Finite Group Databasebeta

← Group #10591214

Character table — Group #10591214

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
χ51111111111111111111111111-1-11111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-111-1-1-1-1-1-111111111-1-1-1-111-1-1
χ61111111111111111111111111-1-11111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-111-1-1-1-11111-1-1-1-11111-1-111
χ71111111111111111111111111-1-11111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-11111-1-1-1-11111-1-1-1-1-1-111
χ81111111111111111111111111-1-11111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1111111-1-1-1-1-1-1-1-1111111-1-1
χ9222222222-122222-1-1-1-1-12-1-12-122-1-1-1-1-1-1-12222-1-1-1-1-1-1-1-1-1-1-1-122220000-1-1-1-1-1-1-1-1000000000000
χ10222222222-122222-1-1-1-1-12-1-12-122-1-1-1-1-1-1-12222-1-1-1-1-1-1-1-1-1-1-1-1-2-2-2-2000011111111000000000000
χ11222222222-122222-1-1-1-1-12-1-12-1-2-2-1-1-1-1-1-1-1-2-2-2-211111111111122-2-200001111-1-1-1-1000000000000
χ12222222222-122222-1-1-1-1-12-1-12-1-2-2-1-1-1-1-1-1-1-2-2-2-2111111111111-2-2220000-1-1-1-11111000000000000
χ1322222222-12-1-1-1-1-122222-122-1-122-1-1-1-1-1-1-1-1-1-1-12222-1-1-1-1-1-1-1-10000222200000000-1-1-1-1-1-1-1-10000
χ1422222222-12-1-1-1-1-122222-122-1-122-1-1-1-1-1-1-1-1-1-1-12222-1-1-1-1-1-1-1-10000-2-2-2-200000000111111110000
χ1522222222-12-1-1-1-1-122222-122-1-1-2-2-1-1-1-1-1-1-11111-2-2-2-211111111000022-2-200000000-1-1-1-111110000
χ1622222222-12-1-1-1-1-122222-122-1-1-2-2-1-1-1-1-1-1-11111-2-2-2-2111111110000-2-222000000001111-1-1-1-10000
χ17222-2-22-2-222222-2-2222-2-2-2-2-2-2200222-2-2-2-20000000000000000000000000000000000000000002-2
χ18222-2-22-2-222222-2-2222-2-2-2-2-2-2200222-2-2-2-2000000000000000000000000000000000000000000-22
χ1922-22-2-22-2222-2-2222-2-222-2-2-2-22002-2-222-2-200000000000000000000000000000000000000002-200
χ2022-22-2-22-2222-2-2222-2-222-2-2-2-22002-2-222-2-20000000000000000000000000000000000000000-2200
χ2122-2-22-2-22222-2-2-2-22-2-2-2-2222222-22-2-2-2-22222-2-222-2-22222-2-2-2-20000000000000000000000000000
χ2222-2-22-2-22222-2-2-2-22-2-2-2-222222-222-2-2-2-222-2-222-2-222-2-2-2-222220000000000000000000000000000
χ2322-2-22-2-222-12-2-2-2-2-111112-1-12-12-2-11111-1-122-2-2-1-111-1-1-1-1111100000000−i3−i3i3i3−i3−i3i3i3000000000000
χ2422-2-22-2-222-12-2-2-2-2-111112-1-12-12-2-11111-1-122-2-2-1-111-1-1-1-1111100000000i3i3−i3−i3i3i3−i3−i3000000000000
χ2522-2-22-2-222-12-2-2-2-2-111112-1-12-1-22-11111-1-1-2-22211-1-11111-1-1-1-100000000−i3−i3i3i3i3i3−i3−i3000000000000
χ2622-2-22-2-222-12-2-2-2-2-111112-1-12-1-22-11111-1-1-2-22211-1-11111-1-1-1-100000000i3i3−i3−i3−i3−i3i3i3000000000000
χ2722-2-22-2-22-12-111112-2-2-2-2-122-1-12-2-11111-1-1-1-11122-2-2-1-1-1-111110000000000000000−i3−i3i3i3−i3−i3i3i30000
χ2822-2-22-2-22-12-111112-2-2-2-2-122-1-12-2-11111-1-1-1-11122-2-2-1-1-1-111110000000000000000i3i3−i3−i3i3i3−i3−i30000
χ2922-2-22-2-22-12-111112-2-2-2-2-122-1-1-22-11111-1-111-1-1-2-2221111-1-1-1-10000000000000000−i3−i3i3i3i3i3−i3−i30000
χ3022-2-22-2-22-12-111112-2-2-2-2-122-1-1-22-11111-1-111-1-1-2-2221111-1-1-1-10000000000000000i3i3−i3−i3−i3−i3i3i30000
χ312-222-2-2-2222-22-22-2-22-22-2-22-22200-22-22-22-200000000000000002i−2i00000000002i−2i2i−2i000000000000
χ322-222-2-2-2222-22-22-2-22-22-2-22-22200-22-22-22-20000000000000000−2i2i0000000000−2i2i−2i2i000000000000
χ332-222-2-2-222-1-22-22-21-11-11-2-112-1001-11-11-1100003−33−333−3−333−3−32i−2i000000−i3i3−i3i3−ii−ii000000000000
χ342-222-2-2-222-1-22-22-21-11-11-2-112-1001-11-11-1100003−33−333−3−333−3−3−2i2i000000i3−i3i3−i3i−ii−i000000000000
χ352-222-2-2-222-1-22-22-21-11-11-2-112-1001-11-11-110000−33−33−3−333−3−3332i−2i000000i3−i3i3−i3−ii−ii000000000000
χ362-222-2-2-222-1-22-22-21-11-11-2-112-1001-11-11-110000−33−33−3−333−3−333−2i2i000000−i3i3−i3i3i−ii−i000000000000
χ372-22-22-22-222-22-2-22-22-2-222-22-2200-22-2-22-2200000000000000000000002i−2i0000000000002i−2i2i−2i0000
χ382-22-22-22-222-22-2-22-22-2-222-22-2200-22-2-22-220000000000000000000000−2i2i000000000000−2i2i−2i2i0000
χ392-22-22-22-2-121-111-1-22-2-22-1-221-1001-111-11-1−i3i3−i3i30000−i3i3−i3i3−i3i3−i3i30000002i−2i000000003−33−3−ii−ii0000
χ402-22-22-22-2-121-111-1-22-2-22-1-221-1001-111-11-1−i3i3−i3i30000−i3i3−i3i3−i3i3−i3i3000000−2i2i00000000−33−33i−ii−i0000
χ412-22-22-22-2-121-111-1-22-2-22-1-221-1001-111-11-1i3−i3i3−i30000i3−i3i3−i3i3−i3i3−i30000002i−2i00000000−33−33−ii−ii0000
χ422-22-22-22-2-121-111-1-22-2-22-1-221-1001-111-11-1i3−i3i3−i30000i3−i3i3−i3i3−i3i3−i3000000−2i2i000000003−33−3i−ii−i0000
χ432-2-2222-2-222-2-222-2-2-222-22-22-2200-2-222-2-22000000000000000000002i−2i00000000002i−2i−2i2i00000000
χ442-2-2222-2-222-2-222-2-2-222-22-22-2200-2-222-2-2200000000000000000000−2i2i0000000000−2i2i2i−2i00000000
χ452-2-2222-2-2-1211-1-11-2-222-2-1-221-10011-1-111-1−i3i3i3−i30000−i3i3−i3i3i3−i3i3−i300002i−2i0000000000−iii−i3−3−330000
χ462-2-2222-2-2-1211-1-11-2-222-2-1-221-10011-1-111-1−i3i3i3−i30000−i3i3−i3i3i3−i3i3−i30000−2i2i0000000000i−i−ii−333−30000
χ472-2-2222-2-2-1211-1-11-2-222-2-1-221-10011-1-111-1i3−i3−i3i30000i3−i3i3−i3−i3i3−i3i300002i−2i0000000000−iii−i−333−30000
χ482-2-2222-2-2-1211-1-11-2-222-2-1-221-10011-1-111-1i3−i3−i3i30000i3−i3i3−i3−i3i3−i3i30000−2i2i0000000000i−i−ii3−3−330000
χ492-2-2-2-222222-2-22-22-2-22-22-22-22200-2-22-222-20000000000000000002-200002-2-220000000000000000
χ502-2-2-2-222222-2-22-22-2-22-22-22-22200-2-22-222-2000000000000000000-220000-222-20000000000000000
χ512-2-2-2-22222-1-2-22-2211-11-1-2-112-10011-11-1-1100003−3−3333−3−3−3−333002-20000-111-13−3−33000000000000
χ522-2-2-2-22222-1-2-22-2211-11-1-2-112-10011-11-1-1100003−3−3333−3−3−3−33300-2200001-1-11−333−3000000000000
χ532-2-2-2-22222-1-2-22-2211-11-1-2-112-10011-11-1-110000−333−3−3−33333−3−3002-20000-111-1−333−3000000000000
χ542-2-2-2-22222-1-2-22-2211-11-1-2-112-10011-11-1-110000−333−3−3−33333−3−300-2200001-1-113−3−33000000000000
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
χ57444-4-44-4-44-2444-4-4-2-2-222-422-4-200-2-2-2222200000000000000000000000000000000000000000000
χ58444-4-44-4-4-24-2-2-222444-4-42-4-42-200-2-2-2222200000000000000000000000000000000000000000000
χ59444-4-44-4-4-2-2-2-2-222-2-2-2222222100111-1-1-1-1000000003i−3i−3i3i3i−3i−3i3i0000000000000000000000000000
χ60444-4-44-4-4-2-2-2-2-222-2-2-2222222100111-1-1-1-100000000−3i3i3i−3i−3i3i3i−3i0000000000000000000000000000
χ6144-44-4-44-44-24-4-444-222-2-2-422-4-200-222-2-22200000000000000000000000000000000000000000000
χ6244-44-4-44-4-24-222-2-24-4-4442-4-42-200-222-2-22200000000000000000000000000000000000000000000
χ6344-44-4-44-4-2-2-222-2-2-222-2-222221001-1-111-1-1000000003i−3i−3i3i−3i3i3i−3i0000000000000000000000000000
χ6444-44-4-44-4-2-2-222-2-2-222-2-222221001-1-111-1-100000000−3i3i3i−3i3i−3i−3i3i0000000000000000000000000000
χ6544-4-44-4-44-2-2-22222-22222-2-2-2-214-41-1-1-1-111-2-222-2-2221111-1-1-1-10000000000000000000000000000
χ6644-4-44-4-44-2-2-22222-22222-2-2-2-21-441-1-1-1-11122-2-222-2-2-1-1-1-111110000000000000000000000000000
χ674-444-4-4-44-242-22-22-44-44-424-4-2-2002-22-22-2200000000000000000000000000000000000000000000
χ684-444-4-4-44-2-22-22-222-22-222-22-2100-11-11-11-1000023−2323−23−3−333−3−3330000000000000000000000000000
χ694-444-4-4-44-2-22-22-222-22-222-22-2100-11-11-11-10000−2323−232333−3−333−3−30000000000000000000000000000
χ704-44-44-44-44-2-44-4-442-222-242-2-4-2002-222-22-200000000000000000000000000000000000000000000
χ714-44-44-44-4-2-22-222-22-222-2-22-22100-11-1-11-11−2i32i3−2i32i30000i3−i3i3−i3i3−i3i3−i30000000000000000000000000000
χ724-44-44-44-4-2-22-222-22-222-2-22-22100-11-1-11-112i3−2i32i3−2i30000−i3i3−i3i3−i3i3−i3i30000000000000000000000000000
χ734-4-4444-4-44-2-4-444-422-2-2242-2-4-20022-2-222-200000000000000000000000000000000000000000000
χ744-4-4444-4-4-2-222-2-2222-2-22-22-22100-1-111-1-11−2i32i32i3−2i30000i3−i3i3−i3−i3i3−i3i30000000000000000000000000000
χ754-4-4444-4-4-2-222-2-2222-2-22-22-22100-1-111-1-112i3−2i3−2i32i30000−i3i3−i3i3i3−i3i3−i30000000000000000000000000000
χ764-4-4-4-4444-2422-22-2-4-44-4424-4-2-20022-22-2-2200000000000000000000000000000000000000000000
χ774-4-4-4-4444-2-222-22-222-22-22-22-2100-1-11-111-1000023−23−2323−3−33333−3−30000000000000000000000000000
χ784-4-4-4-4444-2-222-22-222-22-22-22-2100-1-11-111-10000−232323−2333−3−3−3−3330000000000000000000000000000

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