Finite Group Databasebeta

← Group #11771912

Character table — Group #11771912

Order 1152.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63
size11112222444444444444488888888881818181824242424242424242424242436363636363636363636484848484848
order122244442336666661212121266661212121212128888888824242424242424248816161616161616164412121212
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
χ511111-1-11-111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1ii−i−iiiii−i−i−i−i11iiii−i−i−i−i1-111-1-1
χ611111-1-11-111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1ii−i−iiiii−i−i−i−i11−i−i−i−iiiii-11-1-111
χ711111-1-11-111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1−i−iii−i−i−i−iiiii11iiii−i−i−i−i-11-1-111
χ811111-1-11-111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1−i−iii−i−i−i−iiiii11−i−i−i−iiiii1-111-1-1
χ92222222222222222222222222222222-2-2-2-2000000000000-2-200000000000000
χ1022222-2-22-222222222-2-2-2-2-2-2-2-22222-2-22222000000000000-2-200000000000000
χ112222-222-2-2222222222222-2-2-2-2-2-2-2-22200000000000000000022−2−222−2−2000000
χ122222-222-2-2222222222222-2-2-2-2-2-2-2-222000000000000000000−2−222−2−222000000
χ132222-2-2-2-2222222222-2-2-2-22222-2-2-2-2-2-2000000000000000000−i2−i2i2i2i2i2−i2−i2000000
χ142222-2-2-2-2222222222-2-2-2-22222-2-2-2-2-2-2000000000000000000i2i2−i2−i2−i2−i2i2i2000000
χ152-22-202i−2i00222-2-2-22-22i−2i2i−2i000000002i−2i−i2−i2i2i20000000000002−2ζ11−ζ25−ζ41+ζ43−ζ11+ζ25+ζ41−ζ43−ζ13−ζ29−ζ31−ζ47ζ13+ζ29+ζ31+ζ47−ζ13−ζ29+ζ31+ζ47ζ13+ζ29−ζ31−ζ47ζ11+ζ25+ζ41+ζ43−ζ11−ζ25−ζ41−ζ43000000
χ162-22-202i−2i00222-2-2-22-22i−2i2i−2i000000002i−2i−i2−i2i2i20000000000002−2−ζ11+ζ25+ζ41−ζ43ζ11−ζ25−ζ41+ζ43ζ13+ζ29+ζ31+ζ47−ζ13−ζ29−ζ31−ζ47ζ13+ζ29−ζ31−ζ47−ζ13−ζ29+ζ31+ζ47−ζ11−ζ25−ζ41−ζ43ζ11+ζ25+ζ41+ζ43000000
χ172-22-202i−2i00222-2-2-22-22i−2i2i−2i000000002i−2ii2i2−i2−i2000000000000−22−ζ13−ζ29−ζ31−ζ47ζ13+ζ29+ζ31+ζ47−ζ11+ζ25+ζ41−ζ43ζ11−ζ25−ζ41+ζ43ζ11+ζ25+ζ41+ζ43−ζ11−ζ25−ζ41−ζ43ζ13+ζ29−ζ31−ζ47−ζ13−ζ29+ζ31+ζ47000000
χ182-22-202i−2i00222-2-2-22-22i−2i2i−2i000000002i−2ii2i2−i2−i2000000000000−22ζ13+ζ29+ζ31+ζ47−ζ13−ζ29−ζ31−ζ47ζ11−ζ25−ζ41+ζ43−ζ11+ζ25+ζ41−ζ43−ζ11−ζ25−ζ41−ζ43ζ11+ζ25+ζ41+ζ43−ζ13−ζ29+ζ31+ζ47ζ13+ζ29−ζ31−ζ47000000
χ192-22-20−2i2i00222-2-2-22-2−2i2i−2i2i00000000−2i2i−i2−i2i2i2000000000000−22ζ11+ζ25+ζ41+ζ43−ζ11−ζ25−ζ41−ζ43ζ13+ζ29−ζ31−ζ47−ζ13−ζ29+ζ31+ζ47−ζ13−ζ29−ζ31−ζ47ζ13+ζ29+ζ31+ζ47−ζ11+ζ25+ζ41−ζ43ζ11−ζ25−ζ41+ζ43000000
χ202-22-20−2i2i00222-2-2-22-2−2i2i−2i2i00000000−2i2i−i2−i2i2i2000000000000−22−ζ11−ζ25−ζ41−ζ43ζ11+ζ25+ζ41+ζ43−ζ13−ζ29+ζ31+ζ47ζ13+ζ29−ζ31−ζ47ζ13+ζ29+ζ31+ζ47−ζ13−ζ29−ζ31−ζ47ζ11−ζ25−ζ41+ζ43−ζ11+ζ25+ζ41−ζ43000000
χ212-22-20−2i2i00222-2-2-22-2−2i2i−2i2i00000000−2i2ii2i2−i2−i20000000000002−2−ζ13−ζ29+ζ31+ζ47ζ13+ζ29−ζ31−ζ47ζ11+ζ25+ζ41+ζ43−ζ11−ζ25−ζ41−ζ43ζ11−ζ25−ζ41+ζ43−ζ11+ζ25+ζ41−ζ43−ζ13−ζ29−ζ31−ζ47ζ13+ζ29+ζ31+ζ47000000
χ222-22-20−2i2i00222-2-2-22-2−2i2i−2i2i00000000−2i2ii2i2−i2−i20000000000002−2ζ13+ζ29−ζ31−ζ47−ζ13−ζ29+ζ31+ζ47−ζ11−ζ25−ζ41−ζ43ζ11+ζ25+ζ41+ζ43−ζ11+ζ25+ζ41−ζ43ζ11−ζ25−ζ41+ζ43ζ13+ζ29+ζ31+ζ47−ζ13−ζ29−ζ31−ζ47000000
χ232-2-22200-2022-2-2-22-22000000002-22-2002i−2i2i−2i1+i−1−i1−i−1+i1+i1+i−1−i−1−i1−i1−i−1+i−1+i0000000000000000
χ242-2-22200-2022-2-2-22-22000000002-22-2002i−2i2i−2i−1−i1+i−1+i1−i−1−i−1−i1+i1+i−1+i−1+i1−i1−i0000000000000000
χ252-2-22200-2022-2-2-22-22000000002-22-200−2i2i−2i2i1−i−1+i1+i−1−i1−i1−i−1+i−1+i1+i1+i−1−i−1−i0000000000000000
χ262-2-22200-2022-2-2-22-22000000002-22-200−2i2i−2i2i−1+i1−i−1−i1+i−1+i−1+i1−i1−i−1−i−1−i1+i1+i0000000000000000
χ274444444441-211-21-2-2111111-2-211-2-2-2-200002222-1-1-1-1-1-1-1-10000000000000000
χ284444444441-211-21-2-2111111-2-211-2-2-2-20000-2-2-2-2111111110000000000000000
χ29444444444-21-2-21-211-2-2-2-2-2-211-2-211110000000000000000000000000022-1-1-1-1
χ30444444444-21-2-21-211-2-2-2-2-2-211-2-2111100000000000000000000000000-2-21111
χ3144444-4-44-41-211-21-2-2-1-1-1-1-1-12211-2-22200002i2i−2i−2i−i−i−i−iiiii0000000000000000
χ3244444-4-44-41-211-21-2-2-1-1-1-1-1-12211-2-2220000−2i−2i2i2iiiii−i−i−i−i0000000000000000
χ3344444-4-44-4-21-2-21-211222222-1-1-2-211-1-1000000000000000000000000002-2-1-111
χ3444444-4-44-4-21-2-21-211222222-1-1-2-211-1-100000000000000000000000000-2211-1-1
χ354444-444-4-41-211-21-2-21111-1-122-1-122-2-200000000−i3i3−i3i3−i3i3−i3i30000000000000000
χ364444-444-4-41-211-21-2-21111-1-122-1-122-2-200000000i3−i3i3−i3i3−i3i3−i30000000000000000
χ374444-444-4-4-21-2-21-211-2-2-2-222-1-122-1-1110000000000000000000000000000−i3i3−i3i3
χ384444-444-4-4-21-2-21-211-2-2-2-222-1-122-1-1110000000000000000000000000000i3−i3i3−i3
χ394444-4-4-4-441-211-21-2-2-1-1-1-111-2-2-1-12222000000003−33−3−33−330000000000000000
χ404444-4-4-4-441-211-21-2-2-1-1-1-111-2-2-1-1222200000000−33−333−33−30000000000000000
χ414444-4-4-4-44-21-2-21-2112222-2-21122-1-1-1-10000000000000000000000000000−i3i3i3−i3
χ424444-4-4-4-44-21-2-21-2112222-2-21122-1-1-1-10000000000000000000000000000i3−i3−i3i3
χ4344-4-40000044-444-4-4-40000000000000022−22−22220000000000000000000000000000
χ4444-4-40000044-444-4-4-400000000000000−222222−220000000000000000000000000000
χ454-4-44400-401-2-1-1212-233-3-33-3001-1-220000002-22-2-1-111-1-1110000000000000000
χ464-4-44400-401-2-1-1212-233-3-33-3001-1-22000000-22-2211-1-111-1-10000000000000000
χ474-4-44400-401-2-1-1212-2-3-333-33001-1-220000002i−2i−2i2i−i−iiiii−i−i0000000000000000
χ484-4-44400-401-2-1-1212-2-3-333-33001-1-22000000−2i2i2i−2iii−i−i−i−iii0000000000000000
χ494-4-44-400401-2-1-1212-233-3-3-3300-112-20000000000−i3i3i3−i3−i3i3i3−i30000000000000000
χ504-4-44-400401-2-1-1212-233-3-3-3300-112-20000000000i3−i3−i3i3i3−i3−i3i30000000000000000
χ514-4-44-400401-2-1-1212-2-3-3333-300-112-200000000003−3−33−333−30000000000000000
χ524-4-44-400401-2-1-1212-2-3-3333-300-112-20000000000−333−33−3−330000000000000000
χ534-4-44-4004044-4-4-44-4400000000-44-440000000000000000000000000000000000
χ5488-8-8000002-4-22-4-2446i−6i−6i6i000000000000000000000000000000000000000000
χ5588-8-8000002-4-22-4-244−6i6i6i−6i000000000000000000000000000000000000000000
χ5688-8-800000-424-424-2-20000006-600000000000000000000000000000000000000
χ5788-8-800000-424-424-2-2000000-6600000000000000000000000000000000000000
χ588-88-808i−8i002-42-24-2-442i−2i2i−2i00000000−4i4i00000000000000000000000000000000
χ598-88-808i−8i00-42-44-242-2−4i4i−4i4i000000002i−2i00000000000000000000000000000000
χ608-88-80−8i8i002-42-24-2-44−2i2i−2i2i000000004i−4i00000000000000000000000000000000
χ618-88-80−8i8i00-42-44-242-24i−4i4i−4i00000000−2i2i00000000000000000000000000000000
χ628-8-88800-80-4244-2-4-2200000000-442-20000000000000000000000000000000000
χ638-8-88-80080-4244-2-4-22000000004-4-220000000000000000000000000000000000

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