Finite Group Databasebeta

← Group #10591226

Character table — Group #10591226

Order 576.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78
size1111111122222222222222224444444444444444444444444412121212121212121212121212121212121212121212121236363636
order12222222336666666666666634466666661212121212121212121212121212121244444444121212121212121212121212121212124444
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111111111111111111111111-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1
χ311111111111111111111111111111111111111111111111111-1-1-1-11111-1-1-1-1-1-1-1-111111111-1-1-1-1
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
χ51111111111111111111111111-1-11111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-111-1-11111-1-1-1-11111-1-1-1-111-1-1
χ61111111111111111111111111-1-11111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-1111111-1-1-1-1-1-1-1-11111-1-111
χ71111111111111111111111111-1-11111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-111111111-1-1-1-1-1-111
χ81111111111111111111111111-1-11111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-111-1-1-1-11111-1-1-1-1111111-1-1
χ9222222222-122222-1-1-1-1-12-1-12-122-1-1-1-1-1-1-1-1-1-1-12222-1-1-1-1-1-1-1-122220000-1-1-1-1-1-1-1-1000000000000
χ10222222222-122222-1-1-1-1-12-1-12-122-1-1-1-1-1-1-1-1-1-1-12222-1-1-1-1-1-1-1-1-2-2-2-2000011111111000000000000
χ11222222222-122222-1-1-1-1-12-1-12-1-2-2-1-1-1-1-1-1-11111-2-2-2-21111111122-2-20000-1-1-1-11111000000000000
χ12222222222-122222-1-1-1-1-12-1-12-1-2-2-1-1-1-1-1-1-11111-2-2-2-211111111-2-22200001111-1-1-1-1000000000000
χ1322222222-12-1-1-1-1-122222-122-1-122-1-1-1-1-1-1-12222-1-1-1-1-1-1-1-1-1-1-1-10000222200000000-1-1-1-1-1-1-1-10000
χ1422222222-12-1-1-1-1-122222-122-1-122-1-1-1-1-1-1-12222-1-1-1-1-1-1-1-1-1-1-1-10000-2-2-2-200000000111111110000
χ1522222222-12-1-1-1-1-122222-122-1-1-2-2-1-1-1-1-1-1-1-2-2-2-2111111111111000022-2-200000000-1-1-1-111110000
χ1622222222-12-1-1-1-1-122222-122-1-1-2-2-1-1-1-1-1-1-1-2-2-2-21111111111110000-2-222000000001111-1-1-1-10000
χ172222-2-2-2-22222-2-2-2222-2-22-2-2-2200222-2-2-2-2000000000000000000002-2000000000022-2-200000000
χ182222-2-2-2-22222-2-2-2222-2-22-2-2-2200222-2-2-2-200000000000000000000-220000000000-2-22200000000
χ192222-2-2-2-2-12-1-1111222-2-2-1-2-21-100-1-1-11111000033−3−33333−3−3−3−300002-20000000000-1-11133−3−30000
χ202222-2-2-2-2-12-1-1111222-2-2-1-2-21-100-1-1-11111000033−3−33333−3−3−3−30000-22000000000011-1-1−3−3330000
χ212222-2-2-2-2-12-1-1111222-2-2-1-2-21-100-1-1-111110000−3−333−3−3−3−3333300002-20000000000-1-111−3−3330000
χ222222-2-2-2-2-12-1-1111222-2-2-1-2-21-100-1-1-111110000−3−333−3−3−3−333330000-22000000000011-1-133−3−30000
χ2322-2-22-22-2222-22-2-22-2-2-22-22-222002-2-22-2-2200000000000000000000000000000000000000002i−2i00
χ2422-2-22-22-2222-22-2-22-2-2-22-22-222002-2-22-2-220000000000000000000000000000000000000000−2i2i00
χ2522-2-2-22-22222-2-2222-2-22-2-2-22-22002-2-2-222-200000000000000002i−2i0000002i2i−2i−2i0000000000000000
χ2622-2-2-22-22222-2-2222-2-22-2-2-22-22002-2-2-222-20000000000000000−2i2i000000−2i−2i2i2i0000000000000000
χ2722-2-2-22-222-12-2-222-111-11-21-1-2-100-1111-1-1133−3−3000033−3−333−3−32i−2i000000−i−iii−i3−i3i3i3000000000000
χ2822-2-2-22-222-12-2-222-111-11-21-1-2-100-1111-1-1133−3−3000033−3−333−3−3−2i2i000000ii−i−ii3i3−i3−i3000000000000
χ2922-2-2-22-222-12-2-222-111-11-21-1-2-100-1111-1-11−3−3330000−3−333−3−3332i−2i000000−i−iiii3i3−i3−i3000000000000
χ3022-2-2-22-222-12-2-222-111-11-21-1-2-100-1111-1-11−3−3330000−3−333−3−333−2i2i000000ii−i−i−i3−i3i3i3000000000000
χ312-22-22-2-2222-2222-2-22-22-2-22-2-2200-22-222-2-20000000000000000002i−2i000000002i−2i2i−2i000000000000
χ322-22-22-2-2222-2222-2-22-22-2-22-2-2200-22-222-2-2000000000000000000−2i2i00000000−2i2i−2i2i000000000000
χ332-22-22-2-222-1-2222-21-11-11-2-11-2-1001-11-1-1113−33−300003−33−33−33−3002i−2i0000−i3i3−i3i3−ii−ii000000000000
χ342-22-22-2-222-1-2222-21-11-11-2-11-2-1001-11-1-1113−33−300003−33−33−33−300−2i2i0000i3−i3i3−i3i−ii−i000000000000
χ352-22-22-2-222-1-2222-21-11-11-2-11-2-1001-11-1-111−33−330000−33−33−33−33002i−2i0000i3−i3i3−i3−ii−ii000000000000
χ362-22-22-2-222-1-2222-21-11-11-2-11-2-1001-11-1-111−33−330000−33−33−33−3300−2i2i0000−i3i3−i3i3i−ii−i000000000000
χ372-22-2-222-222-22-2-22-22-2-22-2-222200-22-2-2-2220000000000000000000000000000000000000000002i−2i
χ382-22-2-222-222-22-2-22-22-2-22-2-222200-22-2-2-222000000000000000000000000000000000000000000−2i2i
χ392-2-2222-2-222-2-22-22-2-22-2-2222-2200-2-222-22-200000000000000000000002i−2i0000000000002i−2i2i−2i0000
χ402-2-2222-2-222-2-22-22-2-22-2-2222-2200-2-222-22-20000000000000000000000−2i2i000000000000−2i2i−2i2i0000
χ412-2-2222-2-2-1211-11-1-2-22-2-2-1221-10011-1-11-1100003−33−33−3−33−333−30000002i−2i00000000−i3i3−i3i3−ii−ii0000
χ422-2-2222-2-2-1211-11-1-2-22-2-2-1221-10011-1-11-1100003−33−33−3−33−333−3000000−2i2i00000000i3−i3i3−i3i−ii−i0000
χ432-2-2222-2-2-1211-11-1-2-22-2-2-1221-10011-1-11-110000−33−33−333−33−3−330000002i−2i00000000i3−i3i3−i3−ii−ii0000
χ442-2-2222-2-2-1211-11-1-2-22-2-2-1221-10011-1-11-110000−33−33−333−33−3−33000000−2i2i00000000−i3i3−i3i3i−ii−i0000
χ452-2-22-2-22222-2-2-22-2-2-22222-2-2222-2-2-22-22-222-2-222-2-222-2-222-2-220000000000000000000000000000
χ462-2-22-2-22222-2-2-22-2-2-22222-2-222-22-2-22-22-22-222-2-222-2-222-2-222-20000000000000000000000000000
χ472-2-22-2-2222-1-2-2-22-211-1-1-12112-12-211-11-11-1-111-12-2-22-111-1-111-1000000003−3−33−333−3000000000000
χ482-2-22-2-2222-1-2-2-22-211-1-1-12112-12-211-11-11-1-111-12-2-22-111-1-111-100000000−333−33−3−33000000000000
χ492-2-22-2-2222-1-2-2-22-211-1-1-12112-1-2211-11-11-11-1-11-222-21-1-111-1-11000000003−3−333−3−33000000000000
χ502-2-22-2-2222-1-2-2-22-211-1-1-12112-1-2211-11-11-11-1-11-222-21-1-111-1-1100000000−333−3−333−3000000000000
χ512-2-22-2-222-12111-11-2-2222-1-2-2-1-12-211-11-11-12-2-22-111-1-111-1-111-10000000000000000−i3i3i3−i3−i3i3i3−i30000
χ522-2-22-2-222-12111-11-2-2222-1-2-2-1-12-211-11-11-12-2-22-111-1-111-1-111-10000000000000000i3−i3−i3i3i3−i3−i3i30000
χ532-2-22-2-222-12111-11-2-2222-1-2-2-1-1-2211-11-11-1-222-21-1-111-1-111-1-110000000000000000−i3i3i3−i3i3−i3−i3i30000
χ542-2-22-2-222-12111-11-2-2222-1-2-2-1-1-2211-11-11-1-222-21-1-111-1-111-1-110000000000000000i3−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
χ574444-4-4-4-44-244-4-4-4-2-2-222422-4-200-2-2-2222200000000000000000000000000000000000000000000
χ584444-4-4-4-4-2-2-2-2222-2-2-222-2222100111-1-1-1-100002323−23−23−3−3−3−333330000000000000000000000000000
χ594444-4-4-4-4-2-2-2-2222-2-2-222-2222100111-1-1-1-10000−23−2323233333−3−3−3−30000000000000000000000000000
χ6044-4-44-44-44-24-44-4-4-2222-2-4-224-200-222-222-200000000000000000000000000000000000000000000
χ6144-4-44-44-4-24-22-2224-4-4-4424-4-2-200-222-222-200000000000000000000000000000000000000000000
χ6244-4-44-44-4-2-2-22-222-2222-22-22-21001-1-11-1-110000000033-3-3-3-3330000000000000000000000000000
χ6344-4-44-44-4-2-2-22-222-2222-22-22-21001-1-11-1-1100000000-3-33333-3-30000000000000000000000000000
χ6444-4-4-44-44-24-222-2-24-4-44-42-442-200-2222-2-2200000000000000000000000000000000000000000000
χ6544-4-4-44-44-2-2-222-2-2-222-2222-221001-1-1-111-12323−23−230000−3−333−3−3330000000000000000000000000000
χ6644-4-4-44-44-2-2-222-2-2-222-2222-221001-1-1-111-1−23−232323000033−3−333−3−30000000000000000000000000000
χ674-44-44-4-44-242-2-2-22-44-44-424-42-2002-22-2-22200000000000000000000000000000000000000000000
χ684-44-44-4-44-2-22-2-2-222-22-222-222100-11-111-1-123−2323−230000−33−33−33−330000000000000000000000000000
χ694-44-44-4-44-2-22-2-2-222-22-222-222100-11-111-1-1−2323−232300003−33−33−33−30000000000000000000000000000
χ704-44-4-444-44-2-44-4-442-222-2-42-24-2002-2222-2-200000000000000000000000000000000000000000000
χ714-44-4-444-4-242-222-2-44-4-442-44-2-2002-2222-2-200000000000000000000000000000000000000000000
χ724-44-4-444-4-2-22-222-22-222-222-2-2100-11-1-1-111000000003-33-3-33-330000000000000000000000000000
χ734-44-4-444-4-2-22-222-22-222-222-2-2100-11-1-1-11100000000-33-333-33-30000000000000000000000000000
χ744-4-4444-4-44-2-4-44-4422-2224-2-2-4-20022-2-22-2200000000000000000000000000000000000000000000
χ754-4-4444-4-4-2-222-22-222-222-2-2-22100-1-111-11-1000023−2323−23−333−33−3−330000000000000000000000000000
χ764-4-4444-4-4-2-222-22-222-222-2-2-22100-1-111-11-10000−2323−23233−3−33−333−30000000000000000000000000000
χ774-4-44-4-444-2-2222-2222-2-2-2-222-214-4-1-11-11-11-222-2-222-21-1-111-1-110000000000000000000000000000
χ784-4-44-4-444-2-2222-2222-2-2-2-222-21-44-1-11-11-112-2-222-2-22-111-1-111-10000000000000000000000000000

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