Finite Group Databasebeta

← Group #11799792

Character table — Group #11799792

Order 1152.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63
size11112222444444444444488888888881818181824242424242424242424242436363636363636363636484848484848
order12222244334666666666666121212121212121288884444121212121212121288161616161616161624661212
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
χ51111-1-11111-11-1-1-1-111111-1-11111-1-1-1-1111111-1-11111-1-1-1-1-1-11111-1-1-1-11-111-1-1
χ61111-1-11111-11-1-1-1-111111-1-11111-1-1-1-1111111-1-11111-1-1-1-1-1-1-1-1-1-11111-11-1-111
χ71111-1-11111-11-1-1-1-111111-1-11111-1-1-1-11111-1-111-1-1-1-11111-1-11111-1-1-1-1-11-1-111
χ81111-1-11111-11-1-1-1-111111-1-11111-1-1-1-11111-1-111-1-1-1-11111-1-1-1-1-1-111111-111-1-1
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
χ122222-2-22222-22-2-2-2-222222-2-22222-2-2-2-2-2-2-2-20000000000002200000000000000
χ132222-2-2-2-22222-2-2-2-222222-2-2-2-2-2-2222200000000000000000022−2−2−2−222000000
χ142222-2-2-2-22222-2-2-2-222222-2-2-2-2-2-22222000000000000000000−2−22222−2−2000000
χ152-22-200-22220-20000-222-2-20022-2-2000022-2-2002i−2i00002i2i−2i−2i0000000000000000
χ162-22-200-22220-20000-222-2-20022-2-2000022-2-200−2i2i0000−2i−2i2i2i0000000000000000
χ172-22-200-22220-20000-222-2-20022-2-20000-2-2222i−2i002i2i−2i−2i00000000000000000000
χ182-22-200-22220-20000-222-2-20022-2-20000-2-222−2i2i00−2i−2i2i2i00000000000000000000
χ192-2-222-200220-222-2-2-2-2-2222-2000000002−22−20000000000002−2−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
χ202-2-222-200220-222-2-2-2-2-2222-2000000002−22−20000000000002−2ζ25−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
χ212-2-222-200220-222-2-2-2-2-2222-200000000−22−22000000000000−22ζ11−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
χ222-2-222-200220-222-2-2-2-2-2222-200000000−22−22000000000000−22−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
χ232-2-22-2200220-2-2-222-2-2-222-22000000002−22−2000000000000−22−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
χ242-2-22-2200220-2-2-222-2-2-222-22000000002−22−2000000000000−22ζ25−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
χ252-2-22-2200220-2-2-222-2-2-222-2200000000−22−220000000000002−2ζ11−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
χ262-2-22-2200220-2-2-222-2-2-222-2200000000−22−220000000000002−2−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
χ27444444441-2411111-21-2-21-2-21-21-211-2-200002222-1-1-1-1-1-1-1-10000000000000000
χ28444444441-2411111-21-2-21-2-21-21-211-2-20000-2-2-2-2111111110000000000000000
χ2944444444-214-2-2-2-2-21-211-211-21-21-2-2110000000000000000000000000022-1-1-1-1
χ3044444444-214-2-2-2-2-21-211-211-21-21-2-21100000000000000000000000000-2-21111
χ31444444-4-41-2-411111-21-2-21-2-2-12-12-1-12200000000−i3i3−i3i3−i3i3−i3i30000000000000000
χ32444444-4-41-2-411111-21-2-21-2-2-12-12-1-12200000000i3−i3i3−i3i3−i3i3−i30000000000000000
χ33444444-4-4-21-4-2-2-2-2-21-211-2112-12-122-1-10000000000000000000000000000−i3i3−i3i3
χ34444444-4-4-21-4-2-2-2-2-21-211-2112-12-122-1-10000000000000000000000000000i3−i3i3−i3
χ354444-4-4441-2-41-1-1-1-1-21-2-21221-21-2-1-122000022-2-2-1-1-1-111110000000000000000
χ364444-4-4441-2-41-1-1-1-1-21-2-21221-21-2-1-1220000-2-2221111-1-1-1-10000000000000000
χ374444-4-444-21-4-222221-211-2-1-1-21-2122-1-1000000000000000000000000002-2-1-111
χ384444-4-444-21-4-222221-211-2-1-1-21-2122-1-100000000000000000000000000-2211-1-1
χ394444-4-4-4-41-241-1-1-1-1-21-2-2122-12-1211-2-200000000−i3i3−i3i3i3−i3i3−i30000000000000000
χ404444-4-4-4-41-241-1-1-1-1-21-2-2122-12-1211-2-200000000i3−i3i3−i3−i3i3−i3i30000000000000000
χ414444-4-4-4-4-214-222221-211-2-1-12-12-1-2-2110000000000000000000000000000−i3i3i3−i3
χ424444-4-4-4-4-214-222221-211-2-1-12-12-1-2-2110000000000000000000000000000i3−i3−i3i3
χ4344-4-40000440400004-4-4-4-4000000000022−22−22220000000000000000000000000000
χ4444-4-40000440400004-4-4-4-40000000000−222222−220000000000000000000000000000
χ454-44-4004-41-20-13-33-321-22-100-121-23-300000000003−3−333−3−330000000000000000
χ464-44-4004-41-20-13-33-321-22-100-121-23-30000000000−333−3−333−30000000000000000
χ474-44-4004-41-20-1-33-3321-22-100-121-2-3300000000003−3−33−333−30000000000000000
χ484-44-4004-41-20-1-33-3321-22-100-121-2-330000000000−333−33−3−330000000000000000
χ494-44-4004-4440-40000-444-4-400-4-444000000000000000000000000000000000000
χ504-44-400-441-20-13-33-321-22-1001-2-12-330000002i−2i2i−2i−i−iii−i−iii0000000000000000
χ514-44-400-441-20-13-33-321-22-1001-2-12-33000000−2i2i−2i2iii−i−iii−i−i0000000000000000
χ524-44-400-441-20-1-33-3321-22-1001-2-123-30000002i−2i−2i2i−i−iiiii−i−i0000000000000000
χ534-44-400-441-20-1-33-3321-22-1001-2-123-3000000−2i2i2i−2iii−i−i−i−iii0000000000000000
χ5488-8-800002-4026-6-66-4-244-2000000000000000000000000000000000000000000
χ5588-8-800002-402-666-6-4-244-2000000000000000000000000000000000000000000
χ5688-8-80000-420-4000024-2-24000000006i−6i00000000000000000000000000000000
χ5788-8-80000-420-4000024-2-2400000000−6i6i00000000000000000000000000000000
χ588-88-8008-8-42040000-2-42-24004-2-42000000000000000000000000000000000000
χ598-88-800-88-42040000-2-42-2400-424-2000000000000000000000000000000000000
χ608-8-888-8002-40-222-2-24-24-42-440000000000000000000000000000000000000000
χ618-8-888-800-4204-4-444-24-22-42-20000000000000000000000000000000000000000
χ628-8-88-88002-40-2-2-2224-24-424-40000000000000000000000000000000000000000
χ638-8-88-8800-420444-4-4-24-22-4-220000000000000000000000000000000000000000

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