Finite Group Databasebeta

← Group #13150901

Character table — Group #13150901

Order 1728.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95
size1111222222222222444446666666666661212121212121212121212121212121212121212121212121212181818181818181836363636363636363636363636363636363636363636363672727272
order12223444466612121212266121233666666121212123666666666661212121212121212121212121212222244442444444466661212121212121212121212126121212
χ111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111111111111111111111111-1-111-1-1-11-1-1-11-1-111-1-1111111-1-1-1-1-1-1-1-1-1-1
χ311111111111111111111111111111111111111111111111111111111111-1-111-1-111-1-11-1-1-11-1-1-111-1-1-1-1-1-1111111-1-1-1-1
χ411111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-11-1-111-1-11-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111
χ51111111-1-11111111-1-1-1-1-111111111-1-1-1-11-1-1-1-111-1-1-1-111111-1-11111-1-1-1-11111-1-1111-1-11-11-1-11111-1-1-1-11111-1-1-1-111-1-1
χ61111111-1-11111111-1-1-1-1-111111111-1-1-1-11-1-1-1-111-1-1-1-111111-1-11111-1-1-1-111-1-1-1-1-1-1-1-11-1111111-1-1-1-1-1-111-1-11111-1-111
χ71111111-1-11111111-1-1-1-1-111111111-1-1-1-11-1-1-1-111-1-1-1-111111-1-11111-1-1-1-1-1-1111111-11-1-11-1-11-1-1111111-1-111-1-1-1-1-1-111
χ81111111-1-11111111-1-1-1-1-111111111-1-1-1-11-1-1-1-111-1-1-1-111111-1-11111-1-1-1-1-1-1-1-111-1-11111-1-11-1-1-1-1-11111-1-1-1-1111111-1-1
χ911111-1-111111-1-1-1-1-1-1-1111111111111111-1-1-1-111-1-1-1-11-1-1-1-111-1-1-1-11111111111-1-11-1-1-11-11-1111111-1-1-1-1-1-1-1-1111-11-1
χ1011111-1-111111-1-1-1-1-1-1-1111111111111111-1-1-1-111-1-1-1-11-1-1-1-111-1-1-1-1111111-1-11111-1-111-1-1-1111-1-111-1-1-1-11111-1-1-11-11
χ1111111-1-111111-1-1-1-1-1-1-1111111111111111-1-1-1-111-1-1-1-11-1-1-1-111-1-1-1-11111-1-111-1-1-1-1-11-11-1111-1-111-1-11111-1-1-1-111-11-11
χ1211111-1-111111-1-1-1-1-1-1-1111111111111111-1-1-1-111-1-1-1-11-1-1-1-111-1-1-1-11111-1-1-1-1-1-111111-111-1-1-1-1-1-1-1-111111111-1-11-11-1
χ1311111-1-1-1-1111-1-1-1-1111-1-111111111-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1111-1-1-1-111111-1-111-1-1-1-111-1-11-1-11
χ1411111-1-1-1-1111-1-1-1-1111-1-111111111-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-111-11-111-11-111-1-1-1-111-1-111-1-111-111-1
χ1511111-1-1-1-1111-1-1-1-1111-1-111111111-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1-1-11111-1-111-1-111-1-1-111-1
χ1611111-1-1-1-1111-1-1-1-1111-1-111111111-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111-1-1-1-1111-1-1-1-111-1-11111-1-1111-1-11
χ172222222222222222222222-122-1-12-12222-122-1-1-1-1-1-1-1-1-122-1-1-1-1-1-1-1-1-1-1-1-100000000200220020000000000000000-1-1-1-1
χ182222222222222222222222-122-1-12-12222-122-1-1-1-1-1-1-1-1-122-1-1-1-1-1-1-1-1-1-1-1-100000000-200-2-200-200000000000000001111
χ19222222222222222222222-12-1-122-12-1-1-1-1-1-1-122-1-1-1-1-1-1-1-1-12222-1-1-1-1-1-1-1-1002200220020002000-1-1000000-1-1-1-1-1-10000
χ20222222222222222222222-12-1-122-12-1-1-1-1-1-1-122-1-1-1-1-1-1-1-1-12222-1-1-1-1-1-1-1-100-2-200-2-200-2000-2000110000001111110000
χ212222222-2-22222222-2-2-2-2-22-122-1-12-1-2-2-2-2-1-2-211-1-11111-122-1-111-1-1-1-11111000000002002-200-20000000000000000-1-111
χ222222222-2-22222222-2-2-2-2-22-122-1-12-1-2-2-2-2-1-2-211-1-11111-122-1-111-1-1-1-1111100000000-200-22002000000000000000011-1-1
χ232222222-2-22222222-2-2-2-2-2-12-1-122-121111-111-2-2-1-11111-1-1-122-2-2-1-1-1-111110022002200-2000-2000-1-1000000-1-111110000
χ242222222-2-22222222-2-2-2-2-2-12-1-122-121111-111-2-2-1-11111-1-1-122-2-2-1-1-1-1111100-2-200-2-200200020001100000011-1-1-1-10000
χ2522222-2-222222-2-2-2-2-2-2-2222-122-1-12-12222-1-2-211-1-11111-1-2-211-1-11111-1-1-1-100000000200-2200-20000000000000000-11-11
χ2622222-2-222222-2-2-2-2-2-2-2222-122-1-12-12222-1-2-211-1-11111-1-2-211-1-11111-1-1-1-100000000-2002-200200000000000000001-11-1
χ2722222-2-222222-2-2-2-2-2-2-222-12-1-122-12-1-1-1-1-111-2-2-1-11111-111-2-2221111-1-1-1-1002200-2-200-20002000-1-10000001111-1-10000
χ2822222-2-222222-2-2-2-2-2-2-222-12-1-122-12-1-1-1-1-111-2-2-1-11111-111-2-2221111-1-1-1-100-2-20022002000-200011000000-1-1-1-1110000
χ2922222-2-2-2-2222-2-2-2-2222-2-22-122-1-12-1-2-2-2-2-122-1-1-1-1-1-1-1-1-1-2-211111111111100000000200-2-20020000000000000000-111-1
χ3022222-2-2-2-2222-2-2-2-2222-2-22-122-1-12-1-2-2-2-2-122-1-1-1-1-1-1-1-1-1-2-211111111111100000000-2002200-200000000000000001-1-11
χ3122222-2-2-2-2222-2-2-2-2222-2-2-12-1-122-121111-1-1-122-1-1-1-1-1-1-111-2-2-2-211111111002200-2-2002000-2000-1-100000011-1-1110000
χ3222222-2-2-2-2222-2-2-2-2222-2-2-12-1-122-121111-1-1-122-1-1-1-1-1-1-111-2-2-2-21111111100-2-2002200-2000200011000000-1-111-1-10000
χ3322-2-22002i−2i2-2-200000002i−2i222-22-2-2-22i2i−2i−2i200002-20000-200002i−2i00002i2i−2i−2i2-2002i−2i00000000002-2002i−2i00000000000000
χ3422-2-22002i−2i2-2-200000002i−2i222-22-2-2-22i2i−2i−2i200002-20000-200002i−2i00002i2i−2i−2i-2200−2i2i0000000000-2200−2i2i00000000000000
χ3522-2-2200−2i2i2-2-20000000−2i2i222-22-2-2-2−2i−2i2i2i200002-20000-20000−2i2i0000−2i−2i2i2i2-200−2i2i00000000002-200−2i2i00000000000000
χ3622-2-2200−2i2i2-2-20000000−2i2i222-22-2-2-2−2i−2i2i2i200002-20000-20000−2i2i0000−2i−2i2i2i-22002i−2i0000000000-22002i−2i00000000000000
χ372-22-222i−2i00-22-22i2i−2i−2i0000022-22-22-2-2000020000-220000-22i−2i2i−2i002i2i−2i−2i0000002-2002i−2i00000000002-20000002i−2i00000000
χ382-22-222i−2i00-22-22i2i−2i−2i0000022-22-22-2-2000020000-220000-22i−2i2i−2i002i2i−2i−2i000000-2200−2i2i0000000000-22000000−2i2i00000000
χ392-22-222i−2i00-22-22i2i−2i−2i00000-121-1-221-23−33−3-1−i3i3001-1−i3−i3i3i31−ii2i−2i00−i−iii3−33−3002-2002i−2i0000000000-11000000−ii−i3i33−30000
χ402-22-222i−2i00-22-22i2i−2i−2i00000-121-1-221-23−33−3-1−i3i3001-1−i3−i3i3i31−ii2i−2i00−i−iii3−33−300-2200−2i2i00000000001-1000000i−ii3−i3−330000
χ412-22-222i−2i00-22-22i2i−2i−2i00000-121-1-221-2−33−33-1i3−i3001-1i3i3−i3−i31−ii2i−2i00−i−iii−33−33002-2002i−2i0000000000-11000000−iii3−i3−330000
χ422-22-222i−2i00-22-22i2i−2i−2i00000-121-1-221-2−33−33-1i3−i3001-1i3i3−i3−i31−ii2i−2i00−i−iii−33−3300-2200−2i2i00000000001-1000000i−i−i3i33−30000
χ432-22-22−2i2i00-22-2−2i−2i2i2i0000022-22-22-2-2000020000-220000-2−2i2i−2i2i00−2i−2i2i2i0000002-200−2i2i00000000002-2000000−2i2i00000000
χ442-22-22−2i2i00-22-2−2i−2i2i2i0000022-22-22-2-2000020000-220000-2−2i2i−2i2i00−2i−2i2i2i000000-22002i−2i0000000000-220000002i−2i00000000
χ452-22-22−2i2i00-22-2−2i−2i2i2i00000-121-1-221-23−33−3-1i3−i3001-1i3i3−i3−i31i−i−2i2i00ii−i−i3−33−3002-200−2i2i0000000000-11000000i−ii3−i33−30000
χ462-22-22−2i2i00-22-2−2i−2i2i2i00000-121-1-221-23−33−3-1i3−i3001-1i3i3−i3−i31i−i−2i2i00ii−i−i3−33−300-22002i−2i00000000001-1000000−ii−i3i3−330000
χ472-22-22−2i2i00-22-2−2i−2i2i2i00000-121-1-221-2−33−33-1−i3i3001-1−i3−i3i3i31i−i−2i2i00ii−i−i−33−33002-200−2i2i0000000000-11000000i−i−i3i3−330000
χ482-22-22−2i2i00-22-2−2i−2i2i2i00000-121-1-221-2−33−33-1−i3i3001-1−i3−i3i3i31i−i−2i2i00ii−i−i−33−3300-22002i−2i00000000001-1000000−iii3−i33−30000
χ49444444444444444444444-2-2-2-2-2-2-2-2-2-2-2-21-2-2-2-21111111-2-2-2-2-2-211111111000000000000000000000000000000000000
χ504444444-4-44444444-4-4-4-4-4-2-2-2-2-2-2-2-222221222211-1-1-1-11-2-2-2-2221111-1-1-1-1000000000000000000000000000000000000
χ5144444-4-444444-4-4-4-4-4-4-444-2-2-2-2-2-2-2-2-2-2-2-21222211-1-1-1-112222-2-2-1-1-1-11111000000000000000000000000000000000000
χ5244444-4-4-4-4444-4-4-4-4444-4-4-2-2-2-2-2-2-2-222221-2-2-2-21111111222222-1-1-1-1-1-1-1-1000000000000000000000000000000000000
χ5344-4-44004i−4i4-4-400000004i−4i4-24-4-22-424i4i−4i−4i-20000-22000020000−2i2i0000−2i−2i2i2i000000000000000000000000000000000000
χ5444-4-44004i−4i4-4-400000004i−4i-24-224-42-4−2i−2i2i2i-20000-220000200004i−4i0000−2i−2i2i2i000000000000000000000000000000000000
χ5544-4-44004i−4i4-4-400000004i−4i-2-2-22-2222−2i−2i2i2i100001-13-33-3-10000−2i2i3i−3i3i−3iii−i−i000000000000000000000000000000000000
χ5644-4-44004i−4i4-4-400000004i−4i-2-2-22-2222−2i−2i2i2i100001-1-33-33-10000−2i2i−3i3i−3i3iii−i−i000000000000000000000000000000000000
χ5744-4-4400−4i4i4-4-40000000−4i4i4-24-4-22-42−4i−4i4i4i-20000-220000200002i−2i00002i2i−2i−2i000000000000000000000000000000000000
χ5844-4-4400−4i4i4-4-40000000−4i4i-24-224-42-42i2i−2i−2i-20000-22000020000−4i4i00002i2i−2i−2i000000000000000000000000000000000000
χ5944-4-4400−4i4i4-4-40000000−4i4i-2-2-22-22222i2i−2i−2i100001-13-33-3-100002i−2i−3i3i−3i3i−i−iii000000000000000000000000000000000000
χ6044-4-4400−4i4i4-4-40000000−4i4i-2-2-22-22222i2i−2i−2i100001-1-33-33-100002i−2i3i−3i3i−3i−i−iii000000000000000000000000000000000000
χ614-44-444i−4i00-44-44i4i−4i−4i000004-2-442-2-420000-200002-2000024i−4i−2i2i00−2i−2i2i2i0000000000000000000000000000000000000000
χ624-44-444i−4i00-44-44i4i−4i−4i00000-2-22-22-22223−2323−231−2i32i300-11i3i3−i3−i3-1−2i2i−2i2i00ii−i−i−33−33000000000000000000000000000000000000
χ634-44-444i−4i00-44-44i4i−4i−4i00000-2-22-22-222−2323−232312i3−2i300-11−i3−i3i3i3-1−2i2i−2i2i00ii−i−i3−33−3000000000000000000000000000000000000
χ644-44-44−4i4i00-44-4−4i−4i4i4i000004-2-442-2-420000-200002-200002−4i4i2i−2i002i2i−2i−2i0000000000000000000000000000000000000000
χ654-44-44−4i4i00-44-4−4i−4i4i4i00000-2-22-22-22223−2323−2312i3−2i300-11−i3−i3i3i3-12i−2i2i−2i00−i−iii−33−33000000000000000000000000000000000000
χ664-44-44−4i4i00-44-4−4i−4i4i4i00000-2-22-22-222−2323−23231−2i32i300-11i3i3−i3−i3-12i−2i2i−2i00−i−iii3−33−3000000000000000000000000000000000000
χ674-4-4440000-4-4400000000044-4-4-4-444000040000-4-40000400000000000000000000000000000000000000000000000000
χ684-4-4440000-4-440000000004-2-4-4224-20000-200−2i32i322−2i32i32i3−2i3-200000000000000000000000000000000000000000000000000
χ694-4-4440000-4-440000000004-2-4-4224-20000-2002i3−2i3222i3−2i3−2i32i3-200000000000000000000000000000000000000000000000000
χ704-4-4440000-4-44000000000-2422-4-4-24−2i32i32i3−2i3-20000220000-20000000000−2i32i32i3−2i3000000000000000000000000000000000000
χ714-4-4440000-4-44000000000-2422-4-4-242i3−2i3−2i32i3-20000220000-200000000002i3−2i3−2i32i3000000000000000000000000000000000000
χ724-4-4440000-4-44000000000-2-22222-2-2−2i32i32i3−2i3100−2i32i3-1-1i3−i3−i3i31000000-333-3i3−i3−i3i3000000000000000000000000000000000000
χ734-4-4440000-4-44000000000-2-22222-2-2−2i32i32i3−2i31002i3−2i3-1-1−i3i3i3−i310000003-3-33i3−i3−i3i3000000000000000000000000000000000000
χ744-4-4440000-4-44000000000-2-22222-2-22i3−2i3−2i32i3100−2i32i3-1-1i3−i3−i3i310000003-3-33−i3i3i3−i3000000000000000000000000000000000000
χ754-4-4440000-4-44000000000-2-22222-2-22i3−2i3−2i32i31002i3−2i3-1-1−i3i3i3−i31000000-333-3−i3i3i3−i3000000000000000000000000000000000000
χ766666-36666-3-3-3-3-3-3-36-3-3-3-3000000000000000000000000000000000000002200220002000200-1-100-1-1-1-1-1-10000000000
χ776666-36666-3-3-3-3-3-3-36-3-3-3-300000000000000000000000000000000000000-2-200-2-2000-2000-20011001111110000000000
χ786666-366-6-6-3-3-3-3-3-3-3-63333000000000000000000000000000000000000002200-2-2000-2000200-1-1001111-1-10000000000
χ796666-366-6-6-3-3-3-3-3-3-3-6333300000000000000000000000000000000000000-2-200220002000-2001100-1-1-1-1110000000000
χ806666-3-6-666-3-3-33333-633-3-300000000000000000000000000000000000000220022000-2000-200-1-100-1-111110000000000
χ816666-3-6-666-3-3-33333-633-3-300000000000000000000000000000000000000-2-200-2-20002000200110011-1-1-1-10000000000
χ826666-3-6-6-6-6-3-3-333336-3-333000000000000000000000000000000000000002200-2-20002000-200-1-10011-1-1110000000000
χ836666-3-6-6-6-6-3-3-333336-3-33300000000000000000000000000000000000000-2-20022000-20002001100-1-111-1-10000000000
χ8466-6-6-3006i−6i-33333−3333−330−3i33i3−3i3i000000000000000000000000000000000000002-2002i−2i0000000000-1100−ii−i3i33−30000000000
χ8566-6-6-3006i−6i-33333−3333−330−3i33i3−3i3i00000000000000000000000000000000000000-2200−2i2i00000000001-100i−ii3−i3−330000000000
χ8666-6-6-3006i−6i-333−3333−333303i3−3i3−3i3i000000000000000000000000000000000000002-2002i−2i0000000000-1100−iii3−i3−330000000000
χ8766-6-6-3006i−6i-333−3333−333303i3−3i3−3i3i00000000000000000000000000000000000000-2200−2i2i00000000001-100i−i−i3i33−30000000000
χ8866-6-6-300−6i6i-33333−3333−3303i3−3i33i−3i000000000000000000000000000000000000002-200−2i2i0000000000-1100i−ii3−i33−30000000000
χ8966-6-6-300−6i6i-33333−3333−3303i3−3i33i−3i00000000000000000000000000000000000000-22002i−2i00000000001-100−ii−i3i3−330000000000
χ9066-6-6-300−6i6i-333−3333−33330−3i33i33i−3i000000000000000000000000000000000000002-200−2i2i0000000000-1100i−i−i3i3−330000000000
χ9166-6-6-300−6i6i-333−3333−33330−3i33i33i−3i00000000000000000000000000000000000000-22002i−2i00000000001-100−iii3−i33−30000000000
χ9212-1212-12-612i−12i006-66−6i−6i6i6i0000000000000000000000000000000000000000000000000000000000000000000000000000000
χ9312-1212-12-6−12i12i006-666i6i−6i−6i0000000000000000000000000000000000000000000000000000000000000000000000000000000
χ9412-12-1212-6000066-6−6i36i36i3−6i30000000000000000000000000000000000000000000000000000000000000000000000000000000
χ9512-12-1212-6000066-66i3−6i3−6i36i30000000000000000000000000000000000000000000000000000000000000000000000000000000

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