Finite Group Databasebeta

← Group #11798181

Character table — Group #11798181

Order 1152.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63
size11112222444444444444488888888881818181824242424242424242424242436363636363636363636484848484848
order12222244334666666666666121212121212121288882222666666668816161616161616164412121212
χ1111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ311111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-1
χ411111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1111111
χ51111-1-11111-1111-1-1-1-1111-1-111-1-111-1-1111111-1-11111-1-1-1-1-1-11111-1-1-1-11-111-1-1
χ61111-1-11111-1111-1-1-1-1111-1-111-1-111-1-1111111-1-11111-1-1-1-1-1-1-1-1-1-11111-11-1-111
χ71111-1-11111-1111-1-1-1-1111-1-111-1-111-1-11111-1-111-1-1-1-11111-1-11111-1-1-1-1-11-1-111
χ81111-1-11111-1111-1-1-1-1111-1-111-1-111-1-11111-1-111-1-1-1-11111-1-1-1-1-1-111111-111-1-1
χ92222222222222222222222222222222-2-2-2-2000000000000-2-200000000000000
χ10222222-2-222-2222222222222-2-2-2-2-2-2-2-200000000000000000022−2−222−2−2000000
χ11222222-2-222-2222222222222-2-2-2-2-2-2-2-2000000000000000000−2−222−2−222000000
χ122222-2-22222-2222-2-2-2-2222-2-222-2-222-2-2-2-2-2-20000000000002200000000000000
χ132222-2-2-2-2222222-2-2-2-2222-2-2-2-222-2-22200000000000000000022−2−2−2−222000000
χ142222-2-2-2-2222222-2-2-2-2222-2-2-2-222-2-222000000000000000000−2−22222−2−2000000
χ1522-2-22-20022022-222-2-2-2-2-22-20000000022−2−20000000000002−2−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−ζ43000000
χ1622-2-22-20022022-222-2-2-2-2-22-20000000022−2−20000000000002−2ζ25+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+ζ43000000
χ1722-2-22-20022022-222-2-2-2-2-22-200000000−2−222000000000000−22ζ11+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−ζ47000000
χ1822-2-22-20022022-222-2-2-2-2-22-200000000−2−222000000000000−22−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+ζ47000000
χ1922-2-2-220022022-2-2-222-2-2-2-220000000022−2−2000000000000−22−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+ζ43000000
χ2022-2-2-220022022-2-2-222-2-2-2-220000000022−2−2000000000000−22ζ25+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−ζ43000000
χ2122-2-2-220022022-2-2-222-2-2-2-2200000000−2−2220000000000002−2ζ11+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+ζ47000000
χ2222-2-2-220022022-2-2-222-2-2-2-2200000000−2−2220000000000002−2−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−ζ47000000
χ232-2-2200-22220-2-2-200002-22002-2002-2002-22-2002-2000022-2-20000000000000000
χ242-2-2200-22220-2-2-200002-22002-2002-2002-22-200-220000-2-2220000000000000000
χ252-2-2200-22220-2-2-200002-22002-2002-200-22-222-20022-2-200000000000000000000
χ262-2-2200-22220-2-2-200002-22002-2002-200-22-22-2200-2-22200000000000000000000
χ27444444441-241-2-2-2-2-2-2-21111-2-2-2-211110000000000000000000000000022-1-1-1-1
χ28444444441-241-2-2-2-2-2-2-21111-2-2-2-2111100000000000000000000000000-2-21111
χ2944444444-214-21111111-2-2-2-21111-2-2-2-200002222-1-1-1-1-1-1-1-10000000000000000
χ3044444444-214-21111111-2-2-2-21111-2-2-2-20000-2-2-2-2111111110000000000000000
χ31444444-4-41-2-41-2-2-2-2-2-2-211112222-1-1-1-10000000000000000000000000000−i3i3−i3i3
χ32444444-4-41-2-41-2-2-2-2-2-2-211112222-1-1-1-10000000000000000000000000000i3−i3i3−i3
χ33444444-4-4-21-4-21111111-2-2-2-2-1-1-1-1222200000000−i3i3−i3i3−i3i3−i3i30000000000000000
χ34444444-4-4-21-4-21111111-2-2-2-2-1-1-1-1222200000000i3−i3i3−i3i3−i3i3−i30000000000000000
χ354444-4-4441-2-41-2-22222-211-1-1-2-22211-1-1000000000000000000000000002-2-1-111
χ364444-4-4441-2-41-2-22222-211-1-1-2-22211-1-100000000000000000000000000-2211-1-1
χ374444-4-444-21-4-211-1-1-1-11-2-22211-1-1-2-222000022-2-2-1-1-1-111110000000000000000
χ384444-4-444-21-4-211-1-1-1-11-2-22211-1-1-2-2220000-2-2221111-1-1-1-10000000000000000
χ394444-4-4-4-41-241-2-22222-211-1-122-2-2-1-1110000000000000000000000000000−i3i3i3−i3
χ404444-4-4-4-41-241-2-22222-211-1-122-2-2-1-1110000000000000000000000000000i3−i3−i3i3
χ414444-4-4-4-4-214-211-1-1-1-11-2-222-1-11122-2-200000000−i3i3−i3i3i3−i3i3−i30000000000000000
χ424444-4-4-4-4-214-211-1-1-1-11-2-222-1-11122-2-200000000i3−i3i3−i3−i3i3−i3i30000000000000000
χ434-44-40000440-4-440000-44-4000000000022−22−22220000000000000000000000000000
χ444-44-40000440-4-440000-44-40000000000−222222−220000000000000000000000000000
χ454-4-44004-4440-4-4-400004-4400-4400-440000000000000000000000000000000000
χ464-4-44004-4-2102-1-13-33-312-200-113-32-20000000000−i3i3i3−i3−i3i3i3−i30000000000000000
χ474-4-44004-4-2102-1-13-33-312-200-113-32-20000000000i3−i3−i3i3i3−i3−i3i30000000000000000
χ484-4-44004-4-2102-1-1-33-3312-200-11-332-20000000000−i3i3i3−i3i3−i3−i3i30000000000000000
χ494-4-44004-4-2102-1-1-33-3312-200-11-332-20000000000i3−i3−i3i3−i3i3i3−i30000000000000000
χ504-4-4400-44-2102-1-13-33-312-2001-1-33-220000002-22-2-1-111-1-1110000000000000000
χ514-4-4400-44-2102-1-13-33-312-2001-1-33-22000000-22-2211-1-111-1-10000000000000000
χ524-4-4400-44-2102-1-1-33-3312-2001-13-3-220000002-2-22-1-11111-1-10000000000000000
χ534-4-4400-44-2102-1-1-33-3312-2001-13-3-22000000-222-211-1-1-1-1110000000000000000
χ5488-8-88-8002-402-44-4-4444-2-22-20000000000000000000000000000000000000000
χ5588-8-88-800-420-42-222-2-2-244-440000000000000000000000000000000000000000
χ5688-8-8-88002-402-4444-4-44-2-2-220000000000000000000000000000000000000000
χ5788-8-8-8800-420-42-2-2-222-2444-40000000000000000000000000000000000000000
χ588-88-800002-40-24-4000042-2000000006i−6i00000000000000000000000000000000
χ598-88-800002-40-24-4000042-200000000−6i6i00000000000000000000000000000000
χ608-88-80000-4204-226-6-66-2-44000000000000000000000000000000000000000000
χ618-88-80000-4204-22-666-6-2-44000000000000000000000000000000000000000000
χ628-8-88008-82-40-2440000-4-22004-400-220000000000000000000000000000000000
χ638-8-8800-882-40-2440000-4-2200-44002-20000000000000000000000000000000000

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