Finite Group Databasebeta

← Group #10591345

Character table — Group #10591345

Order 576.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78
size1111111122222222222222224444444444444444444444444412121212121212121212121212121212121212121212121236363636
order12222222336666666666666634466666661212121212121212121212121212121244444444121212121212121212121212121212124444
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1
χ311111111111111111111111111111111111111111111111111-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-1
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
χ61111111111111111111111111-1-11111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-111-1-1-1-111111111-1-1-1-1-1-111
χ71111111111111111111111111-1-11111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-11111-1-1-1-1-1-1-1-11111-1-111
χ81111111111111111111111111-1-11111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-111-1-1-1-11111-1-1-1-1111111-1-1
χ9222222222-122222-1-1-1-12-1-1-12-122-1-1-1-1-1-1-12222-1-1-1-1-1-1-1-1-1-1-1-100002222-1-1-1-1-1-1-1-1000000000000
χ10222222222-122222-1-1-1-12-1-1-12-122-1-1-1-1-1-1-12222-1-1-1-1-1-1-1-1-1-1-1-10000-2-2-2-211111111000000000000
χ11222222222-122222-1-1-1-12-1-1-12-1-2-2-1-1-1-1-1-1-1-2-2-2-2111111111111000022-2-2-1-1-1-11111000000000000
χ12222222222-122222-1-1-1-12-1-1-12-1-2-2-1-1-1-1-1-1-1-2-2-2-21111111111110000-2-2221111-1-1-1-1000000000000
χ1322222222-12-1-1-1-1-12222-1222-1-122-1-1-1-1-1-1-1-1-1-1-12222-1-1-1-1-1-1-1-12222000000000000-1-1-1-1-1-1-1-10000
χ1422222222-12-1-1-1-1-12222-1222-1-122-1-1-1-1-1-1-1-1-1-1-12222-1-1-1-1-1-1-1-1-2-2-2-2000000000000111111110000
χ1522222222-12-1-1-1-1-12222-1222-1-1-2-2-1-1-1-1-1-1-11111-2-2-2-21111111122-2-2000000000000-1-1-1-111110000
χ1622222222-12-1-1-1-1-12222-1222-1-1-2-2-1-1-1-1-1-1-11111-2-2-2-211111111-2-2220000000000001111-1-1-1-10000
χ17222-22-2-2-22222-2-2-222-2-222-2-2-222-222-2-2-2-2222-2-222-2-22222-2-2-2-20000000000000000000000000000
χ18222-22-2-2-22222-2-2-222-2-222-2-2-22-2222-2-2-2-22-2-222-2-222-2-2-2-222220000000000000000000000000000
χ19222-22-2-2-22-122-2-2-2-1-1112-111-2-12-2-1-11111-122-2-2-1-111-1-1-1-111110000000033−3−333−3−3000000000000
χ20222-22-2-2-22-122-2-2-2-1-1112-111-2-12-2-1-11111-122-2-2-1-111-1-1-1-1111100000000−3−333−3−333000000000000
χ21222-22-2-2-22-122-2-2-2-1-1112-111-2-1-22-1-11111-1-2-22211-1-11111-1-1-1-10000000033−3−3−3−333000000000000
χ22222-22-2-2-22-122-2-2-2-1-1112-111-2-1-22-1-11111-1-2-22211-1-11111-1-1-1-100000000−3−33333−3−3000000000000
χ23222-22-2-2-2-12-1-111122-2-2-12-2-21-12-2-1-11111-1-1-11122-2-2-1-1-1-11111000000000000000033−3−333−3−30000
χ24222-22-2-2-2-12-1-111122-2-2-12-2-21-12-2-1-11111-1-1-11122-2-2-1-1-1-111110000000000000000−3−333−3−3330000
χ25222-22-2-2-2-12-1-111122-2-2-12-2-21-1-22-1-11111-111-1-1-2-2221111-1-1-1-1000000000000000033−3−3−3−3330000
χ26222-22-2-2-2-12-1-111122-2-2-12-2-21-1-22-1-11111-111-1-1-2-2221111-1-1-1-10000000000000000−3−33333−3−30000
χ2722-22-22-2-2222-222-22-222-2-2-2-2-22002-222-2-2-200000000000000000000000000000000000000002-200
χ2822-22-22-2-2222-222-22-222-2-2-2-2-22002-222-2-2-20000000000000000000000000000000000000000-2200
χ2922-2-2-2-222222-2-2-222-2-2-2-2-22222002-2-2-222-20000000000000000000000000000000000000000002-2
χ3022-2-2-2-222222-2-2-222-2-2-2-2-22222002-2-2-222-2000000000000000000000000000000000000000000-22
χ312-222-2-22-222-222-2-2-222-2-2-22-22200-222-22-2-200000000000000000000002i−2i00002i−2i2i−2i000000000000
χ322-222-2-22-222-222-2-2-222-2-2-22-22200-222-22-2-20000000000000000000000−2i2i0000−2i2i−2i2i000000000000
χ332-222-2-22-22-1-222-2-21-1-11-21-112-1001-1-11-11100003−33−333−3−333−3−30000002i−2i−i3i3−i3i3−ii−ii000000000000
χ342-222-2-22-22-1-222-2-21-1-11-21-112-1001-1-11-11100003−33−333−3−333−3−3000000−2i2ii3−i3i3−i3i−ii−i000000000000
χ352-222-2-22-22-1-222-2-21-1-11-21-112-1001-1-11-1110000−33−33−3−333−3−3330000002i−2ii3−i3i3−i3−ii−ii000000000000
χ362-222-2-22-22-1-222-2-21-1-11-21-112-1001-1-11-1110000−33−33−3−333−3−333000000−2i2i−i3i3−i3i3i−ii−i000000000000
χ372-22-2-22-2222-22-222-22-22-2-2-22-2200-22-22-22-2000000000000000000002i−2i002i−2i−2i2i0000000000000000
χ382-22-2-22-2222-22-222-22-22-2-2-22-2200-22-22-22-200000000000000000000−2i2i00−2i2i2i−2i0000000000000000
χ392-22-2-22-222-1-22-2221-11-1-211-1-2-1001-11-11-1100003−3−3333−3−3−3−33300002i−2i00−iii−ii3−i3−i3i3000000000000
χ402-22-2-22-222-1-22-2221-11-1-211-1-2-1001-11-11-1100003−3−3333−3−3−3−3330000−2i2i00i−i−ii−i3i3i3−i3000000000000
χ412-22-2-22-222-1-22-2221-11-1-211-1-2-1001-11-11-110000−333−3−3−33333−3−300002i−2i00−iii−i−i3i3i3−i3000000000000
χ422-22-2-22-222-1-22-2221-11-1-211-1-2-1001-11-11-110000−333−3−3−33333−3−30000−2i2i00i−i−iii3−i3−i3i3000000000000
χ432-2-222-2-2222-2-22-22-2-22-222-22-2200-2-22-2-2220000000000000000002i−2i00000000000000002i−2i2i−2i0000
χ442-2-222-2-2222-2-22-22-2-22-222-22-2200-2-22-2-222000000000000000000−2i2i0000000000000000−2i2i−2i2i0000
χ452-2-222-2-22-1211-11-1-2-22-2-12-221-10011-111-1-1−i3i3−i3i30000−i3i3−i3i3−i3i3−i3i3002i−2i0000000000003−33−3−ii−ii0000
χ462-2-222-2-22-1211-11-1-2-22-2-12-221-10011-111-1-1−i3i3−i3i30000−i3i3−i3i3−i3i3−i3i300−2i2i000000000000−33−33i−ii−i0000
χ472-2-222-2-22-1211-11-1-2-22-2-12-221-10011-111-1-1i3−i3i3−i30000i3−i3i3−i3i3−i3i3−i3002i−2i000000000000−33−33−ii−ii0000
χ482-2-222-2-22-1211-11-1-2-22-2-12-221-10011-111-1-1i3−i3i3−i30000i3−i3i3−i3i3−i3i3−i300−2i2i0000000000003−33−3i−ii−i0000
χ492-2-2-2222-222-2-2-22-2-2-2-22222-22200-2-2-222-2200000000000000002-2000000000000002-2-2200000000
χ502-2-2-2222-222-2-2-22-2-2-2-22222-22200-2-2-222-220000000000000000-2200000000000000-222-200000000
χ512-2-2-2222-2-12111-11-2-2-22-122-2-1-100111-1-11-1−i3i3i3−i30000−i3i3−i3i3i3−i3i3−i32-200000000000000-111-1−i3i3i3−i30000
χ522-2-2-2222-2-12111-11-2-2-22-122-2-1-100111-1-11-1−i3i3i3−i30000−i3i3−i3i3i3−i3i3−i3-22000000000000001-1-11i3−i3−i3i30000
χ532-2-2-2222-2-12111-11-2-2-22-122-2-1-100111-1-11-1i3−i3−i3i30000i3−i3i3−i3−i3i3−i3i32-200000000000000-111-1i3−i3−i3i30000
χ542-2-2-2222-2-12111-11-2-2-22-122-2-1-100111-1-11-1i3−i3−i3i30000i3−i3i3−i3−i3i3−i3i3-22000000000000001-1-11−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
χ57444-44-4-4-4-2-2-2-2222-2-222-2-222214-411-1-1-1-11-2-222-2-2221111-1-1-1-10000000000000000000000000000
χ58444-44-4-4-4-2-2-2-2222-2-222-2-22221-4411-1-1-1-1122-2-222-2-2-1-1-1-111110000000000000000000000000000
χ5944-44-44-4-44-24-444-4-22-2-2-4222-4-200-22-2-222200000000000000000000000000000000000000000000
χ6044-44-44-4-4-24-22-2-224-4442-4-4-42-200-22-2-222200000000000000000000000000000000000000000000
χ6144-44-44-4-4-2-2-22-2-22-22-2-2222221001-111-1-1-1000000003i−3i−3i3i3i−3i−3i3i0000000000000000000000000000
χ6244-44-44-4-4-2-2-22-2-22-22-2-2222221001-111-1-1-100000000−3i3i3i−3i−3i3i3i−3i0000000000000000000000000000
χ6344-4-4-4-4444-24-4-4-44-2222-42-2-24-200-2222-2-2200000000000000000000000000000000000000000000
χ6444-4-4-4-444-24-2222-24-4-4-42-444-2-200-2222-2-2200000000000000000000000000000000000000000000
χ6544-4-4-4-444-2-2-2222-2-222222-2-2-21001-1-1-111-1000000003i−3i−3i3i−3i3i3i−3i0000000000000000000000000000
χ6644-4-4-4-444-2-2-2222-2-222222-2-2-21001-1-1-111-100000000−3i3i3i−3i3i−3i−3i3i0000000000000000000000000000
χ674-444-4-44-4-242-2-222-444-42-44-4-2-2002-2-22-22200000000000000000000000000000000000000000000
χ684-444-4-44-4-2-22-2-2222-2-2222-22-2100-111-11-1-1000023−2323−23−3−333−3−3330000000000000000000000000000
χ694-444-4-44-4-2-22-2-2222-2-2222-22-2100-111-11-1-10000−2323−232333−3−333−3−30000000000000000000000000000
χ704-44-4-44-44-242-22-2-2-44-442-4-442-2002-22-22-2200000000000000000000000000000000000000000000
χ714-44-4-44-44-2-22-22-2-22-22-2222-22100-11-11-11-1000023−23−2323−3−33333−3−30000000000000000000000000000
χ724-44-4-44-44-2-22-22-2-22-22-2222-22100-11-11-11-10000−232323−2333−3−3−3−3330000000000000000000000000000
χ734-4-444-4-444-2-4-44-4422-224-22-2-4-20022-222-2-200000000000000000000000000000000000000000000
χ744-4-444-4-44-2-222-22-222-22-2-22-22100-1-11-1-111−2i32i3−2i32i30000i3−i3i3−i3i3−i3i3−i30000000000000000000000000000
χ754-4-444-4-44-2-222-22-222-22-2-22-22100-1-11-1-1112i3−2i32i3−2i30000−i3i3−i3i3−i3i3−i3i30000000000000000000000000000
χ764-4-4-4444-44-2-4-4-44-4222-24-2-224-200222-2-22-200000000000000000000000000000000000000000000
χ774-4-4-4444-4-2-2222-22222-2-2-2-22-2100-1-1-111-11−2i32i32i3−2i30000i3−i3i3−i3−i3i3−i3i30000000000000000000000000000
χ784-4-4-4444-4-2-2222-22222-2-2-2-22-2100-1-1-111-112i3−2i3−2i32i30000−i3i3−i3i3i3−i3i3−i30000000000000000000000000000

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