Finite Group Databasebeta

← Group #10591299

Character table — Group #10591299

Order 576.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78
size1111111122222222222222224444444444444444444444444412121212121212121212121212121212121212121212121236363636
order1222222233666666666666663446666666121212121212121212121212121212122244444466661212121212121212121212124444
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111111111111111-1-111-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1
χ311111111111111111111111111111111111111111111111111-1-111-1-111-1-1-1-1-1-1-1-111111111-1-1-1-1
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
χ61111111111111111111111111-1-11111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-1111111-1-1-1-1-1-1-1-11111-1-111
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
χ81111111111111111111111111-1-11111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1-1-1111111-1-1
χ9222222222-12222-1-1-1-1-12-122-1-122-1-1-1-1-1-1-12222-1-1-1-1-1-1-1-1-1-1-1-122002200-1-1-1-1-1-1-1-1000000000000
χ10222222222-12222-1-1-1-1-12-122-1-122-1-1-1-1-1-1-12222-1-1-1-1-1-1-1-1-1-1-1-1-2-200-2-20011111111000000000000
χ11222222222-12222-1-1-1-1-12-122-1-1-2-2-1-1-1-1-1-1-1-2-2-2-21111111111112200-2-200-1-1-1-11111000000000000
χ12222222222-12222-1-1-1-1-12-122-1-1-2-2-1-1-1-1-1-1-1-2-2-2-2111111111111-2-20022001111-1-1-1-1000000000000
χ1322222222-12-1-1-1-122222-12-1-12-122-1-1-1-1-1-1-1-1-1-1-12222-1-1-1-1-1-1-1-10022002200000000-1-1-1-1-1-1-1-10000
χ1422222222-12-1-1-1-122222-12-1-12-122-1-1-1-1-1-1-1-1-1-1-12222-1-1-1-1-1-1-1-100-2-200-2-200000000111111110000
χ1522222222-12-1-1-1-122222-12-1-12-1-2-2-1-1-1-1-1-1-11111-2-2-2-211111111002200-2-200000000-1-1-1-111110000
χ1622222222-12-1-1-1-122222-12-1-12-1-2-2-1-1-1-1-1-1-11111-2-2-2-21111111100-2-20022000000001111-1-1-1-10000
χ17222-2-22-2-22222-2-222-2-2-2-2-22-22200222-2-2-2-20000000000000000002i−2i0000000000002i2i−2i−2i00000000
χ18222-2-22-2-22222-2-222-2-2-2-2-22-22200222-2-2-2-2000000000000000000−2i2i000000000000−2i−2i2i2i00000000
χ19222-2-22-2-2-12-1-11122-2-2-21-2-112-100-1-1-1111133−3−300003333−3−3−3−3002i−2i000000000000−i−iii−i3−i3i3i30000
χ20222-2-22-2-2-12-1-11122-2-2-21-2-112-100-1-1-1111133−3−300003333−3−3−3−300−2i2i000000000000ii−i−ii3i3−i3−i30000
χ21222-2-22-2-2-12-1-11122-2-2-21-2-112-100-1-1-11111−3−3330000−3−3−3−33333002i−2i000000000000−i−iiii3i3−i3−i30000
χ22222-2-22-2-2-12-1-11122-2-2-21-2-112-100-1-1-11111−3−3330000−3−3−3−3333300−2i2i000000000000ii−i−i−i3−i3i3i30000
χ2322-222-2-2-2222-2-2-22-22-2-222-22-22002-2-22-2-220000000000000000000000000000000000000000002i−2i
χ2422-222-2-2-2222-2-2-22-22-2-222-22-22002-2-22-2-22000000000000000000000000000000000000000000−2i2i
χ2522-2-2-2-222222-2222-2-222-2-2-2-2-22002-2-2-222-2000000000000000000002i−2i0000002i2i−2i−2i000000000000
χ2622-2-2-2-222222-2222-2-222-2-2-2-2-22002-2-2-222-200000000000000000000−2i2i000000−2i−2i2i2i000000000000
χ2722-2-2-2-2222-12-222-111-1-1-21-2-21-100-1111-1-11000033−3−333−3−333−3−300002i−2i00−i3−i3i3i3−i−iii000000000000
χ2822-2-2-2-2222-12-222-111-1-1-21-2-21-100-1111-1-11000033−3−333−3−333−3−30000−2i2i00i3i3−i3−i3ii−i−i000000000000
χ2922-2-2-2-2222-12-222-111-1-1-21-2-21-100-1111-1-110000−3−333−3−333−3−33300002i−2i00i3i3−i3−i3−i−iii000000000000
χ3022-2-2-2-2222-12-222-111-1-1-21-2-21-100-1111-1-110000−3−333−3−333−3−3330000−2i2i00−i3−i3i3i3ii−i−i000000000000
χ312-222-2-22-222-222-2-22-22-222-2-2-2200-22-2-22-2200000000000000000000002i−2i0000000000002i−2i2i−2i0000
χ322-222-2-22-222-222-2-22-22-222-2-2-2200-22-2-22-220000000000000000000000−2i2i000000000000−2i2i−2i2i0000
χ332-222-2-22-2-121-1-11-22-22-2-1211-2-1001-111-11-1−i3i3−i3i30000−i3i3−i3i3−i3i3−i3i30000002i−2i000000003−33−3−ii−ii0000
χ342-222-2-22-2-121-1-11-22-22-2-1211-2-1001-111-11-1−i3i3−i3i30000−i3i3−i3i3−i3i3−i3i3000000−2i2i00000000−33−33i−ii−i0000
χ352-222-2-22-2-121-1-11-22-22-2-1211-2-1001-111-11-1i3−i3i3−i30000i3−i3i3−i3i3−i3i3−i30000002i−2i00000000−33−33−ii−ii0000
χ362-222-2-22-2-121-1-11-22-22-2-1211-2-1001-111-11-1i3−i3i3−i30000i3−i3i3−i3i3−i3i3−i3000000−2i2i000000003−33−3i−ii−i0000
χ372-22-22-2-2222-22-22-222-22-2-2-22-222i−2i-22-22-22-22i−2i−2i2i2i−2i2i−2i2i−2i2i−2i−2i2i−2i2i0000000000000000000000000000
χ382-22-22-2-2222-22-22-222-22-2-2-22-22−2i2i-22-22-22-2−2i2i2i−2i−2i2i−2i2i−2i2i−2i2i2i−2i2i−2i0000000000000000000000000000
χ392-22-22-2-222-1-22-221-1-11-1-21-221-12i−2i1-11-11-112i−2i−2i2i−ii−ii−ii−iii−ii−i00000000−i3i3−i3i33−33−3000000000000
χ402-22-22-2-222-1-22-221-1-11-1-21-221-12i−2i1-11-11-112i−2i−2i2i−ii−ii−ii−iii−ii−i00000000i3−i3i3−i3−33−33000000000000
χ412-22-22-2-222-1-22-221-1-11-1-21-221-1−2i2i1-11-11-11−2i2i2i−2ii−ii−ii−ii−i−ii−ii00000000−i3i3−i3i3−33−33000000000000
χ422-22-22-2-222-1-22-221-1-11-1-21-221-1−2i2i1-11-11-11−2i2i2i−2ii−ii−ii−ii−i−ii−ii00000000i3−i3i3−i33−33−3000000000000
χ432-22-22-2-22-121-11-1-222-221-21-1-2-12i−2i1-11-11-11−iii−i2i−2i2i−2i−ii−iii−ii−i0000000000000000−i3i3i3−i3−333−30000
χ442-22-22-2-22-121-11-1-222-221-21-1-2-12i−2i1-11-11-11−iii−i2i−2i2i−2i−ii−iii−ii−i0000000000000000i3−i3−i3i33−3−330000
χ452-22-22-2-22-121-11-1-222-221-21-1-2-1−2i2i1-11-11-11i−i−ii−2i2i−2i2ii−ii−i−ii−ii0000000000000000−i3i3i3−i33−3−330000
χ462-22-22-2-22-121-11-1-222-221-21-1-2-1−2i2i1-11-11-11i−i−ii−2i2i−2i2ii−ii−i−ii−ii0000000000000000i3−i3−i3i3−333−30000
χ472-2-22-22-2222-2-2-22-2-2-2-22222-22200-2-22-2-22200000000000000002-20000002-2-220000000000000000
χ482-2-22-22-2222-2-2-22-2-2-2-22222-22200-2-22-2-2220000000000000000-22000000-222-20000000000000000
χ492-2-22-22-222-1-2-2-221111-12-12-2-1-10011-111-1-10000−i3i3i3−i3−i3i3i3−i3i3−i3−i3i32-2000000-111-1−i3i3i3−i3000000000000
χ502-2-22-22-222-1-2-2-221111-12-12-2-1-10011-111-1-10000−i3i3i3−i3−i3i3i3−i3i3−i3−i3i3-220000001-1-11i3−i3−i3i3000000000000
χ512-2-22-22-222-1-2-2-221111-12-12-2-1-10011-111-1-10000i3−i3−i3i3i3−i3−i3i3−i3i3i3−i32-2000000-111-1i3−i3−i3i3000000000000
χ522-2-22-22-222-1-2-2-221111-12-12-2-1-10011-111-1-10000i3−i3−i3i3i3−i3−i3i3−i3i3i3−i3-220000001-1-11−i3i3i3−i3000000000000
χ532-2-2-2222-222-2-22-2-2-222-2-2-2222200-2-2222-2-200000000000000000000000000000000000000002-200
χ542-2-2-2222-222-2-22-2-2-222-2-2-2222200-2-2222-2-20000000000000000000000000000000000000000-2200
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
χ57444-4-44-4-44-244-4-4-2-2222-424-4-2-200-2-2-2222200000000000000000000000000000000000000000000
χ58444-4-44-4-4-2-2-2-222-2-222222-22-2100111-1-1-1-12323−23−230000−3−3−3−333330000000000000000000000000000
χ59444-4-44-4-4-2-2-2-222-2-222222-22-2100111-1-1-1-1−23−23232300003333−3−3−3−30000000000000000000000000000
χ6044-444-4-4-44-24-4-4-4-22-2224-2-442-200-222-222-200000000000000000000000000000000000000000000
χ6144-444-4-4-4-24-22224-44-4-4-242-2-4-200-222-222-200000000000000000000000000000000000000000000
χ6244-444-4-4-4-2-2-2222-22-222-2-22-221001-1-11-1-110000000033-3-3-3-3330000000000000000000000000000
χ6344-444-4-4-4-2-2-2222-22-222-2-22-221001-1-11-1-1100000000-3-33333-3-30000000000000000000000000000
χ6444-4-4-4-444-24-22-2-24-4-4442-422-4-200-2222-2-2200000000000000000000000000000000000000000000
χ6544-4-4-4-444-2-2-22-2-2-222-2-2222221001-1-1-111-100002323−23−23−3−333−3−3330000000000000000000000000000
χ6644-4-4-4-444-2-2-22-2-2-222-2-2222221001-1-1-111-10000−23−23232333−3−333−3−30000000000000000000000000000
χ674-444-4-44-44-2-444-42-22-224-2-4-42-2002-222-22-200000000000000000000000000000000000000000000
χ684-444-4-44-4-2-22-2-222-22-22-2-2222100-11-1-11-11−2i32i3−2i32i30000i3−i3i3−i3i3−i3i3−i30000000000000000000000000000
χ694-444-4-44-4-2-22-2-222-22-22-2-2222100-11-1-11-112i3−2i32i3−2i30000−i3i3−i3i3−i3i3−i3i30000000000000000000000000000
χ704-44-44-4-44-2-22-22-22-2-22-2222-2214i−4i-11-11-11-1−2i2i2i−2i−2i2i−2i2ii−ii−i−ii−ii0000000000000000000000000000
χ714-44-44-4-44-2-22-22-22-2-22-2222-221−4i4i-11-11-11-12i−2i−2i2i2i−2i2i−2i−ii−iii−ii−i0000000000000000000000000000
χ724-4-44-44-44-24222-2-4-4-4-44-24-224-20022-222-2-200000000000000000000000000000000000000000000
χ734-4-44-44-44-2-2222-22222-2-2-2-22-2100-1-11-1-1110000−2i32i32i3−2i3i3−i3−i3i3−i3i3i3−i30000000000000000000000000000
χ744-4-44-44-44-2-2222-22222-2-2-2-22-2100-1-11-1-11100002i3−2i3−2i32i3−i3i3i3−i3i3−i3−i3i30000000000000000000000000000
χ754-4-4-4444-44-2-4-44-422-2-22-4244-2-20022-2-2-22200000000000000000000000000000000000000000000
χ764-4-4-4444-4-2422-22-4-444-42-4-2-24-20022-2-2-22200000000000000000000000000000000000000000000
χ774-4-4-4444-4-2-222-2222-2-2222-2-2-2100-1-1111-1-1000000003i−3i−3i3i3i−3i−3i3i0000000000000000000000000000
χ784-4-4-4444-4-2-222-2222-2-2222-2-2-2100-1-1111-1-100000000−3i3i3i−3i−3i3i3i−3i0000000000000000000000000000

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