Finite Group Databasebeta

← Group #13021336

Character table — Group #13021336

Order 1280.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74
size1111222222444444445555888888888888881010101010101616202020202020202020202020202020202020202032323232808080808080
order12224444445888810101022222020202020204040404040404040444444448888888888888888888820202020444444
χ111111111111111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-1-1
χ3111111111111111111111111111111111111111111-1-111111111111111111111-1-1-1-1-1-1-1-1-1-1
χ4111111111111111111111111111111111111111111-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111
χ5111111111111111111-1-1-1-111111111111111-1-1-1-1-1-111-1-1-1-1iiiiiiii−i−i−i−i−i−i−i−i1111-1-1ii−i−i
χ6111111111111111111-1-1-1-111111111111111-1-1-1-1-1-111-1-1-1-1−i−i−i−i−i−i−i−iiiiiiiii1111-1-1−i−iii
χ7111111111111111111-1-1-1-111111111111111-1-1-1-1-1-1-1-1-1-1-1-1iiiiiiii−i−i−i−i−i−i−i−i-1-1-1-111−i−iii
χ8111111111111111111-1-1-1-111111111111111-1-1-1-1-1-1-1-1-1-1-1-1−i−i−i−i−i−i−i−iiiiiiiii-1-1-1-111ii−i−i
χ911111111111-1-1-1-11111111111111-1-1-1-1-1-1-1-11111111-1-1-1-1-11111-1-1-1-11111-1-1-1-111-1-11-11-11-1
χ1011111111111-1-1-1-11111111111111-1-1-1-1-1-1-1-11111111-1-1-1-1-1-1-1-1-11111-1-1-1-1111111-1-11-1-11-11
χ1111111111111-1-1-1-11111111111111-1-1-1-1-1-1-1-1111111-11-1-1-1-11111-1-1-1-11111-1-1-1-1-1-111-11-11-11
χ1211111111111-1-1-1-11111111111111-1-1-1-1-1-1-1-1111111-11-1-1-1-1-1-1-1-11111-1-1-1-11111-1-111-111-11-1
χ1311111111111-1-1-1-1111-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-1-1-11-11111iiii−i−i−i−i−i−i−i−iiiii11-1-1-11i−i−ii
χ1411111111111-1-1-1-1111-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-1-1-11-11111−i−i−i−iiiiiiiii−i−i−i−i11-1-1-11−iii−i
χ1511111111111-1-1-1-1111-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111iiii−i−i−i−i−i−i−i−iiiii-1-1111-1−iii−i
χ1611111111111-1-1-1-1111-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111−i−i−i−iiiiiiiii−i−i−i−i-1-1111-1i−i−ii
χ17222222-2-2-2-220000222222222-2-2-2-200000000-2-222-2-2000000000022-2-2000022-2-20000000000
χ18222222-2-2-2-220000222222222-2-2-2-200000000-2-222-2-20000000000-2-2220000-2-2220000000000
χ19222222-2-2-2-220000222-2-2-2-222-2-2-2-20000000022-2-22200000000002i2i−2i−2i0000−2i−2i2i2i0000000000
χ20222222-2-2-2-220000222-2-2-2-222-2-2-2-20000000022-2-2220000000000−2i−2i2i2i00002i2i−2i−2i0000000000
χ212222-2-222-2-2200002222222-2-222-2-200000000-2-2-2-22200000022-2-2000022-2-200000000000000
χ222222-2-222-2-2200002222222-2-222-2-200000000-2-2-2-222000000-2-2220000-2-22200000000000000
χ232222-2-222-2-220000222-2-2-2-2-2-222-2-2000000002222-2-20000002i2i−2i−2i0000−2i−2i2i2i00000000000000
χ242222-2-222-2-220000222-2-2-2-2-2-222-2-2000000002222-2-2000000−2i−2i2i2i00002i2i−2i−2i00000000000000
χ252222-2-2-2-222222-2-22222222-2-2-2-2222222-2-2-2-222-2-2-2-20022-2-200000000000000000000000000
χ262222-2-2-2-222222-2-2222-2-2-2-2-2-2-2-2222222-2-2-2-2-2-2222200-2-22200000000000000000000000000
χ272222-2-2-2-2222-2-2222222222-2-2-2-222-2-2-2-2222222-2-2-2-200-2-22200000000000000000000000000
χ282222-2-2-2-2222-2-222222-2-2-2-2-2-2-2-222-2-2-2-22222-2-222220022-2-200000000000000000000000000
χ2922-2-2002-20022−22−22-2-222-2-2002-20022−2−222−2−200002-2002−22−2002-22−22−2002-22−22−20000000000
χ3022-2-2002-20022−22−22-2-222-2-2002-20022−2−222−2−200002-2002−22−200-22−22−2200-22−22−220000000000
χ3122-2-2002-20022−22−22-2-2-2-222002-20022−2−222−2−20000-2200−22−22002i−2ii2−i2i2−i200−2i2i−i2i2−i2i20000000000
χ3222-2-2002-20022−22−22-2-2-2-222002-20022−2−222−2−20000-2200−22−2200−2i2i−i2i2−i2i2002i−2ii2−i2i2−i20000000000
χ3322-2-2002-2002−22−222-2-222-2-2002-200−2−222−2−22200002-200−22−22002-2−22−22002-2−22−220000000000
χ3422-2-2002-2002−22−222-2-222-2-2002-200−2−222−2−22200002-200−22−2200-222−22−200-222−22−20000000000
χ3522-2-2002-2002−22−222-2-2-2-222002-200−2−222−2−2220000-22002−22−2002i−2i−i2i2−i2i200−2i2ii2−i2i2−i20000000000
χ3622-2-2002-2002−22−222-2-2-2-222002-200−2−222−2−2220000-22002−22−200−2i2ii2−i2i2−i2002i−2i−i2i2−i2i20000000000
χ3722-2-200-220022−2−222-2-222-2-200-220022−2−2−2−2220000-22002−2−222-2002−2−222-2002−2−220000000000
χ3822-2-200-220022−2−222-2-222-2-200-220022−2−2−2−2220000-22002−2−22-2200−222−2-2200−222−20000000000
χ3922-2-200-220022−2−222-2-2-2-22200-220022−2−2−2−22200002-200−222−22i−2i00i2−i2−i2i2−2i2i00−i2i2i2−i20000000000
χ4022-2-200-220022−2−222-2-2-2-22200-220022−2−2−2−22200002-200−222−2−2i2i00−i2i2i2−i22i−2i00i2−i2−i2i20000000000
χ4122-2-200-22002−222−22-2-222-2-200-2200−2−22222−2−20000-2200−222−22-200−222−22-200−222−20000000000
χ4222-2-200-22002−222−22-2-222-2-200-2200−2−22222−2−20000-2200−222−2-22002−2−22-22002−2−220000000000
χ4322-2-200-22002−222−22-2-2-2-22200-2200−2−22222−2−200002-2002−2−222i−2i00−i2i2i2−i2−2i2i00i2−i2−i2i20000000000
χ4422-2-200-22002−222−22-2-2-2-22200-2200−2−22222−2−200002-2002−2−22−2i2i00i2−i2−i2i22i−2i00−i2i2i2−i20000000000
χ454444444444-14444-1-1-10000-1-1-1-1-1-1-1-1-1-1-1-1-1-10000004400000000000000000000-1-1-1-1000000
χ464444444444-14444-1-1-10000-1-1-1-1-1-1-1-1-1-1-1-1-1-1000000-4-4000000000000000000001111000000
χ474444444444-1-4-4-4-4-1-1-10000-1-1-1-1-1-1111111110000004-400000000000000000000-1-111000000
χ484444444444-1-4-4-4-4-1-1-10000-1-1-1-1-1-111111111000000-440000000000000000000011-1-1000000
χ494444-4-4-4-444-144-4-4-1-1-100001111-1-1-1-1-1-1111100000000000000000000000000005−55−5000000
χ504444-4-4-4-444-144-4-4-1-1-100001111-1-1-1-1-1-111110000000000000000000000000000−55−55000000
χ514444-4-4-4-444-1-4-444-1-1-100001111-1-11111-1-1-1-100000000000000000000000000005−5−55000000
χ524444-4-4-4-444-1-4-444-1-1-100001111-1-11111-1-1-1-10000000000000000000000000000−555−5000000
χ534-44-44-4000040000-44-44-44-44-4000000000000004-40000000000000000000000000000000000
χ544-44-44-4000040000-44-4-44-444-400000000000000-440000000000000000000000000000000000
χ554-44-4-44000040000-44-44-44-4-4400000000000000-440000000000000000000000000000000000
χ564-44-4-44000040000-44-4-44-44-44000000000000004-40000000000000000000000000000000000
χ574-4-4400004-440000-4-444-4-4400004-4000000004-4000000000000000000000000000000000000
χ584-4-4400004-440000-4-44-444-400004-400000000-44000000000000000000000000000000000000
χ594-4-440000-4440000-4-444-4-440000-4400000000-44000000000000000000000000000000000000
χ604-4-440000-4440000-4-44-444-40000-44000000004-4000000000000000000000000000000000000
χ61888888-8-8-8-8-20000-2-2-20000-2-222220000000000000000000000000000000000000000000000
χ628888-8-888-8-8-20000-2-2-2000022-2-2220000000000000000000000000000000000000000000000
χ6388-8-8008-800-242−4242−42-222000000-2200−2−222−2−22200000000000000000000000000000000000000
χ6488-8-8008-800-2−4242−4242-222000000-220022−2−222−2−200000000000000000000000000000000000000
χ6588-8-800-8800-242−42−4242-2220000002-200−2−22222−2−200000000000000000000000000000000000000
χ6688-8-800-8800-2−424242−42-2220000002-20022−2−2−2−22200000000000000000000000000000000000000
χ678-88-88-80000-200002-220000-22000010−1010−1010−1010−1000000000000000000000000000000000000000
χ688-88-88-80000-200002-220000-220000−1010−1010−1010−101000000000000000000000000000000000000000
χ698-88-8-880000-200002-2200002-2000010−1010−10−1010−101000000000000000000000000000000000000000
χ708-88-8-880000-200002-2200002-20000−1010−101010−1010−1000000000000000000000000000000000000000
χ718-8-8800008-8-2000022-200000000-2225−25−2525000000000000000000000000000000000000000000
χ728-8-8800008-8-2000022-200000000-22−252525−25000000000000000000000000000000000000000000
χ738-8-880000-88-2000022-2000000002-2000025−25−252500000000000000000000000000000000000000
χ748-8-880000-88-2000022-2000000002-20000−252525−2500000000000000000000000000000000000000

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