Finite Group Databasebeta

← Group #10591356

Character table — Group #10591356

Order 576.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78
size1111111122222222222222224444444444444444444444444412121212121212121212121212121212121212121212121236363636
order12222222336666666666666634466666661212121212121212121212121212121244444444121212121212121212121212121212124444
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
χ51111111111111111111111111-1-11111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1-1-11111-1-1-1-111-1-1
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
χ81111111111111111111111111-1-11111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1-1-1111111-1-1
χ9222222222-12222-1-1-1-12-122-1-1-122-1-1-1-1-1-1-12222-1-1-1-1-1-1-1-1-1-1-1-10022002200000000-1-1-1-1-1-1-1-10000
χ10222222222-12222-1-1-1-12-122-1-1-122-1-1-1-1-1-1-12222-1-1-1-1-1-1-1-1-1-1-1-100-2-200-2-200000000111111110000
χ11222222222-12222-1-1-1-12-122-1-1-1-2-2-1-1-1-1-1-1-1-2-2-2-2111111111111002200-2-200000000-1-1-1-111110000
χ12222222222-12222-1-1-1-12-122-1-1-1-2-2-1-1-1-1-1-1-1-2-2-2-211111111111100-2-20022000000001111-1-1-1-10000
χ1322222222-12-1-1-1-12222-12-1-122-122-1-1-1-1-1-1-1-1-1-1-12222-1-1-1-1-1-1-1-122002200-1-1-1-1-1-1-1-1000000000000
χ1422222222-12-1-1-1-12222-12-1-122-122-1-1-1-1-1-1-1-1-1-1-12222-1-1-1-1-1-1-1-1-2-200-2-20011111111000000000000
χ1522222222-12-1-1-1-12222-12-1-122-1-2-2-1-1-1-1-1-1-11111-2-2-2-2111111112200-2-200-1-1-1-11111000000000000
χ1622222222-12-1-1-1-12222-12-1-122-1-2-2-1-1-1-1-1-1-11111-2-2-2-211111111-2-20022001111-1-1-1-1000000000000
χ17222-22-2-2-222222-222-2-2-2-2-2-22-2200222-2-2-2-20000000000000000002-200000000000022-2-200000000
χ18222-22-2-2-222222-222-2-2-2-2-2-22-2200222-2-2-2-2000000000000000000-22000000000000-2-22200000000
χ19222-22-2-2-22-1222-2-1-111-21-2-2-11-100-1-1-11111000033−3−33333−3−3−3−3002-2000000000000-1-11133−3−30000
χ20222-22-2-2-22-1222-2-1-111-21-2-2-11-100-1-1-11111000033−3−33333−3−3−3−300-2200000000000011-1-1−3−3330000
χ21222-22-2-2-22-1222-2-1-111-21-2-2-11-100-1-1-111110000−3−333−3−3−3−33333002-2000000000000-1-111−3−3330000
χ22222-22-2-2-22-1222-2-1-111-21-2-2-11-100-1-1-111110000−3−333−3−3−3−3333300-2200000000000011-1-133−3−30000
χ2322-22-22-2-2222-2-222-222-2-22-2-2-22002-2-222-2-200000000000000002-200000022-2-20000000000000000
χ2422-22-22-2-2222-2-222-222-2-22-2-2-22002-2-222-2-20000000000000000-22000000-2-2220000000000000000
χ2522-22-22-2-2-12-111-12-2221-2-11-2-2-100-111-1-11133−3−3000033−3−333−3−32-2000000-1-11133−3−3000000000000
χ2622-22-22-2-2-12-111-12-2221-2-11-2-2-100-111-1-11133−3−3000033−3−333−3−3-2200000011-1-1−3−333000000000000
χ2722-22-22-2-2-12-111-12-2221-2-11-2-2-100-111-1-111−3−3330000−3−333−3−3332-2000000-1-111−3−333000000000000
χ2822-22-22-2-2-12-111-12-2221-2-11-2-2-100-111-1-111−3−3330000−3−333−3−333-2200000011-1-133−3−3000000000000
χ2922-2-2-2-222222-2-2-22-2-2-222-22-222002-2-2-2-22200000000000000000000000000000000000000002-200
χ3022-2-2-2-222222-2-2-22-2-2-222-22-222002-2-2-2-2220000000000000000000000000000000000000000-2200
χ312-222-2-2-2222-22-22-222-2-2-2-22-2222i−2i-22-22-22-22i−2i2i−2i2i−2i2i−2i2i−2i2i−2i2i−2i2i−2i0000000000000000000000000000
χ322-222-2-2-2222-22-22-222-2-2-2-22-222−2i2i-22-22-22-2−2i2i−2i2i−2i2i−2i2i−2i2i−2i2i−2i2i−2i2i0000000000000000000000000000
χ332-222-2-2-222-1-22-221-1-11-21-221-1-12i−2i1-11-11-112i−2i2i−2i−ii−ii−ii−ii−ii−ii00000000000000003−33−3−i3i3−i3i30000
χ342-222-2-2-222-1-22-221-1-11-21-221-1-12i−2i1-11-11-112i−2i2i−2i−ii−ii−ii−ii−ii−ii0000000000000000−33−33i3−i3i3−i30000
χ352-222-2-2-222-1-22-221-1-11-21-221-1-1−2i2i1-11-11-11−2i2i−2i2ii−ii−ii−ii−ii−ii−i00000000000000003−33−3i3−i3i3−i30000
χ362-222-2-2-222-1-22-221-1-11-21-221-1-1−2i2i1-11-11-11−2i2i−2i2ii−ii−ii−ii−ii−ii−i0000000000000000−33−33−i3i3−i3i30000
χ372-222-2-2-22-121-11-1-222-21-21-1-22-12i−2i1-11-11-11−ii−ii2i−2i2i−2i−ii−ii−ii−ii000000003−33−3−i3i3−i3i3000000000000
χ382-222-2-2-22-121-11-1-222-21-21-1-22-12i−2i1-11-11-11−ii−ii2i−2i2i−2i−ii−ii−ii−ii00000000−33−33i3−i3i3−i3000000000000
χ392-222-2-2-22-121-11-1-222-21-21-1-22-1−2i2i1-11-11-11i−ii−i−2i2i−2i2ii−ii−ii−ii−i000000003−33−3i3−i3i3−i3000000000000
χ402-222-2-2-22-121-11-1-222-21-21-1-22-1−2i2i1-11-11-11i−ii−i−2i2i−2i2ii−ii−ii−ii−i00000000−33−33−i3i3−i3i3000000000000
χ412-22-2-222-222-22-2-2-22-22222-2-2-2200-22-2-22-2200000000000000000000002i−2i0000000000002i−2i−2i2i0000
χ422-22-2-222-222-22-2-2-22-22222-2-2-2200-22-2-22-220000000000000000000000−2i2i000000000000−2i2i2i−2i0000
χ432-22-2-222-22-1-22-2-21-11-12-12-211-1001-111-11-10000−i3i3i3−i3−i3i3−i3i3i3−i3i3−i30000002i−2i00000000−333−3−iii−i0000
χ442-22-2-222-22-1-22-2-21-11-12-12-211-1001-111-11-10000−i3i3i3−i3−i3i3−i3i3i3−i3i3−i3000000−2i2i000000003−3−33i−i−ii0000
χ452-22-2-222-22-1-22-2-21-11-12-12-211-1001-111-11-10000i3−i3−i3i3i3−i3i3−i3−i3i3−i3i30000002i−2i000000003−3−33−iii−i0000
χ462-22-2-222-22-1-22-2-21-11-12-12-211-1001-111-11-10000i3−i3−i3i3i3−i3i3−i3−i3i3−i3i3000000−2i2i00000000−333−3i−i−ii0000
χ472-2-222-22-222-2-222-2-22-222-2-22-2200-2-222-2-22000000000000000000002i−2i0000002i−2i−2i2i000000000000
χ482-2-222-22-222-2-222-2-22-222-2-22-2200-2-222-2-2200000000000000000000−2i2i000000−2i2i2i−2i000000000000
χ492-2-222-22-2-1211-1-1-2-22-2-12112-2-10011-1-111-1−i3i3i3−i30000−i3i3i3−i3−i3i3i3−i300002i−2i00−333−3−iii−i000000000000
χ502-2-222-22-2-1211-1-1-2-22-2-12112-2-10011-1-111-1−i3i3i3−i30000−i3i3i3−i3−i3i3i3−i30000−2i2i003−3−33i−i−ii000000000000
χ512-2-222-22-2-1211-1-1-2-22-2-12112-2-10011-1-111-1i3−i3−i3i30000i3−i3−i3i3i3−i3−i3i300002i−2i003−3−33−iii−i000000000000
χ522-2-222-22-2-1211-1-1-2-22-2-12112-2-10011-1-111-1i3−i3−i3i30000i3−i3−i3i3i3−i3−i3i30000−2i2i00−333−3i−i−ii000000000000
χ532-2-2-222-2222-2-22-2-2-2-22-2-22222200-2-22-222-20000000000000000000000000000000000000000002-2
χ542-2-2-222-2222-2-22-2-2-2-22-2-22222200-2-22-222-2000000000000000000000000000000000000000000-22
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
χ57444-44-4-4-4-24-2-2-2244-4-42-4224-4-200-2-2-2222200000000000000000000000000000000000000000000
χ58444-44-4-4-4-2-2-2-2-22-2-2222222-22100111-1-1-1-100002323−23−23−3−3−3−333330000000000000000000000000000
χ59444-44-4-4-4-2-2-2-2-22-2-2222222-22100111-1-1-1-10000−23−2323233333−3−3−3−30000000000000000000000000000
χ6044-44-44-4-44-24-4-44-22-2-2-424-422-200-222-2-22200000000000000000000000000000000000000000000
χ6144-44-44-4-4-2-2-222-2-22-2-222-22221001-1-111-1-12323−23−230000−3−333−3−3330000000000000000000000000000
χ6244-44-44-4-4-2-2-222-2-22-2-222-22221001-1-111-1-1−23−232323000033−3−333−3−30000000000000000000000000000
χ6344-4-4-4-4444-24-4-4-4-22224-2-442-2-200-22222-2-200000000000000000000000000000000000000000000
χ6444-4-4-4-444-24-22224-4-4-4-242-2-44-200-22222-2-200000000000000000000000000000000000000000000
χ6544-4-4-4-444-2-2-2222-2222-2-22-22-21001-1-1-1-1110000000033-3-3-3-3330000000000000000000000000000
χ6644-4-4-4-444-2-2-2222-2222-2-22-22-21001-1-1-1-11100000000-3-33333-3-30000000000000000000000000000
χ674-444-4-4-44-2-22-22-22-2-22222-22-214i−4i-11-11-11-1−2i2i−2i2i−2i2i−2i2ii−ii−ii−ii−i0000000000000000000000000000
χ684-444-4-4-44-2-22-22-22-2-22222-22-21−4i4i-11-11-11-12i−2i2i−2i2i−2i2i−2i−ii−ii−ii−ii0000000000000000000000000000
χ694-44-4-444-4-242-222-44-44-24-22-4-4-2002-222-22-200000000000000000000000000000000000000000000
χ704-44-4-444-4-2-22-2222-22-2-2-2-2222100-11-1-11-110000−2i32i32i3−2i3i3−i3i3−i3−i3i3−i3i30000000000000000000000000000
χ714-44-4-444-4-2-22-2222-22-2-2-2-2222100-11-1-11-1100002i3−2i3−2i32i3−i3i3−i3i3i3−i3i3−i30000000000000000000000000000
χ724-4-444-44-44-2-4-44422-224-2-4-4-22-20022-2-222-200000000000000000000000000000000000000000000
χ734-4-444-44-4-2-222-2-222-22-2-222-22100-1-111-1-11−2i32i32i3−2i30000i3−i3−i3i3i3−i3−i3i30000000000000000000000000000
χ744-4-444-44-4-2-222-2-222-22-2-222-22100-1-111-1-112i3−2i3−2i32i30000−i3i3i3−i3−i3i3i3−i30000000000000000000000000000
χ754-4-4-444-444-2-4-44-4222-2-4244-2-2-20022-22-2-2200000000000000000000000000000000000000000000
χ764-4-4-444-44-2422-22-4-4-442-4-2-244-20022-22-2-2200000000000000000000000000000000000000000000
χ774-4-4-444-44-2-222-22222-222-2-2-2-2100-1-11-111-1000000003i−3i−3i3i−3i3i3i−3i0000000000000000000000000000
χ784-4-4-444-44-2-222-22222-222-2-2-2-2100-1-11-111-100000000−3i3i3i−3i3i−3i−3i3i0000000000000000000000000000

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