Finite Group Databasebeta

← Group #10591691

Character table — Group #10591691

Order 576.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78
size1111111122222222222222224444444444444444444444444412121212121212121212121212121212121212121212121236363636
order1222222233666666666666662236666666666666666666666644444444121212121212121212121212121212124444
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
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
χ6111111111111111111111111-1-11-1-1-1-1-1-1-1-11111111-1-1-1-1-1-1-1-111-1-1-1-1111111-1-1-1-1-1-1-1-11111-1-111
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
χ8111111111111111111111111-1-11-1-1-1-1-1-1-1-11111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1-1-1111111-1-1
χ9222222222-122222-1-1-1-1-122-1-122-12222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-10022002200000000-1-1-1-1-1-1-1-10000
χ10222222222-122222-1-1-1-1-122-1-122-12222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-100-2-200-2-200000000111111110000
χ11222222222-122222-1-1-1-1-122-1-1-2-2-1-2-2-2-21111-1-1-1-1-1-1-111111111002200-2-200000000-1-1-1-111110000
χ12222222222-122222-1-1-1-1-122-1-1-2-2-1-2-2-2-21111-1-1-1-1-1-1-11111111100-2-20022000000001111-1-1-1-10000
χ1322222222-12-1-1-1-1-122222-1-12222-1-1-1-1-12222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-122002200-1-1-1-1-1-1-1-1000000000000
χ1422222222-12-1-1-1-1-122222-1-12222-1-1-1-1-12222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-2-200-2-20011111111000000000000
χ1522222222-12-1-1-1-1-122222-1-122-2-2-11111-2-2-2-2-1-1-1-1-1-1-1111111112200-2-200-1-1-1-11111000000000000
χ1622222222-12-1-1-1-1-122222-1-122-2-2-11111-2-2-2-2-1-1-1-1-1-1-111111111-2-20022001111-1-1-1-1000000000000
χ172222-2-2-2-222222-2-2222-2-2-2-2-2-22-2222-2-222-2-2222-2-2-2-22222-2-2-2-20000000000000000000000000000
χ182222-2-2-2-222222-2-2222-2-2-2-2-2-2-222-2-222-2-222222-2-2-2-2-2-2-2-222220000000000000000000000000000
χ192222-2-2-2-22-1222-2-2-1-1-111-2-2112-2-122-2-2-1-111-1-1-11111-1-1-1-11111000000000000000033−3−333−3−30000
χ202222-2-2-2-22-1222-2-2-1-1-111-2-2112-2-122-2-2-1-111-1-1-11111-1-1-1-111110000000000000000−3−333−3−3330000
χ212222-2-2-2-22-1222-2-2-1-1-111-2-211-22-1-2-22211-1-1-1-1-111111111-1-1-1-1000000000000000033−3−3−3−3330000
χ222222-2-2-2-22-1222-2-2-1-1-111-2-211-22-1-2-22211-1-1-1-1-111111111-1-1-1-10000000000000000−3−33333−3−30000
χ232222-2-2-2-2-12-1-1-111222-2-211-2-22-2-1-1-11122-2-2-1-1-11111-1-1-1-111110000000033−3−333−3−3000000000000
χ242222-2-2-2-2-12-1-1-111222-2-211-2-22-2-1-1-11122-2-2-1-1-11111-1-1-1-1111100000000−3−333−3−333000000000000
χ252222-2-2-2-2-12-1-1-111222-2-211-2-2-22-111-1-1-2-222-1-1-111111111-1-1-1-10000000033−3−3−3−333000000000000
χ262222-2-2-2-2-12-1-1-111222-2-211-2-2-22-111-1-1-2-222-1-1-111111111-1-1-1-100000000−3−33333−3−3000000000000
χ2722-2-222-2-2222-2-22-22-2-22-22-22-2002000000002-2-222-2-200000000000000000000000000000000002i−2i
χ2822-2-222-2-2222-2-22-22-2-22-22-22-2002000000002-2-222-2-20000000000000000000000000000000000−2i2i
χ2922-2-2-2-222222-2-2-222-2-2-22-22-22002000000002-2-2-2-222000000000000000000000000000000002-200
χ3022-2-2-2-222222-2-2-222-2-2-22-22-22002000000002-2-2-2-22200000000000000000000000000000000-2200
χ312-22-22-22-222-22-222-22-22-2-2-2-2200200000000-22-22-22-20000000000002i−2i0000002i−2i2i−2i000000000000
χ322-22-22-22-222-22-222-22-22-2-2-2-2200200000000-22-22-22-2000000000000−2i2i000000−2i2i−2i2i000000000000
χ332-22-22-22-2-121-11-1-1-22-22-211-2200-1−i3i3−i3i300001-11-11-11−i3−i3i3i3−i3−i3i3i300002i−2i003−33−3−ii−ii000000000000
χ342-22-22-22-2-121-11-1-1-22-22-211-2200-1−i3i3−i3i300001-11-11-11−i3−i3i3i3−i3−i3i3i30000−2i2i00−33−33i−ii−i000000000000
χ352-22-22-22-2-121-11-1-1-22-22-211-2200-1i3−i3i3−i300001-11-11-11i3i3−i3−i3i3i3−i3−i300002i−2i00−33−33−ii−ii000000000000
χ362-22-22-22-2-121-11-1-1-22-22-211-2200-1i3−i3i3−i300001-11-11-11i3i3−i3−i3i3i3−i3−i30000−2i2i003−33−3i−ii−i000000000000
χ372-22-2-22-2222-22-2-2-2-22-2-22222-200200000000-22-2-22-22000000002-20000002-2-220000000000000000
χ382-22-2-22-2222-22-2-2-2-22-2-22222-200200000000-22-2-22-2200000000-22000000-222-20000000000000000
χ392-22-2-22-22-121-1111-22-2-22-1-12-200-1−i3i3i3−i300001-111-11-1−i3−i3i3i3i3i3−i3−i32-2000000-111-1−i3i3i3−i3000000000000
χ402-22-2-22-22-121-1111-22-2-22-1-12-200-1−i3i3i3−i300001-111-11-1−i3−i3i3i3i3i3−i3−i3-220000001-1-11i3−i3−i3i3000000000000
χ412-22-2-22-22-121-1111-22-2-22-1-12-200-1i3−i3−i3i300001-111-11-1i3i3−i3−i3−i3−i3i3i32-2000000-111-1i3−i3−i3i3000000000000
χ422-22-2-22-22-121-1111-22-2-22-1-12-200-1i3−i3−i3i300001-111-11-1i3i3−i3−i3−i3−i3i3i3-220000001-1-11−i3i3i3−i3000000000000
χ432-2-222-2-2222-2-222-2-2-2222-22-2-200200000000-2-222-2-2200000000002i−2i0000000000002i−2i2i−2i00000000
χ442-2-222-2-2222-2-222-2-2-2222-22-2-200200000000-2-222-2-220000000000−2i2i000000000000−2i2i−2i2i00000000
χ452-2-222-2-222-1-2-222-211-1-1-1-221100-10000−i3i3−i3i311-1-111-1−i3i3−i3i3−i3i3−i3i3002i−2i000000000000−ii−ii3−33−30000
χ462-2-222-2-222-1-2-222-211-1-1-1-221100-10000−i3i3−i3i311-1-111-1−i3i3−i3i3−i3i3−i3i300−2i2i000000000000i−ii−i−33−330000
χ472-2-222-2-222-1-2-222-211-1-1-1-221100-10000i3−i3i3−i311-1-111-1i3−i3i3−i3i3−i3i3−i3002i−2i000000000000−ii−ii−33−330000
χ482-2-222-2-222-1-2-222-211-1-1-1-221100-10000i3−i3i3−i311-1-111-1i3−i3i3−i3i3−i3i3−i300−2i2i000000000000i−ii−i3−33−30000
χ492-2-22-222-222-2-22-22-2-22-2-22-22200200000000-2-22-222-2000000000000002-20000000000002-2-220000
χ502-2-22-222-222-2-22-22-2-22-2-22-22200200000000-2-22-222-200000000000000-22000000000000-222-20000
χ512-2-22-222-22-1-2-22-2211-1112-2-1-100-10000−i3i3i3−i311-11-1-11−i3i3−i3i3i3−i3i3−i30000002-200000000−i3i3i3−i3-111-10000
χ522-2-22-222-22-1-2-22-2211-1112-2-1-100-10000−i3i3i3−i311-11-1-11−i3i3−i3i3i3−i3i3−i3000000-2200000000i3−i3−i3i31-1-110000
χ532-2-22-222-22-1-2-22-2211-1112-2-1-100-10000i3−i3−i3i311-11-1-11i3−i3i3−i3−i3i3−i3i30000002-200000000i3−i3−i3i3-111-10000
χ542-2-22-222-22-1-2-22-2211-1112-2-1-100-10000i3−i3−i3i311-11-1-11i3−i3i3−i3−i3i3−i3i3000000-2200000000−i3i3i3−i31-1-110000
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
χ574444-4-4-4-4-2-2-2-2-222-2-2-22222224-41-2-222-2-222111-1-1-1-11111-1-1-1-10000000000000000000000000000
χ584444-4-4-4-4-2-2-2-2-222-2-2-2222222-44122-2-222-2-2111-1-1-1-1-1-1-1-111110000000000000000000000000000
χ5944-4-444-4-44-24-4-44-4-222-224-4-2200-200000000-222-2-222000000000000000000000000000000000000
χ6044-4-444-4-4-24-222-224-4-44-4-224-400-200000000-222-2-222000000000000000000000000000000000000
χ6144-4-444-4-4-2-2-222-22-222-22-22-22001000000001-1-111-1-13-3-333-3-330000000000000000000000000000
χ6244-4-444-4-4-2-2-222-22-222-22-22-22001000000001-1-111-1-1-333-3-333-30000000000000000000000000000
χ6344-4-4-4-4444-24-4-4-44-2222-2-442-200-200000000-22222-2-2000000000000000000000000000000000000
χ6444-4-4-4-444-24-2222-24-4-4-442-2-4400-200000000-22222-2-2000000000000000000000000000000000000
χ6544-4-4-4-444-2-2-2222-2-2222-22-22-2001000000001-1-1-1-1113-3-33-333-30000000000000000000000000000
χ6644-4-4-4-444-2-2-2222-2-2222-22-22-2001000000001-1-1-1-111-333-33-3-330000000000000000000000000000
χ674-44-44-44-44-2-44-4442-22-22-4-42-200-2000000002-22-22-22000000000000000000000000000000000000
χ684-44-44-44-4-2-22-22-2-22-22-22222-2001−2i32i3−2i32i30000-11-11-11-1i3i3−i3−i3i3i3−i3−i30000000000000000000000000000
χ694-44-44-44-4-2-22-22-2-22-22-22222-20012i3−2i32i3−2i30000-11-11-11-1−i3−i3i3i3−i3−i3i3i30000000000000000000000000000
χ704-44-4-44-444-2-44-4-4-42-222-244-2200-2000000002-222-22-2000000000000000000000000000000000000
χ714-44-4-44-44-2-22-22222-222-2-2-2-22001−2i32i32i3−2i30000-11-1-11-11i3i3−i3−i3−i3−i3i3i30000000000000000000000000000
χ724-44-4-44-44-2-22-22222-222-2-2-2-220012i3−2i3−2i32i30000-11-1-11-11−i3−i3i3i3i3i3−i3−i30000000000000000000000000000
χ734-4-444-4-44-2422-2-22-4-44442-2-4-400-20000000022-2-222-2000000000000000000000000000000000000
χ744-4-444-4-44-2-222-2-2222-2-2-22-2220010000−2i32i3−2i32i3-1-111-1-11i3−i3i3−i3i3−i3i3−i30000000000000000000000000000
χ754-4-444-4-44-2-222-2-2222-2-2-22-22200100002i3−2i32i3−2i3-1-111-1-11−i3i3−i3i3−i3i3−i3i30000000000000000000000000000
χ764-4-44-444-4-2422-22-2-4-44-4-4-224400-20000000022-22-2-22000000000000000000000000000000000000
χ774-4-44-444-4-2-222-22-222-222-22-2-20010000−2i32i32i3−2i3-1-11-111-1i3−i3i3−i3−i3i3−i3i30000000000000000000000000000
χ784-4-44-444-4-2-222-22-222-222-22-2-200100002i3−2i3−2i32i3-1-11-111-1−i3i3−i3i3i3−i3i3−i30000000000000000000000000000

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