Finite Group Databasebeta

← Group #10591217

Character table — Group #10591217

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
χ51111111111111111111111111-1-11111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1-1-11111-1-1-1-1-1-111
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
χ81111111111111111111111111-1-11111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1-1-11111-1-111
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
χ17222-2-2-22-222222-2222-2-2-2-2-2-2-2200222-2-2-2-200000000000000000000000000000000000000002-200
χ18222-2-2-22-222222-2222-2-2-2-2-2-2-2200222-2-2-2-20000000000000000000000000000000000000000-2200
χ1922-22-22-2-2222-2-222-2-2-2-2-22-2222002-2-222-2-200000000000000002i−2i0000002i2i−2i−2i0000000000000000
χ2022-22-22-2-2222-2-222-2-2-2-2-22-2222002-2-222-2-20000000000000000−2i2i000000−2i−2i2i2i0000000000000000
χ2122-22-22-2-2-12-111-12-2-2-21-2-1122-100-111-1-11133−3−300003333−3−3−3−32i−2i000000−i−iii−i3−i3i3i3000000000000
χ2222-22-22-2-2-12-111-12-2-2-21-2-1122-100-111-1-11133−3−300003333−3−3−3−3−2i2i000000ii−i−ii3i3−i3−i3000000000000
χ2322-22-22-2-2-12-111-12-2-2-21-2-1122-100-111-1-111−3−3330000−3−3−3−333332i−2i000000−i−iiii3i3−i3−i3000000000000
χ2422-22-22-2-2-12-111-12-2-2-21-2-1122-100-111-1-111−3−3330000−3−3−3−33333−2i2i000000ii−i−i−i3−i3i3i3000000000000
χ2522-2-22-2-22222-2-2-22-2-2222-22-2-22002-2-2-2-22200000000000000000000002i−2i0000000000002i2i−2i−2i0000
χ2622-2-22-2-22222-2-2-22-2-2222-22-2-22002-2-2-2-2220000000000000000000000−2i2i000000000000−2i−2i2i2i0000
χ2722-2-22-2-222-12-2-2-2-111-12-1-2211-100-11111-1-10000−i3−i3i3i3−i3−i3i3i3−i3−i3i3i30000002i−2i0000000033−3−3−i−iii0000
χ2822-2-22-2-222-12-2-2-2-111-12-1-2211-100-11111-1-10000−i3−i3i3i3−i3−i3i3i3−i3−i3i3i3000000−2i2i00000000−3−333ii−i−i0000
χ2922-2-22-2-222-12-2-2-2-111-12-1-2211-100-11111-1-10000i3i3−i3−i3i3i3−i3−i3i3i3−i3−i30000002i−2i00000000−3−333−i−iii0000
χ3022-2-22-2-222-12-2-2-2-111-12-1-2211-100-11111-1-10000i3i3−i3−i3i3i3−i3−i3i3i3−i3−i3000000−2i2i0000000033−3−3ii−i−i0000
χ312-222-2-2-2222-22-22-22-2-222-2-22-2200-22-22-2-22000000000000000000002i−2i0000002i−2i2i−2i000000000000
χ322-222-2-2-2222-22-22-22-2-222-2-22-2200-22-22-2-2200000000000000000000−2i2i000000−2i2i−2i2i000000000000
χ332-222-2-2-22-121-11-1-22-2-2-12112-2-1001-11-111-1−i3i3−i3i30000−i3i3−i3i3−i3i3−i3i300002i−2i003−33−3−ii−ii000000000000
χ342-222-2-2-22-121-11-1-22-2-2-12112-2-1001-11-111-1−i3i3−i3i30000−i3i3−i3i3−i3i3−i3i30000−2i2i00−33−33i−ii−i000000000000
χ352-222-2-2-22-121-11-1-22-2-2-12112-2-1001-11-111-1i3−i3i3−i30000i3−i3i3−i3i3−i3i3−i300002i−2i00−33−33−ii−ii000000000000
χ362-222-2-2-22-121-11-1-22-2-2-12112-2-1001-11-111-1i3−i3i3−i30000i3−i3i3−i3i3−i3i3−i30000−2i2i003−33−3i−ii−i000000000000
χ372-22-222-2-222-22-2-2-22-22-2-222-22200-22-2-222-20000000000000000002i−2i0000000000002i−2i2i−2i00000000
χ382-22-222-2-222-22-2-2-22-22-2-222-22200-22-2-222-2000000000000000000−2i2i000000000000−2i2i−2i2i00000000
χ392-22-222-2-22-1-22-2-21-11-1-21221-1-1001-111-1-1100003−33−33−3−33−333−3002i−2i000000000000−ii−ii−i3i3−i3i30000
χ402-22-222-2-22-1-22-2-21-11-1-21221-1-1001-111-1-1100003−33−33−3−33−333−300−2i2i000000000000i−ii−ii3−i3i3−i30000
χ412-22-222-2-22-1-22-2-21-11-1-21221-1-1001-111-1-110000−33−33−333−33−3−33002i−2i000000000000−ii−iii3−i3i3−i30000
χ422-22-222-2-22-1-22-2-21-11-1-21221-1-1001-111-1-110000−33−33−333−33−3−3300−2i2i000000000000i−ii−i−i3i3−i3i30000
χ432-2-222-22-222-2-222-2-222-2-2-222-222i−2i-2-222-22-22i−2i−2i2i2i−2i−2i2i2i−2i2i−2i−2i2i−2i2i0000000000000000000000000000
χ442-2-222-22-222-2-222-2-222-2-2-222-22−2i2i-2-222-22-2−2i2i2i−2i−2i2i2i−2i−2i2i−2i2i2i−2i2i−2i0000000000000000000000000000
χ452-2-222-22-22-1-2-22211-1-1-21-22-11-12i−2i11-1-11-112i−2i−2i2i−iii−i−ii−iii−ii−i0000000000000000−i3i3i3−i3−333−30000
χ462-2-222-22-22-1-2-22211-1-1-21-22-11-12i−2i11-1-11-112i−2i−2i2i−iii−i−ii−iii−ii−i0000000000000000i3−i3−i3i33−3−330000
χ472-2-222-22-22-1-2-22211-1-1-21-22-11-1−2i2i11-1-11-11−2i2i2i−2ii−i−iii−ii−i−ii−ii0000000000000000−i3i3i3−i33−3−330000
χ482-2-222-22-22-1-2-22211-1-1-21-22-11-1−2i2i11-1-11-11−2i2i2i−2ii−i−iii−ii−i−ii−ii0000000000000000i3−i3−i3i3−333−30000
χ492-2-222-22-2-1211-1-1-2-2221-21-12-2-12i−2i11-1-11-11−iii−i2i−2i−2i2i−ii−iii−ii−i00000000−i3i3i3−i3−333−3000000000000
χ502-2-222-22-2-1211-1-1-2-2221-21-12-2-12i−2i11-1-11-11−iii−i2i−2i−2i2i−ii−iii−ii−i00000000i3−i3−i3i33−3−33000000000000
χ512-2-222-22-2-1211-1-1-2-2221-21-12-2-1−2i2i11-1-11-11i−i−ii−2i2i2i−2ii−ii−i−ii−ii00000000−i3i3i3−i33−3−33000000000000
χ522-2-222-22-2-1211-1-1-2-2221-21-12-2-1−2i2i11-1-11-11i−i−ii−2i2i2i−2ii−ii−i−ii−ii00000000i3−i3−i3i3−333−3000000000000
χ532-2-2-2-222222-2-22-2-2-22-2222-2-22200-2-22-22-220000000000000000000000000000000000000000002-2
χ542-2-2-2-222222-2-22-2-2-22-2222-2-22200-2-22-22-22000000000000000000000000000000000000000000-22
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
χ57444-4-4-44-44-2444-4-2-2-22-42-4-422-200-2-2-2222200000000000000000000000000000000000000000000
χ58444-4-4-44-4-24-2-2-22444-42-422-4-4-200-2-2-2222200000000000000000000000000000000000000000000
χ59444-4-4-44-4-2-2-2-2-22-2-2-22222222100111-1-1-1-1000000003i3i−3i−3i−3i−3i3i3i0000000000000000000000000000
χ60444-4-4-44-4-2-2-2-2-22-2-2-22222222100111-1-1-1-100000000−3i−3i3i3i3i3i−3i−3i0000000000000000000000000000
χ6144-44-44-4-44-24-4-44-2222-424-4-2-2-200-222-2-22200000000000000000000000000000000000000000000
χ6244-44-44-4-4-2-2-222-2-222222-22-2-21001-1-111-1-12323−23−230000−3−3−3−333330000000000000000000000000000
χ6344-44-44-4-4-2-2-222-2-222222-22-2-21001-1-111-1-1−23−23232300003333−3−3−3−30000000000000000000000000000
χ6444-4-44-4-44-24-22224-4-44-242-2-4-4-200-22222-2-200000000000000000000000000000000000000000000
χ6544-4-44-4-44-2-2-2222-222-2-2-22-2221001-1-1-1-1110000−2i3−2i32i32i3i3i3−i3−i3i3i3−i3−i30000000000000000000000000000
χ6644-4-44-4-44-2-2-2222-222-2-2-22-2221001-1-1-1-11100002i32i3−2i3−2i3−i3−i3i3i3−i3−i3i3i30000000000000000000000000000
χ674-444-4-4-444-2-44-442-2224-2-4-4-22-2002-22-222-200000000000000000000000000000000000000000000
χ684-444-4-4-44-2-22-22-22-222-2-222-22100-11-11-1-11−2i32i3−2i32i30000i3−i3i3−i3i3−i3i3−i30000000000000000000000000000
χ694-444-4-4-44-2-22-22-22-222-2-222-22100-11-11-1-112i3−2i32i3−2i30000−i3i3−i3i3−i3i3−i3i30000000000000000000000000000
χ704-44-444-4-4-242-222-44-442-4-2-2-44-2002-222-2-2200000000000000000000000000000000000000000000
χ714-44-444-4-4-2-22-2222-22-222-2-22-2100-11-1-111-1000023−2323−23−333−33−3−330000000000000000000000000000
χ724-44-444-4-4-2-22-2222-22-222-2-22-2100-11-1-111-10000−2323−23233−3−33−333−30000000000000000000000000000
χ734-4-444-44-4-2-222-2-222-2-2222-2-2214i−4i-1-111-11-1−2i2i2i−2i−2i2i2i−2ii−ii−i−ii−ii0000000000000000000000000000
χ744-4-444-44-4-2-222-2-222-2-2222-2-221−4i4i-1-111-11-12i−2i−2i2i2i−2i−2i2i−ii−iii−ii−i0000000000000000000000000000
χ754-4-4-4-44444-2-4-44-422-224-24-42-2-20022-22-22-200000000000000000000000000000000000000000000
χ764-4-4-4-4444-2422-22-4-44-4-24-22-44-20022-22-22-200000000000000000000000000000000000000000000
χ774-4-4-4-4444-2-222-2222-22-2-2-222-2100-1-11-11-11000000003-3-333-3-330000000000000000000000000000
χ784-4-4-4-4444-2-222-2222-22-2-2-222-2100-1-11-11-1100000000-333-3-333-30000000000000000000000000000

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