Finite Group Databasebeta

← Group #10591319

Character table — Group #10591319

Order 576.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78
size1111111122222222222222224444444444444444444444444412121212121212121212121212121212121212121212121236363636
order1222222233666666666666663446666666121212121212121212121212121212122244444466661212121212121212121212124444
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111111111111111-1-111-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1
χ311111111111111111111111111111111111111111111111111-1-111-1-111-1-1-1-1-1-1-1-111111111-1-1-1-1
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
χ51111111111111111111111111-1-11111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1-1-1-1-1-1-1111111-1-1
χ61111111111111111111111111-1-11111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-1111111-1-1-1-11111-1-1-1-1-1-111
χ71111111111111111111111111-1-11111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-11111-1-1-1-11111-1-111
χ81111111111111111111111111-1-11111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-111111111-1-1-1-111-1-1
χ9222222222-122222-1-1-1-1-1-12-12-122-1-1-1-1-1-1-1-1-1-1-12222-1-1-1-1-1-1-1-122002200-1-1-1-1-1-1-1-1000000000000
χ10222222222-122222-1-1-1-1-1-12-12-122-1-1-1-1-1-1-1-1-1-1-12222-1-1-1-1-1-1-1-1-2-200-2-20011111111000000000000
χ11222222222-122222-1-1-1-1-1-12-12-1-2-2-1-1-1-1-1-1-11111-2-2-2-2111111112200-2-200-1-1-1-11111000000000000
χ12222222222-122222-1-1-1-1-1-12-12-1-2-2-1-1-1-1-1-1-11111-2-2-2-211111111-2-20022001111-1-1-1-1000000000000
χ1322222222-12-1-1-1-1-1222222-12-1-122-1-1-1-1-1-1-12222-1-1-1-1-1-1-1-1-1-1-1-10022002200000000-1-1-1-1-1-1-1-10000
χ1422222222-12-1-1-1-1-1222222-12-1-122-1-1-1-1-1-1-12222-1-1-1-1-1-1-1-1-1-1-1-100-2-200-2-200000000111111110000
χ1522222222-12-1-1-1-1-1222222-12-1-1-2-2-1-1-1-1-1-1-1-2-2-2-2111111111111002200-2-2000000001111-1-1-1-10000
χ1622222222-12-1-1-1-1-1222222-12-1-1-2-2-1-1-1-1-1-1-1-2-2-2-211111111111100-2-2002200000000-1-1-1-111110000
χ172222-2-2-2-222222-2-2222-2-2-2-2-2-2200222-2-2-2-200000000000000002-200000022-2-20000000000000000
χ182222-2-2-2-222222-2-2222-2-2-2-2-2-2200222-2-2-2-20000000000000000-22000000-2-2220000000000000000
χ192222-2-2-2-22-1222-2-2-1-1-1111-21-2-100-1-1-1111133−3−300003333−3−3−3−32-2000000-1-11133−3−3000000000000
χ202222-2-2-2-22-1222-2-2-1-1-1111-21-2-100-1-1-1111133−3−300003333−3−3−3−3-2200000011-1-1−3−333000000000000
χ212222-2-2-2-22-1222-2-2-1-1-1111-21-2-100-1-1-11111−3−3330000−3−3−3−333332-2000000-1-111−3−333000000000000
χ222222-2-2-2-22-1222-2-2-1-1-1111-21-2-100-1-1-11111−3−3330000−3−3−3−33333-2200000011-1-133−3−3000000000000
χ2322-2-222-2-2222-2-22-22-2-22-22-2-222002-2-22-2-220000000000000000000000000000000000000000002i−2i
χ2422-2-222-2-2222-2-22-22-2-22-22-2-222002-2-22-2-22000000000000000000000000000000000000000000−2i2i
χ2522-2-2-2-222222-2-2-222-2-2-22-222-22002-2-2-222-200000000000000000000002-20000000022-2-200000000
χ2622-2-2-2-222222-2-2-222-2-2-22-222-22002-2-2-222-20000000000000000000000-2200000000-2-22200000000
χ2722-2-2-2-222-12-1111-12-2-2-22-2-121-100-1111-1-11000033−3−333−3−333−3−30000002-200000000-1-11133−3−30000
χ2822-2-2-2-222-12-1111-12-2-2-22-2-121-100-1111-1-11000033−3−333−3−333−3−3000000-220000000011-1-1−3−3330000
χ2922-2-2-2-222-12-1111-12-2-2-22-2-121-100-1111-1-110000−3−333−3−333−3−3330000002-200000000-1-111−3−3330000
χ3022-2-2-2-222-12-1111-12-2-2-22-2-121-100-1111-1-110000−3−333−3−333−3−333000000-220000000011-1-133−3−30000
χ312-22-22-22-222-22-22-2-22-22-2-222-2200-22-222-2-20000000000000000002i−2i00000000000000002i−2i2i−2i0000
χ322-22-22-22-222-22-22-2-22-22-2-222-2200-22-222-2-2000000000000000000−2i2i0000000000000000−2i2i−2i2i0000
χ332-22-22-22-2-121-11-11-22-22-2-2-121-1001-11-1-11100003−33−33−33−33−33−3002i−2i000000000000−i3i3−i3i3−ii−ii0000
χ342-22-22-22-2-121-11-11-22-22-2-2-121-1001-11-1-11100003−33−33−33−33−33−300−2i2i000000000000i3−i3i3−i3i−ii−i0000
χ352-22-22-22-2-121-11-11-22-22-2-2-121-1001-11-1-1110000−33−33−33−33−33−33002i−2i000000000000i3−i3i3−i3−ii−ii0000
χ362-22-22-22-2-121-11-11-22-22-2-2-121-1001-11-1-1110000−33−33−33−33−33−3300−2i2i000000000000−i3i3−i3i3i−ii−i0000
χ372-22-2-22-2222-22-2-22-22-2-222-2-22200-22-2-2-22200000000000000000000000000000000000000002-200
χ382-22-2-22-2222-22-2-22-22-2-222-2-22200-22-2-2-2220000000000000000000000000000000000000000-2200
χ392-2-222-2-2222-2-2222-2-2222-2-2-2-2200-2-222-22-2000000000000000000002i−2i0000002i−2i2i−2i000000000000
χ402-2-222-2-2222-2-2222-2-2222-2-2-2-2200-2-222-22-200000000000000000000−2i2i000000−2i2i−2i2i000000000000
χ412-2-222-2-222-1-2-222211-1-1-11-21-2-10011-1-11-113−33−300003−3−33−333−300002i−2i00−i3i3−i3i3−ii−ii000000000000
χ422-2-222-2-222-1-2-222211-1-1-11-21-2-10011-1-11-113−33−300003−3−33−333−30000−2i2i00i3−i3i3−i3i−ii−i000000000000
χ432-2-222-2-222-1-2-222211-1-1-11-21-2-10011-1-11-11−33−330000−333−33−3−3300002i−2i00i3−i3i3−i3−ii−ii000000000000
χ442-2-222-2-222-1-2-222211-1-1-11-21-2-10011-1-11-11−33−330000−333−33−3−330000−2i2i00−i3i3−i3i3i−ii−i000000000000
χ452-2-22-222-222-2-22-2-2-2-22-2-2222222-2-2-22-22-222-2-222-2-222-2-222-2-220000000000000000000000000000
χ462-2-22-222-222-2-22-2-2-2-22-2-222222-22-2-22-22-22-222-2-222-2-222-2-222-20000000000000000000000000000
χ472-2-22-222-22-1-2-22-2-211-111-12-12-12-211-11-11-1-111-12-2-22-111-1-111-100000000−i3i3i3−i3−i3i3i3−i3000000000000
χ482-2-22-222-22-1-2-22-2-211-111-12-12-12-211-11-11-1-111-12-2-22-111-1-111-100000000i3−i3−i3i3i3−i3−i3i3000000000000
χ492-2-22-222-22-1-2-22-2-211-111-12-12-1-2211-11-11-11-1-11-222-21-1-111-1-1100000000−i3i3i3−i3i3−i3−i3i3000000000000
χ502-2-22-222-22-1-2-22-2-211-111-12-12-1-2211-11-11-11-1-11-222-21-1-111-1-1100000000i3−i3−i3i3−i3i3i3−i3000000000000
χ512-2-22-222-2-1211-111-2-22-2-22-12-1-12-211-11-11-12-2-22-111-1-111-1-111-10000000000000000−i3i3i3−i3−i3i3i3−i30000
χ522-2-22-222-2-1211-111-2-22-2-22-12-1-12-211-11-11-12-2-22-111-1-111-1-111-10000000000000000i3−i3−i3i3i3−i3−i3i30000
χ532-2-22-222-2-1211-111-2-22-2-22-12-1-1-2211-11-11-1-222-21-1-111-1-111-1-110000000000000000−i3i3i3−i3i3−i3−i3i30000
χ542-2-22-222-2-1211-111-2-22-2-22-12-1-1-2211-11-11-1-222-21-1-111-1-111-1-110000000000000000i3−i3−i3i3−i3i3i3−i30000
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
χ574444-4-4-4-4-24-2-2-222444-4-4-42-42-200-2-2-2222200000000000000000000000000000000000000000000
χ584444-4-4-4-4-2-2-2-2-222-2-2-2222222100111-1-1-1-12323−23−230000−3−3−3−333330000000000000000000000000000
χ594444-4-4-4-4-2-2-2-2-222-2-2-2222222100111-1-1-1-1−23−23232300003333−3−3−3−30000000000000000000000000000
χ6044-4-444-4-44-24-4-44-4-222-22-2-424-200-222-222-200000000000000000000000000000000000000000000
χ6144-4-444-4-4-24-222-224-4-44-442-4-2-200-222-222-200000000000000000000000000000000000000000000
χ6244-4-444-4-4-2-2-222-22-222-22-222-21001-1-11-1-110000000033-3-3-3-3330000000000000000000000000000
χ6344-4-444-4-4-2-2-222-22-222-22-222-21001-1-11-1-1100000000-3-33333-3-30000000000000000000000000000
χ6444-4-4-4-4444-24-4-4-44-2222-224-2-4-200-2222-2-2200000000000000000000000000000000000000000000
χ6544-4-4-4-444-2-2-2222-2-2222-22-2-221001-1-1-111-100002323−23−23−3−333−3−3330000000000000000000000000000
χ6644-4-4-4-444-2-2-2222-2-2222-22-2-221001-1-1-111-10000−23−23232333−3−333−3−30000000000000000000000000000
χ674-44-44-44-44-2-44-44-42-22-2224-2-4-2002-22-2-22200000000000000000000000000000000000000000000
χ684-44-44-44-4-2-22-22-222-22-222-2-22100-11-111-1-1000023−2323−23−33−33−33−330000000000000000000000000000
χ694-44-44-44-4-2-22-22-222-22-222-2-22100-11-111-1-10000−2323−23233−33−33−33−30000000000000000000000000000
χ704-44-4-44-444-2-44-4-442-222-2-2-424-2002-2222-2-200000000000000000000000000000000000000000000
χ714-44-4-44-44-242-222-2-44-4-4442-4-2-2002-2222-2-200000000000000000000000000000000000000000000
χ724-44-4-44-44-2-22-222-22-222-2-222-2100-11-1-1-111000000003-33-3-33-330000000000000000000000000000
χ734-44-4-44-44-2-22-222-22-222-2-222-2100-11-1-1-11100000000-33-333-33-30000000000000000000000000000
χ744-4-444-4-44-2422-2-2-2-4-4444-42-42-20022-2-22-2200000000000000000000000000000000000000000000
χ754-4-444-4-44-2-222-2-2-222-2-2-22222100-1-111-11-123−2323−230000−333−33−3−330000000000000000000000000000
χ764-4-444-4-44-2-222-2-2-222-2-2-22222100-1-111-11-1−2323−232300003−3−33−333−30000000000000000000000000000
χ774-4-44-444-4-2-222-22222-222-2-2-2-214-4-1-11-11-11-222-2-222-21-1-111-1-110000000000000000000000000000
χ784-4-44-444-4-2-222-22222-222-2-2-2-21-44-1-11-11-112-2-222-2-22-111-1-111-10000000000000000000000000000

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