-2-22-2-222222222-2-2-2-222-2-22-2-220000-22000000000000000000000000000000002-2
χ282222-2-22-2-222222222-2-2-2-222-2-22-2-220000-2200000000000000000000000000000000-22
χ292222-2-22-2-222-2-2222-222-2-2-2-2-2-2222200002-200000000002-200002-22-200000000000000
χ302222-2-22-2-222-2-2222-222-2-2-2-2-2-2222200002-20000000000-220000-22-2200000000000000
χ312222-2-2-122-2-2-2-2-1-1-122-21111-1-111112i2i−2i−2i-1-1−i−iii−i−iii0000−i3i3−i3i33−3−3300000000000000
χ322222-2-2-122-2-2-2-2-1-1-122-21111-1-111112i2i−2i−2i-1-1−i−iii−i−iii0000i3−i3i3−i3−333−300000000000000
χ332222-2-2-122-2-2-2-2-1-1-122-21111-1-11111−2i−2i2i2i-1-1ii−i−iii−i−i0000−i3i3−i3i3−333−300000000000000
χ342222-2-2-122-2-2-2-2-1-1-122-21111-1-11111−2i−2i2i2i-1-1ii−i−iii−i−i0000i3−i3i3−i33−3−3300000000000000
χ352222-2-2-1-2-222-2-2-1-1-1-222111111-1-1-1-10000-11−i3−i3i3i3i3i3−i3−i3002-2−i3i3i3−i3-11-1100000000000000
χ362222-2-2-1-2-222-2-2-1-1-1-222111111-1-1-1-10000-11−i3−i3i3i3i3i3−i3−i300-22i3−i3−i3i31-11-100000000000000
χ372222-2-2-1-2-222-2-2-1-1-1-222111111-1-1-1-10000-11i3i3−i3−i3−i3−i3i3i3002-2i3−i3−i3i3-11-1100000000000000
χ382222-2-2-1-2-222-2-2-1-1-1-222111111-1-1-1-10000-11i3i3−i3−i3−i3−i3i3i300-22−i3i3i3−i31-11-100000000000000
χ392-2-222-222-22-200-2-220002-2002-2200-2−i2i2−i2i200−i2i2−i2i2−i2i2−i2i2000000000000002i−2i00002−22−200
χ402-2-222-222-22-200-2-220002-2002-2200-2−i2i2−i2i200−i2i2−i2i2−i2i2−i2i200000000000000−2i2i0000−22−2200
χ412-2-222-222-22-200-2-220002-2002-2200-2i2−i2i2−i200i2−i2i2−i2i2−i2i2−i2000000000000002i−2i0000−22−2200
χ422-2-222-222-22-200-2-220002-2002-2200-2i2−i2i2−i200i2−i2i2−i2i2−i2i2−i200000000000000−2i2i00002−22−200
χ432-2-22-2222-2-2200-2-22000-22002-2-20022−2−22002−2−222−2−220000000000002-20000002−2−2200
χ442-2-22-2222-2-2200-2-22000-22002-2-20022−2−22002−2−222−2−22000000000000-22000000−222−200
χ452-2-22-2222-2-2200-2-22000-22002-2-2002−222−200−222−2−222−20000000000002-2000000−222−200
χ462-2-22-2222-2-2200-2-22000-22002-2-2002−222−200−222−2−222−2000000000000-220000002−2−2200
χ47444444-24444-4-4-2-2-2-4-4-4-2-222-2-2-222-20000220000000000000000000000000000000000
χ48444444-2-4-4-4-4-4-4-2-2-24-44-2-222222-2-2200002-20000000000000000000000000000000000
χ494444-4-4-244-4-444-2-2-2-4-4422-2-2-2-22-2-220000220000000000000000000000000000000000
χ504444-4-4-2-4-44444-2-2-24-4-422-2-222-222-200002-20000000000000000000000000000000000
χ514-44-400400004-44-4-4000004-40000000000000000000000000000000000002i−2i2i−2i000000
χ524-44-400400004-44-4-4000004-4000000000000000000000000000000000000−2i2i−2i2i000000
χ534-44-40040000-444-4-400000-440000000000000000000000000000000000002i−2i−2i2i000000
χ544-44-40040000-444-4-400000-44000000000000000000000000000000000000−2i2i2i−2i000000
χ554-4-444-44-44-4400-4-440004-400-44-40040000000000000000000000000000000000000000
χ564-4-444-4-24-44-40022-2000-2200-22-2002−2i22i2−2i22i200i2−i2i2−i2i2−i2i2−i200000000000000000000000000
χ574-4-444-4-24-44-40022-2000-2200-22-20022i2−2i22i2−2i200−i2i2−i2i2−i2i2−i2i200000000000000000000000000
χ584-4-444-4-2-44-440022-2000-22002-2200-2000000i6−i6i6−i6−i6i6−i6i600000000000000000000000000
χ594-4-444-4-2-44-440022-2000-22002-2200-2000000−i6i6−i6i6i6−i6i6−i600000000000000000000000000
χ604-4-44-444-444-400-4-44000-4400-44400-40000000000000000000000000000000000000000
χ614-4-44-44-24-4-440022-20002-200-22200-222−22−222200−222−2−222−200000000000000000000000000
χ624-4-44-44-24-4-440022-20002-200-22200-2−222222−22002−2−222−2−2200000000000000000000000000
χ634-4-44-44-2-444-40022-20002-2002-2-20020000006−6−66−666−600000000000000000000000000
χ644-4-44-44-2-444-40022-20002-2002-2-2002000000−666−66−6−6600000000000000000000000000
χ6588-8-8008000000-88-800000000000000000000000000000000000000000000000000000
χ6688-8-800-40000004-440000000000−4i34i300000000000000000000000000000000000000000
χ6788-8-800-40000004-4400000000004i3−4i300000000000000000000000000000000000000000
χ688-88-800-400008-8-44400000-440000000000000000000000000000000000000000000000
χ698-88-800-40000-88-444000004-40000000000000000000000000000000000000000000000

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