Finite Group Databasebeta

← Group #13165617

Character table — Group #13165617

Order 1728.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72
size1111222244444444668888888818181818181824242424242424242424242424242424242424242424363636363636545454545454727272727272
order1222366633666666223366666644888824666666666666121212121212121212122424242444888824661212
χ1111111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111-1-1-1-111-1-111-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1
χ31111111111111111111111111111-1-1-1-11-1111111111111-1-1-1-1-1-1-1-111-1-1-1-111-1-1-1-1-11-1-111
χ41111111111111111111111111111-1-1-1-1-11-1-111-1-111-1-1-1-11111111111-1-1-1-111-1-1-1-11-111-1-1
χ51111111111111111-1-1111111111111111111-1-111-1-1111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1
χ61111111111111111-1-111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1111111
χ71111111111111111-1-11111111111-1-1-1-11-111-1-111-1-11111-1-1-1-1-1-1-1-111-1-1-1-1-1-111111-111-1-1
χ81111111111111111-1-11111111111-1-1-1-1-11-1-1-1-1-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-11111-11-1-111
χ922222222222222222222222222-2-200000000220022000000000000-2-20000-2-20000000000
χ102222222222222222-2-222222222-2-200000000-2-200-2-2000000000000-2-20000220000000000
χ112222-1-1-1-12222222200-1-1-1-1-1-1-1-122222222-1-1002200-1-1-1-1-1-122-1-1-1-1-1-1-1-1-1-1000000000000
χ122222-1-1-1-12222222200-1-1-1-1-1-1-1-1222222-2-21100-2-200111111-2-21111-1-1-1-1-1-1000000000000
χ132222-1-1-1-12222222200-1-1-1-1-1-1-1-122-2-2-2-22-2-1-1002200-1-1-1-111-2-21111-1-11111000000000000
χ142222-1-1-1-12222222200-1-1-1-1-1-1-1-122-2-2-2-2-221100-2-2001111-1-122-1-1-1-1-1-11111000000000000
χ1522-2-222-2-2222-22-2-2-200222-22-2-2-200−i2−i2i2i2000000000000000000000000−i2−i2i2i22i−2i22−2−2000000
χ1622-2-222-2-2222-22-2-2-200222-22-2-2-200−i2−i2i2i2000000000000000000000000−i2−i2i2i2−2i2i−2−222000000
χ1722-2-222-2-2222-22-2-2-200222-22-2-2-200i2i2−i2−i2000000000000000000000000i2i2−i2−i22i−2i−2−222000000
χ1822-2-222-2-2222-22-2-2-200222-22-2-2-200i2i2−i2−i2000000000000000000000000i2i2−i2−i2−2i2i22−2−2000000
χ192-22-22-22-222-2-2-2-2222-222-2-2-22-22002−22−200002-2002-2000000000000002−22−2002−22−2000000
χ202-22-22-22-222-2-2-2-2222-222-2-2-22-2200−22−2200002-2002-200000000000000−22−2200−22−22000000
χ212-22-22-22-222-2-2-2-222-2222-2-2-22-22002−22−20000-2200-22000000000000002−22−200−22−22000000
χ222-22-22-22-222-2-2-2-222-2222-2-2-22-2200−22−220000-2200-2200000000000000−22−22002−22−2000000
χ232-2-222-2-2222-22-22-2-20022-22-2-22-22-22i−2i−2i2i00000000000000000000002-22i−2i−2i2i000000000000
χ242-2-222-2-2222-22-22-2-20022-22-2-22-22-2−2i2i2i−2i00000000000000000000002-2−2i2i2i−2i000000000000
χ252-2-222-2-2222-22-22-2-20022-22-2-22-2-2200000000000000000000000000-220000002-2-22000000
χ262-2-222-2-2222-22-22-2-20022-22-2-22-2-2200000000000000000000000000-22000000-222-2000000
χ272-2-22-111-122-22-22-2-200-1-11-111-112-22i−2i−2i2i00−i3i3000000−i3−i3i3i33−30033−3−3-11−iii−i000000000000
χ282-2-22-111-122-22-22-2-200-1-11-111-112-22i−2i−2i2i00i3−i3000000i3i3−i3−i3−3300−3−333-11−iii−i000000000000
χ292-2-22-111-122-22-22-2-200-1-11-111-112-2−2i2i2i−2i00−i3i3000000−i3−i3i3i3−3300−3−333-11i−i−ii000000000000
χ302-2-22-111-122-22-22-2-200-1-11-111-112-2−2i2i2i−2i00i3−i3000000i3i3−i3−i33−30033−3−3-11i−i−ii000000000000
χ31444444441-211-2-2-2144-21-2-2111-2000000202211-1-1-2-2-1-1-1-1000000000000000000000200-1-1
χ32444444441-211-2-2-2144-21-2-2111-2000000-20-2-21111-2-21111000000000000000000000-20011
χ33444444441-211-2-2-21-4-4-21-2-2111-20000002022-1-1-1-122-1-1-1-1000000000000000000000-20011
χ34444444441-211-2-2-21-4-4-21-2-2111-2000000-20-2-2-1-111221111000000000000000000000200-1-1
χ3544444444-21-2-2111-2441-211-2-2-210000000200-2-20011000022-1-1-1-1-1-100000000000020-1-100
χ3644444444-21-2-2111-2441-211-2-2-210000000-200-2-200110000-2-2111111000000000000-201100
χ3744444444-21-2-2111-2-4-41-211-2-2-2100000002002200-1-1000022-1-1-1-1-1-1000000000000-201100
χ3844444444-21-2-2111-2-4-41-211-2-2-210000000-2002200-1-10000-2-211111100000000000020-1-100
χ394444-2-2-2-24444444400-2-2-2-2-2-2-2-2-4-400000000000000000000000000220000000000000000
χ4044-4-4-2-222444-44-4-4-400-2-2-22-222200−2i2−2i22i22i2000000000000000000000000i2i2−i2−i2000000000000
χ4144-4-4-2-222444-44-4-4-400-2-2-22-2222002i22i2−2i2−2i2000000000000000000000000−i2−i2i2i2000000000000
χ424-44-44-44-41-2-1-122-214-4-2122-11-1-200000000001-1−i3i3-22−i3i3−i3i3000000000000000000000000−i3i3
χ434-44-44-44-41-2-1-122-214-4-2122-11-1-200000000001-1i3−i3-22i3−i3i3−i3000000000000000000000000i3−i3
χ444-44-44-44-41-2-1-122-21-44-2122-11-1-20000000000-11−i3i32-2−i3i3−i3i3000000000000000000000000i3−i3
χ454-44-44-44-41-2-1-122-21-44-2122-11-1-20000000000-11i3−i32-2i3−i3i3−i3000000000000000000000000−i3i3
χ464-44-44-44-4-2122-1-11-24-41-2-1-12-2210000000000-22001-1000000−i3i3−i3i3−i3i300000000000000−i3i300
χ474-44-44-44-4-2122-1-11-24-41-2-1-12-2210000000000-22001-1000000i3−i3i3−i3i3−i300000000000000i3−i300
χ484-44-44-44-4-2122-1-11-2-441-2-1-12-22100000000002-200-11000000−i3i3−i3i3−i3i300000000000000i3−i300
χ494-44-44-44-4-2122-1-11-2-441-2-1-12-22100000000002-200-11000000i3−i3i3−i3i3−i300000000000000−i3i300
χ504-44-4-22-2244-4-4-4-44400-2-2222-22-20022−2222−22000000000000000000000000−22−22000000000000
χ514-44-4-22-2244-4-4-4-44400-2-2222-22-200−2222−22220000000000000000000000002−22−2000000000000
χ524-4-44-222-244-44-44-4-400-2-22-222-22-44000000000000000000000000002-20000000000000000
χ538888-4-4-4-42-422-4-4-42002-122-1-1-1200000040-2-200-2-200111100000000000000000000000000
χ548888-4-4-4-42-422-4-4-42002-122-1-1-12000000-4022002200-1-1-1-100000000000000000000000000
χ558888-4-4-4-4-42-4-4222-400-12-1-1222-100000004000000000000-2-2-2-21111000000000000000000
χ568888-4-4-4-4-42-4-4222-400-12-1-1222-10000000-40000000000002222-1-1-1-1000000000000000000
χ5788-8-888-8-82-42-2-444-200-42-442-2-240000000000000000000000000000000000000000000000
χ5888-8-888-8-8-42-442-2-24002-42-2-444-20000000000000000000000000000000000000000000000
χ5988-8-8-4-4442-42-2-444-2002-12-2-111-200000000000000003-3-3300000000000000000000000000
χ6088-8-8-4-4442-42-2-444-2002-12-2-111-20000000000000000-333-300000000000000000000000000
χ6188-8-8-4-444-42-442-2-2400-12-112-2-210000000000000000000000003i−3i−3i3i000000000000000000
χ6288-8-8-4-444-42-442-2-2400-12-112-2-21000000000000000000000000−3i3i3i−3i000000000000000000
χ638-88-8-44-442-4-2-244-42002-1-2-21-112000000000000−2i32i300i3−i3i3−i300000000000000000000000000
χ648-88-8-44-442-4-2-244-42002-1-2-21-1120000000000002i3−2i300−i3i3−i3i300000000000000000000000000
χ658-88-8-44-44-4244-2-22-400-1211-22-2-10000000000000000000000−2i32i3i3−i3i3−i3000000000000000000
χ668-88-8-44-44-4244-2-22-400-1211-22-2-100000000000000000000002i3−2i3−i3i3−i3i3000000000000000000
χ678-8-888-8-882-4-224-44-200-424-4-2-2240000000000000000000000000000000000000000000000
χ688-8-888-8-88-424-4-22-24002-4-2244-4-20000000000000000000000000000000000000000000000
χ698-8-88-444-42-4-224-44-2002-1-2211-1-200000000−2i32i3000000i3i3−i3−i300000000000000000000000000
χ708-8-88-444-42-4-224-44-2002-1-2211-1-2000000002i3−2i3000000−i3−i3i3i300000000000000000000000000
χ718-8-88-444-4-424-4-22-2400-121-1-2-2210000000000000000000023−2300−3−333000000000000000000
χ728-8-88-444-4-424-4-22-2400-121-1-2-22100000000000000000000−23230033−3−3000000000000000000

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