Finite Group Databasebeta

← Group #10705560

Character table — Group #10705560

Order 768.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69
size111122222233334444446688888888888888888121212121616161616161616161616161624242424242424242424242424
order12222236664444444466444444488888888121212122244121212121224242424242424242444488888888
χ1111111111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111-1-1-1-1-1-1-1-11111111111111-1-1-1-1-1-1-1-111111-1-1-1-1-1-1-1-1
χ311111111111111111111111-1-1-1-11111-1-1-1-1111111111-1-1-1-1-1-1-1-111111-1-1-1-1-1-1-1-11111
χ411111111111111111111111-1-1-1-1-1-1-1-11111111111111-1-1-1-11111-1-1-1-11-1-1-1-11111-1-1-1-1
χ511111111111111-1-1-1-11111111-1-1ii−i−iii−i−i-1-1-1-1-1-1-1-1111-1-1ii−i−iii−i−i111-1-1ii−i−iii−i−i
χ611111111111111-1-1-1-11111111-1-1−i−iii−i−iii-1-1-1-1-1-1-1-1111-1-1−i−iii−i−iii111-1-1−i−iii−i−iii
χ711111111111111-1-1-1-111111-1-111ii−i−i−i−iii-1-1-1-1-1-1-1-11-1-111−i−iiiii−i−i1-1-111−i−iiiii−i−i
χ811111111111111-1-1-1-111111-1-111−i−iiiii−i−i-1-1-1-1-1-1-1-11-1-111ii−i−i−i−iii1-1-111ii−i−i−i−iii
χ91111111111-1-1-1-1111111-1-111111111111111111-1-1-1-11111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1
χ101111111111-1-1-1-1111111-1-111111-1-1-1-1-1-1-1-11111-1-1-1-111111-1-1-1-1-1-1-1-1-1-1-1-1-111111111
χ111111111111-1-1-1-1111111-1-11-1-1-1-11111-1-1-1-11111-1-1-1-11-1-1-1-1-1-1-1-11111-111111111-1-1-1-1
χ121111111111-1-1-1-1111111-1-11-1-1-1-1-1-1-1-111111111-1-1-1-11-1-1-1-11111-1-1-1-1-11111-1-1-1-11111
χ131111111111-1-1-1-1-1-1-1-111-1-1111-1-1ii−i−iii−i−i-1-1-1-11111111-1-1ii−i−iii−i−i-1-1-111−i−iii−i−iii
χ141111111111-1-1-1-1-1-1-1-111-1-1111-1-1−i−iii−i−iii-1-1-1-11111111-1-1−i−iii−i−iii-1-1-111ii−i−iii−i−i
χ151111111111-1-1-1-1-1-1-1-111-1-11-1-111ii−i−i−i−iii-1-1-1-111111-1-111−i−iiiii−i−i-111-1-1ii−i−i−i−iii
χ161111111111-1-1-1-1-1-1-1-111-1-11-1-111−i−iiiii−i−i-1-1-1-111111-1-111ii−i−i−i−iii-111-1-1−i−iiiii−i−i
χ17222222222222222-2-222222-20000000000002-2-22-2-222-2000000000000-2000000000000
χ1822222222222222-222-22222-2000000000000-222-222-2-2-2000000000000-2000000000000
χ192222222222-2-2-2-22-2-2222-2-2-20000000000002-2-2222-2-2-20000000000002000000000000
χ202222222222-2-2-2-2-222-222-2-2-2000000000000-222-2-2-222-20000000000002000000000000
χ21222222-1-1-1-100002222-1-1002222222222222-1-1-1-10000-1-1-1-1-1-1-1-1-1-1-1-1-10000000000000
χ22222222-1-1-1-100002222-1-10022222-2-2-2-2-2-2-2-2-1-1-1-10000-1-1-1-1-1111111110000000000000
χ23222222-1-1-1-100002222-1-1002-2-2-2-22222-2-2-2-2-1-1-1-10000-111111111-1-1-1-10000000000000
χ24222222-1-1-1-100002222-1-1002-2-2-2-2-2-2-2-22222-1-1-1-10000-11111-1-1-1-111110000000000000
χ25222222-1-1-1-10000-2-2-2-2-1-100222-2-22i2i−2i−2i2i2i−2i−2i11110000-1-1-111−i−iii−i−iii0000000000000
χ26222222-1-1-1-10000-2-2-2-2-1-100222-2-2−2i−2i2i2i−2i−2i2i2i11110000-1-1-111ii−i−iii−i−i0000000000000
χ27222222-1-1-1-10000-2-2-2-2-1-1002-2-2222i2i−2i−2i−2i−2i2i2i11110000-111-1-1ii−i−i−i−iii0000000000000
χ28222222-1-1-1-10000-2-2-2-2-1-1002-2-222−2i−2i2i2i2i2i−2i−2i11110000-111-1-1−i−iiiii−i−i0000000000000
χ292-2-222-222-2-22i2i−2i−2i02i−2i0-222i−2i000001+i−1−i1−i−1+i000002i−2i02-2000000000001+i−1−i1−i−1+i0000000001−i−1+i1+i−1−i
χ302-2-222-222-2-22i2i−2i−2i02i−2i0-222i−2i00000−1−i1+i−1+i1−i000002i−2i02-200000000000−1−i1+i−1+i1−i000000000−1+i1−i−1−i1+i
χ312-2-222-222-2-22i2i−2i−2i0−2i2i0-222i−2i000001−i−1+i1+i−1−i00000−2i2i0-22000000000001−i−1+i1+i−1−i000000000−1−i1+i−1+i1−i
χ322-2-222-222-2-22i2i−2i−2i0−2i2i0-222i−2i00000−1+i1−i−1−i1+i00000−2i2i0-2200000000000−1+i1−i−1−i1+i0000000001+i−1−i1−i−1+i
χ332-2-222-222-2-2−2i−2i2i2i02i−2i0-22−2i2i000001+i−1−i1−i−1+i000002i−2i0-22000000000001+i−1−i1−i−1+i000000000−1+i1−i−1−i1+i
χ342-2-222-222-2-2−2i−2i2i2i02i−2i0-22−2i2i00000−1−i1+i−1+i1−i000002i−2i0-2200000000000−1−i1+i−1+i1−i0000000001−i−1+i1+i−1−i
χ352-2-222-222-2-2−2i−2i2i2i0−2i2i0-22−2i2i000001−i−1+i1+i−1−i00000−2i2i02-2000000000001−i−1+i1+i−1−i0000000001+i−1−i1−i−1+i
χ362-2-222-222-2-2−2i−2i2i2i0−2i2i0-22−2i2i00000−1+i1−i−1−i1+i00000−2i2i02-200000000000−1+i1−i−1−i1+i000000000−1−i1+i−1+i1−i
χ372-2-22-2222-2-22i2i−2i−2i200-22-2−2i2i000000000i2−i2i2−i2-2002002i−2i00000i2−i2i2−i20000000002−22−20000
χ382-2-22-2222-2-22i2i−2i−2i200-22-2−2i2i000000000−i2i2−i2i2-2002002i−2i00000−i2i2−i2i2000000000−22−220000
χ392-2-22-2222-2-22i2i−2i−2i-20022-2−2i2i0000000002−2−22200-200−2i2i000002−2−22000000000−i2i2i2−i20000
χ402-2-22-2222-2-22i2i−2i−2i-20022-2−2i2i000000000−222−2200-200−2i2i00000−222−2000000000i2−i2−i2i20000
χ412-2-22-2222-2-2−2i−2i2i2i200-22-22i−2i000000000i2−i2i2−i2-200200−2i2i00000i2−i2i2−i2000000000−22−220000
χ422-2-22-2222-2-2−2i−2i2i2i200-22-22i−2i000000000−i2i2−i2i2-200200−2i2i00000−i2i2−i2i20000000002−22−20000
χ432-2-22-2222-2-2−2i−2i2i2i-20022-22i−2i0000000002−2−22200-2002i−2i000002−2−22000000000i2−i2−i2i20000
χ442-2-22-2222-2-2−2i−2i2i2i-20022-22i−2i000000000−222−2200-2002i−2i00000−222−2000000000−i2i2i2−i20000
χ45444444-2-2-2-200004-4-44-2-200-4000000000000-222-2000020000000000000000000000000
χ46444444-2-2-2-20000-444-4-2-200-40000000000002-2-22000020000000000000000000000000
χ474444-4-4444444440000-4-4-4-400000000000000000000000000000000000000000000000
χ484444-4-44444-4-4-4-40000-4-44400000000000000000000000000000000000000000000000
χ4944-4-4004-44-44-44-40000000002i−2i00000000000000000002i−2i000000000002i−2i0000000000
χ5044-4-4004-44-44-44-4000000000−2i2i0000000000000000000−2i2i00000000000−2i2i0000000000
χ5144-4-4004-44-4-44-440000000002i−2i00000000000000000002i−2i00000000000−2i2i0000000000
χ5244-4-4004-44-4-44-44000000000−2i2i0000000000000000000−2i2i000000000002i−2i0000000000
χ534-44-4004-4-444i−4i−4i4i000000000002i−2i00000000000000000002i−2i000000000002-200000000
χ544-44-4004-4-444i−4i−4i4i00000000000−2i2i0000000000000000000−2i2i00000000000-2200000000
χ554-44-4004-4-44−4i4i4i−4i000000000002i−2i00000000000000000002i−2i00000000000-2200000000
χ564-44-4004-4-44−4i4i4i−4i00000000000−2i2i0000000000000000000−2i2i000000000002-200000000
χ574-4-444-4-2-222000004i−4i02-200000002+2i−2−2i2−2i−2+2i00000−2i2i00000000000000−1−i1+i−1+i1−i0000000000000
χ584-4-444-4-2-222000004i−4i02-20000000−2−2i2+2i−2+2i2−2i00000−2i2i000000000000001+i−1−i1−i−1+i0000000000000
χ594-4-444-4-2-22200000−4i4i02-200000002−2i−2+2i2+2i−2−2i000002i−2i00000000000000−1+i1−i−1−i1+i0000000000000
χ604-4-444-4-2-22200000−4i4i02-20000000−2+2i2−2i−2−2i2+2i000002i−2i000000000000001−i−1+i1+i−1−i0000000000000
χ614-4-44-44-2-2220000400-4-22000000000002i2−2i22i2−2i2200-2000000000−i2i2−i2i200000000000000000
χ624-4-44-44-2-2220000400-4-2200000000000−2i22i2−2i22i2200-2000000000i2−i2i2−i200000000000000000
χ634-4-44-44-2-2220000-4004-220000000000022−22−2222-2002000000000−222−200000000000000000
χ644-4-44-44-2-2220000-4004-2200000000000−222222−22-20020000000002−2−2200000000000000000
χ658888-8-8-4-4-4-400000000440000000000000000000000000000000000000000000000000
χ6688-8-800-44-4400000000000004i−4i0000000000000000000−2i2i00000000000000000000000
χ6788-8-800-44-440000000000000−4i4i00000000000000000002i−2i00000000000000000000000
χ688-88-800-444-40000000000000004i−4i0000000000000000000−2i2i000000000000000000000
χ698-88-800-444-4000000000000000−4i4i00000000000000000002i−2i000000000000000000000

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