Finite Group Databasebeta

← Group #11800112

Character table — Group #11800112

Order 1152.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66
size111122222244444444888888888888181818181818181818181818181818181818181818181818484848484848484848484848
order1222444444336666661212121212121212121212128888888816161616161616161616161616161616244466121212121212
χ1111111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1
χ311111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-11111-1-1-1-1
χ411111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-11111
χ51111-1-1-1-1111111111111-1-1-1-111-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-11-11-111-1-111-1-1
χ61111-1-1-1-1111111111111-1-1-1-111-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-1-11-11-1-111-1-111
χ71111-1-1-1-1111111111111-1-1-1-111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1111111111-1-1111-1-1-1-111
χ81111-1-1-1-1111111111111-1-1-1-111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-111111111-111-1-1-11111-1-1
χ9222222222222222222222222222222-2-2-2-2-2-2-2-20000000000000000000000000000
χ10222222-2-2-2-222222222-2-222-2-2-2-222-2-2000000002222−2−2−2−22222−2−2−2−2000000000000
χ11222222-2-2-2-222222222-2-222-2-2-2-222-2-200000000−2−2−2−22222−2−2−2−22222000000000000
χ122222-2-222-2-222222222-2-2-2-222-2-2-2-222000000002222−2−2−2−2−2−2−2−22222000000000000
χ132222-2-222-2-222222222-2-2-2-222-2-2-2-22200000000−2−2−2−222222222−2−2−2−2000000000000
χ142222-2-2-2-2222222222222-2-2-2-222-2-2-2-22222-2-2-2-20000000000000000000000000000
χ1522-2-2002i−2i0022-22-22-2-200002i−2i00002i−2i−i2−i2i2i222−2−2−ζ25−ζ31−ζ41−ζ47−ζ25−ζ31−ζ41−ζ47ζ25+ζ31+ζ41+ζ47ζ25+ζ31+ζ41+ζ47ζ11+ζ13+ζ29+ζ43ζ11+ζ13+ζ29+ζ43−ζ11−ζ13−ζ29−ζ43−ζ11−ζ13−ζ29−ζ43−ζ25+ζ31−ζ41+ζ47−ζ25+ζ31−ζ41+ζ47ζ25−ζ31+ζ41−ζ47ζ25−ζ31+ζ41−ζ47ζ11−ζ13−ζ29+ζ43ζ11−ζ13−ζ29+ζ43−ζ11+ζ13+ζ29−ζ43−ζ11+ζ13+ζ29−ζ43000000000000
χ1622-2-2002i−2i0022-22-22-2-200002i−2i00002i−2i−i2−i2i2i222−2−2ζ25+ζ31+ζ41+ζ47ζ25+ζ31+ζ41+ζ47−ζ25−ζ31−ζ41−ζ47−ζ25−ζ31−ζ41−ζ47−ζ11−ζ13−ζ29−ζ43−ζ11−ζ13−ζ29−ζ43ζ11+ζ13+ζ29+ζ43ζ11+ζ13+ζ29+ζ43ζ25−ζ31+ζ41−ζ47ζ25−ζ31+ζ41−ζ47−ζ25+ζ31−ζ41+ζ47−ζ25+ζ31−ζ41+ζ47−ζ11+ζ13+ζ29−ζ43−ζ11+ζ13+ζ29−ζ43ζ11−ζ13−ζ29+ζ43ζ11−ζ13−ζ29+ζ43000000000000
χ1722-2-2002i−2i0022-22-22-2-200002i−2i00002i−2ii2i2−i2−i2−2−222ζ11+ζ13+ζ29+ζ43ζ11+ζ13+ζ29+ζ43−ζ11−ζ13−ζ29−ζ43−ζ11−ζ13−ζ29−ζ43ζ25+ζ31+ζ41+ζ47ζ25+ζ31+ζ41+ζ47−ζ25−ζ31−ζ41−ζ47−ζ25−ζ31−ζ41−ζ47−ζ11+ζ13+ζ29−ζ43−ζ11+ζ13+ζ29−ζ43ζ11−ζ13−ζ29+ζ43ζ11−ζ13−ζ29+ζ43−ζ25+ζ31−ζ41+ζ47−ζ25+ζ31−ζ41+ζ47ζ25−ζ31+ζ41−ζ47ζ25−ζ31+ζ41−ζ47000000000000
χ1822-2-2002i−2i0022-22-22-2-200002i−2i00002i−2ii2i2−i2−i2−2−222−ζ11−ζ13−ζ29−ζ43−ζ11−ζ13−ζ29−ζ43ζ11+ζ13+ζ29+ζ43ζ11+ζ13+ζ29+ζ43−ζ25−ζ31−ζ41−ζ47−ζ25−ζ31−ζ41−ζ47ζ25+ζ31+ζ41+ζ47ζ25+ζ31+ζ41+ζ47ζ11−ζ13−ζ29+ζ43ζ11−ζ13−ζ29+ζ43−ζ11+ζ13+ζ29−ζ43−ζ11+ζ13+ζ29−ζ43ζ25−ζ31+ζ41−ζ47ζ25−ζ31+ζ41−ζ47−ζ25+ζ31−ζ41+ζ47−ζ25+ζ31−ζ41+ζ47000000000000
χ1922-2-200−2i2i0022-22-22-2-20000−2i2i0000−2i2i−i2−i2i2i2−2−222ζ11+ζ13+ζ29+ζ43ζ11+ζ13+ζ29+ζ43−ζ11−ζ13−ζ29−ζ43−ζ11−ζ13−ζ29−ζ43ζ25+ζ31+ζ41+ζ47ζ25+ζ31+ζ41+ζ47−ζ25−ζ31−ζ41−ζ47−ζ25−ζ31−ζ41−ζ47ζ11−ζ13−ζ29+ζ43ζ11−ζ13−ζ29+ζ43−ζ11+ζ13+ζ29−ζ43−ζ11+ζ13+ζ29−ζ43ζ25−ζ31+ζ41−ζ47ζ25−ζ31+ζ41−ζ47−ζ25+ζ31−ζ41+ζ47−ζ25+ζ31−ζ41+ζ47000000000000
χ2022-2-200−2i2i0022-22-22-2-20000−2i2i0000−2i2i−i2−i2i2i2−2−222−ζ11−ζ13−ζ29−ζ43−ζ11−ζ13−ζ29−ζ43ζ11+ζ13+ζ29+ζ43ζ11+ζ13+ζ29+ζ43−ζ25−ζ31−ζ41−ζ47−ζ25−ζ31−ζ41−ζ47ζ25+ζ31+ζ41+ζ47ζ25+ζ31+ζ41+ζ47−ζ11+ζ13+ζ29−ζ43−ζ11+ζ13+ζ29−ζ43ζ11−ζ13−ζ29+ζ43ζ11−ζ13−ζ29+ζ43−ζ25+ζ31−ζ41+ζ47−ζ25+ζ31−ζ41+ζ47ζ25−ζ31+ζ41−ζ47ζ25−ζ31+ζ41−ζ47000000000000
χ2122-2-200−2i2i0022-22-22-2-20000−2i2i0000−2i2ii2i2−i2−i222−2−2−ζ25−ζ31−ζ41−ζ47−ζ25−ζ31−ζ41−ζ47ζ25+ζ31+ζ41+ζ47ζ25+ζ31+ζ41+ζ47ζ11+ζ13+ζ29+ζ43ζ11+ζ13+ζ29+ζ43−ζ11−ζ13−ζ29−ζ43−ζ11−ζ13−ζ29−ζ43ζ25−ζ31+ζ41−ζ47ζ25−ζ31+ζ41−ζ47−ζ25+ζ31−ζ41+ζ47−ζ25+ζ31−ζ41+ζ47−ζ11+ζ13+ζ29−ζ43−ζ11+ζ13+ζ29−ζ43ζ11−ζ13−ζ29+ζ43ζ11−ζ13−ζ29+ζ43000000000000
χ2222-2-200−2i2i0022-22-22-2-20000−2i2i0000−2i2ii2i2−i2−i222−2−2ζ25+ζ31+ζ41+ζ47ζ25+ζ31+ζ41+ζ47−ζ25−ζ31−ζ41−ζ47−ζ25−ζ31−ζ41−ζ47−ζ11−ζ13−ζ29−ζ43−ζ11−ζ13−ζ29−ζ43ζ11+ζ13+ζ29+ζ43ζ11+ζ13+ζ29+ζ43−ζ25+ζ31−ζ41+ζ47−ζ25+ζ31−ζ41+ζ47ζ25−ζ31+ζ41−ζ47ζ25−ζ31+ζ41−ζ47ζ11−ζ13−ζ29+ζ43ζ11−ζ13−ζ29+ζ43−ζ11+ζ13+ζ29−ζ43−ζ11+ζ13+ζ29−ζ43000000000000
χ232-22-200002-2222-2-2-2-222-200002-2000000002-22-2000000002i−2i2i−2i2i−2i2i−2i000000000000
χ242-22-200002-2222-2-2-2-222-200002-2000000002-22-200000000−2i2i−2i2i−2i2i−2i2i000000000000
χ252-22-200002-2222-2-2-2-222-200002-200000000-22-222i−2i2i−2i2i−2i2i−2i00000000000000000000
χ262-22-200002-2222-2-2-2-222-200002-200000000-22-22−2i2i−2i2i−2i2i−2i2i00000000000000000000
χ272-22-20000-22222-2-2-2-22-220000-2200002-22-20000−i2i2−i2i2i2−i2i2−i2−i2i2−i2i2i2−i2i2−i2000000000000
χ282-22-20000-22222-2-2-2-22-220000-2200002-22-20000i2−i2i2−i2−i2i2−i2i2i2−i2i2−i2−i2i2−i2i2000000000000
χ292-22-20000-22222-2-2-2-22-220000-220000-22-220000−i2i2−i2i2i2−i2i2−i2i2−i2i2−i2−i2i2−i2i2000000000000
χ302-22-20000-22222-2-2-2-22-220000-220000-22-220000i2−i2i2−i2−i2i2−i2i2−i2i2−i2i2i2−i2i2−i2000000000000
χ312-2-222i−2i000022-2-22-22-2002i−2i00002i−2i00−i2i2i2−i22−2−22−ζ25+ζ31−ζ41+ζ47ζ25−ζ31+ζ41−ζ47ζ25−ζ31+ζ41−ζ47−ζ25+ζ31−ζ41+ζ47−ζ11+ζ13+ζ29−ζ43ζ11−ζ13−ζ29+ζ43ζ11−ζ13−ζ29+ζ43−ζ11+ζ13+ζ29−ζ43ζ11+ζ13+ζ29+ζ43−ζ11−ζ13−ζ29−ζ43−ζ11−ζ13−ζ29−ζ43ζ11+ζ13+ζ29+ζ43−ζ25−ζ31−ζ41−ζ47ζ25+ζ31+ζ41+ζ47ζ25+ζ31+ζ41+ζ47−ζ25−ζ31−ζ41−ζ47000000000000
χ322-2-222i−2i000022-2-22-22-2002i−2i00002i−2i00−i2i2i2−i22−2−22ζ25−ζ31+ζ41−ζ47−ζ25+ζ31−ζ41+ζ47−ζ25+ζ31−ζ41+ζ47ζ25−ζ31+ζ41−ζ47ζ11−ζ13−ζ29+ζ43−ζ11+ζ13+ζ29−ζ43−ζ11+ζ13+ζ29−ζ43ζ11−ζ13−ζ29+ζ43−ζ11−ζ13−ζ29−ζ43ζ11+ζ13+ζ29+ζ43ζ11+ζ13+ζ29+ζ43−ζ11−ζ13−ζ29−ζ43ζ25+ζ31+ζ41+ζ47−ζ25−ζ31−ζ41−ζ47−ζ25−ζ31−ζ41−ζ47ζ25+ζ31+ζ41+ζ47000000000000
χ332-2-222i−2i000022-2-22-22-2002i−2i00002i−2i00i2−i2−i2i2−222−2ζ11−ζ13−ζ29+ζ43−ζ11+ζ13+ζ29−ζ43−ζ11+ζ13+ζ29−ζ43ζ11−ζ13−ζ29+ζ43−ζ25+ζ31−ζ41+ζ47ζ25−ζ31+ζ41−ζ47ζ25−ζ31+ζ41−ζ47−ζ25+ζ31−ζ41+ζ47−ζ25−ζ31−ζ41−ζ47ζ25+ζ31+ζ41+ζ47ζ25+ζ31+ζ41+ζ47−ζ25−ζ31−ζ41−ζ47−ζ11−ζ13−ζ29−ζ43ζ11+ζ13+ζ29+ζ43ζ11+ζ13+ζ29+ζ43−ζ11−ζ13−ζ29−ζ43000000000000
χ342-2-222i−2i000022-2-22-22-2002i−2i00002i−2i00i2−i2−i2i2−222−2−ζ11+ζ13+ζ29−ζ43ζ11−ζ13−ζ29+ζ43ζ11−ζ13−ζ29+ζ43−ζ11+ζ13+ζ29−ζ43ζ25−ζ31+ζ41−ζ47−ζ25+ζ31−ζ41+ζ47−ζ25+ζ31−ζ41+ζ47ζ25−ζ31+ζ41−ζ47ζ25+ζ31+ζ41+ζ47−ζ25−ζ31−ζ41−ζ47−ζ25−ζ31−ζ41−ζ47ζ25+ζ31+ζ41+ζ47ζ11+ζ13+ζ29+ζ43−ζ11−ζ13−ζ29−ζ43−ζ11−ζ13−ζ29−ζ43ζ11+ζ13+ζ29+ζ43000000000000
χ352-2-22−2i2i000022-2-22-22-200−2i2i0000−2i2i00−i2i2i2−i2−222−2ζ11−ζ13−ζ29+ζ43−ζ11+ζ13+ζ29−ζ43−ζ11+ζ13+ζ29−ζ43ζ11−ζ13−ζ29+ζ43−ζ25+ζ31−ζ41+ζ47ζ25−ζ31+ζ41−ζ47ζ25−ζ31+ζ41−ζ47−ζ25+ζ31−ζ41+ζ47ζ25+ζ31+ζ41+ζ47−ζ25−ζ31−ζ41−ζ47−ζ25−ζ31−ζ41−ζ47ζ25+ζ31+ζ41+ζ47ζ11+ζ13+ζ29+ζ43−ζ11−ζ13−ζ29−ζ43−ζ11−ζ13−ζ29−ζ43ζ11+ζ13+ζ29+ζ43000000000000
χ362-2-22−2i2i000022-2-22-22-200−2i2i0000−2i2i00−i2i2i2−i2−222−2−ζ11+ζ13+ζ29−ζ43ζ11−ζ13−ζ29+ζ43ζ11−ζ13−ζ29+ζ43−ζ11+ζ13+ζ29−ζ43ζ25−ζ31+ζ41−ζ47−ζ25+ζ31−ζ41+ζ47−ζ25+ζ31−ζ41+ζ47ζ25−ζ31+ζ41−ζ47−ζ25−ζ31−ζ41−ζ47ζ25+ζ31+ζ41+ζ47ζ25+ζ31+ζ41+ζ47−ζ25−ζ31−ζ41−ζ47−ζ11−ζ13−ζ29−ζ43ζ11+ζ13+ζ29+ζ43ζ11+ζ13+ζ29+ζ43−ζ11−ζ13−ζ29−ζ43000000000000
χ372-2-22−2i2i000022-2-22-22-200−2i2i0000−2i2i00i2−i2−i2i22−2−22−ζ25+ζ31−ζ41+ζ47ζ25−ζ31+ζ41−ζ47ζ25−ζ31+ζ41−ζ47−ζ25+ζ31−ζ41+ζ47−ζ11+ζ13+ζ29−ζ43ζ11−ζ13−ζ29+ζ43ζ11−ζ13−ζ29+ζ43−ζ11+ζ13+ζ29−ζ43−ζ11−ζ13−ζ29−ζ43ζ11+ζ13+ζ29+ζ43ζ11+ζ13+ζ29+ζ43−ζ11−ζ13−ζ29−ζ43ζ25+ζ31+ζ41+ζ47−ζ25−ζ31−ζ41−ζ47−ζ25−ζ31−ζ41−ζ47ζ25+ζ31+ζ41+ζ47000000000000
χ382-2-22−2i2i000022-2-22-22-200−2i2i0000−2i2i00i2−i2−i2i22−2−22ζ25−ζ31+ζ41−ζ47−ζ25+ζ31−ζ41+ζ47−ζ25+ζ31−ζ41+ζ47ζ25−ζ31+ζ41−ζ47ζ11−ζ13−ζ29+ζ43−ζ11+ζ13+ζ29−ζ43−ζ11+ζ13+ζ29−ζ43ζ11−ζ13−ζ29+ζ43ζ11+ζ13+ζ29+ζ43−ζ11−ζ13−ζ29−ζ43−ζ11−ζ13−ζ29−ζ43ζ11+ζ13+ζ29+ζ43−ζ25−ζ31−ζ41−ζ47ζ25+ζ31+ζ41+ζ47ζ25+ζ31+ζ41+ζ47−ζ25−ζ31−ζ41−ζ47000000000000
χ3944444444441-21-2-211-211-2-2-2-2-2-2111100000000000000000000000000220000-1-1-1-1
χ4044444444441-21-2-211-211-2-2-2-2-2-2111100000000000000000000000000-2-200001111
χ414444444444-21-211-2-21-2-2111111-2-2-2-20000000000000000000000002200-1-1-1-10000
χ424444444444-21-211-2-21-2-2111111-2-2-2-2000000000000000000000000-2-20011110000
χ43444444-4-4-4-41-21-2-211-2-1-1-2-2222211-1-100000000000000000000000000000000−i3i3−i3i3
χ44444444-4-4-4-41-21-2-211-2-1-1-2-2222211-1-100000000000000000000000000000000i3−i3i3−i3
χ45444444-4-4-4-4-21-211-2-212211-1-1-1-1-2-2220000000000000000000000000000−i3i3−i3i30000
χ46444444-4-4-4-4-21-211-2-212211-1-1-1-1-2-2220000000000000000000000000000i3−i3i3−i30000
χ474444-4-444-4-41-21-2-211-2-1-122-2-222-1-11100000000000000000000000000000000−i3i3i3−i3
χ484444-4-444-4-41-21-2-211-2-1-122-2-222-1-11100000000000000000000000000000000i3−i3−i3i3
χ494444-4-444-4-4-21-211-2-2122-1-111-1-122-2-20000000000000000000000000000−i3i3i3−i30000
χ504444-4-444-4-4-21-211-2-2122-1-111-1-122-2-20000000000000000000000000000i3−i3−i3i30000
χ514444-4-4-4-4441-21-2-211-2112222-2-2-1-1-1-1000000000000000000000000002-20000-1-111
χ524444-4-4-4-4441-21-2-211-2112222-2-2-1-1-1-100000000000000000000000000-22000011-1-1
χ534444-4-4-4-444-21-211-2-21-2-2-1-1-1-11122220000000000000000000000002-200-1-1110000
χ544444-4-4-4-444-21-211-2-21-2-2-1-1-1-1112222000000000000000000000000-220011-1-10000
χ5588-8-8008i−8i002-4-2-442-240000−4i4i00002i−2i000000000000000000000000000000000000
χ5688-8-8008i−8i00-4242-2-44-200002i−2i0000−4i4i000000000000000000000000000000000000
χ5788-8-800−8i8i002-4-2-442-2400004i−4i0000−2i2i000000000000000000000000000000000000
χ5888-8-800−8i8i00-4242-2-44-20000−2i2i00004i−4i000000000000000000000000000000000000
χ598-88-800008-82-4244-2-2-42-20000-440000000000000000000000000000000000000000
χ608-88-800008-8-42-4-2-2442-4400002-20000000000000000000000000000000000000000
χ618-88-80000-882-4244-2-2-4-2200004-40000000000000000000000000000000000000000
χ628-88-80000-88-42-4-2-24424-40000-220000000000000000000000000000000000000000
χ638-8-888i−8i00002-4-24-4-22400−4i4i00002i−2i00000000000000000000000000000000000000
χ648-8-888i−8i0000-424-224-4-2002i−2i0000−4i4i00000000000000000000000000000000000000
χ658-8-88−8i8i00002-4-24-4-224004i−4i0000−2i2i00000000000000000000000000000000000000
χ668-8-88−8i8i0000-424-224-4-200−2i2i00004i−4i00000000000000000000000000000000000000

Here ζ is a primitive root of unity of order 48 (ζ48 = 1); i = ζ12.