Finite Group Databasebeta

← Group #10591297

Character table — Group #10591297

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
χ51111111111111111111111111-1-11111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-111-1-11111-1-1-1-11111-1-1-1-1-1-111
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
χ81111111111111111111111111-1-11111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-111-1-1-1-11111-1-1-1-11111-1-111
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
χ17222-2-2-2-222222-2-2222-2-2-2-22-2-222i−2i222-2-2-2-22i2i−2i−2i2i2i−2i−2i2i2i2i2i−2i−2i−2i−2i0000000000000000000000000000
χ18222-2-2-2-222222-2-2222-2-2-2-22-2-22−2i2i222-2-2-2-2−2i−2i2i2i−2i−2i2i2i−2i−2i−2i−2i2i2i2i2i0000000000000000000000000000
χ19222-2-2-2-222-122-2-2-1-1-111-212-21-12i−2i-1-1-111112i2i−2i−2i−i−iii−i−i−i−iiiii00000000−i3−i3i3i333−3−3000000000000
χ20222-2-2-2-222-122-2-2-1-1-111-212-21-12i−2i-1-1-111112i2i−2i−2i−i−iii−i−i−i−iiiii00000000i3i3−i3−i3−3−333000000000000
χ21222-2-2-2-222-122-2-2-1-1-111-212-21-1−2i2i-1-1-11111−2i−2i2i2iii−i−iiiii−i−i−i−i00000000−i3−i3i3i3−3−333000000000000
χ22222-2-2-2-222-122-2-2-1-1-111-212-21-1−2i2i-1-1-11111−2i−2i2i2iii−i−iiiii−i−i−i−i00000000i3i3−i3−i333−3−3000000000000
χ23222-2-2-2-22-12-1-111222-2-21-2-11-2-12i−2i-1-1-11111−i−iii2i2i−2i−2i−i−i−i−iiiii000000000000000033−3−3−i3−i3i3i30000
χ24222-2-2-2-22-12-1-111222-2-21-2-11-2-12i−2i-1-1-11111−i−iii2i2i−2i−2i−i−i−i−iiiii0000000000000000−3−333i3i3−i3−i30000
χ25222-2-2-2-22-12-1-111222-2-21-2-11-2-1−2i2i-1-1-11111ii−i−i−2i−2i2i2iiiii−i−i−i−i000000000000000033−3−3i3i3−i3−i30000
χ26222-2-2-2-22-12-1-111222-2-21-2-11-2-1−2i2i-1-1-11111ii−i−i−2i−2i2i2iiiii−i−i−i−i0000000000000000−3−333−i3−i3i3i30000
χ2722-222-2-2-2222-2-2-22-2-22-222-22-22002-2-22-2-2200000000000000000000000000000000000000002i−2i00
χ2822-222-2-2-2222-2-2-22-2-22-222-22-22002-2-22-2-220000000000000000000000000000000000000000−2i2i00
χ2922-2-2-222-2222-2222-2-2-22-2-2-2-222002-2-2-222-20000000000000000000000000000000000000000002i−2i
χ3022-2-2-222-2222-2222-2-2-22-2-2-2-222002-2-2-222-2000000000000000000000000000000000000000000−2i2i
χ312-222-2-22-222-222-2-22-2-2222-2-2-2200-22-2-22-22000000000000000000002i−2i00000000002i−2i2i−2i00000000
χ322-222-2-22-222-222-2-22-2-2222-2-2-2200-22-2-22-2200000000000000000000−2i2i0000000000−2i2i−2i2i00000000
χ332-222-2-22-2-121-1-11-22-2-22-1211-2-1001-111-11-1−i3i3−i3i30000−i3−i3i3i3−i3−i3i3i300002i−2i0000000000−ii−ii3−33−30000
χ342-222-2-22-2-121-1-11-22-2-22-1211-2-1001-111-11-1−i3i3−i3i30000−i3−i3i3i3−i3−i3i3i30000−2i2i0000000000i−ii−i−33−330000
χ352-222-2-22-2-121-1-11-22-2-22-1211-2-1001-111-11-1i3−i3i3−i30000i3i3−i3−i3i3i3−i3−i300002i−2i0000000000−ii−ii−33−330000
χ362-222-2-22-2-121-1-11-22-2-22-1211-2-1001-111-11-1i3−i3i3−i30000i3i3−i3−i3i3i3−i3−i30000−2i2i0000000000i−ii−i3−33−30000
χ372-22-222-2-222-22-22-22-22-2-2-2-222200-22-22-22-200000000000000000000002i−2i0000000000002i−2i−2i2i0000
χ382-22-222-2-222-22-22-22-22-2-2-2-222200-22-22-22-20000000000000000000000−2i2i000000000000−2i2i2i−2i0000
χ392-22-222-2-2-121-11-1-22-22-21-21-12-1001-11-11-113−3−33000033−3−3−3−3330000002i−2i00000000i3−i3−i3i3−iii−i0000
χ402-22-222-2-2-121-11-1-22-22-21-21-12-1001-11-11-113−3−33000033−3−3−3−333000000−2i2i00000000−i3i3i3−i3i−i−ii0000
χ412-22-222-2-2-121-11-1-22-22-21-21-12-1001-11-11-11−333−30000−3−33333−3−30000002i−2i00000000−i3i3i3−i3−iii−i0000
χ422-22-222-2-2-121-11-1-22-22-21-21-12-1001-11-11-11−333−30000−3−33333−3−3000000−2i2i00000000i3−i3−i3i3i−i−ii0000
χ432-2-22-22-2222-2-2-22-2-22-2-2222-22200-2-22-2-2220000000000000000002-2000000002-22-2000000000000
χ442-2-22-22-2222-2-2-22-2-22-2-2222-22200-2-22-2-222000000000000000000-2200000000-22-22000000000000
χ452-2-22-22-222-1-2-2-2211-1112-12-2-1-10011-111-1-10000−i3i3−i3i3−i3i3−i3i3−i3i3−i3i3002-20000−i3i3−i3i3-11-11000000000000
χ462-2-22-22-222-1-2-2-2211-1112-12-2-1-10011-111-1-10000−i3i3−i3i3−i3i3−i3i3−i3i3−i3i300-220000i3−i3i3−i31-11-1000000000000
χ472-2-22-22-222-1-2-2-2211-1112-12-2-1-10011-111-1-10000i3−i3i3−i3i3−i3i3−i3i3−i3i3−i3002-20000i3−i3i3−i3-11-11000000000000
χ482-2-22-22-222-1-2-2-2211-1112-12-2-1-10011-111-1-10000i3−i3i3−i3i3−i3i3−i3i3−i3i3−i300-220000−i3i3−i3i31-11-1000000000000
χ492-2-2-22-22222-2-22-2-2-2222-2-222-2200-2-2222-2-200000000000000002-20000002-2-220000000000000000
χ502-2-2-22-22222-2-22-2-2-2222-2-222-2200-2-2222-2-20000000000000000-22000000-222-20000000000000000
χ512-2-2-22-2222-1-2-22-211-1-1-1-21221-10011-1-1-11100003−3−333−33−3−33−332-2000000-111-13−3−33000000000000
χ522-2-2-22-2222-1-2-22-211-1-1-1-21221-10011-1-1-11100003−3−333−33−3−33−33-220000001-1-11−333−3000000000000
χ532-2-2-22-2222-1-2-22-211-1-1-1-21221-10011-1-1-1110000−333−3−33−333−33−32-2000000-111-1−333−3000000000000
χ542-2-2-22-2222-1-2-22-211-1-1-1-21221-10011-1-1-1110000−333−3−33−333−33−3-220000001-1-113−3−33000000000000
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
χ57444-4-4-4-44-2-2-2-222-2-2-22222-22214i−4i111-1-1-1-1−2i−2i2i2i−2i−2i2i2iiiii−i−i−i−i0000000000000000000000000000
χ58444-4-4-4-44-2-2-2-222-2-2-22222-2221−4i4i111-1-1-1-12i2i−2i−2i2i2i−2i−2i−i−i−i−iiiii0000000000000000000000000000
χ5944-444-4-4-44-24-4-4-4-222-224-2-442-200-222-222-200000000000000000000000000000000000000000000
χ6044-444-4-4-4-24-22224-4-44-4-242-2-4-200-222-222-200000000000000000000000000000000000000000000
χ6144-444-4-4-4-2-2-2222-222-22-2-22-221001-1-11-1-11000000003-3-333-3-330000000000000000000000000000
χ6244-444-4-4-4-2-2-2222-222-22-2-22-221001-1-11-1-1100000000-333-3-333-30000000000000000000000000000
χ6344-4-4-444-44-24-444-2222-2-42-4-4-2-200-2222-2-2200000000000000000000000000000000000000000000
χ6444-4-4-444-4-24-22-2-24-4-4-442-4224-200-2222-2-2200000000000000000000000000000000000000000000
χ6544-4-4-444-4-2-2-22-2-2-2222-22222-21001-1-1-111-1000000003i−3i−3i3i−3i3i3i−3i0000000000000000000000000000
χ6644-4-4-444-4-2-2-22-2-2-2222-22222-21001-1-1-111-100000000−3i3i3i−3i3i−3i−3i3i0000000000000000000000000000
χ674-444-4-44-44-2-444-42-222-24-2-4-42-2002-222-22-200000000000000000000000000000000000000000000
χ684-444-4-44-4-2-22-2-222-222-2-2-2222100-11-1-11-11−2i32i3−2i32i30000i3i3−i3−i3i3i3−i3−i30000000000000000000000000000
χ694-444-4-44-4-2-22-2-222-222-2-2-2222100-11-1-11-112i3−2i32i3−2i30000−i3−i3i3i3−i3−i3i3i30000000000000000000000000000
χ704-44-444-4-44-2-44-442-22-22-42-44-2-2002-22-22-2200000000000000000000000000000000000000000000
χ714-44-444-4-4-2-22-22-22-22-22222-2-2100-11-11-11-123−23−23230000−3−33333−3−30000000000000000000000000000
χ724-44-444-4-4-2-22-22-22-22-22222-2-2100-11-11-11-1−232323−23000033−3−3−3−3330000000000000000000000000000
χ734-4-44-44-44-24222-2-4-44-4-4-24-224-20022-222-2-200000000000000000000000000000000000000000000
χ744-4-44-44-44-2-2222-222-222-2-2-22-2100-1-11-1-1110000−2i32i3−2i32i3i3−i3i3−i3i3−i3i3−i30000000000000000000000000000
χ754-4-44-44-44-2-2222-222-222-2-2-22-2100-1-11-1-11100002i3−2i32i3−2i3−i3i3−i3i3−i3i3−i3i30000000000000000000000000000
χ764-4-4-44-444-2422-22-4-44442-4-2-2-4-20022-2-2-22200000000000000000000000000000000000000000000
χ774-4-4-44-444-2-222-2222-2-2-222-2-22100-1-1111-1-1000023−23−2323−33−333−33−30000000000000000000000000000
χ784-4-4-44-444-2-222-2222-2-2-222-2-22100-1-1111-1-10000−232323−233−33−3−33−330000000000000000000000000000

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