Finite Group Databasebeta

← Group #13181149

Character table — Group #13181149

Order 1728.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72
size112222244444448888888888161616161616181818181818181818181818363636363636363636363636363636363636363636363636727272727272
order122234633666612336666661212666612122444881212242424242222224466666888121224242424242466661212
χ1111111111111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111111111111-1-1-1-1-1-1-1-11-1-1-1-111111111111-1-1-1-1-1-1
χ31111111111111111111111111111111111-1-111-1-1-1-1111-1-1-11-1111-1-1-1-1-111-1-1-1-1-1-111-1-11-1
χ41111111111111111111111111111111111-1-111-1-1-1-1-1-1-1111-111-1-111-1-1-111-1-1-1-1-1-1-1-111-11
χ5111-11-11111-111-11111-1-111-1-111-1-1-1-1-11-111111111111-111-1-1-1-111111-1-11-111-1-1-1-11-11-1-1-1
χ6111-11-11111-111-11111-1-111-1-111-1-1-1-1-11-1111111111-1-11-1-1111-1-1-1-1-11-1-11-111-1-1-1-1-11-1111
χ7111-11-11111-111-11111-1-111-1-111-1-1-1-1-11-11-1-111-1-1-1-111-1-1-11-11-111-1-1-1111-1-1-111111-1-11-11
χ8111-11-11111-111-11111-1-111-1-111-1-1-1-1-11-11-1-111-1-1-1-1-1-1111-11-1-1-1-111-1111-1-1-11111-111-11-1
χ911-111-1111-1111-111-1-11111-1-1-1-111-1-1-1-111111111111-111-11-1-1-11111-11-1-11-1-111-1-1-11-11-1-1
χ1011-111-1111-1111-111-1-11111-1-1-1-111-1-1-1-11111111111-11-1-11-111-1-1-1-1-1-11-1-11-1-111-1-11-11-111
χ1111-111-1111-1111-111-1-11111-1-1-1-111-1-1-1-111-1-111-1-1-1-11-11-11-1-11-111-1-11-11-1111-1-111-111-1-11
χ1211-111-1111-1111-111-1-11111-1-1-1-111-1-1-1-111-1-111-1-1-1-1-11-11-111-1-1-1-1111-11-1111-1-1111-1-111-1
χ1311-1-111111-1-111111-1-1-1-11111-1-1-1-1111-1-11111111111-1-11-1-11111111-1-11-1-1-1-1-1-111-1-1-1-111
χ1411-1-111111-1-111111-1-1-1-11111-1-1-1-1111-1-1111111111-111-111-1-11-1-1-1-1-1-11-1-1-1-1-1-1111111-1-1
χ1511-1-111111-1-111111-1-1-1-11111-1-1-1-1111-1-11-1-111-1-1-1-11-1-1-1111-1111-1-111-1-1-11111-1-1-1-1111-1
χ1611-1-111111-1-111111-1-1-1-11111-1-1-1-1111-1-11-1-111-1-1-1-1-1111-1-1-111-1-11111-1-1-11111-1-111-1-1-11
χ17222222222222222222222222222222-2-2-2-200-2-2000000000000-20000000-2-2000000000000
χ182222-12-122-1-122-1-1-12222-1-122-1-1-1-1-1-1222222-1-1-1-1-1-100000000-10000222-1-1-1-1-1-1-1-1000000
χ192222-12-122-1-122-1-1-12222-1-122-1-1-1-1-1-12222-2-2-1-1111100000000-10000-2-2-2-1-1111111000000
χ202222-12-122-1-122-1-1-12222-1-122-1-1-1-1-1-1-2-2-2-2001133−3−30000000010000000113−33−33−3000000
χ212222-12-122-1-122-1-1-12222-1-122-1-1-1-1-1-1-2-2-2-20011−3−333000000001000000011−33−33−33000000
χ22222-22-22222-222-22222-2-222-2-222-2-2-2-22-22-200-2-200000000000020000000-22000000000000
χ23222-2-1-2-122-11221-1-122-2-2-1-1-2-2-1-111112-22-2001133−3−300000000-100000001-13−3−33−33000000
χ24222-2-1-2-122-11221-1-122-2-2-1-1-2-2-1-111112-22-20011−3−33300000000-100000001-1−333−33−3000000
χ25222-2-1-2-122-11221-1-122-2-2-1-1-2-2-1-11111-22-2222-1-1-1-1-1-100000000100002-2-2-11-1-11111000000
χ26222-2-1-2-122-11221-1-122-2-2-1-1-2-2-1-11111-22-22-2-2-1-111110000000010000-222-1111-1-1-1-1000000
χ2722-222-2222-2222-222-2-22222-2-2-2-222-2-222-2-200-2-2000000000000200000002-2000000000000
χ2822-22-1-2-1221-1221-1-1-2-222-1-1-2-211-1-11122-2-2001133−3−300000000-10000000-11−333−3−33000000
χ2922-22-1-2-1221-1221-1-1-2-222-1-1-2-211-1-11122-2-20011−3−33300000000-10000000-113−3−333−3000000
χ3022-22-1-2-1221-1221-1-1-2-222-1-1-2-211-1-111-2-22222-1-1-1-1-1-10000000010000-22-21-111-1-111000000
χ3122-22-1-2-1221-1221-1-1-2-222-1-1-2-211-1-111-2-222-2-2-1-1111100000000100002-221-1-1-111-1-1000000
χ3222-2-222222-2-222222-2-2-2-22222-2-2-2-222-222-200-2-2000000000000-2000000022000000000000
χ3322-2-2-12-1221122-1-1-1-2-2-2-2-1-1221111-1-12-2-2222-1-1-1-1-1-100000000-10000-2-22111111-1-1000000
χ3422-2-2-12-1221122-1-1-1-2-2-2-2-1-1221111-1-12-2-22-2-2-1-1111100000000-1000022-211-1-1-1-111000000
χ3522-2-2-12-1221122-1-1-1-2-2-2-2-1-1221111-1-1-222-2001133−3−30000000010000000-1-1−33−333−3000000
χ3622-2-2-12-1221122-1-1-1-2-2-2-2-1-1221111-1-1-222-20011−3−3330000000010000000-1-13−33−3−33000000
χ3744444441-2441-241-21-21-21-21-21-21-21-200000000000000022202000-1-10000000000000-1-10-1
χ3844444441-2441-241-21-21-21-21-21-21-21-2000000000000000-2-2-20-20001100000000000001101
χ394444444-2144-214-21-21-21-21-21-21-21-21000000000000222000200-1-10000000000000-1-100-10
χ404444444-2144-214-21-21-21-21-21-21-21-21000000000000-2-2-2000-200110000000000000110010
χ41444-44-441-24-41-2-41-21-2-121-2-121-2-12-1200000000000000022-20-2000-1-10000000000000-1101
χ42444-44-441-24-41-2-41-21-2-121-2-121-2-12-12000000000000000-2-22020001100000000000001-10-1
χ43444-44-44-214-4-21-4-21-212-1-212-1-212-12-100000000000022-2000-200-1-10000000000000-110010
χ44444-44-44-214-4-21-4-21-212-1-212-1-212-12-1000000000000-2-220002001100000000000001-100-10
χ4544-444-441-2-441-2-41-2-121-21-2-12-121-2-120000000000000002-220-2000-1-100000000000001-101
χ4644-444-441-2-441-2-41-2-121-21-2-12-121-2-12000000000000000-22-202000110000000000000-110-1
χ4744-444-44-21-44-21-4-212-1-21-212-12-1-212-10000000000002-22000-200-1-100000000000001-10010
χ4844-444-44-21-44-21-4-212-1-21-212-12-1-212-1000000000000-22-2000200110000000000000-1100-10
χ4944-4-44441-2-4-41-241-2-12-121-21-2-12-121-20000000000000002-2-202000-1-10000000000000110-1
χ5044-4-44441-2-4-41-241-2-12-121-21-2-12-121-2000000000000000-2220-2000110000000000000-1-101
χ5144-4-4444-21-4-4-214-212-12-1-21-212-12-1-210000000000002-2-2000200-1-100000000000001100-10
χ5244-4-4444-21-4-4-214-212-12-1-21-212-12-1-21000000000000-222000-200110000000000000-1-10010
χ534-40040-44400-4-40440000-4-400000000000022−220022−2222−22000000000000000000000000000000
χ544-40040-44400-4-40440000-4-4000000000000−222200−2222−2222000000000000000000000000000000
χ554-400-2024400-4-40-2-200002200000000000022−2223−232ζ5−2ζ7−2ζ5+2ζ72ζ13−2ζ23−2ζ13+2ζ23000000000000000000000000000000
χ564-400-2024400-4-40-2-200002200000000000022−22−23232ζ13−2ζ23−2ζ13+2ζ232ζ5−2ζ7−2ζ5+2ζ7000000000000000000000000000000
χ574-400-2024400-4-40-2-2000022000000000000−222223−23−2ζ5+2ζ72ζ5−2ζ7−2ζ13+2ζ232ζ13−2ζ23000000000000000000000000000000
χ584-400-2024400-4-40-2-2000022000000000000−2222−2323−2ζ13+2ζ232ζ13−2ζ23−2ζ5+2ζ72ζ5−2ζ7000000000000000000000000000000
χ598888-48-42-4-4-42-4-4-122-42-4-122-4-12-12-12000000000000000000000000000000000000000000
χ608888-48-4-42-4-4-42-42-1-42-422-1-422-12-12-1000000000000000000000000000000000000000000
χ61888-8-4-8-42-4-442-44-122-4-24-12-24-121-21-2000000000000000000000000000000000000000000
χ62888-8-4-8-4-42-44-4242-1-424-22-14-22-1-21-21000000000000000000000000000000000000000000
χ6388-88-4-8-42-44-42-44-12-242-4-12-241-2-121-2000000000000000000000000000000000000000000
χ6488-88-4-8-4-424-4-4242-14-2-422-14-2-212-1-21000000000000000000000000000000000000000000
χ6588-8-8-48-42-4442-4-4-12-24-24-122-41-21-2-12000000000000000000000000000000000000000000
χ6688-8-8-48-4-4244-42-42-14-24-22-1-42-21-212-1000000000000000000000000000000000000000000
χ678-80080-82-400-2402-40000-240000000000000000000000000000000−2i32i300000000000000000
χ688-80080-82-400-2402-40000-2400000000000000000000000000000002i3−2i300000000000000000
χ698-80080-8-42004-20-4200004-200000000000000000000000000000−2i32i30000000000000000000
χ708-80080-8-42004-20-4200004-2000000000000000000000000000002i3−2i30000000000000000000
χ7116-1600-8084-800-480-2400002-400000000000000000000000000000000000000000000000000
χ7216-1600-808-84008-404-20000-4200000000000000000000000000000000000000000000000000

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