Finite Group Databasebeta

← Group #13181150

Character table — Group #13181150

Order 1728.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72
size112222244444448888888888161616161616181818181818181818181818363636363636363636363636363636363636363636363636727272727272
order122234633666612336666661212666612122444881212242424242222444466688812121212242424242424666121212
χ1111111111111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111111111111-1-1-1-1-1-1-1-11-1-111111-1-1111111-1-1-1-1-1-1
χ31111111111111111111111111111111111-1-111-1-1-1-1111-11-1-1-1111-1-1-111-1-1-1-1-1-1-1-1-1111-1-1
χ41111111111111111111111111111111111-1-111-1-1-1-1-1-1-11-11111-1-1-1-1-11111-1-1-1-1-1-11-1-1-111
χ5111-11-11111-111-1111-11-111-1-111-1-1-1-1-11-111111111111-1-1-111-1-1111-1-11-11111-1-1-1-1-11-1-11-1
χ6111-11-11111-111-1111-11-111-1-111-1-1-1-1-11-1111111111-1-1111-1-11-1-1-11-1-11-1-1-111-1-1-1-11-111-11
χ7111-11-11111-111-1111-11-111-1-111-1-1-1-1-11-11-1-111-1-1-1-111-11-1-1-11-111-1111-1-1-1-1-1111111-1-1-11
χ8111-11-11111-111-1111-11-111-1-111-1-1-1-1-11-11-1-111-1-1-1-1-1-11-1111-1-1-1-1-1111-111-1-11111-1-1111-1
χ911-111-1111-1111-111-11-1111-1-1-1-111-1-1-1-111111111111-11-1-11-11-111-11-1-1111-1-111-1-1-1-11-1-11
χ1011-111-1111-1111-111-11-1111-1-1-1-111-1-1-1-11111111111-11-111-11-1-1-1-1-11-1-11-1-1-1-111-1-111-111-1
χ1111-111-1111-1111-111-11-1111-1-1-1-111-1-1-1-111-1-111-1-1-1-11-111-1-11-1-1111-11-11-1-111-1-1111-11-11-1
χ1211-111-1111-1111-111-11-1111-1-1-1-111-1-1-1-111-1-111-1-1-1-1-11-1-111-11-1-1-11-11-111111-1-111-11-11-11
χ1311-1-111111-1-111111-1-1-1-11111-1-1-1-1111-1-11111111111-1-1111-1-1111-1-11-1-111-1-1-1-1111-1-11-1-1
χ1411-1-111111-1-111111-1-1-1-11111-1-1-1-1111-1-1111111111-111-1-1-1111-1-1-1-11-1-1-1-1-1-1-1-111-111-111
χ1511-1-111111-1-111111-1-1-1-11111-1-1-1-1111-1-11-1-111-1-1-1-11-1-1-11-11111111-1-1-1-1-11111-1-1-1-1-1111
χ1611-1-111111-1-111111-1-1-1-11111-1-1-1-1111-1-11-1-111-1-1-1-1-1111-11-1-11-1-111-1-1-1111111-1-1111-1-1-1
χ17222222222222222222222222222222-2-2-2-200-2-2000000000000-200000-2-200000000000000
χ182222-12-122-1-122-1-1-12222-1-122-1-1-1-1-1-1222222-1-1-1-1-1-100000000-100222-1-100-1-1-1-1-1-1000000
χ192222-12-122-1-122-1-1-12222-1-122-1-1-1-1-1-12222-2-2-1-1111100000000-100-2-2-2-1-100111111000000
χ202222-12-122-1-122-1-1-12222-1-122-1-1-1-1-1-1-2-2-2-2001133−3−30000000010000011003−33−33−3000000
χ212222-12-122-1-122-1-1-12222-1-122-1-1-1-1-1-1-2-2-2-20011−3−333000000001000001100−33−33−33000000
χ22222-22-22222-222-2222-22-222-2-222-2-2-2-22-22-200-2-2000000000000200000-2200000000000000
χ23222-2-1-2-122-11221-1-12-22-2-1-1-2-2-1-111112-22-2001133−3−300000000-1000001-1003−3−33−33000000
χ24222-2-1-2-122-11221-1-12-22-2-1-1-2-2-1-111112-22-20011−3−33300000000-1000001-100−333−33−3000000
χ25222-2-1-2-122-11221-1-12-22-2-1-1-2-2-1-11111-22-2222-1-1-1-1-1-1000000001002-2-2-1100-1-11111000000
χ26222-2-1-2-122-11221-1-12-22-2-1-1-2-2-1-11111-22-22-2-2-1-1111100000000100-222-110011-1-1-1-1000000
χ2722-222-2222-2222-222-22-2222-2-2-2-222-2-222-2-200-2-20000000000002000002-200000000000000
χ2822-22-1-2-1221-1221-1-1-22-22-1-1-2-211-1-11122-2-2001133−3−300000000-100000-1100−333−3−33000000
χ2922-22-1-2-1221-1221-1-1-22-22-1-1-2-211-1-11122-2-20011−3−33300000000-100000-11003−3−333−3000000
χ3022-22-1-2-1221-1221-1-1-22-22-1-1-2-211-1-111-2-22222-1-1-1-1-1-100000000100-22-21-10011-1-111000000
χ3122-22-1-2-1221-1221-1-1-22-22-1-1-2-211-1-111-2-222-2-2-1-11111000000001002-221-100-1-111-1-1000000
χ3222-2-222222-2-222222-2-2-2-22222-2-2-2-222-222-200-2-2000000000000-2000002200000000000000
χ3322-2-2-12-1221122-1-1-1-2-2-2-2-1-1221111-1-12-2-2222-1-1-1-1-1-100000000-100-2-2211001111-1-1000000
χ3422-2-2-12-1221122-1-1-1-2-2-2-2-1-1221111-1-12-2-22-2-2-1-1111100000000-10022-21100-1-1-1-111000000
χ3522-2-2-12-1221122-1-1-1-2-2-2-2-1-1221111-1-1-222-2001133−3−300000000100000-1-100−33−333−3000000
χ3622-2-2-12-1221122-1-1-1-2-2-2-2-1-1221111-1-1-222-20011−3−33300000000100000-1-1003−33−3−33000000
χ3744444441-244-2141-211-2-21-2-211-21-21-20000000000000002022200000000-1-1000000-1000-1-1
χ3844444441-244-2141-211-2-21-2-211-21-21-2000000000000000-20-2-2-20000000011000000100011
χ394444444-21441-24-21-2-211-211-2-21-21-21000000000000222020000-1-100000000000000-1-1-100
χ404444444-21441-24-21-2-211-211-2-21-21-21000000000000-2-2-20-20000110000000000000011100
χ41444-44-441-24-4-21-41-21-1-221-22-11-2-12-1200000000000000020-2-220000000011000000-10001-1
χ42444-44-441-24-4-21-41-21-1-221-22-11-2-12-12000000000000000-2022-200000000-1-10000001000-11
χ43444-44-44-214-41-2-4-21-221-1-21-12-212-12-100000000000022-20-20000-1-100000000000000-11100
χ44444-44-44-214-41-2-4-21-221-1-21-12-212-12-1000000000000-2-2202000011000000000000001-1-100
χ4544-444-441-2-44-21-41-2-112-21-22-1-121-2-1200000000000000020-22-20000000011000000-1000-11
χ4644-444-441-2-44-21-41-2-112-21-22-1-121-2-12000000000000000-202-2200000000-1-100000010001-1
χ4744-444-44-21-441-2-4-212-2-11-21-122-1-212-10000000000002-220-20000-1-1000000000000001-1100
χ4844-444-44-21-441-2-4-212-2-11-21-122-1-212-1000000000000-22-20200001100000000000000-11-100
χ4944-4-44441-2-4-4-2141-2-1-1221-2-21-12-121-2000000000000000202-2-200000000-1-1000000-100011
χ5044-4-44441-2-4-4-2141-2-1-1221-2-21-12-121-2000000000000000-20-22200000000110000001000-1-1
χ5144-4-4444-21-4-41-24-2122-1-1-211-22-12-1-210000000000002-2-2020000-1-10000000000000011-100
χ5244-4-4444-21-4-41-24-2122-1-1-211-22-12-1-21000000000000-2220-200001100000000000000-1-1100
χ534-40040-44400-4-40440000-4-4000000000000−2i22i200−2i22i2−2i22i2000000000000000000000000000000
χ544-40040-44400-4-40440000-4-40000000000002i2−2i2002i2−2i22i2−2i2000000000000000000000000000000
χ554-400-2024400-4-40-2-2000022000000000000−2i22i223−232ζ5+2ζ7−2ζ5−2ζ72ζ13+2ζ23−2ζ13−2ζ23000000000000000000000000000000
χ564-400-2024400-4-40-2-2000022000000000000−2i22i2−23232ζ13+2ζ23−2ζ13−2ζ232ζ5+2ζ7−2ζ5−2ζ7000000000000000000000000000000
χ574-400-2024400-4-40-2-20000220000000000002i2−2i223−23−2ζ5−2ζ72ζ5+2ζ7−2ζ13−2ζ232ζ13+2ζ23000000000000000000000000000000
χ584-400-2024400-4-40-2-20000220000000000002i2−2i2−2323−2ζ13−2ζ232ζ13+2ζ23−2ζ5−2ζ72ζ5+2ζ7000000000000000000000000000000
χ598888-48-42-4-4-4-42-4-1222-4-4-12-42-12-12-12000000000000000000000000000000000000000000
χ608888-48-4-42-4-42-4-42-1-4-4222-12-42-12-12-1000000000000000000000000000000000000000000
χ61888-8-4-8-42-4-44-424-122-2-44-124-2-121-21-2000000000000000000000000000000000000000000
χ62888-8-4-8-4-42-442-442-1-442-22-1-242-1-21-21000000000000000000000000000000000000000000
χ6388-88-4-8-42-44-4-424-12-224-4-124-21-2-121-2000000000000000000000000000000000000000000
χ6488-88-4-8-4-424-42-442-14-4-222-1-24-212-1-21000000000000000000000000000000000000000000
χ6588-8-8-48-42-444-42-4-12-2-244-12-421-21-2-12000000000000000000000000000000000000000000
χ6688-8-8-48-4-42442-4-42-144-2-22-12-4-21-212-1000000000000000000000000000000000000000000
χ678-80080-82-4004-202-40000-2400000000000000000000000000000000000023−23000000000000
χ688-80080-82-4004-202-40000-24000000000000000000000000000000000000−2323000000000000
χ698-80080-8-4200-240-4200004-200000000000000000000000000000−2i32i30000000000000000000
χ708-80080-8-4200-240-4200004-2000000000000000000000000000002i3−2i30000000000000000000
χ7116-1600-8084-8008-40-2400002-400000000000000000000000000000000000000000000000000
χ7216-1600-808-8400-4804-20000-4200000000000000000000000000000000000000000000000000

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