Finite Group Databasebeta

← Group #13167494

Character table — Group #13167494

Order 1728.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75
size111122224444444444488888888888888888888181818181818181836363636363636363636363636363636363672727272727272727272
order122236663346666661212336666661212121212121212121212124444121212122244888812122424242424242424226666661212
χ1111111111111111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111111111111111111111-1-1-1-111-1-1-1-1-1-1-1-1-1-111-1-1-1-111
χ311111111111111111111111111111111111111111111111-1-1-1-111111111111111-1-1-1-1-1-1-1-1-1-1
χ411111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-111-1-11111-1-1
χ51111111111-1111111-1-111111111-1-1-1-1-1-1-1-1-1-1-1-11-1-11111111-1-111-1-1-1-11111-1-1-1-11-11111-1-1-1-1
χ61111111111-1111111-1-111111111-1-1-1-1-1-1-1-1-1-1-1-11-1-11111111-1-1-1-111-1-1-1-1-1-11111-1111-1-111-1-1
χ71111111111-1111111-1-111111111-1-1-1-1-1-1-1-1-1-1-1-11-1-111111-1-11111-1-1-1-11111-1-1-1-1-11-1-1-1-11111
χ81111111111-1111111-1-111111111-1-1-1-1-1-1-1-1-1-1-1-11-1-111111-1-111-1-111-1-1-1-1-1-111111-1-1-111-1-111
χ9222222222222222222222222222222222222222-2-2-2-2-2-2-2-200000000-2-2000000000000000000
χ102222222222-2222222-2-222222222-2-2-2-2-2-2-2-2-2-2-2-2-222-2-2-2-2-20000000022000000000000000000
χ112222-1-1-1-1222222222-1-1-1-1-1-1-1-1-1-12222-1-1-1-1-1-1-1-12222-1-1-1-100002222-1-1-1-1-1-1-1-1-1-10000000000
χ122222-1-1-1-1222222222-1-1-1-1-1-1-1-1-1-12222-1-1-1-1-1-1-1-12222-1-1-1-10000-2-2-2-2-1-1111111110000000000
χ132222-1-1-1-1222222222-1-1-1-1-1-1-1-1-1-12222-1-1-1-1-1-1-1-1-2-2-2-21111000000001133−3−333−3−30000000000
χ142222-1-1-1-1222222222-1-1-1-1-1-1-1-1-1-12222-1-1-1-1-1-1-1-1-2-2-2-211110000000011−3−333−3−3330000000000
χ152222-1-1-1-122-222222211-1-1-1-1-1-1-1-1-2-2-2-2111111112-2-22-1-1-1-1000022-2-211-1-1-1-111110000000000
χ162222-1-1-1-122-222222211-1-1-1-1-1-1-1-1-2-2-2-2111111112-2-22-1-1-1-10000-2-222111111-1-1-1-10000000000
χ172222-1-1-1-122-222222211-1-1-1-1-1-1-1-1-2-2-2-211111111-222-2111100000000-1-133−3−3−3−3330000000000
χ182222-1-1-1-122-222222211-1-1-1-1-1-1-1-1-2-2-2-211111111-222-2111100000000-1-1−3−33333−3−30000000000
χ192-22-22-22-222022-2-2-2-2002222-2-2-2-2000000000000200-222-2-2002i−2i00000000000000000000002i−2i
χ202-22-22-22-222022-2-2-2-2002222-2-2-2-2000000000000200-222-2-200−2i2i0000000000000000000000−2i2i
χ212-22-22-22-222022-2-2-2-2002222-2-2-2-2000000000000-2002-2-2222-20000000000000000002-2000000
χ222-22-22-22-222022-2-2-2-2002222-2-2-2-2000000000000-2002-2-222-22000000000000000000-22000000
χ232-2-222-2-22220-2-22-2-220022-2-222-2-200000000000002-20000000002−22−22-22−22−22−22−20000000000
χ242-2-222-2-22220-2-22-2-220022-2-222-2-200000000000002-2000000000−22−222-2−22−22−22−220000000000
χ252-2-222-2-22220-2-22-2-220022-2-222-2-20000000000000-220000000002−2−22-222−22−2−22−220000000000
χ262-2-222-2-22220-2-22-2-220022-2-222-2-20000000000000-22000000000−222−2-22−22−222−22−20000000000
χ272-2-22-111-1220-2-22-2-223−3-1-111-1-11100003333−3−3−3−302-203−33−300002−22−2-11ζ5−ζ7−ζ5+ζ7ζ13−ζ23−ζ13+ζ23ζ13−ζ23−ζ13+ζ23ζ5−ζ7−ζ5+ζ70000000000
χ282-2-22-111-1220-2-22-2-223−3-1-111-1-11100003333−3−3−3−302-203−33−30000−22−22-11−ζ5+ζ7ζ5−ζ7−ζ13+ζ23ζ13−ζ23−ζ13+ζ23ζ13−ζ23−ζ5+ζ7ζ5−ζ70000000000
χ292-2-22-111-1220-2-22-2-223−3-1-111-1-11100003333−3−3−3−30-220−33−3300002−2−221-1ζ13−ζ23−ζ13+ζ23ζ5−ζ7−ζ5+ζ7−ζ5+ζ7ζ5−ζ7−ζ13+ζ23ζ13−ζ230000000000
χ302-2-22-111-1220-2-22-2-223−3-1-111-1-11100003333−3−3−3−30-220−33−330000−222−21-1−ζ13+ζ23ζ13−ζ23−ζ5+ζ7ζ5−ζ7ζ5−ζ7−ζ5+ζ7ζ13−ζ23−ζ13+ζ230000000000
χ312-2-22-111-1220-2-22-2-22−33-1-111-1-1110000−3−3−3−3333302-20−33−3300002−22−2-11ζ13−ζ23−ζ13+ζ23ζ5−ζ7−ζ5+ζ7ζ5−ζ7−ζ5+ζ7ζ13−ζ23−ζ13+ζ230000000000
χ322-2-22-111-1220-2-22-2-22−33-1-111-1-1110000−3−3−3−3333302-20−33−330000−22−22-11−ζ13+ζ23ζ13−ζ23−ζ5+ζ7ζ5−ζ7−ζ5+ζ7ζ5−ζ7−ζ13+ζ23ζ13−ζ230000000000
χ332-2-22-111-1220-2-22-2-22−33-1-111-1-1110000−3−3−3−333330-2203−33−300002−2−221-1ζ5−ζ7−ζ5+ζ7ζ13−ζ23−ζ13+ζ23−ζ13+ζ23ζ13−ζ23−ζ5+ζ7ζ5−ζ70000000000
χ342-2-22-111-1220-2-22-2-22−33-1-111-1-1110000−3−3−3−333330-2203−33−30000−222−21-1−ζ5+ζ7ζ5−ζ7−ζ13+ζ23ζ13−ζ23ζ13−ζ23−ζ13+ζ23ζ5−ζ7−ζ5+ζ70000000000
χ35444444441-241-2-21-21441-21-21-21-211-2-211-2-211-2-20000000022220000000000000000-1-10000-1-1
χ36444444441-241-2-21-21441-21-21-21-211-2-211-2-211-2-200000000-2-2-2-2000000000000000011000011
χ37444444441-2-41-2-21-21-4-41-21-21-21-2-1-122-1-122-1-1220000000022-2-20000000000000000-1-1000011
χ38444444441-2-41-2-21-21-4-41-21-21-21-2-1-122-1-122-1-12200000000-2-2220000000000000000110000-1-1
χ3944444444-214-211-21-244-21-21-21-21-2-211-2-211-2-211000000000000000000000000002200-1-1-1-100
χ4044444444-214-211-21-244-21-21-21-21-2-211-2-211-2-21100000000000000000000000000-2-200111100
χ4144444444-21-4-211-21-2-4-4-21-21-21-2122-1-122-1-122-1-1000000000000000000000000002-200-1-11100
χ4244444444-21-4-211-21-2-4-4-21-21-21-2122-1-122-1-122-1-100000000000000000000000000-220011-1-100
χ4344-4-444-4-4440-4-4-444-40044-4-4-4-444000000000000000000000000000000000000000000000000
χ4444-4-444-4-4-2102-1-1-21200-212-12-1-21003-3003-3003-3000000000000000000000000000000−i3i3−i3i300
χ4544-4-444-4-4-2102-1-1-21200-212-12-1-21003-3003-3003-3000000000000000000000000000000i3−i3i3−i300
χ4644-4-444-4-4-2102-1-1-21200-212-12-1-2100-3300-3300-33000000000000000000000000000000−i3i3i3−i300
χ4744-4-444-4-4-2102-1-1-21200-212-12-1-2100-3300-3300-33000000000000000000000000000000i3−i3−i3i300
χ4844-4-4-2-222440-4-4-444-400-2-22222-2-2000000000000000023−23−23230000000000000000000000000000
χ4944-4-4-2-222440-4-4-444-400-2-22222-2-20000000000000000−232323−230000000000000000000000000000
χ504-44-44-44-41-201-22-12-1001-21-2-12-123i−3i003i−3i003i−3i00000000002-22i−2i0000000000000000-110000−ii
χ514-44-44-44-41-201-22-12-1001-21-2-12-123i−3i003i−3i003i−3i0000000000-22−2i2i00000000000000001-10000i−i
χ524-44-44-44-41-201-22-12-1001-21-2-12-12−3i3i00−3i3i00−3i3i00000000002-2−2i2i0000000000000000-110000i−i
χ534-44-44-44-41-201-22-12-1001-21-2-12-12−3i3i00−3i3i00−3i3i0000000000-222i−2i00000000000000001-10000−ii
χ544-44-4-22-2244044-4-4-4-400-2-2-2-22222000000000000400-4-2-2220000000000000000000000000000
χ554-44-4-22-2244044-4-4-4-400-2-2-2-22222000000000000-400422-2-20000000000000000000000000000
χ568888-4-4-4-42-482-4-42-42-4-4-12-12-12-1222-4-4-1-122-1-122000000000000000000000000000000000000
χ578888-4-4-4-42-4-82-4-42-4244-12-12-12-12-2-24411-2-211-2-2000000000000000000000000000000000000
χ588888-4-4-4-4-428-422-42-4-4-42-12-12-12-1-4-42222-1-122-1-1000000000000000000000000000000000000
χ598888-4-4-4-4-42-8-422-42-4442-12-12-12-144-2-2-2-211-2-211000000000000000000000000000000000000
χ6088-8-888-8-82-40-2442-4-2002-4-24-242-4000000000000000000000000000000000000000000000000
χ6188-8-8-4-4442-40-2442-4-200-121-21-2-120000−3i33i3003i3−3i300000000000000000000000000000000000000
χ6288-8-8-4-4442-40-2442-4-200-121-21-2-1200003i3−3i300−3i33i300000000000000000000000000000000000000
χ6388-8-8-4-444-4204-2-2-424002-1-21-212-1006-600-3300-33000000000000000000000000000000000000
χ6488-8-8-4-444-4204-2-2-424002-1-21-212-100-66003-3003-3000000000000000000000000000000000000
χ658-88-88-88-8-420-42-24-2400-42-424-24-2000000000000000000000000000000000000000000000000
χ668-88-8-44-442-402-44-24-200-12-121-21-26i−6i00−3i3i00−3i3i00000000000000000000000000000000000000
χ678-88-8-44-442-402-44-24-200-12-121-21-2−6i6i003i−3i003i−3i00000000000000000000000000000000000000
χ688-88-8-44-44-420-42-24-24002-12-1-21-2100000033−3300−3333000000000000000000000000000000000000
χ698-88-8-44-44-420-42-24-24002-12-1-21-21000000−33330033−33000000000000000000000000000000000000
χ708-8-888-8-882-40-24-4-242002-4-242-4-24000000000000000000000000000000000000000000000000
χ718-8-888-8-88-4204-224-2-400-424-2-424-2000000000000000000000000000000000000000000000000
χ728-8-88-444-42-40-24-4-24243−43-121-2-121-2000033−23−23−3−32323000000000000000000000000000000000000
χ738-8-88-444-42-40-24-4-242−4343-121-2-121-20000−3−3232333−23−23000000000000000000000000000000000000
χ748-8-88-444-4-4204-224-2-443−432-1-212-1-210000−23−23332323−3−3000000000000000000000000000000000000
χ758-8-88-444-4-4204-224-2-4−43432-1-212-1-2100002323−3−3−23−2333000000000000000000000000000000000000

Here ζ is a primitive root of unity of order 24 (ζ24 = 1); i = ζ6.