Finite Group Databasebeta

← Group #13167532

Character table — Group #13167532

Order 1728.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78
size11112222444444444448888888888888888888899991818181836363636363636363636363636363636363636363636367272727272727272
order1222366633466666612123366666612121212121212121212121222226666222244444444412121212121212121212666612121212
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111111111111-1-1111-1-1-1-1-1-111-1-1-1-1-1-1-1-111-1-111-1-1
χ311111111111111111111111111111111111111111111111-1-1111-1-111-1-1-1-111-1-1-1-1-1-1-1-1-1-111-1-111
χ411111111111111111111111111111111111111111111111-1-1-1-11-1-1-1-111111111111111-1-1-1-1-1-1-1-1
χ51111111111-1111111-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-1-111-1-1-1-11111-1-1-1-11111-1-1-1-1
χ61111111111-1111111-1-111111111-1-1-1-1-1-1-1-1-1-1-1-11111111111-1-1-1-1-111-1-111-1-1-1-1-1-1111111-1-1-1-111
χ71111111111-1111111-1-111111111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-111-111-1-1-1-111-1-1-1-1-1-11111-1-11111-1-1
χ81111111111-1111111-1-111111111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1111111-1-1-1-11111-1-1-1-1-1-1-1-11111
χ9222222222222222222222222222222222222222-2-2-2-2-2-2-2-20000-200000000-2-20000000000000000
χ102222222222-2222222-2-222222222-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-20000200000000220000000000000000
χ112222-1-1-1-1222222222-1-1-1-1-1-1-1-1-1-12222-1-1-1-1-1-1-1-12222-1-1-1-10000200002222-1-1-1-1-1-1-1-1-1-100000000
χ122222-1-1-1-1222222222-1-1-1-1-1-1-1-1-1-12222-1-1-1-1-1-1-1-12222-1-1-1-1000020000-2-2-2-2-1-11111111100000000
χ132222-1-1-1-1222222222-1-1-1-1-1-1-1-1-1-12222-1-1-1-1-1-1-1-1-2-2-2-211110000-2000000001133−3−333−3−300000000
χ142222-1-1-1-1222222222-1-1-1-1-1-1-1-1-1-12222-1-1-1-1-1-1-1-1-2-2-2-211110000-20000000011−3−333−3−33300000000
χ152222-1-1-1-122-222222211-1-1-1-1-1-1-1-1-2-2-2-2111111112222-1-1-1-10000-2000022-2-211-1-1-1-1111100000000
χ162222-1-1-1-122-222222211-1-1-1-1-1-1-1-1-2-2-2-2111111112222-1-1-1-10000-20000-2-222111111-1-1-1-100000000
χ172222-1-1-1-122-222222211-1-1-1-1-1-1-1-1-2-2-2-211111111-2-2-2-211110000200000000-1-133−3−3−3−33300000000
χ182222-1-1-1-122-222222211-1-1-1-1-1-1-1-1-2-2-2-211111111-2-2-2-211110000200000000-1-1−3−33333−3−300000000
χ1922-2-22-2-22220-2-222-2-20022-2-2-2-22200000000000022-2-222-2-2000000000002i−2i0000002i−2i2i−2i00000000
χ2022-2-22-2-22220-2-222-2-20022-2-2-2-22200000000000022-2-222-2-200000000000−2i2i000000−2i2i−2i2i00000000
χ2122-2-22-2-22220-2-222-2-20022-2-2-2-222000000000000-2-222-2-2220000000002-200002-22-2000000000000
χ2222-2-22-2-22220-2-222-2-20022-2-2-2-222000000000000-2-222-2-222000000000-220000-22-22000000000000
χ2322-2-2-111-1220-2-222-2-2−i3i3-1-11111-1-10000−i3−i3−i3−i3i3i3i3i322-2-2-1-111000000000002i−2i−i3i33−3−33−ii−ii00000000
χ2422-2-2-111-1220-2-222-2-2−i3i3-1-11111-1-10000−i3−i3−i3−i3i3i3i3i322-2-2-1-11100000000000−2i2i−i3i3−333−3i−ii−i00000000
χ2522-2-2-111-1220-2-222-2-2−i3i3-1-11111-1-10000−i3−i3−i3−i3i3i3i3i3-2-22211-1-10000000002-200i3−i3-11-11−i3i3i3−i300000000
χ2622-2-2-111-1220-2-222-2-2−i3i3-1-11111-1-10000−i3−i3−i3−i3i3i3i3i3-2-22211-1-1000000000-2200i3−i31-11-1i3−i3−i3i300000000
χ2722-2-2-111-1220-2-222-2-2i3−i3-1-11111-1-10000i3i3i3i3−i3−i3−i3−i322-2-2-1-111000000000002i−2ii3−i3−333−3−ii−ii00000000
χ2822-2-2-111-1220-2-222-2-2i3−i3-1-11111-1-10000i3i3i3i3−i3−i3−i3−i322-2-2-1-11100000000000−2i2ii3−i33−3−33i−ii−i00000000
χ2922-2-2-111-1220-2-222-2-2i3−i3-1-11111-1-10000i3i3i3i3−i3−i3−i3−i3-2-22211-1-10000000002-200−i3i3-11-11i3−i3−i3i300000000
χ3022-2-2-111-1220-2-222-2-2i3−i3-1-11111-1-10000i3i3i3i3−i3−i3−i3−i3-2-22211-1-1000000000-2200−i3i31-11-1−i3i3i3−i300000000
χ312-22-222-2-22202-2-2-22-2002222-2-2-2-20000000000002-22-22-22-200000002i−2i000000000000000000002i−2i
χ322-22-222-2-22202-2-2-22-2002222-2-2-2-20000000000002-22-22-22-20000000−2i2i00000000000000000000−2i2i
χ332-22-222-2-22202-2-2-22-2002222-2-2-2-2000000000000-22-22-22-22002-20000000000000000000002-20000
χ342-22-222-2-22202-2-2-22-2002222-2-2-2-2000000000000-22-22-22-2200-22000000000000000000000-220000
χ352-2-222-22-2220-22-2-2-220022-2-222-2-20000000000002-2-222-2-222-20000000000000000000002-2000000
χ362-2-222-22-2220-22-2-2-220022-2-222-2-20000000000002-2-222-2-22-22000000000000000000000-22000000
χ372-2-222-22-2220-22-2-2-220022-2-222-2-2000000000000-222-2-222-2000002i−2i000000000000000000002i−2i00
χ382-2-222-22-2220-22-2-2-220022-2-222-2-2000000000000-222-2-222-200000−2i2i00000000000000000000−2i2i00
χ39444444441-241-21-2-21441-21-21-21-211-2-211-2-211-2-2000000000022000220000000000000000-1-100-1-1
χ40444444441-241-21-2-21441-21-21-21-211-2-211-2-211-2-20000000000-2-2000-2-20000000000000000110011
χ41444444441-2-41-21-2-21-4-41-21-21-21-2-1-122-1-122-1-122000000000022000-2-20000000000000000-1-10011
χ42444444441-2-41-21-2-21-4-41-21-21-21-2-1-122-1-122-1-1220000000000-2-20002200000000000000001100-1-1
χ4344444444-214-21-211-244-21-21-21-21-2-211-2-211-2-2110000000022000220000000000000000-1-100-1-100
χ4444444444-214-21-211-244-21-21-21-21-2-211-2-211-2-21100000000-2-2000-2-2000000000000000011001100
χ4544444444-21-4-21-211-2-4-4-21-21-21-2122-1-122-1-122-1-10000000022000-2-20000000000000000-1-1001100
χ4644444444-21-4-21-211-2-4-4-21-21-21-2122-1-122-1-122-1-100000000-2-20002200000000000000001100-1-100
χ474-44-444-4-41-2012-12-2-1001-21-2-12-123i−3i003i−3i003i−3i0000000000002-20002i−2i0000000000000000-1100−ii
χ484-44-444-4-41-2012-12-2-1001-21-2-12-123i−3i003i−3i003i−3i000000000000-22000−2i2i00000000000000001-100i−i
χ494-44-444-4-41-2012-12-2-1001-21-2-12-12−3i3i00−3i3i00−3i3i0000000000002-2000−2i2i0000000000000000-1100i−i
χ504-44-444-4-41-2012-12-2-1001-21-2-12-12−3i3i00−3i3i00−3i3i000000000000-220002i−2i00000000000000001-100−ii
χ514-44-4-2-2224404-4-4-44-400-2-2-2-222220000000000004-44-4-22-220000000000000000000000000000000
χ524-44-4-2-2224404-4-4-44-400-2-2-2-22222000000000000-44-442-22-20000000000000000000000000000000
χ534-4-444-44-4-210212-1-1-200-212-1-212-1003i−3i003i−3i003i−3i000000002-20002i−2i0000000000000000-1100−ii00
χ544-4-444-44-4-210212-1-1-200-212-1-212-1003i−3i003i−3i003i−3i00000000-22000−2i2i00000000000000001-100i−i00
χ554-4-444-44-4-210212-1-1-200-212-1-212-100−3i3i00−3i3i00−3i3i000000002-2000−2i2i0000000000000000-1100i−i00
χ564-4-444-44-4-210212-1-1-200-212-1-212-100−3i3i00−3i3i00−3i3i00000000-220002i−2i00000000000000001-100−ii00
χ574-4-44-22-22440-44-4-4-4400-2-222-2-2220000000000004-4-44-222-20000000000000000000000000000000
χ584-4-44-22-22440-44-4-4-4400-2-222-2-222000000000000-444-42-2-220000000000000000000000000000000
χ598888-4-4-4-42-482-42-4-42-4-4-12-12-12-1222-4-4-1-122-1-122000000000000000000000000000000000000000
χ608888-4-4-4-42-4-82-42-4-4244-12-12-12-12-2-24411-2-211-2-2000000000000000000000000000000000000000
χ618888-4-4-4-4-428-42-422-4-4-42-12-12-12-1-4-42222-1-122-1-1000000000000000000000000000000000000000
χ628888-4-4-4-4-42-8-42-422-4442-12-12-12-144-2-2-2-211-2-211000000000000000000000000000000000000000
χ6388-8-88-8-882-40-242-44-2002-4-24-242-4000000000000000000000000000000000000000000000000000
χ6488-8-88-8-88-4204-2-42-2400-424-24-2-42000000000000000000000000000000000000000000000000000
χ6588-8-8-444-42-40-242-44-2−4i34i3-121-21-2-120000−i3−i32i32i3i3i3−2i3−2i3000000000000000000000000000000000000000
χ6688-8-8-444-42-40-242-44-24i3−4i3-121-21-2-120000i3i3−2i3−2i3−i3−i32i32i3000000000000000000000000000000000000000
χ6788-8-8-444-4-4204-2-42-24−4i34i32-1-21-212-100002i32i3−i3−i3−2i3−2i3i3i3000000000000000000000000000000000000000
χ6888-8-8-444-4-4204-2-42-244i3−4i32-1-21-212-10000−2i3−2i3i3i32i32i3−i3−i3000000000000000000000000000000000000000
χ698-88-888-8-8-420-4-24-22400-42-424-24-2000000000000000000000000000000000000000000000000000
χ708-88-8-4-4442-4024-24-4-200-12-121-21-26i−6i00−3i3i00−3i3i00000000000000000000000000000000000000000
χ718-88-8-4-4442-4024-24-4-200-12-121-21-2−6i6i003i−3i003i−3i00000000000000000000000000000000000000000
χ728-88-8-4-444-420-4-24-224002-12-1-21-2100000033−3300−3333000000000000000000000000000000000000000
χ738-88-8-4-444-420-4-24-224002-12-1-21-21000000−33330033−33000000000000000000000000000000000000000
χ748-8-888-88-82-40-2-4-2442002-4-242-4-24000000000000000000000000000000000000000000000000000
χ758-8-88-44-442-40-2-4-244200-121-2-121-2000033−3300−333300000000000000000000000000000000000000000
χ768-8-88-44-442-40-2-4-244200-121-2-121-20000−33330033−3300000000000000000000000000000000000000000
χ778-8-88-44-44-420424-2-2-4002-1-212-1-21006i−6i00−3i3i00−3i3i000000000000000000000000000000000000000
χ788-8-88-44-44-420424-2-2-4002-1-212-1-2100−6i6i003i−3i003i−3i000000000000000000000000000000000000000

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