Finite Group Databasebeta

← Group #10591390

Character table — Group #10591390

Order 576.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78
size1111111122222222222222224444444444444444444444444412121212121212121212121212121212121212121212121236363636
order122222223366666666666666344666666612121212121212121212121212121212222244446666666612121212121212124444
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111111111111111-1-111-1-11111-1-1-1-11111-1-1-1-1-1-1-1-1
χ311111111111111111111111111111111111111111111111111-1-111-1-111-1-1-1-11111-1-1-1-11111-1-1-1-1
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
χ51111111111111111111111111-1-11111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-111111111-1-1-1-1-1-1-1-1-1-111
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
χ81111111111111111111111111-1-11111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-111111111-1-111
χ9222222222-122222-1-1-1-1-12-12-1-122-1-1-1-1-1-1-12222-1-1-1-1-1-1-1-1-1-1-1-1002200220000-1-1-1-10000-1-1-1-10000
χ10222222222-122222-1-1-1-1-12-12-1-122-1-1-1-1-1-1-12222-1-1-1-1-1-1-1-1-1-1-1-100-2-200-2-200001111000011110000
χ11222222222-122222-1-1-1-1-12-12-1-1-2-2-1-1-1-1-1-1-1-2-2-2-2111111111111002200-2-20000-1-1-1-1000011110000
χ12222222222-122222-1-1-1-1-12-12-1-1-2-2-1-1-1-1-1-1-1-2-2-2-211111111111100-2-20022000011110000-1-1-1-10000
χ1322222222-12-1-1-1-1-122222-12-12-122-1-1-1-1-1-1-1-1-1-1-12222-1-1-1-1-1-1-1-122002200-1-1-1-10000-1-1-1-100000000
χ1422222222-12-1-1-1-1-122222-12-12-122-1-1-1-1-1-1-1-1-1-1-12222-1-1-1-1-1-1-1-1-2-200-2-20011110000111100000000
χ1522222222-12-1-1-1-1-122222-12-12-1-2-2-1-1-1-1-1-1-11111-2-2-2-2111111112200-2-200-1-1-1-10000111100000000
χ1622222222-12-1-1-1-1-122222-12-12-1-2-2-1-1-1-1-1-1-11111-2-2-2-211111111-2-200220011110000-1-1-1-100000000
χ17222-22-2-2-22222-2-2-222-2-2-222-2-220022-2-2-2-2200000000000000000000000000000000000000002i−2i00
χ18222-22-2-2-22222-2-2-222-2-2-222-2-220022-2-2-2-220000000000000000000000000000000000000000−2i2i00
χ1922-22-22-2-2222-22-2-22-222-2-2-22-22002-222-2-2-200000000000000000000002i−2i0000000000002i2i−2i−2i0000
χ2022-22-22-2-2222-22-2-22-222-2-2-22-22002-222-2-2-20000000000000000000000−2i2i000000000000−2i−2i2i2i0000
χ2122-22-22-2-22-12-22-2-2-11-1-11-2121-100-11-1-1111000033−3−33333−3−3−3−30000002i−2i0000−i3−i3i3i30000−i−iii0000
χ2222-22-22-2-22-12-22-2-2-11-1-11-2121-100-11-1-1111000033−3−33333−3−3−3−3000000−2i2i0000i3i3−i3−i30000ii−i−i0000
χ2322-22-22-2-22-12-22-2-2-11-1-11-2121-100-11-1-11110000−3−333−3−3−3−333330000002i−2i0000i3i3−i3−i30000−i−iii0000
χ2422-22-22-2-22-12-22-2-2-11-1-11-2121-100-11-1-11110000−3−333−3−3−3−33333000000−2i2i0000−i3−i3i3i30000ii−i−i0000
χ2522-2-2-2-222222-2-2222-2-2-22-2-2-222002-2-2-222-200000000000000002-200000022-2-20000000000000000
χ2622-2-2-2-222222-2-2222-2-2-22-2-2-222002-2-2-222-20000000000000000-22000000-2-2220000000000000000
χ2722-2-2-2-222-12-111-1-12-2-2-221-212-100-1111-1-1133−3−3000033−3−333−3−32-2000000-1-111000033−3−300000000
χ2822-2-2-2-222-12-111-1-12-2-2-221-212-100-1111-1-1133−3−3000033−3−333−3−3-2200000011-1-10000−3−33300000000
χ2922-2-2-2-222-12-111-1-12-2-2-221-212-100-1111-1-11−3−3330000−3−333−3−3332-2000000-1-1110000−3−33300000000
χ3022-2-2-2-222-12-111-1-12-2-2-221-212-100-1111-1-11−3−3330000−3−333−3−333-2200000011-1-1000033−3−300000000
χ312-222-2-22-222-2222-2-222-22-2-2-2-222i−2i-222-22-2-22i−2i2i−2i2i−2i2i−2i2i−2i2i−2i2i−2i2i−2i0000000000000000000000000000
χ322-222-2-22-222-2222-2-222-22-2-2-2-22−2i2i-222-22-2-2−2i2i−2i2i−2i2i−2i2i−2i2i−2i2i−2i2i−2i2i0000000000000000000000000000
χ332-222-2-22-22-1-2222-21-1-11-1-21-21-12i−2i1-1-11-1112i−2i2i−2i−ii−ii−ii−ii−ii−ii000000000000−i3i3−i3i300003−33−30000
χ342-222-2-22-22-1-2222-21-1-11-1-21-21-12i−2i1-1-11-1112i−2i2i−2i−ii−ii−ii−ii−ii−ii000000000000i3−i3i3−i30000−33−330000
χ352-222-2-22-22-1-2222-21-1-11-1-21-21-1−2i2i1-1-11-111−2i2i−2i2ii−ii−ii−ii−ii−ii−i000000000000−i3i3−i3i30000−33−330000
χ362-222-2-22-22-1-2222-21-1-11-1-21-21-1−2i2i1-1-11-111−2i2i−2i2ii−ii−ii−ii−ii−ii−i000000000000i3−i3i3−i300003−33−30000
χ372-222-2-22-2-121-1-1-11-222-221-21-2-12i−2i1-1-11-111−ii−ii2i−2i2i−2i−ii−ii−ii−ii00000000−i3i3−i3i300003−33−300000000
χ382-222-2-22-2-121-1-1-11-222-221-21-2-12i−2i1-1-11-111−ii−ii2i−2i2i−2i−ii−ii−ii−ii00000000i3−i3i3−i30000−33−3300000000
χ392-222-2-22-2-121-1-1-11-222-221-21-2-1−2i2i1-1-11-111i−ii−i−2i2i−2i2ii−ii−ii−ii−i00000000−i3i3−i3i30000−33−3300000000
χ402-222-2-22-2-121-1-1-11-222-221-21-2-1−2i2i1-1-11-111i−ii−i−2i2i−2i2ii−ii−ii−ii−i00000000i3−i3i3−i300003−33−300000000
χ412-22-2-22-2222-22-2-22-22-22-2-2-222200-22-22-22-20000000000000000000000000000000000000000002-2
χ422-22-2-22-2222-22-2-22-22-22-2-2-222200-22-22-22-2000000000000000000000000000000000000000000-22
χ432-2-222-2-2222-2-22-22-2-22-2-222-22200-2-22-2-2220000000000000000002-2000000002-2-22000000000000
χ442-2-222-2-2222-2-22-22-2-22-2-222-22200-2-22-2-222000000000000000000-2200000000-222-2000000000000
χ452-2-222-2-222-1-2-22-2211-1112-1-2-1-10011-111-1-10000−i3i3i3−i3−i3i3−i3i3i3−i3i3−i3002-200000000-111-10000−i3i3i3−i30000
χ462-2-222-2-222-1-2-22-2211-1112-1-2-1-10011-111-1-10000−i3i3i3−i3−i3i3−i3i3i3−i3i3−i300-22000000001-1-110000i3−i3−i3i30000
χ472-2-222-2-222-1-2-22-2211-1112-1-2-1-10011-111-1-10000i3−i3−i3i3i3−i3i3−i3−i3i3−i3i3002-200000000-111-10000i3−i3−i3i30000
χ482-2-222-2-222-1-2-22-2211-1112-1-2-1-10011-111-1-10000i3−i3−i3i3i3−i3i3−i3−i3i3−i3i300-22000000001-1-110000−i3i3i3−i30000
χ492-2-2-2222-222-2-2-22-2-2-2-222222-2200-2-2-222-22000000000000000000002-200000000002-2-2200000000
χ502-2-2-2222-222-2-2-22-2-2-2-222222-2200-2-2-222-2200000000000000000000-220000000000-222-200000000
χ512-2-2-2222-2-12111-11-2-2-222-12-1-2-100111-1-11-1−i3i3i3−i30000−i3i3i3−i3−i3i3i3−i300002-200−i3i3i3−i30000-111-100000000
χ522-2-2-2222-2-12111-11-2-2-222-12-1-2-100111-1-11-1−i3i3i3−i30000−i3i3i3−i3−i3i3i3−i30000-2200i3−i3−i3i300001-1-1100000000
χ532-2-2-2222-2-12111-11-2-2-222-12-1-2-100111-1-11-1i3−i3−i3i30000i3−i3−i3i3i3−i3−i3i300002-200i3−i3−i3i30000-111-100000000
χ542-2-2-2222-2-12111-11-2-2-222-12-1-2-100111-1-11-1i3−i3−i3i30000i3−i3−i3i3i3−i3−i3i30000-2200−i3i3i3−i300001-1-1100000000
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
χ57444-44-4-4-44-244-4-4-4-2-22224-2-42-200-2-22222-200000000000000000000000000000000000000000000
χ58444-44-4-4-4-24-2-222244-4-4-4-242-4-200-2-22222-200000000000000000000000000000000000000000000
χ59444-44-4-4-4-2-2-2-2222-2-2222-2-22210011-1-1-1-110000000033-3-3-3-3330000000000000000000000000000
χ60444-44-4-4-4-2-2-2-2222-2-2222-2-22210011-1-1-1-1100000000-3-33333-3-30000000000000000000000000000
χ6144-44-44-4-4-24-22-2224-444-42-4-2-4-200-22-2-222200000000000000000000000000000000000000000000
χ6244-44-44-4-4-2-2-22-222-22-2-2222-221001-111-1-1-100002323−23−23−3−3−3−333330000000000000000000000000000
χ6344-44-44-4-4-2-2-22-222-22-2-2222-221001-111-1-1-10000−23−2323233333−3−3−3−30000000000000000000000000000
χ6444-4-4-4-4444-24-4-444-2222-2-42-4-2-200-2222-2-2200000000000000000000000000000000000000000000
χ6544-4-4-4-444-2-2-222-2-2-2222-2222-21001-1-1-111-12323−23−230000−3−333−3−3330000000000000000000000000000
χ6644-4-4-4-444-2-2-222-2-2-2222-2222-21001-1-1-111-1−23−232323000033−3−333−3−30000000000000000000000000000
χ674-444-4-44-4-2-22-2-2-222-2-22-2222214i−4i-111-11-1-1−2i2i−2i2i−2i2i−2i2ii−ii−ii−ii−i0000000000000000000000000000
χ684-444-4-44-4-2-22-2-2-222-2-22-222221−4i4i-111-11-1-12i−2i2i−2i2i−2i2i−2i−ii−ii−ii−ii0000000000000000000000000000
χ694-44-4-44-444-2-44-4-442-22-22-424-2-2002-22-22-2200000000000000000000000000000000000000000000
χ704-44-4-44-44-242-222-2-44-44-42-4-24-2002-22-22-2200000000000000000000000000000000000000000000
χ714-44-4-44-44-2-22-222-22-22-2222-2-2100-11-11-11-1000000003i−3i−3i3i−3i3i3i−3i0000000000000000000000000000
χ724-44-4-44-44-2-22-222-22-22-2222-2-2100-11-11-11-100000000−3i3i3i−3i3i−3i−3i3i0000000000000000000000000000
χ734-4-444-4-44-2422-22-2-4-44-4-4-2424-20022-222-2-200000000000000000000000000000000000000000000
χ744-4-444-4-44-2-222-22-222-222-2-22-2100-1-11-1-1110000−2i32i32i3−2i3i3−i3i3−i3−i3i3−i3i30000000000000000000000000000
χ754-4-444-4-44-2-222-22-222-222-2-22-2100-1-11-1-11100002i3−2i3−2i32i3−i3i3−i3i3i3−i3i3−i30000000000000000000000000000
χ764-4-4-4444-44-2-4-4-44-4222-2-24-242-200222-2-22-200000000000000000000000000000000000000000000
χ774-4-4-4444-4-2-2222-22222-2-2-2-2-22100-1-1-111-11−2i32i32i3−2i30000i3−i3−i3i3i3−i3−i3i30000000000000000000000000000
χ784-4-4-4444-4-2-2222-22222-2-2-2-2-22100-1-1-111-112i3−2i3−2i32i30000−i3i3i3−i3−i3i3i3−i30000000000000000000000000000

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