Finite Group Databasebeta

← Group #10591203

Character table — Group #10591203

Order 576.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78
size1111111122222222222222224444444444444444444444444412121212121212121212121212121212121212121212121236363636
order12222222336666666666666634466666661212121212121212121212121212121244444444121212121212121212121212121212122244
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111111111111111-1-111-1-11111-1-1-1-11111-1-1-1-1-1-1-1-1
χ311111111111111111111111111111111111111111111111111-1-111-1-111-1-1-1-11111-1-1-1-11111-1-1-1-1
χ411111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111
χ51111111111111111111111111-1-11111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-111111111-1-1-1-1-1-1-1-1-1-111
χ61111111111111111111111111-1-11111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-1111111-1-1-1-1-1-1-1-1111111-1-1
χ71111111111111111111111111-1-11111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-111111111-1-1-1-111-1-1
χ81111111111111111111111111-1-11111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-111111111-1-111
χ9222222222-122222-1-1-1-1-12-12-1-122-1-1-1-1-1-1-12222-1-1-1-1-1-1-1-1-1-1-1-1002200220000-1-1-1-10000-1-1-1-10000
χ10222222222-122222-1-1-1-1-12-12-1-122-1-1-1-1-1-1-12222-1-1-1-1-1-1-1-1-1-1-1-100-2-200-2-200001111000011110000
χ11222222222-122222-1-1-1-1-12-12-1-1-2-2-1-1-1-1-1-1-1-2-2-2-2111111111111002200-2-20000-1-1-1-1000011110000
χ12222222222-122222-1-1-1-1-12-12-1-1-2-2-1-1-1-1-1-1-1-2-2-2-211111111111100-2-20022000011110000-1-1-1-10000
χ1322222222-12-1-1-1-1-122222-12-12-122-1-1-1-1-1-1-1-1-1-1-12222-1-1-1-1-1-1-1-122002200-1-1-1-10000-1-1-1-100000000
χ1422222222-12-1-1-1-1-122222-12-12-122-1-1-1-1-1-1-1-1-1-1-12222-1-1-1-1-1-1-1-1-2-200-2-20011110000111100000000
χ1522222222-12-1-1-1-1-122222-12-12-1-2-2-1-1-1-1-1-1-11111-2-2-2-2111111112200-2-200-1-1-1-10000111100000000
χ1622222222-12-1-1-1-1-122222-12-12-1-2-2-1-1-1-1-1-1-11111-2-2-2-211111111-2-200220011110000-1-1-1-100000000
χ172222-2-2-2-222222-2-2222-2-2-2-2-2-2200222-2-2-2-200000000000000000000000000000000000000002-200
χ182222-2-2-2-222222-2-2222-2-2-2-2-2-2200222-2-2-2-20000000000000000000000000000000000000000-2200
χ1922-2-222-2-2222-2-22-22-2-22-222-2-222i−2i2-2-222-2-22i2i−2i−2i2i2i−2i−2i2i2i2i2i−2i−2i−2i−2i0000000000000000000000000000
χ2022-2-222-2-2222-2-22-22-2-22-222-2-22−2i2i2-2-222-2-2−2i−2i2i2i−2i−2i2i2i−2i−2i−2i−2i2i2i2i2i0000000000000000000000000000
χ2122-2-222-2-22-12-2-22-2-111-112-1-21-12i−2i-111-1-1112i2i−2i−2i−i−iii−i−i−i−iiiii000000000000−i3−i3i3i3000033−3−30000
χ2222-2-222-2-22-12-2-22-2-111-112-1-21-12i−2i-111-1-1112i2i−2i−2i−i−iii−i−i−i−iiiii000000000000i3i3−i3−i30000−3−3330000
χ2322-2-222-2-22-12-2-22-2-111-112-1-21-1−2i2i-111-1-111−2i−2i2i2iii−i−iiiii−i−i−i−i000000000000−i3−i3i3i30000−3−3330000
χ2422-2-222-2-22-12-2-22-2-111-112-1-21-1−2i2i-111-1-111−2i−2i2i2iii−i−iiiii−i−i−i−i000000000000i3i3−i3−i3000033−3−30000
χ2522-2-222-2-2-12-111-112-2-22-2-121-2-12i−2i-111-1-111−i−iii2i2i−2i−2i−i−i−i−iiiii00000000−i3−i3i3i3000033−3−300000000
χ2622-2-222-2-2-12-111-112-2-22-2-121-2-12i−2i-111-1-111−i−iii2i2i−2i−2i−i−i−i−iiiii00000000i3i3−i3−i30000−3−33300000000
χ2722-2-222-2-2-12-111-112-2-22-2-121-2-1−2i2i-111-1-111ii−i−i−2i−2i2i2iiiii−i−i−i−i00000000−i3−i3i3i30000−3−33300000000
χ2822-2-222-2-2-12-111-112-2-22-2-121-2-1−2i2i-111-1-111ii−i−i−2i−2i2i2iiiii−i−i−i−i00000000i3i3−i3−i3000033−3−300000000
χ2922-2-2-2-222222-2-2-222-2-2-22-2-2222002-2-2-2-2220000000000000000000000000000000000000000002-2
χ3022-2-2-2-222222-2-2-222-2-2-22-2-2222002-2-2-2-222000000000000000000000000000000000000000000-22
χ312-22-22-22-222-22-22-2-22-2-2-2-2222200-22-22-2-220000000000000000002-2000000002-22-2000000000000
χ322-22-22-22-222-22-22-2-22-2-2-2-2222200-22-22-2-22000000000000000000-2200000000-22-22000000000000
χ332-22-22-22-22-1-22-22-21-1111-2-12-1-1001-11-111-10000−i3i3−i3i3−i3−i3i3i3−i3−i3i3i3002-200000000-11-110000−i3i3−i3i30000
χ342-22-22-22-22-1-22-22-21-1111-2-12-1-1001-11-111-10000−i3i3−i3i3−i3−i3i3i3−i3−i3i3i300-22000000001-11-10000i3−i3i3−i30000
χ352-22-22-22-22-1-22-22-21-1111-2-12-1-1001-11-111-10000i3−i3i3−i3i3i3−i3−i3i3i3−i3−i3002-200000000-11-110000i3−i3i3−i30000
χ362-22-22-22-22-1-22-22-21-1111-2-12-1-1001-11-111-10000i3−i3i3−i3i3i3−i3−i3i3i3−i3−i300-22000000001-11-10000−i3i3−i3i30000
χ372-22-2-22-2222-22-2-22-22-2222-2-2-2200-22-2-222-2000000000000000000002i−2i00000000002i−2i2i−2i00000000
χ382-22-2-22-2222-22-2-22-22-2222-2-2-2200-22-2-222-200000000000000000000−2i2i0000000000−2i2i−2i2i00000000
χ392-22-2-22-22-121-111-1-22-222-1-21-2-1001-111-1-113−33−300003−33−33−33−300002i−2i00−i3i3−i3i30000−ii−ii00000000
χ402-22-2-22-22-121-111-1-22-222-1-21-2-1001-111-1-113−33−300003−33−33−33−30000−2i2i00i3−i3i3−i30000i−ii−i00000000
χ412-22-2-22-22-121-111-1-22-222-1-21-2-1001-111-1-11−33−330000−33−33−33−3300002i−2i00i3−i3i3−i30000−ii−ii00000000
χ422-22-2-22-22-121-111-1-22-222-1-21-2-1001-111-1-11−33−330000−33−33−33−330000−2i2i00−i3i3−i3i30000i−ii−i00000000
χ432-2-222-2-2222-2-2222-2-22-22-22-2-2200-2-222-22-200000000000000000000002i−2i0000000000002i−2i−2i2i0000
χ442-2-222-2-2222-2-2222-2-22-22-22-2-2200-2-222-22-20000000000000000000000−2i2i000000000000−2i2i2i−2i0000
χ452-2-222-2-222-1-2-222211-11-1-2-1-21-10011-1-11-1100003−3−3333−3−3−3−3330000002i−2i0000−i3i3i3−i30000−iii−i0000
χ462-2-222-2-222-1-2-222211-11-1-2-1-21-10011-1-11-1100003−3−3333−3−3−3−333000000−2i2i0000i3−i3−i3i30000i−i−ii0000
χ472-2-222-2-222-1-2-222211-11-1-2-1-21-10011-1-11-110000−333−3−3−33333−3−30000002i−2i0000i3−i3−i3i30000−iii−i0000
χ482-2-222-2-222-1-2-222211-11-1-2-1-21-10011-1-11-110000−333−3−3−33333−3−3000000−2i2i0000−i3i3i3−i30000i−i−ii0000
χ492-2-22-222-222-2-22-2-2-2-222-22-222200-2-22-22-2200000000000000002-20000002-2-220000000000000000
χ502-2-22-222-222-2-22-2-2-2-222-22-222200-2-22-22-220000000000000000-22000000-222-20000000000000000
χ512-2-22-222-2-1211-111-2-222-2-1-2-12-10011-11-11-1−i3i3i3−i30000−i3i3−i3i3i3−i3i3−i32-2000000-111-10000−i3i3i3−i300000000
χ522-2-22-222-2-1211-111-2-222-2-1-2-12-10011-11-11-1−i3i3i3−i30000−i3i3−i3i3i3−i3i3−i3-220000001-1-110000i3−i3−i3i300000000
χ532-2-22-222-2-1211-111-2-222-2-1-2-12-10011-11-11-1i3−i3−i3i30000i3−i3i3−i3−i3i3−i3i32-2000000-111-10000i3−i3−i3i300000000
χ542-2-22-222-2-1211-111-2-222-2-1-2-12-10011-11-11-1i3−i3−i3i30000i3−i3i3−i3−i3i3−i3i3-220000001-1-110000−i3i3i3−i300000000
χ5544444444-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-21441111111-2-2-2-2-2-2-2-2111111110000000000000000000000000000
χ5644444444-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-21-4-4111111122222222-1-1-1-1-1-1-1-10000000000000000000000000000
χ574444-4-4-4-44-2444-4-4-2-2-222-42-42-200-2-2-2222200000000000000000000000000000000000000000000
χ584444-4-4-4-4-24-2-2-222444-4-42-42-4-200-2-2-2222200000000000000000000000000000000000000000000
χ594444-4-4-4-4-2-2-2-2-222-2-2-2222222100111-1-1-1-1000000003i−3i−3i3i3i−3i−3i3i0000000000000000000000000000
χ604444-4-4-4-4-2-2-2-2-222-2-2-2222222100111-1-1-1-100000000−3i3i3i−3i−3i3i3i−3i0000000000000000000000000000
χ6144-4-444-4-4-2-2-222-22-222-22-2-22214i−4i1-1-111-1-1−2i−2i2i2i−2i−2i2i2iiiii−i−i−i−i0000000000000000000000000000
χ6244-4-444-4-4-2-2-222-22-222-22-2-2221−4i4i1-1-111-1-12i2i−2i−2i2i2i−2i−2i−i−i−i−iiiii0000000000000000000000000000
χ6344-4-4-4-4444-24-4-4-44-2222-2-424-2-200-22222-2-200000000000000000000000000000000000000000000
χ6444-4-4-4-444-24-2222-24-4-4-442-4-24-200-22222-2-200000000000000000000000000000000000000000000
χ6544-4-4-4-444-2-2-2222-2-2222-222-2-21001-1-1-1-111000000003-3-33-333-30000000000000000000000000000
χ6644-4-4-4-444-2-2-2222-2-2222-222-2-21001-1-1-1-11100000000-333-33-3-330000000000000000000000000000
χ674-44-44-44-4-242-22-22-44-4-4-424-24-2002-22-222-200000000000000000000000000000000000000000000
χ684-44-44-44-4-2-22-22-222-22222-2-2-2100-11-11-1-110000−2i32i3−2i32i3i3i3−i3−i3i3i3−i3−i30000000000000000000000000000
χ694-44-44-44-4-2-22-22-222-22222-2-2-2100-11-11-1-1100002i3−2i32i3−2i3−i3−i3i3i3−i3−i3i3i30000000000000000000000000000
χ704-44-4-44-444-2-44-4-442-22-2-242-42-2002-222-2-2200000000000000000000000000000000000000000000
χ714-44-4-44-44-2-22-222-22-22-2-2-2222100-11-1-111-123−2323−230000−33−33−33−330000000000000000000000000000
χ724-44-4-44-44-2-22-222-22-22-2-2-2222100-11-1-111-1−2323−232300003−33−33−33−30000000000000000000000000000
χ734-4-444-4-44-2422-2-2-2-4-44-44242-4-20022-2-22-2200000000000000000000000000000000000000000000
χ744-4-444-4-44-2-222-2-2-222-22-22-222100-1-111-11-1000023−23−2323−3−33333−3−30000000000000000000000000000
χ754-4-444-4-44-2-222-2-2-222-22-22-222100-1-111-11-10000−232323−2333−3−3−3−3330000000000000000000000000000
χ764-4-44-444-44-2-4-44-4-422-2-22424-2-20022-22-22-200000000000000000000000000000000000000000000
χ774-4-44-444-4-2-222-22222-2-22-22-2-2100-1-11-11-11−2i32i32i3−2i30000i3−i3i3−i3−i3i3−i3i30000000000000000000000000000
χ784-4-44-444-4-2-222-22222-2-22-22-2-2100-1-11-11-112i3−2i3−2i32i30000−i3i3−i3i3i3−i3i3−i30000000000000000000000000000

Here i is the imaginary unit (i² = −1).