Finite Group Databasebeta

← Group #10591717

Character table — Group #10591717

Order 576.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78
size1111111122222222222222224444444444444444444444444412121212121212121212121212121212121212121212121236363636
order1222222233666666666666662236666666666666666666666644444444121212121212121212121212121212124444
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
χ5111111111111111111111111-1-11-1-1-1-1-1-1-1-11111111-1-1-1-1-1-1-1-111-1-111-1-11111-1-1-1-11111-1-1-1-111-1-1
χ6111111111111111111111111-1-11-1-1-1-1-1-1-1-11111111-1-1-1-1-1-1-1-111-1-1-1-1111111-1-1-1-1-1-1-1-11111-1-111
χ7111111111111111111111111-1-11-1-1-1-1-1-1-1-11111111-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-111111111-1-1-1-1-1-111
χ8111111111111111111111111-1-11-1-1-1-1-1-1-1-11111111-1-1-1-1-1-1-1-1-1-111-1-111-1-1-1-11111-1-1-1-1111111-1-1
χ9222222222-122222-1-1-1-1-122-1-122-12222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-10000222200000000-1-1-1-1-1-1-1-10000
χ10222222222-122222-1-1-1-1-122-1-122-12222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-10000-2-2-2-200000000111111110000
χ11222222222-122222-1-1-1-1-122-1-1-2-2-1-2-2-2-21111-1-1-1-1-1-1-111111111000022-2-200000000-1-1-1-111110000
χ12222222222-122222-1-1-1-1-122-1-1-2-2-1-2-2-2-21111-1-1-1-1-1-1-1111111110000-2-222000000001111-1-1-1-10000
χ1322222222-12-1-1-1-1-122222-1-12222-1-1-1-1-12222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-122220000-1-1-1-1-1-1-1-1000000000000
χ1422222222-12-1-1-1-1-122222-1-12222-1-1-1-1-12222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-2-2-2-2000011111111000000000000
χ1522222222-12-1-1-1-1-122222-1-122-2-2-11111-2-2-2-2-1-1-1-1-1-1-11111111122-2-20000-1-1-1-11111000000000000
χ1622222222-12-1-1-1-1-122222-1-122-2-2-11111-2-2-2-2-1-1-1-1-1-1-111111111-2-22200001111-1-1-1-1000000000000
χ17222-2-2-2-2222222-2-222-2-2-2-2-22-200200000000222-2-2-2-200000000002i−2i000000002i2i−2i−2i000000000000
χ18222-2-2-2-2222222-2-222-2-2-2-2-22-200200000000222-2-2-2-20000000000−2i2i00000000−2i−2i2i2i000000000000
χ19222-2-2-2-22-12-1-1-11122-2-2-2112-200-1−i3−i3i3i30000-1-1-11111−i3−i3−i3−i3i3i3i3i3002i−2i000033−3−3−i−iii000000000000
χ20222-2-2-2-22-12-1-1-11122-2-2-2112-200-1−i3−i3i3i30000-1-1-11111−i3−i3−i3−i3i3i3i3i300−2i2i0000−3−333ii−i−i000000000000
χ21222-2-2-2-22-12-1-1-11122-2-2-2112-200-1i3i3−i3−i30000-1-1-11111i3i3i3i3−i3−i3−i3−i3002i−2i0000−3−333−i−iii000000000000
χ22222-2-2-2-22-12-1-1-11122-2-2-2112-200-1i3i3−i3−i30000-1-1-11111i3i3i3i3−i3−i3−i3−i300−2i2i000033−3−3ii−i−i000000000000
χ2322-222-2-2-2222-2-22-22-22-2-22-2-22002000000002-2-222-2-200000000000000000000000000000000002i−2i
χ2422-222-2-2-2222-2-22-22-22-2-22-2-22002000000002-2-222-2-20000000000000000000000000000000000−2i2i
χ2522-2-2-222-2222-2-2-222-2-222-22-2-2002000000002-2-2-2-2220000000000002i−2i00000000002i2i−2i−2i00000000
χ2622-2-2-222-2222-2-2-222-2-222-22-2-2002000000002-2-2-2-222000000000000−2i2i0000000000−2i−2i2i2i00000000
χ2722-2-2-222-22-12-2-2-22-111-1-1-221100-10000−i3−i3i3i3-11111-1-1−i3−i3i3i3−i3−i3i3i300002i−2i0000000000−i−iii33−3−30000
χ2822-2-2-222-22-12-2-2-22-111-1-1-221100-10000−i3−i3i3i3-11111-1-1−i3−i3i3i3−i3−i3i3i30000−2i2i0000000000ii−i−i−3−3330000
χ2922-2-2-222-22-12-2-2-22-111-1-1-221100-10000i3i3−i3−i3-11111-1-1i3i3−i3−i3i3i3−i3−i300002i−2i0000000000−i−iii−3−3330000
χ3022-2-2-222-22-12-2-2-22-111-1-1-221100-10000i3i3−i3−i3-11111-1-1i3i3−i3−i3i3i3−i3−i30000−2i2i0000000000ii−i−i33−3−30000
χ312-222-22-2-222-22-22-2-22-22-2-22-2200200000000-22-22-22-2000000000000000000000000000000002i−2i00
χ322-222-22-2-222-22-22-2-22-22-2-22-2200200000000-22-22-22-200000000000000000000000000000000−2i2i00
χ332-22-22-22-222-22-2-22-222-222-2-2-200200000000-22-2-22-22000000000000002i−2i0000000000002i−2i2i−2i0000
χ342-22-22-22-222-22-2-22-222-222-2-2-200200000000-22-2-22-2200000000000000−2i2i000000000000−2i2i−2i2i0000
χ352-22-22-22-22-1-22-2-221-1-11-12-21100-10000−i3i3−i3i31-111-11-1−i3i3−i3i3−i3i3−i3i30000002i−2i000000003−33−3−ii−ii0000
χ362-22-22-22-22-1-22-2-221-1-11-12-21100-10000−i3i3−i3i31-111-11-1−i3i3−i3i3−i3i3−i3i3000000−2i2i00000000−33−33i−ii−i0000
χ372-22-22-22-22-1-22-2-221-1-11-12-21100-10000i3−i3i3−i31-111-11-1i3−i3i3−i3i3−i3i3−i30000002i−2i00000000−33−33−ii−ii0000
χ382-22-22-22-22-1-22-2-221-1-11-12-21100-10000i3−i3i3−i31-111-11-1i3−i3i3−i3i3−i3i3−i3000000−2i2i000000003−33−3i−ii−i0000
χ392-2-22-2-22222-2-2222-2-2-2-22-2-2222-222-22-22-2-22-2-222-2-222-2-222-2-220000000000000000000000000000
χ402-2-22-2-22222-2-2222-2-2-2-22-2-222-222-22-22-222-2-2-222-2-22-222-2-222-20000000000000000000000000000
χ412-2-22-2-2222-1-2-22221111-1-2-2-1-12-2-12-22-2-111-111-1-111-1-111-1-111-10000000000000000−i3i3i3−i3−i3i3i3−i30000
χ422-2-22-2-2222-1-2-22221111-1-2-2-1-12-2-12-22-2-111-111-1-111-1-111-1-111-10000000000000000i3−i3−i3i3i3−i3−i3i30000
χ432-2-22-2-2222-1-2-22221111-1-2-2-1-1-22-1-22-221-1-1111-1-111-11-1-111-1-110000000000000000−i3i3i3−i3i3−i3−i3i30000
χ442-2-22-2-2222-1-2-22221111-1-2-2-1-1-22-1-22-221-1-1111-1-111-11-1-111-1-110000000000000000i3−i3−i3i3−i3i3i3−i30000
χ452-2-22-2-222-1211-1-1-1-2-2-2-2211222-2-1-11-112-2-2211-1-111-1-111-1-111-1000000003−33−33−33−3000000000000
χ462-2-22-2-222-1211-1-1-1-2-2-2-2211222-2-1-11-112-2-2211-1-111-1-111-1-111-100000000−33−33−33−33000000000000
χ472-2-22-2-222-1211-1-1-1-2-2-2-221122-22-11-11-1-222-211-1-111-11-1-111-1-11000000003−33−3−33−33000000000000
χ482-2-22-2-222-1211-1-1-1-2-2-2-221122-22-11-11-1-222-211-1-111-11-1-111-1-1100000000−33−333−33−3000000000000
χ492-2-2-222-2222-2-22-2-2-2-222-2222-200200000000-2-22-222-2000000002-20000002-2-220000000000000000
χ502-2-2-222-2222-2-22-2-2-2-222-2222-200200000000-2-22-222-200000000-22000000-222-20000000000000000
χ512-2-2-222-22-1211-111-2-222-2-1-12-200-1−i3i3i3−i3000011-11-1-11−i3i3i3−i3i3−i3−i3i32-2000000-111-1−i3i3i3−i3000000000000
χ522-2-2-222-22-1211-111-2-222-2-1-12-200-1−i3i3i3−i3000011-11-1-11−i3i3i3−i3i3−i3−i3i3-220000001-1-11i3−i3−i3i3000000000000
χ532-2-2-222-22-1211-111-2-222-2-1-12-200-1i3−i3−i3i3000011-11-1-11i3−i3−i3i3−i3i3i3−i32-2000000-111-1i3−i3−i3i3000000000000
χ542-2-2-222-22-1211-111-2-222-2-1-12-200-1i3−i3−i3i3000011-11-1-11i3−i3−i3i3−i3i3i3−i3-220000001-1-11−i3i3i3−i3000000000000
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
χ57444-4-4-4-444-2444-4-4-2-2222-4-4-2200-200000000-2-2-22222000000000000000000000000000000000000
χ58444-4-4-4-44-2-2-2-2-222-2-222222-22001−2i3−2i32i32i30000111-1-1-1-1i3i3i3i3−i3−i3−i3−i30000000000000000000000000000
χ59444-4-4-4-44-2-2-2-2-222-2-222222-220012i32i3−2i3−2i30000111-1-1-1-1−i3−i3−i3−i3i3i3i3i30000000000000000000000000000
χ6044-444-4-4-44-24-4-44-4-22-2224-42-200-200000000-222-2-222000000000000000000000000000000000000
χ6144-444-4-4-4-24-222-224-44-4-4-22-4400-200000000-222-2-222000000000000000000000000000000000000
χ6244-444-4-4-4-2-2-222-22-22-222-222-2001000000001-1-111-1-133-3-3-3-3330000000000000000000000000000
χ6344-444-4-4-4-2-2-222-22-22-222-222-2001000000001-1-111-1-1-3-33333-3-30000000000000000000000000000
χ6444-4-4-444-4-24-2222-24-4-4442-2-4-400-200000000-22222-2-2000000000000000000000000000000000000
χ6544-4-4-444-4-2-2-2222-2-222-2-22-2220010000−2i3−2i32i32i31-1-1-1-111i3i3−i3−i3i3i3−i3−i30000000000000000000000000000
χ6644-4-4-444-4-2-2-2222-2-222-2-22-22200100002i32i3−2i3−2i31-1-1-1-111−i3−i3i3i3−i3−i3i3i30000000000000000000000000000
χ674-444-44-4-44-2-44-44-42-22-22-442-200-2000000002-22-22-22000000000000000000000000000000000000
χ684-444-44-4-4-242-22-22-44-44-42-2-4400-2000000002-22-22-22000000000000000000000000000000000000
χ694-444-44-4-4-2-22-22-222-22-222-22-200100000000-11-11-11-13-33-3-33-330000000000000000000000000000
χ704-444-44-4-4-2-22-22-222-22-222-22-200100000000-11-11-11-1-33-333-33-30000000000000000000000000000
χ714-44-44-44-4-242-222-2-444-44-22-4-400-2000000002-222-22-2000000000000000000000000000000000000
χ724-44-44-44-4-2-22-222-22-2-22-2-22220010000−2i32i3−2i32i3-11-1-11-11i3−i3i3−i3i3−i3i3−i30000000000000000000000000000
χ734-44-44-44-4-2-22-222-22-2-22-2-222200100002i3−2i32i3−2i3-11-1-11-11−i3i3−i3i3−i3i3−i3i30000000000000000000000000000
χ744-4-44-4-444-2-222-2-2-22222-222-2-24-41-22-22-222-2-1-111-1-111-1-111-1-110000000000000000000000000000
χ754-4-44-4-444-2-222-2-2-22222-222-2-2-4412-22-22-2-22-1-111-1-11-111-1-111-10000000000000000000000000000
χ764-4-4-444-444-2-4-44-4-422-2-2244-2200-20000000022-22-2-22000000000000000000000000000000000000
χ774-4-4-444-44-2-222-22222-2-22-2-2-22001−2i32i32i3−2i30000-1-11-111-1i3−i3−i3i3−i3i3i3−i30000000000000000000000000000
χ784-4-4-444-44-2-222-22222-2-22-2-2-220012i3−2i3−2i32i30000-1-11-111-1−i3i3i3−i3i3−i3−i3i30000000000000000000000000000

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