Finite Group Databasebeta

← Group #10948975

Character table — Group #10948975

Order 768.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75
size11112222222222224444444444466666688888888888888888881212121212161616161616242424242424242432324848
order122222344666888846688121224242424222244222212161616162424484848484848484848888446666222216161616121224
χ1111111111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111-1-1-1-111-1-1-1-1-1-1-1-111111-1-111111111-1-1-1-1-1-1-1-1
χ3111111111111111111111111111111111-1-1-1-111111111111111111111-1-1-1-1-1-1-1-1-1-11111-1-1-1-1
χ4111111111111111111111111111111111-1-1-1-11-1-1-1-111-1-1-1-1-1-1-1-11111111-1-1-1-1-1-1-1-1-1-1-1-11111
χ5111111111111111111111111111-1-1-1-1-1-11111111111111111111-1-1-1-1-1111111-1-1-1-1-1-1-1-111-1-1
χ6111111111111111111111111111-1-1-1-1-1-111111-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-11111-1-111
χ7111111111111111111111111111-1-1-1-1-1-1-1-1-1-1111111111111111-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-111
χ8111111111111111111111111111-1-1-1-1-1-1-1-1-1-11-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-11111111111-1-1
χ91111-1-11111111111-1-1-1-1-111111111-1-11111-1-1-111-1-1-1-11111-1-1-1-1-111-1-11-111-1-111-1-111-1-11-1-11
χ101111-1-11111111111-1-1-1-1-111111111-1-11111-1-1-1-1-111-1-1-1-1-1-11111-111-1-1-1111-1-111-1-1-1-111-111-1
χ111111-1-11111111111-1-1-1-1-111111111-1-111-1-111-111-1-1-1-11111-1-1-1-1-111-1-1-11-1-111-1-11111-1-1-111-1
χ121111-1-11111111111-1-1-1-1-111111111-1-111-1-111-1-1-111-1-1-1-1-1-11111-111-1-11-1-1-111-1-111-1-1111-1-11
χ131111-1-11111111111-1-1-1-1-1111111-1-111-1-111-1-1-111-1-1-1-11111-1-1-1-11-1-1111-111-1-1-1-111-1-1111-11-1
χ141111-1-11111111111-1-1-1-1-1111111-1-111-1-111-1-1-1-1-111-1-1-1-1-1-111111-1-111-1111-1-1-1-11111-1-1-11-11
χ151111-1-11111111111-1-1-1-1-1111111-1-111-1-1-1-111-111-1-1-1-11111-1-1-1-11-1-111-11-1-11111-1-1-1-111-11-11
χ161111-1-11111111111-1-1-1-1-1111111-1-111-1-1-1-111-1-1-111-1-1-1-1-1-111111-1-1111-1-1-11111-1-111-1-11-11-1
χ17222222222222-2-2-2-2222-2-222-2-2-2-2222222000020000-2-2000000002-2-2-2-2000000000000000000
χ18222222222222-2-2-2-2222-2-222-2-2-2-2-2-2-2-2-2-2000020000-2-200000000-22222000000000000000000
χ192222222-2-22220000-22200-2-200002222-2-20000-22−22−20022−2−222−2−2-2000000000000002−22−20000
χ202222222-2-22220000-22200-2-200002222-2-20000-2−22−2200−2−222−2−222-200000000000000−22−220000
χ212222222-2-22220000-22200-2-20000-2-2-2-2220000-22−22−20022−2−222−2−2200000000000000−22−220000
χ222222222-2-22220000-22200-2-20000-2-2-2-2220000-2−22−2200−2−222−2−2222000000000000002−22−20000
χ23222222-122-1-1-122222-1-122-1-1-1-1-1-10000002222-12222-1-1-1-1-1-1-1-1-1-10000022-1-1-1-100000000-1-100
χ24222222-122-1-1-122222-1-122-1-1-1-1-1-10000002222-1-2-2-2-2-1-11111111100000-2-2-1-1-1-1000000001100
χ25222222-122-1-1-122222-1-122-1-1-1-1-1-1000000-2-2-2-2-12222-1-1-1-1-1-1-1-1-1-100000-2-21111000000001100
χ26222222-122-1-1-122222-1-122-1-1-1-1-1-1000000-2-2-2-2-1-2-2-2-2-1-1111111110000022111100000000-1-100
χ272222-2-2222222-2-2-2-2-2-2-22222-2-2-2-222-2-2220000-200002200000000-2-2-222000000000000000000
χ282222-2-2222222-2-2-2-2-2-2-22222-2-2-2-2-2-222-2-20000-200002200000000222-2-2000000000000000000
χ292222-2-22-2-222200002-2-200-2-2000022-2-2-2-2000022−2−220022−2−2−2−2222000000000000002−2−220000
χ302222-2-22-2-222200002-2-200-2-2000022-2-2-2-200002−222−200−2−22222−2−2200000000000000−222−20000
χ312222-2-22-2-222200002-2-200-2-20000-2-22222000022−2−220022−2−2−2−222-200000000000000−222−20000
χ322222-2-22-2-222200002-2-200-2-20000-2-2222200002−222−200−2−22222−2−2-2000000000000002−2−220000
χ332222-2-2-122-1-1-12222-211-2-2-1-1-1-1-1-100000022-2-2122-2-211-1-1-1-11111000002-2-1-11100000000-1100
χ342222-2-2-122-1-1-12222-211-2-2-1-1-1-1-1-100000022-2-21-2-222111111-1-1-1-100000-22-1-111000000001-100
χ352222-2-2-122-1-1-12222-211-2-2-1-1-1-1-1-1000000-2-222122-2-211-1-1-1-1111100000-2211-1-1000000001-100
χ362222-2-2-122-1-1-12222-211-2-2-1-1-1-1-1-1000000-2-2221-2-222111111-1-1-1-1000002-211-1-100000000-1100
χ372-22-2002-22-2-2222-2-200000-2222-2-22-2002-2002-200000000000000002-20000002-2002-200000000
χ382-22-2002-22-2-2222-2-200000-2222-2-22-2002-200-2200000000000000002-2000000-2200-2200000000
χ392-22-2002-22-2-2222-2-200000-2222-2-2-2200-22002-20000000000000000-220000002-200-2200000000
χ402-22-2002-22-2-2222-2-200000-2222-2-2-2200-2200-220000000000000000-22000000-22002-200000000
χ412-22-2002-22-2-22-2-22200000-22-2-2222-2002-22-2000000000000000000-2200002-2002-20000000000
χ422-22-2002-22-2-22-2-22200000-22-2-2222-2002-2-22000000000000000000-220000-2200-220000000000
χ432-22-2002-22-2-22-2-22200000-22-2-222-2200-222-20000000000000000002-200002-200-220000000000
χ442-22-2002-22-2-22-2-22200000-22-2-222-2200-22-220000000000000000002-20000-22002-20000000000
χ45444444-244-2-2-2-4-4-4-44-2-2-4-4-2-222220000000000-20000220000000000000000000000000000000
χ46444444-2-4-4-2-2-20000-4-2-2002200000000000000222−2222−2200−2−222−2−22200000000000000000000000
χ47444444-2-4-4-2-2-20000-4-2-20022000000000000002−2222−22220022−2−222−2−200000000000000000000000
χ484444-4-4-244-2-2-2-4-4-4-4-42244-2-22222000000000020000-2-20000000000000000000000000000000
χ494444-4-4-2-4-4-2-2-20000422002200000000000000-222−22−222200−2−22222−2−200000000000000000000000
χ504444-4-4-2-4-4-2-2-20000422002200000000000000-2−222222−220022−2−2−2−22200000000000000000000000
χ5144-4-400400-44-422−2222−22000000022−2222−22004-400000000000000000000000022−22000000000000000000
χ5244-4-400400-44-422−2222−22000000022−2222−2200-44000000000000000000000000−2222000000000000000000
χ5344-4-400400-44-4−2222−22220000000−2222−2222004-4000000000000000000000000−2222000000000000000000
χ5444-4-400400-44-4−2222−22220000000−2222−222200-4400000000000000000000000022−22000000000000000000
χ554-44-40044-4-4-440000000004-400004-400-44000000000000000000000000000000000000000000
χ564-44-40044-4-4-440000000004-40000-44004-4000000000000000000000000000000000000000000
χ574-44-400-2-4422-244-4-4000002-2-2-222000000004-4000000000000000000000000-22000000000000
χ584-44-400-2-4422-244-4-4000002-2-2-22200000000-440000000000000000000000002-2000000000000
χ594-44-400-2-4422-2-4-444000002-222-2-20000004-4000000000000000000000000-2200000000000000
χ604-44-400-2-4422-2-4-444000002-222-2-2000000-440000000000000000000000002-200000000000000
χ614-4-444-44004-4-422−22−222204-422−220022−22−222200000000000000022−220000000000000000000000000000000
χ624-4-444-44004-4-4−222222−2204-4−222200−222222−22000000000000000−22220000000000000000000000000000000
χ634-4-444-4-200-22222−22−22220-2222−2200−222−2000000000000000−22−ζ11+ζ13−ζ29+ζ43ζ11−ζ13+ζ29−ζ43−ζ25−ζ31+ζ41+ζ47ζ25+ζ31−ζ41−ζ47−ζ11+ζ13−ζ29+ζ43ζ11−ζ13+ζ29−ζ43−ζ25−ζ31+ζ41+ζ47ζ25+ζ31−ζ41−ζ4700000000000000000000000
χ644-4-444-4-200-22222−22−22220-2222−2200−222−2000000000000000−22ζ11−ζ13+ζ29−ζ43−ζ11+ζ13−ζ29+ζ43ζ25+ζ31−ζ41−ζ47−ζ25−ζ31+ζ41+ζ47ζ11−ζ13+ζ29−ζ43−ζ11+ζ13−ζ29+ζ43ζ25+ζ31−ζ41−ζ47−ζ25−ζ31+ζ41+ζ4700000000000000000000000
χ654-4-444-4-200-222−222222−220-22−2222002−2−220000000000000002−2−ζ25−ζ31+ζ41+ζ47ζ25+ζ31−ζ41−ζ47ζ11−ζ13+ζ29−ζ43−ζ11+ζ13−ζ29+ζ43−ζ25−ζ31+ζ41+ζ47ζ25+ζ31−ζ41−ζ47ζ11−ζ13+ζ29−ζ43−ζ11+ζ13−ζ29+ζ4300000000000000000000000
χ664-4-444-4-200-222−222222−220-22−2222002−2−220000000000000002−2ζ25+ζ31−ζ41−ζ47−ζ25−ζ31+ζ41+ζ47−ζ11+ζ13−ζ29+ζ43ζ11−ζ13+ζ29−ζ43ζ25+ζ31−ζ41−ζ47−ζ25−ζ31+ζ41+ζ47−ζ11+ζ13−ζ29+ζ43ζ11−ζ13+ζ29−ζ4300000000000000000000000
χ674-4-44-444004-4-422−22−22220-44−22220022−22−2222000000000000000−22220000000000000000000000000000000
χ684-4-44-444004-4-4−222222−220-4422−2200−222222−2200000000000000022−220000000000000000000000000000000
χ694-4-44-44-200-22222−22−222202-2−222200−222−20000000000000002−2−ζ11+ζ13−ζ29+ζ43ζ11−ζ13+ζ29−ζ43−ζ25−ζ31+ζ41+ζ47ζ25+ζ31−ζ41−ζ47ζ11−ζ13+ζ29−ζ43−ζ11+ζ13−ζ29+ζ43ζ25+ζ31−ζ41−ζ47−ζ25−ζ31+ζ41+ζ4700000000000000000000000
χ704-4-44-44-200-22222−22−222202-2−222200−222−20000000000000002−2ζ11−ζ13+ζ29−ζ43−ζ11+ζ13−ζ29+ζ43ζ25+ζ31−ζ41−ζ47−ζ25−ζ31+ζ41+ζ47−ζ11+ζ13−ζ29+ζ43ζ11−ζ13+ζ29−ζ43−ζ25−ζ31+ζ41+ζ47ζ25+ζ31−ζ41−ζ4700000000000000000000000
χ714-4-44-44-200-222−222222−2202-222−22002−2−22000000000000000−22−ζ25−ζ31+ζ41+ζ47ζ25+ζ31−ζ41−ζ47ζ11−ζ13+ζ29−ζ43−ζ11+ζ13−ζ29+ζ43ζ25+ζ31−ζ41−ζ47−ζ25−ζ31+ζ41+ζ47−ζ11+ζ13−ζ29+ζ43ζ11−ζ13+ζ29−ζ4300000000000000000000000
χ724-4-44-44-200-222−222222−2202-222−22002−2−22000000000000000−22ζ25+ζ31−ζ41−ζ47−ζ25−ζ31+ζ41+ζ47−ζ11+ζ13−ζ29+ζ43ζ11−ζ13+ζ29−ζ43−ζ25−ζ31+ζ41+ζ47ζ25+ζ31−ζ41−ζ47ζ11−ζ13+ζ29−ζ43−ζ11+ζ13−ζ29+ζ4300000000000000000000000
χ7388-8-800-4004-4442−4242−420000000−2222−2222000000000000000000000000000000000000000000000000
χ7488-8-800-4004-44−4242−4242000000022−2222−22000000000000000000000000000000000000000000000000
χ758-88-800-48-844-4000000000-440000000000000000000000000000000000000000000000000000

Here ζ is a primitive root of unity of order 48 (ζ48 = 1).