Finite Group Databasebeta

← Group #10591347

Character table — Group #10591347

Order 576.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78
size1111111122222222222222224444444444444444444444444412121212121212121212121212121212121212121212121236363636
order12222222336666666666666634466666661212121212121212121212121212121244444444121212121212121212121212121212122244
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111111111111111111111111-1-1-1-11111-1-1-1-1-1-1-1-11111-1-1-1-1
χ311111111111111111111111111111111111111111111111111-1-1-1-11111-1-1-1-111111111-1-1-1-1-1-1-1-1
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
χ51111111111111111111111111-1-11111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-111-1-1-1-1-1-11111-1-1-1-1111111-1-1
χ61111111111111111111111111-1-11111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-111-1-1-1-1-1-1-1-111111111-1-111
χ71111111111111111111111111-1-11111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-111111111-1-1-1-1-1-1-1-1-1-111
χ81111111111111111111111111-1-11111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1111111-1-1-1-11111-1-1-1-111-1-1
χ9222222222-122222-1-1-1-1-12-1-12-122-1-1-1-1-1-1-1-1-1-1-12222-1-1-1-1-1-1-1-1000022220000-1-1-1-1-1-1-1-100000000
χ10222222222-122222-1-1-1-1-12-1-12-122-1-1-1-1-1-1-1-1-1-1-12222-1-1-1-1-1-1-1-10000-2-2-2-200001111111100000000
χ11222222222-122222-1-1-1-1-12-1-12-1-2-2-1-1-1-1-1-1-11111-2-2-2-211111111000022-2-20000-1-1-1-1111100000000
χ12222222222-122222-1-1-1-1-12-1-12-1-2-2-1-1-1-1-1-1-11111-2-2-2-2111111110000-2-22200001111-1-1-1-100000000
χ1322222222-12-1-1-1-1-122222-122-1-122-1-1-1-1-1-1-12222-1-1-1-1-1-1-1-1-1-1-1-122220000-1-1-1-100000000-1-1-1-10000
χ1422222222-12-1-1-1-1-122222-122-1-122-1-1-1-1-1-1-12222-1-1-1-1-1-1-1-1-1-1-1-1-2-2-2-2000011110000000011110000
χ1522222222-12-1-1-1-1-122222-122-1-1-2-2-1-1-1-1-1-1-1-2-2-2-211111111111122-2-20000111100000000-1-1-1-10000
χ1622222222-12-1-1-1-1-122222-122-1-1-2-2-1-1-1-1-1-1-1-2-2-2-2111111111111-2-2220000-1-1-1-10000000011110000
χ172222-2-2-2-222222-2-2222-2-2-2-2-2-2200222-2-2-2-200000000000000000000000000000000000000002-200
χ182222-2-2-2-222222-2-2222-2-2-2-2-2-2200222-2-2-2-20000000000000000000000000000000000000000-2200
χ1922-2-222-2-2222-2-22-22-2-222-2-2-222002-2-22-2-2200000000000000000000002i−2i000000002i2i−2i−2i00000000
χ2022-2-222-2-2222-2-22-22-2-222-2-2-222002-2-22-2-220000000000000000000000−2i2i00000000−2i−2i2i2i00000000
χ2122-2-222-2-22-12-2-22-2-111-1-1-2112-100-111-111-1−i3−i3i3i30000−i3−i3−i3−i3i3i3i3i30000002i−2i000033−3−3−i−iii00000000
χ2222-2-222-2-22-12-2-22-2-111-1-1-2112-100-111-111-1−i3−i3i3i30000−i3−i3−i3−i3i3i3i3i3000000−2i2i0000−3−333ii−i−i00000000
χ2322-2-222-2-22-12-2-22-2-111-1-1-2112-100-111-111-1i3i3−i3−i30000i3i3i3i3−i3−i3−i3−i30000002i−2i0000−3−333−i−iii00000000
χ2422-2-222-2-22-12-2-22-2-111-1-1-2112-100-111-111-1i3i3−i3−i30000i3i3i3i3−i3−i3−i3−i3000000−2i2i000033−3−3ii−i−i00000000
χ2522-2-2-2-222222-2-2-222-2-2-2-2222-22002-2-2-222-20000000000000000002-2000022-2-20000000000000000
χ2622-2-2-2-222222-2-2-222-2-2-2-2222-22002-2-2-222-2000000000000000000-220000-2-2220000000000000000
χ2722-2-2-2-222-12-1111-12-2-2-2-2-1221-100-1111-1-11000033−3−333−3−333−3−3002-20000-1-1110000000033−3−30000
χ2822-2-2-2-222-12-1111-12-2-2-2-2-1221-100-1111-1-11000033−3−333−3−333−3−300-22000011-1-100000000−3−3330000
χ2922-2-2-2-222-12-1111-12-2-2-2-2-1221-100-1111-1-110000−3−333−3−333−3−333002-20000-1-11100000000−3−3330000
χ3022-2-2-2-222-12-1111-12-2-2-2-2-1221-100-1111-1-110000−3−333−3−333−3−33300-22000011-1-10000000033−3−30000
χ312-22-22-22-222-22-22-2-22-22-222-2-222i−2i-22-222-2-22i−2i2i−2i2i−2i2i−2i2i−2i2i−2i2i−2i2i−2i0000000000000000000000000000
χ322-22-22-22-222-22-22-2-22-22-222-2-22−2i2i-22-222-2-2−2i2i−2i2i−2i2i−2i2i−2i2i−2i2i−2i2i−2i2i0000000000000000000000000000
χ332-22-22-22-22-1-22-22-21-11-112-11-2-12i−2i1-11-1-111−ii−ii2i−2i2i−2i−ii−ii−ii−ii000000000000−i3i3−i3i33−33−300000000
χ342-22-22-22-22-1-22-22-21-11-112-11-2-12i−2i1-11-1-111−ii−ii2i−2i2i−2i−ii−ii−ii−ii000000000000i3−i3i3−i3−33−3300000000
χ352-22-22-22-22-1-22-22-21-11-112-11-2-1−2i2i1-11-1-111i−ii−i−2i2i−2i2ii−ii−ii−ii−i000000000000−i3i3−i3i3−33−3300000000
χ362-22-22-22-22-1-22-22-21-11-112-11-2-1−2i2i1-11-1-111i−ii−i−2i2i−2i2ii−ii−ii−ii−i000000000000i3−i3i3−i33−33−300000000
χ372-22-22-22-2-121-11-11-22-22-2-12-21-12i−2i1-11-1-1112i−2i2i−2i−ii−ii−ii−ii−ii−ii00000000−i3i3−i3i3000000003−33−30000
χ382-22-22-22-2-121-11-11-22-22-2-12-21-12i−2i1-11-1-1112i−2i2i−2i−ii−ii−ii−ii−ii−ii00000000i3−i3i3−i300000000−33−330000
χ392-22-22-22-2-121-11-11-22-22-2-12-21-1−2i2i1-11-1-111−2i2i−2i2ii−ii−ii−ii−ii−ii−i00000000−i3i3−i3i300000000−33−330000
χ402-22-22-22-2-121-11-11-22-22-2-12-21-1−2i2i1-11-1-111−2i2i−2i2ii−ii−ii−ii−ii−ii−i00000000i3−i3i3−i3000000003−33−30000
χ412-22-2-22-2222-22-2-22-22-2-22-2-222200-22-2-2-2220000000000000000000000000000000000000000002-2
χ422-22-2-22-2222-22-2-22-22-2-22-2-222200-22-2-2-222000000000000000000000000000000000000000000-22
χ432-2-222-2-2222-2-2222-2-222-2-2-22-2200-2-222-22-2000000000000000000002i−2i0000002i−2i−2i2i000000000000
χ442-2-222-2-2222-2-2222-2-222-2-2-22-2200-2-222-22-200000000000000000000−2i2i000000−2i2i2i−2i000000000000
χ452-2-222-2-222-1-2-222211-1-11-21-1-2-10011-1-11-113−3−3300003−33−3−33−3300002i−2i000000−iii−ii3−i3−i3i300000000
χ462-2-222-2-222-1-2-222211-1-11-21-1-2-10011-1-11-113−3−3300003−33−3−33−330000−2i2i000000i−i−ii−i3i3i3−i300000000
χ472-2-222-2-222-1-2-222211-1-11-21-1-2-10011-1-11-11−333−30000−33−333−33−300002i−2i000000−iii−i−i3i3i3−i300000000
χ482-2-222-2-222-1-2-222211-1-11-21-1-2-10011-1-11-11−333−30000−33−333−33−30000−2i2i000000i−i−iii3−i3−i3i300000000
χ492-2-22-222-222-2-22-2-2-2-22-2222-22200-2-22-22-2200000000000000002-20000000000000000002-2-220000
χ502-2-22-222-222-2-22-2-2-2-22-2222-22200-2-22-22-220000000000000000-22000000000000000000-222-20000
χ512-2-22-222-2-1211-111-2-22-22-12-2-1-10011-11-11-10000−i3i3i3−i3−i3i3i3−i3−i3i3i3−i32-2000000−i3i3i3−i300000000-111-10000
χ522-2-22-222-2-1211-111-2-22-22-12-2-1-10011-11-11-10000−i3i3i3−i3−i3i3i3−i3−i3i3i3−i3-22000000i3−i3−i3i3000000001-1-110000
χ532-2-22-222-2-1211-111-2-22-22-12-2-1-10011-11-11-10000i3−i3−i3i3i3−i3−i3i3i3−i3−i3i32-2000000i3−i3−i3i300000000-111-10000
χ542-2-22-222-2-1211-111-2-22-22-12-2-1-10011-11-11-10000i3−i3−i3i3i3−i3−i3i3i3−i3−i3i3-22000000−i3i3i3−i3000000001-1-110000
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
χ574444-4-4-4-44-2444-4-4-2-2-222-422-4-200-2-2-2222200000000000000000000000000000000000000000000
χ584444-4-4-4-4-24-2-2-222444-4-42-4-42-200-2-2-2222200000000000000000000000000000000000000000000
χ594444-4-4-4-4-2-2-2-2-222-2-2-2222222100111-1-1-1-1000000003i3i−3i−3i−3i−3i3i3i0000000000000000000000000000
χ604444-4-4-4-4-2-2-2-2-222-2-2-2222222100111-1-1-1-100000000−3i−3i3i3i3i3i−3i−3i0000000000000000000000000000
χ6144-4-444-4-4-24-222-224-4-4442-4-4-2-200-222-222-200000000000000000000000000000000000000000000
χ6244-4-444-4-4-2-2-222-22-222-2-2222-21001-1-11-1-11−2i3−2i32i32i30000i3i3i3i3−i3−i3−i3−i30000000000000000000000000000
χ6344-4-444-4-4-2-2-222-22-222-2-2222-21001-1-11-1-112i32i3−2i3−2i30000−i3−i3−i3−i3i3i3i3i30000000000000000000000000000
χ6444-4-4-4-4444-24-4-4-44-222224-2-2-4-200-2222-2-2200000000000000000000000000000000000000000000
χ6544-4-4-4-444-2-2-2222-2-22222-2-2-221001-1-1-111-100002323−23−23−3−333−3−3330000000000000000000000000000
χ6644-4-4-4-444-2-2-2222-2-22222-2-2-221001-1-1-111-10000−23−23232333−3−333−3−30000000000000000000000000000
χ674-44-44-44-4-2-22-22-222-22-22-2-22214i−4i-11-111-1-1−2i2i−2i2i−2i2i−2i2ii−ii−ii−ii−i0000000000000000000000000000
χ684-44-44-44-4-2-22-22-222-22-22-2-2221−4i4i-11-111-1-12i−2i2i−2i2i−2i2i−2i−ii−ii−ii−ii0000000000000000000000000000
χ694-44-4-44-444-2-44-4-442-222-2-42-24-2002-2222-2-200000000000000000000000000000000000000000000
χ704-44-4-44-44-242-222-2-44-4-442-44-2-2002-2222-2-200000000000000000000000000000000000000000000
χ714-44-4-44-44-2-22-222-22-222-222-2-2100-11-1-1-111000000003-3-33-333-30000000000000000000000000000
χ724-44-4-44-44-2-22-222-22-222-222-2-2100-11-1-1-11100000000-333-33-3-330000000000000000000000000000
χ734-4-444-4-44-2422-2-2-2-4-444-42-442-20022-2-22-2200000000000000000000000000000000000000000000
χ744-4-444-4-44-2-222-2-2-222-2-2222-22100-1-111-11-123−23−23230000−33−333−33−30000000000000000000000000000
χ754-4-444-4-44-2-222-2-2-222-2-2222-22100-1-111-11-1−232323−2300003−33−3−33−330000000000000000000000000000
χ764-4-44-444-44-2-4-44-4-422-22-24-224-20022-22-22-200000000000000000000000000000000000000000000
χ774-4-44-444-4-2-222-22222-22-2-2-22-2100-1-11-11-110000−2i32i32i3−2i3i3−i3−i3i3i3−i3−i3i30000000000000000000000000000
χ784-4-44-444-4-2-222-22222-22-2-2-22-2100-1-11-11-1100002i3−2i3−2i32i3−i3i3i3−i3−i3i3i3−i30000000000000000000000000000

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