Finite Group Databasebeta

← Group #13181154

Character table — Group #13181154

Order 1728.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75
size1122222444444488888888889916161616161618181818181818181818181818181836363636363636363636363636363636363636363636727272727272
order122234633666612336666661212226666121222444444466121212122244444446612121212121212121212126612121212
χ1111111111111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111-1-1-1-111-1-1-1-11-111-1-1-1-1-111111-1-1-1-1-1-1-1-11-111-1-1
χ311111111111111111111111111111111111-1-111-1-111-1-1-1-1-11-1-111-1-1-1111-1-111-1-1-1-1-1-1-11-1-111
χ411111111111111111111111111111111111-1-1-1-111111111-1-1-1-1-1-1111111-1-1-1-1111111-1-1-1-1-1-1
χ5111-11-11111-111-11111-1-111-1-11111-1-1-1-11-1-1111111111111-1-11-11-1-11-11-1-11111-1-111-1-1-1-11-11-1
χ6111-11-11111-111-11111-1-111-1-11111-1-1-1-11-1-111-1-1-1-111-1-1-1-1-111-1-111-111-1-111-1-111-1-111-111-1-11
χ7111-11-11111-111-11111-1-111-1-11111-1-1-1-11-1-1-1-111-1-111-1-1-1-11-1-111-11-111-1-1-1-11111-1-1111-1-111-1
χ8111-11-11111-111-11111-1-111-1-11111-1-1-1-11-1-1-1-1-1-11111111111-11-11-11-11-1-1-1-1-1-1-1-111-1-111-11-11
χ911-111-1111-1111-111-1-11111-1-111-1-111-1-1-11-1111111111111-1-1-11-11-1-11-11-11111-1-1-1-111-1-1-11-11
χ1011-111-1111-1111-111-1-11111-1-111-1-111-1-1-11-111-1-1-1-111-1-1-1-1-11-111-111-1-11-111-1-11111-1-1-11-111-1
χ1111-111-1111-1111-111-1-11111-1-111-1-111-1-1-11-1-1-111-1-111-1-1-1-11-11-1-1111-1-11-1-1-1111111-1-11-11-1-11
χ1211-111-1111-1111-111-1-11111-1-111-1-111-1-1-11-1-1-1-1-111111111111-11-1-1-11-11-1-1-1-1-1-1-1-1-111111-11-1
χ1311-1-111111-1-111111-1-1-1-1111111-1-1-1-111-1-1111111111111111-1-1-1-11-1-1-1-11111111-1-1-1-111-1-1-1-1
χ1411-1-111111-1-111111-1-1-1-1111111-1-1-1-111-1-1111-1-1-1-111-1-1-1-11-1-1-111-111-1-1111-1-1-1-111111-1-1-111
χ1511-1-111111-1-111111-1-1-1-1111111-1-1-1-111-1-11-1-111-1-111-1-1-1-1-1111-1-1-111-1-11-1-111-1-11111-1111-1-1
χ1611-1-111111-1-111111-1-1-1-1111111-1-1-1-111-1-11-1-1-1-111111111-1-111111-1-1-1-11-1-1-1-111-1-1-1-1-1-11111
χ17222222222222222222222222-2-2222222-2-2-2000000-2-20000000000000-2-2-20000000000000000
χ182222-12-122-1-122-1-1-12222-1-12222-1-1-1-1-1-1222000022-1-1-1-1-1-1000000222-1-1-10000-1-1-1-1-1-1000000
χ192222-12-122-1-122-1-1-12222-1-12222-1-1-1-1-1-12220000-2-2-1-11111000000-2-2-2-1-1-10000111111000000
χ202222-12-122-1-122-1-1-12222-1-122-2-2-1-1-1-1-1-1-2-2-20000001133−3−300000000011100003−33−33−3000000
χ212222-12-122-1-122-1-1-12222-1-122-2-2-1-1-1-1-1-1-2-2-200000011−3−3330000000001110000−33−33−33000000
χ22222-22-22222-222-22222-2-222-2-2-2-222-2-2-2-2-222000000-2-20000000000000-2220000000000000000
χ23222-2-1-2-122-11221-1-122-2-2-1-1-2-222-1-111112-2-2000022-1-1-1-1-1-1000000-22-2-111000011-1-111000000
χ24222-2-1-2-122-11221-1-122-2-2-1-1-2-222-1-111112-2-20000-2-2-1-111110000002-22-1110000-1-111-1-1000000
χ25222-2-1-2-122-11221-1-122-2-2-1-1-2-2-2-2-1-11111-2220000001133−3−30000000001-1-10000−333−3−33000000
χ26222-2-1-2-122-11221-1-122-2-2-1-1-2-2-2-2-1-11111-22200000011−3−3330000000001-1-100003−3−333−3000000
χ2722-222-2222-2222-222-2-22222-2-2-2-2-2-222-2-22-22000000-2-200000000000002-220000000000000000
χ2822-22-1-2-1221-1221-1-1-2-222-1-1-2-22211-1-111-22-2000022-1-1-1-1-1-1000000-2-221-1100001111-1-1000000
χ2922-22-1-2-1221-1221-1-1-2-222-1-1-2-22211-1-111-22-20000-2-2-1-1111100000022-21-110000-1-1-1-111000000
χ3022-22-1-2-1221-1221-1-1-2-222-1-1-2-2-2-211-1-1112-220000001133−3−3000000000-11-10000−33−333−3000000
χ3122-22-1-2-1221-1221-1-1-2-222-1-1-2-2-2-211-1-1112-2200000011−3−333000000000-11-100003−33−3−33000000
χ3222-2-222222-2-222222-2-2-2-22222-2-2-2-2-2-22222-2000000-2-2000000000000022-20000000000000000
χ3322-2-2-12-1221122-1-1-1-2-2-2-2-1-122221111-1-1-2-22000022-1-1-1-1-1-10000002-2-211-10000-1-11111000000
χ3422-2-2-12-1221122-1-1-1-2-2-2-2-1-122221111-1-1-2-220000-2-2-1-11111000000-22211-1000011-1-1-1-1000000
χ3522-2-2-12-1221122-1-1-1-2-2-2-2-1-122-2-21111-1-122-20000001133−3−3000000000-1-1100003−3−33−33000000
χ3622-2-2-12-1221122-1-1-1-2-2-2-2-1-122-2-21111-1-122-200000011−3−333000000000-1-110000−333−33−3000000
χ372-20020-22200-2-20220000-2-200-220000000002i−2i2i−2i2-2-222-22-20000000000002i−2i2i−2i000000000000
χ382-20020-22200-2-20220000-2-200-220000000002i−2i−2i2i-22-22-22-220000000000002i−2i−2i2i000000000000
χ392-20020-22200-2-20220000-2-200-22000000000−2i2i2i−2i-22-22-22-22000000000000−2i2i2i−2i000000000000
χ402-20020-22200-2-20220000-2-200-22000000000−2i2i−2i2i2-2-222-22-2000000000000−2i2i−2i2i000000000000
χ4144444441-2441-241-21-21-21-21-2001-21-21-200000220000000002002200000000-1-10000000-100-1-1
χ4244444441-2441-241-21-21-21-21-2001-21-21-200000-2-2000000000-200-2-20000000011000000010011
χ434444444-2144-214-21-21-21-21-2100-21-21-21000220000000000202200000000-1-100000000-10-1-100
χ444444444-2144-214-21-21-21-21-2100-21-21-21000-2-20000000000-20-2-2000000001100000000101100
χ45444-44-441-24-41-2-41-21-2-121-2-12001-2-12-120000022000000000-2002-200000000-1-10000000100-11
χ46444-44-441-24-41-2-41-21-2-121-2-12001-2-12-1200000-2-2000000000200-2200000000110000000-1001-1
χ47444-44-44-214-4-21-4-21-212-1-212-100-212-12-1000220000000000-202-200000000-1-10000000010-1100
χ48444-44-44-214-4-21-4-21-212-1-212-100-212-12-1000-2-2000000000020-22000000001100000000-101-100
χ4944-444-441-2-441-2-41-2-121-21-2-1200-121-2-120000022000000000-200-2200000000-1-100000001001-1
χ5044-444-441-2-441-2-41-2-121-21-2-1200-121-2-1200000-2-20000000002002-200000000110000000-100-11
χ5144-444-44-21-44-21-4-212-1-21-212-1002-1-212-1000220000000000-20-2200000000-1-100000000101-100
χ5244-444-44-21-44-21-4-212-1-21-212-1002-1-212-1000-2-20000000000202-2000000001100000000-10-1100
χ5344-4-44441-2-4-41-241-2-12-121-21-200-12-121-20000022000000000200-2-200000000-1-10000000-10011
χ5444-4-44441-2-4-41-241-2-12-121-21-200-12-121-200000-2-2000000000-2002200000000110000000100-1-1
χ5544-4-4444-21-4-4-214-212-12-1-21-21002-12-1-2100022000000000020-2-200000000-1-100000000-101100
χ5644-4-4444-21-4-4-214-212-12-1-21-21002-12-1-21000-2-20000000000-202200000000110000000010-1-100
χ574-40040-44400-4-40440000-4-4004-40000000000000004-400000000000000000000000000000000
χ584-400-2024400-4-40-2-2000022004-4000000000000000-2223−23−23230000000000000000000000000000
χ594-400-2024400-4-40-2-2000022004-4000000000000000-22−232323−230000000000000000000000000000
χ604-400-2024400-4-40-2-200002200-4400000000000004-42-2-22-220000000000000000000000000000
χ614-400-2024400-4-40-2-200002200-440000000000000-442-22-22-20000000000000000000000000000
χ628888-48-42-4-4-42-4-4-122-42-4-122-400-12-12-120000000000000000000000000000000000000000000
χ638888-48-4-42-4-4-42-42-1-42-422-1-42002-12-12-10000000000000000000000000000000000000000000
χ64888-8-4-8-42-4-442-44-122-4-24-12-2400-121-21-20000000000000000000000000000000000000000000
χ65888-8-4-8-4-42-44-4242-1-424-22-14-2002-1-21-210000000000000000000000000000000000000000000
χ6688-88-4-8-42-44-42-44-12-242-4-12-24001-2-121-20000000000000000000000000000000000000000000
χ6788-88-4-8-4-424-4-4242-14-2-422-14-200-212-1-210000000000000000000000000000000000000000000
χ6888-8-8-48-42-4442-4-4-12-24-24-122-4001-21-2-120000000000000000000000000000000000000000000
χ6988-8-8-48-4-4244-42-42-14-24-22-1-4200-21-212-10000000000000000000000000000000000000000000
χ708-80080-82-400-2402-40000-240000000000000004i−4i0000000000000000000000−2i2i000000000000
χ718-80080-82-400-2402-40000-24000000000000000−4i4i00000000000000000000002i−2i000000000000
χ728-80080-8-42004-20-4200004-200000000000004i−4i0000000000000000000000−2i2i00000000000000
χ738-80080-8-42004-20-4200004-20000000000000−4i4i00000000000000000000002i−2i00000000000000
χ7416-1600-8084-800-480-2400002-400000000000000000000000000000000000000000000000000000
χ7516-1600-808-84008-404-20000-4200000000000000000000000000000000000000000000000000000

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