Finite Group Databasebeta

← Group #10591304

Character table — Group #10591304

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
χ9222222222-1222222-1-1-1-1-1-1-12-122-1-1-1-1-1-1-1-1-1-1-12222-1-1-1-1-1-1-1-122220000-1-1-1-1-1-1-1-1000000000000
χ10222222222-1222222-1-1-1-1-1-1-12-122-1-1-1-1-1-1-1-1-1-1-12222-1-1-1-1-1-1-1-1-2-2-2-2000011111111000000000000
χ11222222222-1222222-1-1-1-1-1-1-12-1-2-2-1-1-1-1-1-1-11111-2-2-2-21111111122-2-20000-1-1-1-11111000000000000
χ12222222222-1222222-1-1-1-1-1-1-12-1-2-2-1-1-1-1-1-1-11111-2-2-2-211111111-2-22200001111-1-1-1-1000000000000
χ1322222222-12-1-1-1-1-1-12222222-1-122-1-1-1-1-1-1-12222-1-1-1-1-1-1-1-1-1-1-1-10000222200000000-1-1-1-1-1-1-1-10000
χ1422222222-12-1-1-1-1-1-12222222-1-122-1-1-1-1-1-1-12222-1-1-1-1-1-1-1-1-1-1-1-10000-2-2-2-200000000111111110000
χ1522222222-12-1-1-1-1-1-12222222-1-1-2-2-1-1-1-1-1-1-1-2-2-2-2111111111111000022-2-200000000-1-1-1-111110000
χ1622222222-12-1-1-1-1-1-12222222-1-1-2-2-1-1-1-1-1-1-1-2-2-2-21111111111110000-2-222000000001111-1-1-1-10000
χ172222-2-2-2-222222-2-2-2222-2-2-2-2-2200222-2-2-2-200000000000000002-200000022-2-20000000000000000
χ182222-2-2-2-222222-2-2-2222-2-2-2-2-2200222-2-2-2-20000000000000000-22000000-2-2220000000000000000
χ192222-2-2-2-22-1222-2-2-2-1-1-11111-2-100-1-1-1111133−3−300003333−3−3−3−32-2000000-1-11133−3−3000000000000
χ202222-2-2-2-22-1222-2-2-2-1-1-11111-2-100-1-1-1111133−3−300003333−3−3−3−3-2200000011-1-1−3−333000000000000
χ212222-2-2-2-22-1222-2-2-2-1-1-11111-2-100-1-1-11111−3−3330000−3−3−3−333332-2000000-1-111−3−333000000000000
χ222222-2-2-2-22-1222-2-2-2-1-1-11111-2-100-1-1-11111−3−3330000−3−3−3−33333-2200000011-1-133−3−3000000000000
χ2322-2-222-2-2222-2-22-2-22-2-2-2-222222-22-2-22-2-222-22-222-2-222-2-222-2-20000000000000000000000000000
χ2422-2-222-2-2222-2-22-2-22-2-2-2-22222-222-2-22-2-22-22-22-2-222-2-222-2-2220000000000000000000000000000
χ2522-2-222-2-22-12-2-22-2-2-11111-1-12-12-2-111-111-1-11-1122-2-2-1-111-1-11100000000−i3i3−i3i3−i3i3−i3i3000000000000
χ2622-2-222-2-22-12-2-22-2-2-11111-1-12-12-2-111-111-1-11-1122-2-2-1-111-1-11100000000i3−i3i3−i3i3−i3i3−i3000000000000
χ2722-2-222-2-22-12-2-22-2-2-11111-1-12-1-22-111-111-11-11-1-2-22211-1-111-1-100000000−i3i3−i3i3i3−i3i3−i3000000000000
χ2822-2-222-2-22-12-2-22-2-2-11111-1-12-1-22-111-111-11-11-1-2-22211-1-111-1-100000000i3−i3i3−i3−i3i3−i3i3000000000000
χ2922-2-222-2-2-12-111-1112-2-2-2-222-1-12-2-111-111-12-22-2-1-111-1-111-1-1110000000000000000−i3−i3i3i3−i3−i3i3i30000
χ3022-2-222-2-2-12-111-1112-2-2-2-222-1-12-2-111-111-12-22-2-1-111-1-111-1-1110000000000000000i3i3−i3−i3i3i3−i3−i30000
χ3122-2-222-2-2-12-111-1112-2-2-2-222-1-1-22-111-111-1-22-2211-1-111-1-111-1-10000000000000000−i3−i3i3i3i3i3−i3−i30000
χ3222-2-222-2-2-12-111-1112-2-2-2-222-1-1-22-111-111-1-22-2211-1-111-1-111-1-10000000000000000i3i3−i3−i3−i3−i3i3i30000
χ3322-2-2-2-222222-2-2-2222-2-222-2-2-22002-2-2-222-20000000000000000002i−2i000000002i−2i−2i2i000000000000
χ3422-2-2-2-222222-2-2-2222-2-222-2-2-22002-2-2-222-2000000000000000000−2i2i00000000−2i2i2i−2i000000000000
χ3522-2-2-2-2222-12-2-2-222-111-1-111-2-100-1111-1-113−3−33000033−3−3−3−333002i−2i0000−i3i3i3−i3−iii−i000000000000
χ3622-2-2-2-2222-12-2-2-222-111-1-111-2-100-1111-1-113−3−33000033−3−3−3−33300−2i2i0000i3−i3−i3i3i−i−ii000000000000
χ3722-2-2-2-2222-12-2-2-222-111-1-111-2-100-1111-1-11−333−30000−3−33333−3−3002i−2i0000i3−i3−i3i3−iii−i000000000000
χ3822-2-2-2-2222-12-2-2-222-111-1-111-2-100-1111-1-11−333−30000−3−33333−3−300−2i2i0000−i3i3i3−i3i−i−ii000000000000
χ392-22-22-22-222-22-222-2-22-22-2-22-2200-22-222-2-20000000000000000000000000000000000000000002i−2i
χ402-22-22-22-222-22-222-2-22-22-2-22-2200-22-222-2-2000000000000000000000000000000000000000000−2i2i
χ412-22-2-22-2222-22-2-2-22-22-2-222-22200-22-2-2-22200000000000000000000002-20000000000002-22-20000
χ422-22-2-22-2222-22-2-2-22-22-2-222-22200-22-2-2-2220000000000000000000000-22000000000000-22-220000
χ432-22-2-22-22-121-1111-1-22-2-222-2-1-1001-1111-1-10000−i3i3−i3i3−i3i3−i3i3−i3i3−i3i30000002-200000000−i3i3−i3i3-11-110000
χ442-22-2-22-22-121-1111-1-22-2-222-2-1-1001-1111-1-10000−i3i3−i3i3−i3i3−i3i3−i3i3−i3i3000000-2200000000i3−i3i3−i31-11-10000
χ452-22-2-22-22-121-1111-1-22-2-222-2-1-1001-1111-1-10000i3−i3i3−i3i3−i3i3−i3i3−i3i3−i30000002-200000000i3−i3i3−i3-11-110000
χ462-22-2-22-22-121-1111-1-22-2-222-2-1-1001-1111-1-10000i3−i3i3−i3i3−i3i3−i3i3−i3i3−i3000000-2200000000−i3i3−i3i31-11-10000
χ472-2-222-2-2222-2-222-22-2-22-22-22-2200-2-222-22-200000000000000000000000000000000000000002i−2i00
χ482-2-222-2-2222-2-222-22-2-22-22-22-2200-2-222-22-20000000000000000000000000000000000000000−2i2i00
χ492-2-22-222-222-2-22-22-2-2-222-22-22200-2-22-22-22000000000000000000002-200000000002-2-2200000000
χ502-2-22-222-222-2-22-22-2-2-222-22-22200-2-22-22-2200000000000000000000-220000000000-222-200000000
χ512-2-22-222-2-1211-11-11-2-222-22-2-1-10011-11-11-10000−i3i3i3−i3−i3i3i3−i3−i3i3i3−i300002-20000000000-111-1−i3i3i3−i30000
χ522-2-22-222-2-1211-11-11-2-222-22-2-1-10011-11-11-10000−i3i3i3−i3−i3i3i3−i3−i3i3i3−i30000-2200000000001-1-11i3−i3−i3i30000
χ532-2-22-222-2-1211-11-11-2-222-22-2-1-10011-11-11-10000i3−i3−i3i3i3−i3−i3i3i3−i3−i3i300002-20000000000-111-1i3−i3−i3i30000
χ542-2-22-222-2-1211-11-11-2-222-22-2-1-10011-11-11-10000i3−i3−i3i3i3−i3−i3i3i3−i3−i3i30000-2200000000001-1-11−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
χ574444-4-4-4-4-24-2-2-2222444-4-4-4-42-200-2-2-2222200000000000000000000000000000000000000000000
χ584444-4-4-4-4-2-2-2-2-2222-2-2-222222100111-1-1-1-12323−23−230000−3−3−3−333330000000000000000000000000000
χ594444-4-4-4-4-2-2-2-2-2222-2-2-222222100111-1-1-1-1−23−23232300003333−3−3−3−30000000000000000000000000000
χ6044-4-444-4-4-2-2-222-222-22222-2-2-214-41-1-11-1-11-22-22-2-22211-1-111-1-10000000000000000000000000000
χ6144-4-444-4-4-2-2-222-222-22222-2-2-21-441-1-11-1-112-22-222-2-2-1-111-1-1110000000000000000000000000000
χ6244-4-4-4-444-24-2222-2-24-4-444-4-42-200-2222-2-2200000000000000000000000000000000000000000000
χ6344-4-4-4-444-2-2-2222-2-2-222-2-22221001-1-1-111-123−23−23230000−3−33333−3−30000000000000000000000000000
χ6444-4-4-4-444-2-2-2222-2-2-222-2-22221001-1-1-111-1−232323−23000033−3−3−3−3330000000000000000000000000000
χ654-44-44-44-44-2-44-444-42-22-222-2-4-2002-22-2-22200000000000000000000000000000000000000000000
χ664-44-44-44-4-242-22-2-22-44-44-4-442-2002-22-2-22200000000000000000000000000000000000000000000
χ674-44-44-44-4-2-22-22-2-222-22-222-22100-11-111-1-1000000003i−3i3i−3i−3i3i−3i3i0000000000000000000000000000
χ684-44-44-44-4-2-22-22-2-222-22-222-22100-11-111-1-100000000−3i3i−3i3i3i−3i3i−3i0000000000000000000000000000
χ694-44-4-44-444-2-44-4-4-442-222-2-224-2002-2222-2-200000000000000000000000000000000000000000000
χ704-44-4-44-44-2-22-2222-22-222-2-22-2100-11-1-1-1110000−2i32i3−2i32i3i3−i3i3−i3i3−i3i3−i30000000000000000000000000000
χ714-44-4-44-44-2-22-2222-22-222-2-22-2100-11-1-1-11100002i3−2i32i3−2i3−i3i3−i3i3−i3i3−i3i30000000000000000000000000000
χ724-4-444-4-444-2-4-444-4422-22-22-2-4-20022-2-22-2200000000000000000000000000000000000000000000
χ734-4-444-4-44-2422-2-22-2-4-44-44-442-20022-2-22-2200000000000000000000000000000000000000000000
χ744-4-444-4-44-2-222-2-22-222-22-22-22100-1-111-11-1000000003i−3i−3i3i−3i3i3i−3i0000000000000000000000000000
χ754-4-444-4-44-2-222-2-22-222-22-22-22100-1-111-11-100000000−3i3i3i−3i3i−3i−3i3i0000000000000000000000000000
χ764-4-44-444-44-2-4-44-44-422-2-22-224-20022-22-22-200000000000000000000000000000000000000000000
χ774-4-44-444-4-2-222-22-2222-2-22-22-2100-1-11-11-110000−2i32i32i3−2i3i3−i3−i3i3i3−i3−i3i30000000000000000000000000000
χ784-4-44-444-4-2-222-22-2222-2-22-22-2100-1-11-11-1100002i3−2i3−2i32i3−i3i3i3−i3−i3i3i3−i30000000000000000000000000000

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