Finite Group Databasebeta

← Group #10591709

Character table — Group #10591709

Order 576.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78
size1111111122222222222222224444444444444444444444444412121212121212121212121212121212121212121212121236363636
order122222223366666666666666223666666666666666666666662244444466661212121212121212121212124444
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111111111111111-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-1-1-1
χ311111111111111111111111111111111111111111111111111-1-11111-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1
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
χ5111111111111111111111111-1-11-1-1-1-1-1-1-1-11111111-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1-1-11111-1-1-1-111-1-1
χ6111111111111111111111111-1-11-1-1-1-1-1-1-1-11111111-1-1-1-1-1-1-1-111-1-111-1-11111-1-1-1-1-1-1-1-11111-1-111
χ7111111111111111111111111-1-11-1-1-1-1-1-1-1-11111111-1-1-1-1-1-1-1-1-1-111-1-111-1-1-1-111111111-1-1-1-1-1-111
χ8111111111111111111111111-1-11-1-1-1-1-1-1-1-11111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1-1-1111111-1-1
χ9222222222-122222-1-1-1-1-1-122-122-12222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-122000022-1-1-1-1-1-1-1-1000000000000
χ10222222222-122222-1-1-1-1-1-122-122-12222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-2-20000-2-211111111000000000000
χ11222222222-122222-1-1-1-1-1-122-1-2-2-1-2-2-2-21111-1-1-1-1-1-1-111111111220000-2-2-1-1-1-11111000000000000
χ12222222222-122222-1-1-1-1-1-122-1-2-2-1-2-2-2-21111-1-1-1-1-1-1-111111111-2-20000221111-1-1-1-1000000000000
χ1322222222-12-1-1-1-1-1222222-1-1222-1-1-1-1-12222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-10022220000000000-1-1-1-1-1-1-1-10000
χ1422222222-12-1-1-1-1-1222222-1-1222-1-1-1-1-12222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-100-2-2-2-20000000000111111110000
χ1522222222-12-1-1-1-1-1222222-1-12-2-2-11111-2-2-2-2-1-1-1-1-1-1-1111111110022-2-20000000000-1-1-1-111110000
χ1622222222-12-1-1-1-1-1222222-1-12-2-2-11111-2-2-2-2-1-1-1-1-1-1-11111111100-2-22200000000001111-1-1-1-10000
χ17222-22-2-2-22222-2-2-2222-2-2-22-2-200200000000222-2-2-2-200000000000000000000000000000000002i−2i
χ18222-22-2-2-22222-2-2-2222-2-2-22-2-200200000000222-2-2-2-20000000000000000000000000000000000−2i2i
χ1922-22-22-2-2222-22-2-22-2-222-2-22-2002000000002-2-222-2-2000000000000000000000000000000002i−2i00
χ2022-22-22-2-2222-22-2-22-2-222-2-22-2002000000002-2-222-2-200000000000000000000000000000000−2i2i00
χ2122-2-2-2-222222-2-2222-2-2-2-22-2-222-2222-2-222-2-22-2-2-2-2222222-2-2-2-20000000000000000000000000000
χ2222-2-2-2-222222-2-2222-2-2-2-22-2-22-222-2-222-2-2222-2-2-2-222-2-2-2-222220000000000000000000000000000
χ2322-2-2-2-2222-12-2-222-11111-1-2-2-12-2-122-2-2-1-111-11111-1-1-1-1-1-1111100000000−i3−i3i3i3−i3−i3i3i3000000000000
χ2422-2-2-2-2222-12-2-222-11111-1-2-2-12-2-122-2-2-1-111-11111-1-1-1-1-1-1111100000000i3i3−i3−i3i3i3−i3−i3000000000000
χ2522-2-2-2-2222-12-2-222-11111-1-2-2-1-22-1-2-22211-1-1-11111-1-11111-1-1-1-100000000−i3−i3i3i3i3i3−i3−i3000000000000
χ2622-2-2-2-2222-12-2-222-11111-1-2-2-1-22-1-2-22211-1-1-11111-1-11111-1-1-1-100000000i3i3−i3−i3−i3−i3i3i3000000000000
χ2722-2-2-2-222-12-111-1-12-2-2-2-221122-2-1-1-11122-2-2-11111-1-1-1-1-1-11111000000000000000033−3−333−3−30000
χ2822-2-2-2-222-12-111-1-12-2-2-2-221122-2-1-1-11122-2-2-11111-1-1-1-1-1-111110000000000000000−3−333−3−3330000
χ2922-2-2-2-222-12-111-1-12-2-2-2-22112-22-111-1-1-2-222-11111-1-11111-1-1-1-1000000000000000033−3−3−3−3330000
χ3022-2-2-2-222-12-111-1-12-2-2-2-22112-22-111-1-1-2-222-11111-1-11111-1-1-1-10000000000000000−3−33333−3−30000
χ312-222-2-22-222-2222-2-22-22-22-2-2-200200000000-22-22-22-20000000000002i−2i000000000000002i−2i2i−2i0000
χ322-222-2-22-222-2222-2-22-22-22-2-2-200200000000-22-22-22-2000000000000−2i2i00000000000000−2i2i−2i2i0000
χ332-222-2-22-2-121-1-1-11-22-22-2211-200-1−i3i3−i3i300001-11-11-11−i3−i3i3i3−i3−i3i3i300002i−2i00000000003−33−3−ii−ii0000
χ342-222-2-22-2-121-1-1-11-22-22-2211-200-1−i3i3−i3i300001-11-11-11−i3−i3i3i3−i3−i3i3i30000−2i2i0000000000−33−33i−ii−i0000
χ352-222-2-22-2-121-1-1-11-22-22-2211-200-1i3−i3i3−i300001-11-11-11i3i3−i3−i3i3i3−i3−i300002i−2i0000000000−33−33−ii−ii0000
χ362-222-2-22-2-121-1-1-11-22-22-2211-200-1i3−i3i3−i300001-11-11-11i3i3−i3−i3i3i3−i3−i30000−2i2i00000000003−33−3i−ii−i0000
χ372-22-2-22-2222-22-2-22-22-2-22-2-22200200000000-22-2-22-22000000002-20000002-22-20000000000000000
χ382-22-2-22-2222-22-2-22-22-2-22-2-22200200000000-22-2-22-2200000000-22000000-22-220000000000000000
χ392-22-2-22-222-1-22-2-221-111-11-22-100-10000−i3i3−i3i31-111-11-1−i3i3−i3i3−i3i3−i3i32-2000000-11-11−i3i3−i3i3000000000000
χ402-22-2-22-222-1-22-2-221-111-11-22-100-10000−i3i3−i3i31-111-11-1−i3i3−i3i3−i3i3−i3i3-220000001-11-1i3−i3i3−i3000000000000
χ412-22-2-22-222-1-22-2-221-111-11-22-100-10000i3−i3i3−i31-111-11-1i3−i3i3−i3i3−i3i3−i32-2000000-11-11i3−i3i3−i3000000000000
χ422-22-2-22-222-1-22-2-221-111-11-22-100-10000i3−i3i3−i31-111-11-1i3−i3i3−i3i3−i3i3−i3-220000001-11-1−i3i3−i3i3000000000000
χ432-2-222-2-2222-2-22-22-2-222-2-22-2200200000000-2-222-2-22000000000000002-200002-2-22000000000000
χ442-2-222-2-2222-2-22-22-2-222-2-22-2200200000000-2-222-2-2200000000000000-220000-222-2000000000000
χ452-2-222-2-222-1-2-22-2211-1-1112-2-100-10000−i3i3i3−i311-1-111-1−i3i3−i3i3i3−i3i3−i30000002-2−i3i3i3−i3-111-1000000000000
χ462-2-222-2-222-1-2-22-2211-1-1112-2-100-10000−i3i3i3−i311-1-111-1−i3i3−i3i3i3−i3i3−i3000000-22i3−i3−i3i31-1-11000000000000
χ472-2-222-2-222-1-2-22-2211-1-1112-2-100-10000i3−i3−i3i311-1-111-1i3−i3i3−i3−i3i3−i3i30000002-2i3−i3−i3i3-111-1000000000000
χ482-2-222-2-222-1-2-22-2211-1-1112-2-100-10000i3−i3−i3i311-1-111-1i3−i3i3−i3−i3i3−i3i3000000-22−i3i3i3−i31-1-11000000000000
χ492-2-2-2222-222-2-2-22-2-2-22-22222-200200000000-2-22-222-200000000002-20000000000002-2-2200000000
χ502-2-2-2222-222-2-2-22-2-2-22-22222-200200000000-2-22-222-20000000000-22000000000000-222-200000000
χ512-2-2-2222-2-12111-11-2-22-222-1-1-200-1−i3i3i3−i3000011-11-1-11−i3−i3i3i3i3i3−i3−i3002-2000000000000-111-1−i3i3i3−i30000
χ522-2-2-2222-2-12111-11-2-22-222-1-1-200-1−i3i3i3−i3000011-11-1-11−i3−i3i3i3i3i3−i3−i300-220000000000001-1-11i3−i3−i3i30000
χ532-2-2-2222-2-12111-11-2-22-222-1-1-200-1i3−i3−i3i3000011-11-1-11i3i3−i3−i3−i3−i3i3i3002-2000000000000-111-1i3−i3−i3i30000
χ542-2-2-2222-2-12111-11-2-22-222-1-1-200-1i3−i3−i3i3000011-11-1-11i3i3−i3−i3−i3−i3i3i300-220000000000001-1-11−i3i3i3−i30000
χ5544444444-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2441-2-2-2-2-2-2-2-21111111111111110000000000000000000000000000
χ5644444444-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-4-41222222221111111-1-1-1-1-1-1-1-10000000000000000000000000000
χ57444-44-4-4-44-244-4-4-4-2-2-22224-4200-200000000-2-2-22222000000000000000000000000000000000000
χ58444-44-4-4-4-24-2-2222444-4-4-4-22-400-200000000-2-2-22222000000000000000000000000000000000000
χ59444-44-4-4-4-2-2-2-2222-2-2-2222-22200100000000111-1-1-1-13-3-333-3-330000000000000000000000000000
χ60444-44-4-4-4-2-2-2-2222-2-2-2222-22200100000000111-1-1-1-1-333-3-333-30000000000000000000000000000
χ6144-44-44-4-44-24-44-4-4-222-2-22-44200-200000000-222-2-222000000000000000000000000000000000000
χ6244-44-44-4-4-24-22-2224-4-444-42-2-400-200000000-222-2-222000000000000000000000000000000000000
χ6344-44-44-4-4-2-2-22-222-222-2-222-22001000000001-1-111-1-13-3-33-333-30000000000000000000000000000
χ6444-44-44-4-4-2-2-22-222-222-2-222-22001000000001-1-111-1-1-333-33-3-330000000000000000000000000000
χ6544-4-4-4-444-2-2-222-2-2-22222-222-24-41-2-222-2-2221-1-1-1-1111111-1-1-1-10000000000000000000000000000
χ6644-4-4-4-444-2-2-222-2-2-22222-222-2-44122-2-222-2-21-1-1-1-111-1-1-1-111110000000000000000000000000000
χ674-444-4-44-44-2-4444-42-22-22-2-4-4200-2000000002-22-22-22000000000000000000000000000000000000
χ684-444-4-44-4-2-22-2-2-222-22-22-2222001−2i32i3−2i32i30000-11-11-11-1i3i3−i3−i3i3i3−i3−i30000000000000000000000000000
χ694-444-4-44-4-2-22-2-2-222-22-22-22220012i3−2i32i3−2i30000-11-11-11-1−i3−i3i3i3−i3−i3i3i30000000000000000000000000000
χ704-44-4-44-44-242-222-2-44-4-44-42-2400-2000000002-222-22-2000000000000000000000000000000000000
χ714-44-4-44-44-2-22-222-22-222-222-2-20010000−2i32i3−2i32i3-11-1-11-11i3−i3i3−i3i3−i3i3−i30000000000000000000000000000
χ724-44-4-44-44-2-22-222-22-222-222-2-200100002i3−2i32i3−2i3-11-1-11-11−i3i3−i3i3−i3i3−i3i30000000000000000000000000000
χ734-4-444-4-44-2422-22-2-4-444-4-4-22400-20000000022-2-222-2000000000000000000000000000000000000
χ744-4-444-4-44-2-222-22-222-2-222-22-20010000−2i32i32i3−2i3-1-111-1-11i3−i3i3−i3−i3i3−i3i30000000000000000000000000000
χ754-4-444-4-44-2-222-22-222-2-222-22-200100002i3−2i3−2i32i3-1-111-1-11−i3i3−i3i3i3−i3i3−i30000000000000000000000000000
χ764-4-4-4444-44-2-4-4-44-422-22-2-244200-20000000022-22-2-22000000000000000000000000000000000000
χ774-4-4-4444-4-2-2222-2222-22-2-2-2-22001−2i32i32i3−2i30000-1-11-111-1i3i3−i3−i3−i3−i3i3i30000000000000000000000000000
χ784-4-4-4444-4-2-2222-2222-22-2-2-2-220012i3−2i3−2i32i30000-1-11-111-1−i3−i3i3i3i3i3−i3−i30000000000000000000000000000

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