Finite Group Databasebeta

← Group #10591315

Character table — Group #10591315

Order 576.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78
size1111111122222222222222224444444444444444444444444412121212121212121212121212121212121212121212121236363636
order1222222233666666666666663446666666121212121212121212121212121212122244444466661212121212121212121212124444
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
χ51111111111111111111111111-1-11111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-111-1-11111-1-1-1-11111-1-1-1-111-1-1
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
χ81111111111111111111111111-1-11111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-111-1-1-1-11111-1-1-1-1111111-1-1
χ9222222222-12222-1-1-1-1-12-122-1-122-1-1-1-1-1-1-12222-1-1-1-1-1-1-1-1-1-1-1-122220000-1-1-1-1-1-1-1-1000000000000
χ10222222222-12222-1-1-1-1-12-122-1-122-1-1-1-1-1-1-12222-1-1-1-1-1-1-1-1-1-1-1-1-2-2-2-2000011111111000000000000
χ11222222222-12222-1-1-1-1-12-122-1-1-2-2-1-1-1-1-1-1-1-2-2-2-211111111111122-2-20000-1-1-1-11111000000000000
χ12222222222-12222-1-1-1-1-12-122-1-1-2-2-1-1-1-1-1-1-1-2-2-2-2111111111111-2-22200001111-1-1-1-1000000000000
χ1322222222-12-1-1-1-122222-12-1-12-122-1-1-1-1-1-1-1-1-1-1-12222-1-1-1-1-1-1-1-10000222200000000-1-1-1-1-1-1-1-10000
χ1422222222-12-1-1-1-122222-12-1-12-122-1-1-1-1-1-1-1-1-1-1-12222-1-1-1-1-1-1-1-10000-2-2-2-200000000111111110000
χ1522222222-12-1-1-1-122222-12-1-12-1-2-2-1-1-1-1-1-1-11111-2-2-2-211111111000022-2-200000000-1-1-1-111110000
χ1622222222-12-1-1-1-122222-12-1-12-1-2-2-1-1-1-1-1-1-11111-2-2-2-2111111110000-2-222000000001111-1-1-1-10000
χ17222-2-2-2-2222222-2222-2-2-2-2-2-2-2200222-2-2-2-20000000000000000002i−2i000000002i2i−2i−2i000000000000
χ18222-2-2-2-2222222-2222-2-2-2-2-2-2-2200222-2-2-2-2000000000000000000−2i2i00000000−2i−2i2i2i000000000000
χ19222-2-2-2-222-1222-2-1-1-111-21-2-21-100-1-1-11111000033−3−33333−3−3−3−3002i−2i0000−i3−i3i3i3−i−iii000000000000
χ20222-2-2-2-222-1222-2-1-1-111-21-2-21-100-1-1-11111000033−3−33333−3−3−3−300−2i2i0000i3i3−i3−i3ii−i−i000000000000
χ21222-2-2-2-222-1222-2-1-1-111-21-2-21-100-1-1-111110000−3−333−3−3−3−33333002i−2i0000i3i3−i3−i3−i−iii000000000000
χ22222-2-2-2-222-1222-2-1-1-111-21-2-21-100-1-1-111110000−3−333−3−3−3−3333300−2i2i0000−i3−i3i3i3ii−i−i000000000000
χ2322-222-2-2-2222-2-2-22-2-22-2222-2-22002-2-22-2-220000000000000000000000000000000000000000002i−2i
χ2422-222-2-2-2222-2-2-22-2-22-2222-2-22002-2-22-2-22000000000000000000000000000000000000000000−2i2i
χ2522-2-2-222-2222-2-222-2-2-22-2-2-2222002-2-2-222-2000000000000000000002i−2i00000000002i2i−2i−2i00000000
χ2622-2-2-222-2222-2-222-2-2-22-2-2-2222002-2-2-222-200000000000000000000−2i2i0000000000−2i−2i2i2i00000000
χ2722-2-2-222-2-12-111-12-2-2-221-21-12-100-1111-1-1133−3−3000033−3−333−3−300002i−2i0000000000−i−iii−i3−i3i3i30000
χ2822-2-2-222-2-12-111-12-2-2-221-21-12-100-1111-1-1133−3−3000033−3−333−3−30000−2i2i0000000000ii−i−ii3i3−i3−i30000
χ2922-2-2-222-2-12-111-12-2-2-221-21-12-100-1111-1-11−3−3330000−3−333−3−33300002i−2i0000000000−i−iiii3i3−i3−i30000
χ3022-2-2-222-2-12-111-12-2-2-221-21-12-100-1111-1-11−3−3330000−3−333−3−3330000−2i2i0000000000ii−i−i−i3−i3i3i30000
χ312-222-22-2-222-22-2-2-22-2-2222-22-2200-22-2-22-2200000000000000000000000000000000000000002i−2i00
χ322-222-22-2-222-22-2-2-22-2-2222-22-2200-22-2-22-220000000000000000000000000000000000000000−2i2i00
χ332-22-22-22-222-22-22-22-22-2-2-22-22200-22-22-22-200000000000000000000002i−2i0000000000002i−2i2i−2i0000
χ342-22-22-22-222-22-22-22-22-2-2-22-22200-22-22-22-20000000000000000000000−2i2i000000000000−2i2i−2i2i0000
χ352-22-22-22-2-121-11-1-22-22-21-2-112-1001-11-11-113−33−300003−33−33−33−30000002i−2i00000000−i3i3−i3i3−ii−ii0000
χ362-22-22-22-2-121-11-1-22-22-21-2-112-1001-11-11-113−33−300003−33−33−33−3000000−2i2i00000000i3−i3i3−i3i−ii−i0000
χ372-22-22-22-2-121-11-1-22-22-21-2-112-1001-11-11-11−33−330000−33−33−33−330000002i−2i00000000i3−i3i3−i3−ii−ii0000
χ382-22-22-22-2-121-11-1-22-22-21-2-112-1001-11-11-11−33−330000−33−33−33−33000000−2i2i00000000−i3i3−i3i3i−ii−i0000
χ392-2-22-2-22222-2-222-2-22-2-222-2-2222-2-2-22-2-2222-2-222-22-22-2-222-2-220000000000000000000000000000
χ402-2-22-2-22222-2-222-2-22-2-222-2-222-22-2-22-2-222-222-2-22-22-222-2-222-20000000000000000000000000000
χ412-2-22-2-2222-1-2-22211-1112-1-2-2-1-12-211-111-1-12-2-22-11-11-111-1-111-100000000−i3i3−i3i3−i3i3−i3i3000000000000
χ422-2-22-2-2222-1-2-22211-1112-1-2-2-1-12-211-111-1-12-2-22-11-11-111-1-111-100000000i3−i3i3−i3i3−i3i3−i3000000000000
χ432-2-22-2-2222-1-2-22211-1112-1-2-2-1-1-2211-111-1-1-222-21-11-11-1-111-1-1100000000−i3i3−i3i3i3−i3i3−i3000000000000
χ442-2-22-2-2222-1-2-22211-1112-1-2-2-1-1-2211-111-1-1-222-21-11-11-1-111-1-1100000000i3−i3i3−i3−i3i3−i3i3000000000000
χ452-2-22-2-222-1211-1-1-2-22-2-2-12112-12-211-111-1-1-111-12-22-2-111-1-111-100000000000000003−3−33−333−30000
χ462-2-22-2-222-1211-1-1-2-22-2-2-12112-12-211-111-1-1-111-12-22-2-111-1-111-10000000000000000−333−33−3−330000
χ472-2-22-2-222-1211-1-1-2-22-2-2-12112-1-2211-111-1-11-1-11-22-221-1-111-1-1100000000000000003−3−333−3−330000
χ482-2-22-2-222-1211-1-1-2-22-2-2-12112-1-2211-111-1-11-1-11-22-221-1-111-1-110000000000000000−333−3−333−30000
χ492-2-2-222-2222-2-22-2-2-2222-2-222-2200-2-2222-2-200000000000000002-20000002-2-220000000000000000
χ502-2-2-222-2222-2-22-2-2-2222-2-222-2200-2-2222-2-20000000000000000-22000000-222-20000000000000000
χ512-2-2-222-222-1-2-22-211-1-1-1-21221-10011-1-1-11100003−3−333−3−33−333−32-2000000-111-13−3−33000000000000
χ522-2-2-222-222-1-2-22-211-1-1-1-21221-10011-1-1-11100003−3−333−3−33−333−3-220000001-1-11−333−3000000000000
χ532-2-2-222-222-1-2-22-211-1-1-1-21221-10011-1-1-1110000−333−3−333−33−3−332-2000000-111-1−333−3000000000000
χ542-2-2-222-222-1-2-22-211-1-1-1-21221-10011-1-1-1110000−333−3−333−33−3−33-220000001-1-113−3−33000000000000
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
χ57444-4-4-4-44-24-2-2-22444-4-42-422-4-200-2-2-2222200000000000000000000000000000000000000000000
χ58444-4-4-4-44-2-2-2-2-22-2-2-22222222100111-1-1-1-100002323−23−23−3−3−3−333330000000000000000000000000000
χ59444-4-4-4-44-2-2-2-2-22-2-2-22222222100111-1-1-1-10000−23−2323233333−3−3−3−30000000000000000000000000000
χ6044-444-4-4-44-24-4-4-4-222-224-24-42-200-222-222-200000000000000000000000000000000000000000000
χ6144-444-4-4-4-24-22224-4-44-4-24-22-4-200-222-222-200000000000000000000000000000000000000000000
χ6244-444-4-4-4-2-2-2222-222-22-2-2-2221001-1-11-1-110000000033-3-3-3-3330000000000000000000000000000
χ6344-444-4-4-4-2-2-2222-222-22-2-2-2221001-1-11-1-1100000000-3-33333-3-30000000000000000000000000000
χ6444-4-4-444-44-24-4-44-2222-2-42-44-2-200-2222-2-2200000000000000000000000000000000000000000000
χ6544-4-4-444-4-2-2-222-2-2222-2222-2-21001-1-1-111-12323−23−230000−3−333−3−3330000000000000000000000000000
χ6644-4-4-444-4-2-2-222-2-2222-2222-2-21001-1-1-111-1−23−232323000033−3−333−3−30000000000000000000000000000
χ674-444-44-4-44-2-44-4-42-222-24-2-442-2002-222-22-200000000000000000000000000000000000000000000
χ684-444-44-4-4-242-222-44-4-44-242-2-4-2002-222-22-200000000000000000000000000000000000000000000
χ694-444-44-4-4-2-22-2222-222-2-2-22-22100-11-1-11-11000000003-33-3-33-330000000000000000000000000000
χ704-444-44-4-4-2-22-2222-222-2-2-22-22100-11-1-11-1100000000-33-333-33-30000000000000000000000000000
χ714-44-44-44-44-2-44-442-22-22-424-4-2-2002-22-22-2200000000000000000000000000000000000000000000
χ724-44-44-44-4-2-22-22-22-22-2222-22-2100-11-11-11-123−2323−230000−33−33−33−330000000000000000000000000000
χ734-44-44-44-4-2-22-22-22-22-2222-22-2100-11-11-11-1−2323−232300003−33−33−33−30000000000000000000000000000
χ744-4-44-4-444-2-222-2-222-222-2-222-214-4-1-11-1-111-222-2-22-221-1-111-1-110000000000000000000000000000
χ754-4-44-4-444-2-222-2-222-222-2-222-21-44-1-11-1-1112-2-222-22-2-111-1-111-10000000000000000000000000000
χ764-4-4-444-44-2422-22-4-44442-4-2-2-4-20022-2-2-22200000000000000000000000000000000000000000000
χ774-4-4-444-44-2-222-2222-2-2-222-2-22100-1-1111-1-1000023−23−2323−333−33−3−330000000000000000000000000000
χ784-4-4-444-44-2-222-2222-2-2-222-2-22100-1-1111-1-10000−232323−233−3−33−333−30000000000000000000000000000

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