Finite Group Databasebeta

← Group #11800608

Character table — Group #11800608

Order 1152.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54
size11222224444444448888888888881818181836363636363636363636484848484848484848484848
order12244883366668121261212122424242424242424161616161616323232323232323222246666661212
χ1111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1
χ31111111111111111111111111111111111-1-1-1-1-1-1-1-111-1-1-1-11111-1-1
χ41111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-11111-1-1-1-111
χ511-1-111111-1-111-1-1-1-1-1111111-1-1-1-11111-1-11111-1-1-1-11-11-11111-1-1-1-1
χ611-1-111111-1-111-1-1-1-1-1111111-1-1-1-11111-1-11111-1-1-1-1-11-11-1-1-1-11111
χ711-1-111111-1-111-1-1-1-1-1111111-1-1-1-11111-1-1-1-1-1-111111-1-11-1-111-1-111
χ811-1-111111-1-111-1-1-1-1-1111111-1-1-1-11111-1-1-1-1-1-11111-111-111-1-111-1-1
χ92222222222222222222222222222-2-2-2-2-2-200000000000000000000
χ1022222-2-2222222-2222222-2-2-2-2-2-2-2-200000022−2−222−2−2000000000000
χ1122222-2-2222222-2222222-2-2-2-2-2-2-2-2000000−2−222−2−222000000000000
χ12222-2-2002222220-2-22-2-2-20000000022−2−22−2−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−ζ43000000000000
χ13222-2-2002222220-2-22-2-2-20000000022−2−22−2ζ25−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+ζ43000000000000
χ14222-2-2002222220-2-22-2-2-200000000−2−222−22ζ11−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+ζ47000000000000
χ15222-2-2002222220-2-22-2-2-200000000−2−222−22−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−ζ47000000000000
χ1622-22-20022-2-222022-22-2-20000000022−2−2−22−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+ζ43000000000000
χ1722-22-20022-2-222022-22-2-20000000022−2−2−22ζ25−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−ζ43000000000000
χ1822-22-20022-2-222022-22-2-200000000−2−2222−2ζ11−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−ζ47000000000000
χ1922-22-20022-2-222022-22-2-200000000−2−2222−2−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+ζ47000000000000
χ2022-2-222222-2-222-2-2-2-2-2222222-2-2-2-2-2-2-2-22200000000000000000000
χ2122-2-22-2-222-2-2222-2-2-2-222-2-2-2-2222200000022−2−2−2−222000000000000
χ2222-2-22-2-222-2-2222-2-2-2-222-2-2-2-22222000000−2−22222−2−2000000000000
χ2344444441-2-2-2-214111-2-2111-2-211-2-2000000000000000022-1-10000-1-1
χ2444444441-2-2-2-214111-2-2111-2-211-2-20000000000000000-2-211000011
χ254444444-21111-24-2-2-211-2-2-211-2-21100000000000000220000-1-1-1-100
χ264444444-21111-24-2-2-211-2-2-211-2-21100000000000000-2-20000111100
χ2744444-4-41-2-2-2-21-4111-2-21-1-122-1-122000000000000000000−i3i30000−i3i3
χ2844444-4-41-2-2-2-21-4111-2-21-1-122-1-122000000000000000000i3−i30000i3−i3
χ2944444-4-4-21111-2-4-2-2-211-222-1-122-1-100000000000000000000−i3i3−i3i300
χ3044444-4-4-21111-2-4-2-2-211-222-1-122-1-100000000000000000000i3−i3i3−i300
χ3144-4-44441-222-21-4-1-1-12-2111-2-2-1-12200000000000000002-2-1-1000011
χ3244-4-44441-222-21-4-1-1-12-2111-2-2-1-1220000000000000000-22110000-1-1
χ3344-4-4444-21-1-11-2-4222-11-2-2-21122-1-1000000000000002-20000-1-11100
χ3444-4-4444-21-1-11-2-4222-11-2-2-21122-1-100000000000000-22000011-1-100
χ3544-4-44-4-41-222-214-1-1-12-21-1-12211-2-2000000000000000000−i3i30000i3−i3
χ3644-4-44-4-41-222-214-1-1-12-21-1-12211-2-2000000000000000000i3−i30000−i3i3
χ3744-4-44-4-4-21-1-11-24222-11-222-1-1-2-21100000000000000000000−i3i3i3−i300
χ3844-4-44-4-4-21-1-11-24222-11-222-1-1-2-21100000000000000000000i3−i3−i3i300
χ394-400022−224400-4-4000000022−2222−220000−2ζ25+2ζ31−2ζ41+2ζ472ζ25−2ζ31+2ζ41−2ζ472ζ11−2ζ13−2ζ29+2ζ43−2ζ11+2ζ13+2ζ29−2ζ430000000000000000000000
χ404-400022−224400-4-4000000022−2222−2200002ζ25−2ζ31+2ζ41−2ζ47−2ζ25+2ζ31−2ζ41+2ζ47−2ζ11+2ζ13+2ζ29−2ζ432ζ11−2ζ13−2ζ29+2ζ430000000000000000000000
χ414-4000−22224400-4-40000000−2222−222200002ζ11−2ζ13−2ζ29+2ζ43−2ζ11+2ζ13+2ζ29−2ζ432ζ25−2ζ31+2ζ41−2ζ47−2ζ25+2ζ31−2ζ41+2ζ470000000000000000000000
χ424-4000−22224400-4-40000000−2222−22220000−2ζ11+2ζ13+2ζ29−2ζ432ζ11−2ζ13−2ζ29+2ζ43−2ζ25+2ζ31−2ζ41+2ζ472ζ25−2ζ31+2ζ41−2ζ470000000000000000000000
χ43888-8-8002-4-4-4-420-2-2244-20000000000000000000000000000000000
χ44888-8-800-42222-4044-4-2-240000000000000000000000000000000000
χ4588-88-8002-444-42022-2-44-20000000000000000000000000000000000
χ4688-88-800-42-2-22-40-4-442-240000000000000000000000000000000000
χ478-800042−422-4004-206i−6i00002−2−2222−3i23i20000000000000000000000000000
χ488-800042−422-4004-20−6i6i00002−2−22223i2−3i20000000000000000000000000000
χ498-800042−42-426-6-240000000−22222−20032−3200000000000000000000000000
χ508-800042−42-42-66-240000000−22222−200−323200000000000000000000000000
χ518-8000−42422-4004-206i−6i0000−2222−223i2−3i20000000000000000000000000000
χ528-8000−42422-4004-20−6i6i0000−2222−22−3i23i20000000000000000000000000000
χ538-8000−4242-426-6-24000000022−22−2200−323200000000000000000000000000
χ548-8000−4242-42-66-24000000022−22−220032−3200000000000000000000000000

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