Finite Group Databasebeta

← Group #10770365

Character table — Group #10770365

Order 768.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69
size111122222222222244444444488888888888888888888161616161616161616162424242424242424242424244848
order1222223446666666444441212121222444444121212121212121212121212446612121212121222244444888888
χ1111111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ311111111111111111111111111111-1-1-1-111-1-1-1-1-1-1-1-111-1-11111-1-1-1-111111111-1-1-1-1-1-1
χ411111111111111111111111111111-1-1-1-111-1-1-1-1-1-1-1-111-1-11111-1-1-1-1-1-1-1-1-1-1-1-1111111
χ51111111111111111111111111-1-1-1-11111111111111111-1-1-1-1-1-1-1-1-1-111-1-1-111-1-1-1-1-111
χ61111111111111111111111111-1-1-1-11111111111111111-1-1-1-1-1-1-1-1-1-1-1-1111-1-111111-1-1
χ71111111111111111111111111-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-11111-1-1-1-1111111-1-1-111-11111-1-1
χ81111111111111111111111111-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1111-1-11-1-1-1-111
χ91111111-1-11111111-1-1-111-1-1-1-11-11-111-1-1111111-1-1-1-1-1-11-11-11-111-1-11-11-1-11-1111-1-11-1
χ101111111-1-11111111-1-1-111-1-1-1-11-11-111-1-1111111-1-1-1-1-1-11-11-11-111-1-1-11-111-11-1-1-111-11
χ111111111-1-11111111-1-1-111-1-1-1-11-11-1-1-11111-1-1-1-11111-1-1-111-11-1-1-1111-11-1-11-11-1-111-11
χ121111111-1-11111111-1-1-111-1-1-1-11-11-1-1-11111-1-1-1-11111-1-1-111-11-1-1-111-11-111-11-111-1-11-1
χ131111111-1-11111111-1-1-111-1-1-1-1-11-1111-1-1111111-1-1-1-1-1-1-11-11-11-1-1111-1-1111-1-1-1-1111-1
χ141111111-1-11111111-1-1-111-1-1-1-1-11-1111-1-1111111-1-1-1-1-1-1-11-11-11-1-111-111-1-1-11111-1-1-11
χ151111111-1-11111111-1-1-111-1-1-1-1-11-11-1-11111-1-1-1-11111-1-11-1-11-1111-1-11-1-1111-1-111-1-1-11
χ161111111-1-11111111-1-1-111-1-1-1-1-11-11-1-11111-1-1-1-11111-1-11-1-11-1111-1-1-111-1-1-111-1-1111-1
χ1722222222222222222-2-2-2-2222222-2-20000-2-200000000-2-20022-2-2000000000000000000
χ1822222222222222222-2-2-2-22222-2-2220000-2-200000000-2-200-2-222000000000000000000
χ192222222-2-22222222-222-2-2-2-2-2-22-2-220000-2-20000000022002-2-22000000000000000000
χ202222222-2-22222222-222-2-2-2-2-2-2-222-20000-2-2000000002200-222-2000000000000000000
χ21222222-122-1-1-1-1-1-1-122222-1-1-1-122222222-1-1-1-1-1-1-1-1-1-1-1-122-1-1-1-1-1-1-1-100000000000000
χ22222222-122-1-1-1-1-1-1-122222-1-1-1-12222-2-2-2-2-1-111111111-1-1-2-2-1-1-1-1111100000000000000
χ23222222-122-1-1-1-1-1-1-122222-1-1-1-1-2-2-2-22222-1-1-1-1-1-1-1-1-1-1-1-1-2-21111111100000000000000
χ24222222-122-1-1-1-1-1-1-122222-1-1-1-1-2-2-2-2-2-2-2-2-1-111111111-1-1221111-1-1-1-100000000000000
χ25222222-122-1-1-1-1-1-1-12-2-2-2-2-1-1-1-122-2-2000011−i3−i3i3i3−i3−i3i3i31100-1-111−i3i3−i3i300000000000000
χ26222222-122-1-1-1-1-1-1-12-2-2-2-2-1-1-1-122-2-2000011i3i3−i3−i3i3i3−i3−i31100-1-111i3−i3i3−i300000000000000
χ27222222-122-1-1-1-1-1-1-12-2-2-2-2-1-1-1-1-2-222000011−i3−i3i3i3−i3−i3i3i3110011-1-1i3−i3i3−i300000000000000
χ28222222-122-1-1-1-1-1-1-12-2-2-2-2-1-1-1-1-2-222000011i3i3−i3−i3i3i3−i3−i3110011-1-1−i3i3−i3i300000000000000
χ29222222-1-2-2-1-1-1-1-1-1-1-222-2-211112-2-22000011−i3−i3i3i3i3i3−i3−i3-1-100-111-1−i3i3i3−i300000000000000
χ30222222-1-2-2-1-1-1-1-1-1-1-222-2-211112-2-22000011i3i3−i3−i3−i3−i3i3i3-1-100-111-1i3−i3−i3i300000000000000
χ31222222-1-2-2-1-1-1-1-1-1-1-222-2-21111-222-2000011−i3−i3i3i3i3i3−i3−i3-1-1001-1-11i3−i3−i3i300000000000000
χ32222222-1-2-2-1-1-1-1-1-1-1-222-2-21111-222-2000011i3i3−i3−i3−i3−i3i3i3-1-1001-1-11−i3i3i3−i300000000000000
χ33222222-1-2-2-1-1-1-1-1-1-1-2-2-22211112-22-222-2-2-1-1-1-1-1-11111112-2-11-11-1-11100000000000000
χ34222222-1-2-2-1-1-1-1-1-1-1-2-2-22211112-22-2-2-222-1-11111-1-1-1-111-22-11-1111-1-100000000000000
χ35222222-1-2-2-1-1-1-1-1-1-1-2-2-2221111-22-2222-2-2-1-1-1-1-1-1111111-221-11-111-1-100000000000000
χ36222222-1-2-2-1-1-1-1-1-1-1-2-2-2221111-22-22-2-222-1-11111-1-1-1-1112-21-11-1-1-11100000000000000
χ372222-2-22222-2-2-2-222-22-22-222-2-2000000002-2000000002-20000000000002-2200-2000000
χ382222-2-22222-2-2-2-222-22-22-222-2-2000000002-2000000002-2000000000000-22-2002000000
χ392222-2-22222-2-2-2-222-2-22-2222-2-200000000-2200000000-22000000000022000-2-20000000
χ402222-2-22222-2-2-2-222-2-22-2222-2-200000000-2200000000-220000000000-2-2000220000000
χ412222-2-22-2-22-2-2-2-22222-2-22-2-22200000000-22000000002-200000000002-2000-220000000
χ422222-2-22-2-22-2-2-2-22222-2-22-2-22200000000-22000000002-20000000000-220002-20000000
χ432222-2-22-2-22-2-2-2-2222-222-2-2-222000000002-200000000-2200000000000022-200-2000000
χ442222-2-22-2-22-2-2-2-2222-222-2-2-222000000002-200000000-22000000000000-2-22002000000
χ454444-4-4-244-22222-2-2-44-44-4-2-22200000000-2200000000-22000000000000000000000000
χ464444-4-4-244-22222-2-2-4-44-44-2-222000000002-2000000002-2000000000000000000000000
χ474444-4-4-2-4-4-22222-2-244-4-4422-2-2000000002-200000000-22000000000000000000000000
χ484444-4-4-2-4-4-22222-2-24-444-422-2-200000000-22000000002-2000000000000000000000000
χ494-44-40044-4-400004-4000004-40000002i−2i2i−2i002i−2i2i−2i2i−2i2i−2i00000000000000000000000000
χ504-44-40044-4-400004-4000004-4000000−2i2i−2i2i00−2i2i−2i2i−2i2i−2i2i00000000000000000000000000
χ514-44-4004-44-400004-400000-440000002i−2i−2i2i002i−2i2i−2i−2i2i−2i2i00000000000000000000000000
χ524-44-4004-44-400004-400000-44000000−2i2i2i−2i00−2i2i−2i2i2i−2i2i−2i00000000000000000000000000
χ534-44-400-24-42−2i3−2i32i32i3-2200000-22−2i32i300002i−2i2i−2i002ζ14−2ζ142ζ22−2ζ222ζ14−2ζ142ζ22−2ζ2200000000000000000000000000
χ544-44-400-24-42−2i3−2i32i32i3-2200000-22−2i32i30000−2i2i−2i2i00−2ζ142ζ14−2ζ222ζ22−2ζ142ζ14−2ζ222ζ2200000000000000000000000000
χ554-44-400-24-422i32i3−2i3−2i3-2200000-222i3−2i300002i−2i2i−2i002ζ22−2ζ222ζ14−2ζ142ζ22−2ζ222ζ14−2ζ1400000000000000000000000000
χ564-44-400-24-422i32i3−2i3−2i3-2200000-222i3−2i30000−2i2i−2i2i00−2ζ222ζ22−2ζ142ζ14−2ζ222ζ22−2ζ142ζ1400000000000000000000000000
χ574-44-400-2-442−2i3−2i32i32i3-22000002-22i3−2i300002i−2i−2i2i002ζ14−2ζ142ζ22−2ζ22−2ζ142ζ14−2ζ222ζ2200000000000000000000000000
χ584-44-400-2-442−2i3−2i32i32i3-22000002-22i3−2i30000−2i2i2i−2i00−2ζ142ζ14−2ζ222ζ222ζ14−2ζ142ζ22−2ζ2200000000000000000000000000
χ594-44-400-2-4422i32i3−2i3−2i3-22000002-2−2i32i300002i−2i−2i2i002ζ22−2ζ222ζ14−2ζ14−2ζ222ζ22−2ζ142ζ1400000000000000000000000000
χ604-44-400-2-4422i32i3−2i3−2i3-22000002-2−2i32i30000−2i2i2i−2i00−2ζ222ζ22−2ζ142ζ142ζ22−2ζ222ζ14−2ζ1400000000000000000000000000
χ614-4-444-4400-44-44-4-440000000000000000000000000000000000000000000000022−220000
χ624-4-444-4400-44-44-4-4400000000000000000000000000000000000000000000000−22220000
χ634-4-44-44400-4-44-44-44000000000000000000000000000000000000000000000000022−2200
χ644-4-44-44400-4-44-44-440000000000000000000000000000000000000000000000000−222200
χ6588-8-80080080000-8-800000000000000000000000000000000000000000000000000000
χ6688-8-800-400-4−4i34i34i3−4i34400000000000000000000000000000000000000000000000000000
χ6788-8-800-400-44i3−4i3−4i34i34400000000000000000000000000000000000000000000000000000
χ688-8-888-8-4004-44-444-400000000000000000000000000000000000000000000000000000
χ698-8-88-88-40044-44-44-400000000000000000000000000000000000000000000000000000

Here ζ is a primitive root of unity of order 24 (ζ24 = 1); i = ζ6.