Finite Group Databasebeta

← Group #10591308

Character table — Group #10591308

Order 576.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78
size1111111122222222222222224444444444444444444444444412121212121212121212121212121212121212121212121236363636
order1222222233666666666666663446666666121212121212121212121212121212122244444466661212121212121212121212124444
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111111111111111-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-1-1-1
χ311111111111111111111111111111111111111111111111111-1-11111-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1
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
χ61111111111111111111111111-1-11111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-111-1-11111-1-1-1-1-1-1-1-11111-1-111
χ71111111111111111111111111-1-11111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-111-1-1-1-111111111-1-1-1-1-1-111
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
χ9222222222-122222-1-1-1-1-12-1-12-122-1-1-1-1-1-1-12222-1-1-1-1-1-1-1-1-1-1-1-122000022-1-1-1-1-1-1-1-1000000000000
χ10222222222-122222-1-1-1-1-12-1-12-122-1-1-1-1-1-1-12222-1-1-1-1-1-1-1-1-1-1-1-1-2-20000-2-211111111000000000000
χ11222222222-122222-1-1-1-1-12-1-12-1-2-2-1-1-1-1-1-1-1-2-2-2-2111111111111220000-2-2-1-1-1-11111000000000000
χ12222222222-122222-1-1-1-1-12-1-12-1-2-2-1-1-1-1-1-1-1-2-2-2-2111111111111-2-20000221111-1-1-1-1000000000000
χ1322222222-12-1-1-1-1-122222-122-1-122-1-1-1-1-1-1-1-1-1-1-12222-1-1-1-1-1-1-1-10022220000000000-1-1-1-1-1-1-1-10000
χ1422222222-12-1-1-1-1-122222-122-1-122-1-1-1-1-1-1-1-1-1-1-12222-1-1-1-1-1-1-1-100-2-2-2-20000000000111111110000
χ1522222222-12-1-1-1-1-122222-122-1-1-2-2-1-1-1-1-1-1-11111-2-2-2-2111111110022-2-20000000000-1-1-1-111110000
χ1622222222-12-1-1-1-1-122222-122-1-1-2-2-1-1-1-1-1-1-11111-2-2-2-21111111100-2-22200000000001111-1-1-1-10000
χ172222-2-2-2-222222-2-2222-2-2-2-2-2-2200222-2-2-2-200000000000000002-200000022-2-20000000000000000
χ182222-2-2-2-222222-2-2222-2-2-2-2-2-2200222-2-2-2-20000000000000000-22000000-2-2220000000000000000
χ192222-2-2-2-22-1222-2-2-1-1-111-211-2-100-1-1-11111000033−3−33333−3−3−3−32-2000000-1-11133−3−3000000000000
χ202222-2-2-2-22-1222-2-2-1-1-111-211-2-100-1-1-11111000033−3−33333−3−3−3−3-2200000011-1-1−3−333000000000000
χ212222-2-2-2-22-1222-2-2-1-1-111-211-2-100-1-1-111110000−3−333−3−3−3−333332-2000000-1-111−3−333000000000000
χ222222-2-2-2-22-1222-2-2-1-1-111-211-2-100-1-1-111110000−3−333−3−3−3−33333-2200000011-1-133−3−3000000000000
χ2322-2-222-2-2222-2-22-22-2-222-2-2-222002-2-222-2-200000000000000000000002i−2i00002i−2i2i−2i000000000000
χ2422-2-222-2-2222-2-22-22-2-222-2-2-222002-2-222-2-20000000000000000000000−2i2i0000−2i2i−2i2i000000000000
χ2522-2-222-2-22-12-2-22-2-111-1-1-2112-100-111-1-11100003−33−333−3−333−3−30000002i−2i−i3i3−i3i3−ii−ii000000000000
χ2622-2-222-2-22-12-2-22-2-111-1-1-2112-100-111-1-11100003−33−333−3−333−3−3000000−2i2ii3−i3i3−i3i−ii−i000000000000
χ2722-2-222-2-22-12-2-22-2-111-1-1-2112-100-111-1-1110000−33−33−3−333−3−3330000002i−2ii3−i3i3−i3−ii−ii000000000000
χ2822-2-222-2-22-12-2-22-2-111-1-1-2112-100-111-1-1110000−33−33−3−333−3−333000000−2i2i−i3i3−i3i3i−ii−i000000000000
χ2922-2-2-2-222222-2-2-222-2-2-2-2222-222-22-2-2-2-22222-2-22-2-2222-2-2-2-2220000000000000000000000000000
χ3022-2-2-2-222222-2-2-222-2-2-2-2222-22-222-2-2-2-222-2-222-222-2-2-22222-2-20000000000000000000000000000
χ3122-2-2-2-2222-12-2-2-22-111112-1-1-2-12-2-11111-1-122-2-2-111-1-1-11111-1-100000000−i3i3i3−i3−i3i3i3−i3000000000000
χ3222-2-2-2-2222-12-2-2-22-111112-1-1-2-12-2-11111-1-122-2-2-111-1-1-11111-1-100000000i3−i3−i3i3i3−i3−i3i3000000000000
χ3322-2-2-2-2222-12-2-2-22-111112-1-1-2-1-22-11111-1-1-2-2221-1-1111-1-1-1-11100000000−i3i3i3−i3i3−i3−i3i3000000000000
χ3422-2-2-2-2222-12-2-2-22-111112-1-1-2-1-22-11111-1-1-2-2221-1-1111-1-1-1-11100000000i3−i3−i3i3−i3i3i3−i3000000000000
χ3522-2-2-2-222-12-1111-12-2-2-2-2-1221-12-2-11111-1-1-1-1112-2-22-1-11111-1-1000000000000000033−3−333−3−30000
χ3622-2-2-2-222-12-1111-12-2-2-2-2-1221-12-2-11111-1-1-1-1112-2-22-1-11111-1-10000000000000000−3−333−3−3330000
χ3722-2-2-2-222-12-1111-12-2-2-2-2-1221-1-22-11111-1-111-1-1-222-211-1-1-1-111000000000000000033−3−3−3−3330000
χ3822-2-2-2-222-12-1111-12-2-2-2-2-1221-1-22-11111-1-111-1-1-222-211-1-1-1-1110000000000000000−3−33333−3−30000
χ392-22-22-22-222-22-22-2-22-22-222-2-2200-22-22-2-22000000000000000000002i−2i000000000000002i−2i2i−2i0000
χ402-22-22-22-222-22-22-2-22-22-222-2-2200-22-22-2-2200000000000000000000−2i2i00000000000000−2i2i−2i2i0000
χ412-22-22-22-2-121-11-11-22-22-2-12-21-1001-11-111-1−i3i3−i3i30000−i3i3−i3i3−i3i3−i3i300002i−2i00000000003−33−3−ii−ii0000
χ422-22-22-22-2-121-11-11-22-22-2-12-21-1001-11-111-1−i3i3−i3i30000−i3i3−i3i3−i3i3−i3i30000−2i2i0000000000−33−33i−ii−i0000
χ432-22-22-22-2-121-11-11-22-22-2-12-21-1001-11-111-1i3−i3i3−i30000i3−i3i3−i3i3−i3i3−i300002i−2i0000000000−33−33−ii−ii0000
χ442-22-22-22-2-121-11-11-22-22-2-12-21-1001-11-111-1i3−i3i3−i30000i3−i3i3−i3i3−i3i3−i30000−2i2i00000000003−33−3i−ii−i0000
χ452-22-2-22-2222-22-2-22-22-2-22-2-222200-22-2-222-20000000000000000000000000000000000000000002-2
χ462-22-2-22-2222-22-2-22-22-2-22-2-222200-22-2-222-2000000000000000000000000000000000000000000-22
χ472-2-222-2-2222-2-2222-2-222-2-2-22-2200-2-222-22-200000000000000000000000000000000000000002i−2i00
χ482-2-222-2-2222-2-2222-2-222-2-2-22-2200-2-222-22-20000000000000000000000000000000000000000−2i2i00
χ492-2-22-222-222-2-22-2-2-2-22-2222-22200-2-22-22-220000000000000000002-20000000000002-2-2200000000
χ502-2-22-222-222-2-22-2-2-2-22-2222-22200-2-22-22-22000000000000000000-22000000000000-222-200000000
χ512-2-22-222-2-1211-111-2-22-22-12-2-1-10011-11-11-1−i3i3i3−i30000−i3i3i3−i3i3−i3−i3i3002-2000000000000-111-1−i3i3i3−i30000
χ522-2-22-222-2-1211-111-2-22-22-12-2-1-10011-11-11-1−i3i3i3−i30000−i3i3i3−i3i3−i3−i3i300-220000000000001-1-11i3−i3−i3i30000
χ532-2-22-222-2-1211-111-2-22-22-12-2-1-10011-11-11-1i3−i3−i3i30000i3−i3−i3i3−i3i3i3−i3002-2000000000000-111-1i3−i3−i3i30000
χ542-2-22-222-2-1211-111-2-22-22-12-2-1-10011-11-11-1i3−i3−i3i30000i3−i3−i3i3−i3i3i3−i300-220000000000001-1-11−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
χ574444-4-4-4-4-24-2-2-222444-4-42-4-42-200-2-2-2222200000000000000000000000000000000000000000000
χ584444-4-4-4-4-2-2-2-2-222-2-2-2222222100111-1-1-1-100002323−23−23−3−3−3−333330000000000000000000000000000
χ594444-4-4-4-4-2-2-2-2-222-2-2-2222222100111-1-1-1-10000−23−2323233333−3−3−3−30000000000000000000000000000
χ6044-4-444-4-4-24-222-224-4-4442-4-4-2-200-222-2-22200000000000000000000000000000000000000000000
χ6144-4-444-4-4-2-2-222-22-222-2-2222-21001-1-111-1-1000023−2323−23−3−333−3−3330000000000000000000000000000
χ6244-4-444-4-4-2-2-222-22-222-2-2222-21001-1-111-1-10000−2323−232333−3−333−3−30000000000000000000000000000
χ6344-4-4-4-444-2-2-2222-2-22222-2-2-2214-41-1-1-1-111-2-222-222-211-1-1-1-1110000000000000000000000000000
χ6444-4-4-4-444-2-2-2222-2-22222-2-2-221-441-1-1-1-11122-2-22-2-22-1-11111-1-10000000000000000000000000000
χ654-44-44-44-44-2-44-44-42-22-224-22-4-2002-22-222-200000000000000000000000000000000000000000000
χ664-44-44-44-4-2-22-22-222-22-22-2-222100-11-11-1-11−2i32i3−2i32i30000i3−i3i3−i3i3−i3i3−i30000000000000000000000000000
χ674-44-44-44-4-2-22-22-222-22-22-2-222100-11-11-1-112i3−2i32i3−2i30000−i3i3−i3i3−i3i3−i3i30000000000000000000000000000
χ684-44-4-44-444-2-44-4-442-222-2-42-24-2002-222-2-2200000000000000000000000000000000000000000000
χ694-44-4-44-44-242-222-2-44-4-442-44-2-2002-222-2-2200000000000000000000000000000000000000000000
χ704-44-4-44-44-2-22-222-22-222-222-2-2100-11-1-111-1000000003i−3i3i−3i−3i3i−3i3i0000000000000000000000000000
χ714-44-4-44-44-2-22-222-22-222-222-2-2100-11-1-111-100000000−3i3i−3i3i3i−3i3i−3i0000000000000000000000000000
χ724-4-444-4-444-2-4-444422-2-22-42-2-4-20022-2-22-2200000000000000000000000000000000000000000000
χ734-4-444-4-44-2422-2-2-2-4-444-42-442-20022-2-22-2200000000000000000000000000000000000000000000
χ744-4-444-4-44-2-222-2-2-222-2-2222-22100-1-111-11-1000000003i−3i−3i3i3i−3i−3i3i0000000000000000000000000000
χ754-4-444-4-44-2-222-2-2-222-2-2222-22100-1-111-11-100000000−3i3i3i−3i−3i3i3i−3i0000000000000000000000000000
χ764-4-44-444-44-2-4-44-4-422-22-24-224-20022-22-22-200000000000000000000000000000000000000000000
χ774-4-44-444-4-2-222-22222-22-2-2-22-2100-1-11-11-11−2i32i32i3−2i30000i3−i3−i3i3−i3i3i3−i30000000000000000000000000000
χ784-4-44-444-4-2-222-22222-22-2-2-22-2100-1-11-11-112i3−2i3−2i32i30000−i3i3i3−i3i3−i3−i3i30000000000000000000000000000

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