Finite Group Databasebeta

← Group #10699174

Character table — Group #10699174

Order 768.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69
size11112222222222224444444444444888888888888881616161616161616161616162424242424242424242424244848
order1222223444444666444661212121212121212888812122424242424242424226666882424242444448888888824
χ1111111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ31111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-111
χ41111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1
χ511111111111111111111111111111-1-1-1-111-1-1-1-1-1-1-1-1111111-1-1-1-1-1-11111-1-11111-1-1-1-1
χ611111111111111111111111111111-1-1-1-111-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1-1-111-1-1-1-11111
χ711111111111111111111111111111-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-111-1-1
χ811111111111111111111111111111-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-1-1-1-11111-1-111
χ922222222222-2-2222-2-2-2222-2-2-2-222222-2-2-2-22222-2-2-2-200000000000000000000000000
χ1022222222222-2-2222-2-2-2222-2-2-2-2222-2-222-2-2-2-2-2-2222200000000000000000000000000
χ112222222-2-2-2-2222222-2-222-222-2-2-2-2-200002-2000000002-222-2-200000000000000000000
χ122222222-2-2-2-2222222-2-222-222-2-2-2-2-200002-200000000-22-2-22200000000000000000000
χ132222222-2-2-2-2-2-2222-22222-2-2-222-2-2-20000-22000000000000002i−2i2i2i−2i−2i00000000000000
χ142222222-2-2-2-2-2-2222-22222-2-2-222-2-2-20000-2200000000000000−2i2i−2i−2i2i2i00000000000000
χ15222222-1222222-1-1-1222-1-1-1-1-1-1-1-1-1-12222-1-1-1-1-1-1-1-1-1-122-1-1-1-122-1-1-1-100000000000000
χ16222222-1222222-1-1-1222-1-1-1-1-1-1-1-1-1-12222-1-1-1-1-1-1-1-1-1-1-2-21111-2-2111100000000000000
χ17222222-1222222-1-1-1222-1-1-1-1-1-1-1-1-1-1-2-2-2-2-1-11111111122-1-1-1-1-2-2111100000000000000
χ18222222-1222222-1-1-1222-1-1-1-1-1-1-1-1-1-1-2-2-2-2-1-111111111-2-2111122-1-1-1-100000000000000
χ19222222-12222-2-2-1-1-1-2-2-2-1-1-11111-1-1-122-2-211-1-1-1-1111100−i3i3−i3i300−i3i3−i3i300000000000000
χ20222222-12222-2-2-1-1-1-2-2-2-1-1-11111-1-1-122-2-211-1-1-1-1111100i3−i3i3−i300i3−i3i3−i300000000000000
χ21222222-12222-2-2-1-1-1-2-2-2-1-1-11111-1-1-1-2-222111111-1-1-1-100−i3i3−i3i300i3−i3i3−i300000000000000
χ22222222-12222-2-2-1-1-1-2-2-2-1-1-11111-1-1-1-2-222111111-1-1-1-100i3−i3i3−i300−i3i3−i3i300000000000000
χ23222222-1-2-2-2-222-1-1-12-2-2-1-11-1-1111110000-1133−3−333−3−32-2-1-111003−3−3300000000000000
χ24222222-1-2-2-2-222-1-1-12-2-2-1-11-1-1111110000-1133−3−333−3−3-2211-1-100−333−300000000000000
χ25222222-1-2-2-2-222-1-1-12-2-2-1-11-1-1111110000-11−3−333−3−3332-2-1-11100−333−300000000000000
χ26222222-1-2-2-2-222-1-1-12-2-2-1-11-1-1111110000-11−3−333−3−333-2211-1-1003−3−3300000000000000
χ27222222-1-2-2-2-2-2-2-1-1-1-222-1-1111-1-111100001-133−3−3−3−33300−i3i3i3−i32i−2i−i−iii00000000000000
χ28222222-1-2-2-2-2-2-2-1-1-1-222-1-1111-1-111100001-133−3−3−3−33300i3−i3−i3i3−2i2iii−i−i00000000000000
χ29222222-1-2-2-2-2-2-2-1-1-1-222-1-1111-1-111100001-1−3−33333−3−300−i3i3i3−i3−2i2iii−i−i00000000000000
χ30222222-1-2-2-2-2-2-2-1-1-1-222-1-1111-1-111100001-1−3−33333−3−300i3−i3−i3i32i−2i−i−iii00000000000000
χ312222-2-222-2-2222222-22-2-2-2222-2-2-2-220000-22000000000000000000000000000000002-2
χ322222-2-222-2-2222222-22-2-2-2222-2-2-2-220000-2200000000000000000000000000000000-22
χ332222-2-222-2-22-2-22222-22-2-22-2-222-2-2200002-2000000000000000000002i2i−2i−2i0000000000
χ342222-2-222-2-22-2-22222-22-2-22-2-222-2-2200002-200000000000000000000−2i−2i2i2i0000000000
χ352222-2-22-222-222222-2-22-2-2-2222222-20000-2-2000000000000000000000000220000-2-200
χ362222-2-22-222-222222-2-22-2-2-2222222-20000-2-2000000000000000000000000-2-200002200
χ372222-2-22-222-2-2-222222-2-2-2-2-2-2-2-222-2000022000000000000000000000000002i2i−2i−2i0000
χ382222-2-22-222-2-2-222222-2-2-2-2-2-2-2-222-200002200000000000000000000000000−2i−2i2i2i0000
χ392-2-222-2222-2-2002-2-20002-2200002-2-2002i−2i0000002i−2i2i−2i00000000000000002−2−i2i2−i2i22−200
χ402-2-222-2222-2-2002-2-20002-2200002-2-2002i−2i0000002i−2i2i−2i0000000000000000−22i2−i2i2−i2−2200
χ412-2-222-2222-2-2002-2-20002-2200002-2-200−2i2i000000−2i2i−2i2i00000000000000002−2i2−i2i2−i22−200
χ422-2-222-2222-2-2002-2-20002-2200002-2-200−2i2i000000−2i2i−2i2i0000000000000000−22−i2i2−i2i2−2200
χ432-2-22-222-22-22002-2-2000-22-200002-222-200002-22-2000000000000000000002−22−2−22−2200
χ442-2-22-222-22-22002-2-2000-22-200002-222-200002-22-200000000000000000000−22−222−22−200
χ452-2-22-222-22-22002-2-2000-22-200002-22-220000-22-22000000000000000000002−2−222−2−2200
χ462-2-22-222-22-22002-2-2000-22-200002-22-220000-22-2200000000000000000000−222−2−222−200
χ474444-4-4-24-4-4444-2-2-2-44-422-2-2-22222-200002-20000000000000000000000000000000000
χ484444-4-4-24-4-44-4-4-2-2-24-4422-222-2-222-20000-220000000000000000000000000000000000
χ494444-4-4-2-444-444-2-2-2-4-44222-2-2-2-2-2-220000220000000000000000000000000000000000
χ504444-4-4-2-444-4-4-4-2-2-244-42222222-2-220000-2-20000000000000000000000000000000000
χ5144-4-400400004-4-44-40000004-400000000000000000000000000000002i−2i2i−2i0000000000
χ5244-4-400400004-4-44-40000004-40000000000000000000000000000000−2i2i−2i2i0000000000
χ5344-4-40040000-44-44-4000000-4400000000000000000000000000000002-2-220000000000
χ5444-4-40040000-44-44-4000000-440000000000000000000000000000000-222-20000000000
χ554-4-444-44-4-444004-4-40004-4-40000-4440000000000000000000000000000000000000000
χ564-4-444-4-244-4-400-222000-22-20000-222004i−4i000000−2i2i−2i2i00000000000000000000000000
χ574-4-444-4-244-4-400-222000-22-20000-22200−4i4i0000002i−2i2i−2i00000000000000000000000000
χ584-4-444-4-2-4-44400-222000-22200002-2-20000000000−2i32i32i3−2i300000000000000000000000000
χ594-4-444-4-2-4-44400-222000-22200002-2-200000000002i3−2i3−2i32i300000000000000000000000000
χ604-4-44-4444-44-4004-4-4000-4440000-44-40000000000000000000000000000000000000000
χ614-4-44-44-24-44-400-2220002-2-200002-2200000023−23−2323000000000000000000000000000000
χ624-4-44-44-24-44-400-2220002-2-200002-22000000−232323−23000000000000000000000000000000
χ634-4-44-44-2-44-4400-2220002-220000-22-24-40000-22-22000000000000000000000000000000
χ644-4-44-44-2-44-4400-2220002-220000-22-2-4400002-22-2000000000000000000000000000000
χ6588-8-800-400008-84-44000000-44000000000000000000000000000000000000000000000
χ6688-8-800-40000-884-440000004-4000000000000000000000000000000000000000000000
χ678-88-8008000000-8-8800000000000000000000000000000000000000000000000000000
χ688-88-800-400000044-400000000−4i34i30000000000000000000000000000000000000000000
χ698-88-800-400000044-4000000004i3−4i30000000000000000000000000000000000000000000

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