Finite Group Databasebeta

← Group #11798893

Character table — Group #11798893

Order 1152.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63
size11112222444444444444488888888881818181824242424242424242424242436363636363636363636484848484848
order122244443346666661212121212121212121212121212888844441212121212121212881616161616161616226666
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
χ51111-1-11111-1111111-1-1-1-111-1-1-1-111-1-1111111-1-11111-1-1-1-1-1-11111-1-1-1-11-111-1-1
χ61111-1-11111-1111111-1-1-1-111-1-1-1-111-1-1111111-1-11111-1-1-1-1-1-1-1-1-1-11111-11-1-111
χ71111-1-11111-1111111-1-1-1-111-1-1-1-111-1-11111-1-111-1-1-1-11111-1-11111-1-1-1-1-11-1-111
χ81111-1-11111-1111111-1-1-1-111-1-1-1-111-1-11111-1-111-1-1-1-11111-1-1-1-1-1-111111-111-1-1
χ92222222222222222222222222222222-2-2-2-2000000000000-2-200000000000000
χ10222222-2-222-22222222222-2-222-2-2-2-2-2-200000000000000000022−2−222−2−2000000
χ11222222-2-222-22222222222-2-222-2-2-2-2-2-2000000000000000000−2−222−2−222000000
χ122222-2-22222-2222222-2-2-2-222-2-2-2-222-2-2-2-2-2-20000000000002200000000000000
χ132222-2-2-2-2222222222-2-2-2-2-2-2-2-222-2-22200000000000000000022−2−2−2−222000000
χ142222-2-2-2-2222222222-2-2-2-2-2-2-2-222-2-222000000000000000000−2−22222−2−2000000
χ1522-2-22-20022022-2-2-2-222-2-2002-20000002−22−20000000000002−2−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
χ1622-2-22-20022022-2-2-2-222-2-2002-20000002−22−20000000000002−2ζ25+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
χ1722-2-22-20022022-2-2-2-222-2-2002-2000000−22−22000000000000−22ζ11+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
χ1822-2-22-20022022-2-2-2-222-2-2002-2000000−22−22000000000000−22−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
χ1922-2-2-220022022-2-2-2-2-2-22200-220000002−22−2000000000000−22−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
χ2022-2-2-220022022-2-2-2-2-2-22200-220000002−22−2000000000000−22ζ25+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
χ2122-2-2-220022022-2-2-2-2-2-22200-22000000−22−220000000000002−2ζ11+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
χ2222-2-2-220022022-2-2-2-2-2-22200-22000000−22−220000000000002−2−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
χ232-22-2002-2220-2-22-22-200002-200002-20022-2-2002i−2i00002i2i−2i−2i0000000000000000
χ242-22-2002-2220-2-22-22-200002-200002-20022-2-200−2i2i0000−2i−2i2i2i0000000000000000
χ252-22-2002-2220-2-22-22-200002-200002-200-2-2222-20022-2-200000000000000000000
χ262-22-2002-2220-2-22-22-200002-200002-200-2-222-2200-2-22200000000000000000000
χ27444444441-241-2-2-2111111-2-2-2-2-2-2111100002222-1-1-1-1-1-1-1-10000000000000000
χ28444444441-241-2-2-2111111-2-2-2-2-2-211110000-2-2-2-2111111110000000000000000
χ2944444444-214-2111-2-2-2-2-2-2111111-2-2-2-20000000000000000000000000022-1-1-1-1
χ3044444444-214-2111-2-2-2-2-2-2111111-2-2-2-200000000000000000000000000-2-21111
χ31444444-4-41-2-41-2-2-211111122-2-222-1-1-1-100000000−i3i3−i3i3−i3i3−i3i30000000000000000
χ32444444-4-41-2-41-2-2-211111122-2-222-1-1-1-100000000i3−i3i3−i3i3−i3i3−i30000000000000000
χ33444444-4-4-21-4-2111-2-2-2-2-2-2-1-111-1-122220000000000000000000000000000−i3i3−i3i3
χ34444444-4-4-21-4-2111-2-2-2-2-2-2-1-111-1-122220000000000000000000000000000i3−i3i3−i3
χ354444-4-4441-2-41-2-2-211-1-1-1-1-2-2222211-1-1000022-2-2-1-1-1-111110000000000000000
χ364444-4-4441-2-41-2-2-211-1-1-1-1-2-2222211-1-10000-2-2221111-1-1-1-10000000000000000
χ374444-4-444-21-4-2111-2-2222211-1-1-1-1-2-222000000000000000000000000002-2-1-111
χ384444-4-444-21-4-2111-2-2222211-1-1-1-1-2-22200000000000000000000000000-2211-1-1
χ394444-4-4-4-41-241-2-2-211-1-1-1-12222-2-2-1-11100000000−i3i3−i3i3i3−i3i3−i30000000000000000
χ404444-4-4-4-41-241-2-2-211-1-1-1-12222-2-2-1-11100000000i3−i3i3−i3−i3i3−i3i30000000000000000
χ414444-4-4-4-4-214-2111-2-22222-1-1-1-11122-2-20000000000000000000000000000−i3i3i3−i3
χ424444-4-4-4-4-214-2111-2-22222-1-1-1-11122-2-20000000000000000000000000000i3−i3−i3i3
χ434-44-4004-41-20-12-221-13i−3i3i−3i-2200001-13i−3i00002-22i−2i-1-111−i−iii0000000000000000
χ444-44-4004-41-20-12-221-13i−3i3i−3i-2200001-13i−3i0000-22−2i2i11-1-1ii−i−i0000000000000000
χ454-44-4004-41-20-12-221-1−3i3i−3i3i-2200001-1−3i3i00002-2−2i2i-1-111ii−i−i0000000000000000
χ464-44-4004-41-20-12-221-1−3i3i−3i3i-2200001-1−3i3i0000-222i−2i11-1-1−i−iii0000000000000000
χ474-44-400-441-20-12-221-13i−3i3i−3i2-20000-11−3i3i00000000−i3i3i3−i33−3−330000000000000000
χ484-44-400-441-20-12-221-13i−3i3i−3i2-20000-11−3i3i00000000i3−i3−i3i3−333−30000000000000000
χ494-44-400-441-20-12-221-1−3i3i−3i3i2-20000-113i−3i00000000−i3i3i3−i3−333−30000000000000000
χ504-44-400-441-20-12-221-1−3i3i−3i3i2-20000-113i−3i00000000i3−i3−i3i33−3−330000000000000000
χ514-44-400-44440-4-44-44-40000-440000-440000000000000000000000000000000000
χ524-4-440000440-4-4-44-440000000000000022−22−22220000000000000000000000000000
χ534-4-440000440-4-4-44-4400000000000000−222222−220000000000000000000000000000
χ5488-8-88-8002-402-444-2-222-2-200-4400000000000000000000000000000000000000
χ5588-8-88-800-420-42-2-244-4-444002-200000000000000000000000000000000000000
χ5688-8-8-88002-402-444-2-2-2-222004-400000000000000000000000000000000000000
χ5788-8-8-8800-420-42-2-24444-4-400-2200000000000000000000000000000000000000
χ588-88-8008-8-4204-22-2-4400002-20000-440000000000000000000000000000000000
χ598-88-800-88-4204-22-2-440000-2200004-40000000000000000000000000000000000
χ608-8-8800002-40-244-4-226i−6i−6i6i000000000000000000000000000000000000000000
χ618-8-8800002-40-244-4-22−6i6i6i−6i000000000000000000000000000000000000000000
χ628-8-880000-4204-2-224-4000000006-6000000000000000000000000000000000000
χ638-8-880000-4204-2-224-400000000-66000000000000000000000000000000000000

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