Finite Group Databasebeta

← Group #72237939

Character table — Group #72237939

Order 2048.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74
size1122244444444888888888881616161616161616161616163232323232323232323232323232323232323232323264646464646464646464646464646464
order12222222222222224444444422444444444422444444444444444444444444888888888888
χ111111111111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111-11-111-1-111-1-1-1-111111111-1-1-1-11111-1-1-1-1-1-1-1-1
χ3111111111111111111111111111111111111-11-11-1-11111-1-1-1-11111-1-1-1-11-1-11-1-1-1-11111-1-1-1-1
χ4111111111111111111111111111111111111-1-1-1-1-1-1-1-11111111111-1-1-1-1-111-1-1-1-1-1-1-1-1-11111
χ51111111111111111111111111111111-1-1-1-1111111111-1-11111-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1
χ61111111111111111111111111111111-1-1-1-111-11-111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-111111111
χ71111111111111111111111111111111-1-1-1-11-11-11-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-11-1-111111-1-1-1-11111
χ81111111111111111111111111111111-1-1-1-11-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-111-111111111-1-1-1-1
χ9111111111-111-1-1-1-11111-1-1-1-11-11-111-1ii−i−i-11111-1-1-1-1i−i11-1-1ii−i−i11-1-1-11-11ii−i−iii−i−iii−i−i
χ10111111111-111-1-1-1-11111-1-1-1-11-11-111-1ii−i−i-11-11-1-1-111i−i-1-111ii−i−i11-1-11-11-1ii−i−i−i−iii−i−iii
χ11111111111-111-1-1-1-11111-1-1-1-11-11-111-1ii−i−i-1-11-1111-1-1i−i-1-111ii−i−i-1-111-1-111−i−iiiii−i−i−i−iii
χ12111111111-111-1-1-1-11111-1-1-1-11-11-111-1ii−i−i-1-1-1-1-11111i−i11-1-1ii−i−i-1-11111-1-1−i−iii−i−iiiii−i−i
χ13111111111-111-1-1-1-11111-1-1-1-11-11-111-1−i−iii-11111-1-1-1-1−ii11-1-1−i−iii11-1-1-11-11−i−iii−i−iii−i−iii
χ14111111111-111-1-1-1-11111-1-1-1-11-11-111-1−i−iii-11-11-1-1-111−ii-1-111−i−iii11-1-11-11-1−i−iiiii−i−iii−i−i
χ15111111111-111-1-1-1-11111-1-1-1-11-11-111-1−i−iii-1-11-1111-1-1−ii-1-111−i−iii-1-111-1-111ii−i−i−i−iiiii−i−i
χ16111111111-111-1-1-1-11111-1-1-1-11-11-111-1−i−iii-1-1-1-1-11111−ii11-1-1−i−iii-1-11111-1-1ii−i−iii−i−i−i−iii
χ17222222222222222222-2-222-2-222-2-2-2-2-20000-2202022000000000000-2-2-2-20000000000000000
χ18222222222222222222-2-222-2-222-2-2-2-2-20000-2-20-20-2-200000000000022220000000000000000
χ192222222222222222-2-222-2-2-2-2-2-222-2-2-20000200000000002222000000000-2-20000000000000
χ202222222222222222-2-222-2-2-2-2-2-222-2-2-2000020000000000-2-2-2-2000000000220000000000000
χ212222222222222222-2-2-2-2-2-222-2-2-2-22220000-20202002200000000000000-200-2000000000000
χ222222222222222222-2-2-2-2-2-222-2-2-2-22220000-20-20-200-2-2000000000000002002000000000000
χ23222222222-222-2-2-2-222-2-2-2-2222-2-22-2-22000022020-2-2000000000000-2-2220000000000000000
χ24222222222-222-2-2-2-222-2-2-2-2222-2-22-2-2200002-20-202200000000000022-2-20000000000000000
χ25222222222-222-2-2-2-2-2-2222222-222-2-2-220000-2000000000022-2-2000000000-220000000000000
χ26222222222-222-2-2-2-2-2-2222222-222-2-2-220000-20000000000-2-2220000000002-20000000000000
χ27222222222-222-2-2-2-2-2-2-2-222-2-2-22-2222-200002020200-2-200000000000000200-2000000000000
χ28222222222-222-2-2-2-2-2-2-2-222-2-2-22-2222-2000020-20-2002200000000000000-2002000000000000
χ2922222-22-2-22-2222-2-222222222-2-2-222-2-22222-200000000220000-2-2-2-200000000000000000000
χ3022222-22-2-22-2222-2-222222222-2-2-222-2-2-2-2-2-2-200000000-2-20000222200000000000000000000
χ3122222-22-2-22-2222-2-222-2-222-2-2-2-22-2-22200002000000000000000000000000002-22-200000000
χ3222222-22-2-22-2222-2-222-2-222-2-2-2-22-2-2220000200000000000000000000000000-22-2200000000
χ3322222-22-2-22-2222-2-2-2-222-2-2-2-222-22-2220000-200000000000000000000000000000000002i−2i2i−2i
χ3422222-22-2-22-2222-2-2-2-222-2-2-2-222-22-2220000-20000000000000000000000000000000000−2i2i−2i2i
χ3522222-22-2-22-2222-2-2-2-2-2-2-2-222222-22-2-2000020000000000000000000000000000002-22-20000
χ3622222-22-2-22-2222-2-2-2-2-2-2-2-222222-22-2-200002000000000000000000000000000000-22-220000
χ3722222-22-2-2-2-22-2-2222222-2-2-2-2-22-2-22-222i2i−2i−2i2000000002i−2i0000−2i−2i2i2i00000000000000000000
χ3822222-22-2-2-2-22-2-2222222-2-2-2-2-22-2-22-22−2i−2i2i2i200000000−2i2i00002i2i−2i−2i00000000000000000000
χ3922222-22-2-2-2-22-2-22222-2-2-2-222-2222-22-20000-2000000000000000000000000002i−2i−2i2i00000000
χ4022222-22-2-2-2-22-2-22222-2-2-2-222-2222-22-20000-200000000000000000000000000−2i2i2i−2i00000000
χ4122222-22-2-2-2-22-2-222-2-22222222-2-2-2-22-20000200000000000000000000000000000000002-2-22
χ4222222-22-2-2-2-22-2-222-2-22222222-2-2-2-22-2000020000000000000000000000000000000000-222-2
χ4322222-22-2-2-2-22-2-222-2-2-2-222-2-22-2222-220000-20000000000000000000000000000002i−2i−2i2i0000
χ4422222-22-2-2-2-22-2-222-2-2-2-222-2-22-2222-220000-2000000000000000000000000000000−2i2i2i−2i0000
χ45444444-4-4-444-44-44-40000000000000002222000000000-2-200002-22-200000000000000000000
χ46444444-4-4-444-44-44-4000000000000000-2-2-2-2000000000220000-22-2200000000000000000000
χ47444444-4-4-4-44-4-44-440000000000000002i2i−2i−2i000000000−2i2i00002i−2i−2i2i00000000000000000000
χ48444444-4-4-4-44-4-44-44000000000000000−2i−2i2i2i0000000002i−2i0000−2i2i2i−2i00000000000000000000
χ4944444-4-4444-4-44-4-440000000000000002222000000000-2-20000-22-2200000000000000000000
χ5044444-4-4444-4-44-4-44000000000000000-2-2-2-20000000002200002-22-200000000000000000000
χ5144444-4-444-4-4-4-444-40000000000000002i2i−2i−2i000000000−2i2i0000−2i2i2i−2i00000000000000000000
χ5244444-4-444-4-4-4-444-4000000000000000−2i−2i2i2i0000000002i−2i00002i−2i−2i2i00000000000000000000
χ53444-4-4040000-40000004i−4i4-44i−4i00000000000020-202-20000000000002i−2i2i−2i0000000000000000
χ54444-4-4040000-40000004i−4i4-44i−4i000000000000-2020-22000000000000−2i2i−2i2i0000000000000000
χ55444-4-4040000-40000004i−4i-44−4i4i00000000000020-20-220000000000002i−2i−2i2i0000000000000000
χ56444-4-4040000-40000004i−4i-44−4i4i000000000000-20202-2000000000000−2i2i2i−2i0000000000000000
χ57444-4-4040000-4000000−4i4i4-4−4i4i00000000000020-202-2000000000000−2i2i−2i2i0000000000000000
χ58444-4-4040000-4000000−4i4i4-4−4i4i000000000000-2020-220000000000002i−2i2i−2i0000000000000000
χ59444-4-4040000-4000000−4i4i-444i−4i00000000000020-20-22000000000000−2i2i2i−2i0000000000000000
χ60444-4-4040000-4000000−4i4i-444i−4i000000000000-20202-20000000000002i−2i−2i2i0000000000000000
χ61888-8-80-80000800008-800000000000000000000000000000000000000000000000000000000
χ62888-8-80-8000080000-8800000000000000000000000000000000000000000000000000000000
χ6388-88-880000-800000000000000000000000000000000000004i−4i000000000000000000000000
χ6488-88-880000-80000000000000000000000000000000000000−4i4i000000000000000000000000
χ6588-88-8-800008000000000000000000000000000000000004-400000000000000000000000000
χ6688-88-8-80000800000000000000000000000000000000000-4400000000000000000000000000
χ6788-8-88008-80000000000000000000000000000000004-4000000000000000000000000000000
χ6888-8-88008-8000000000000000000000000000000000-44000000000000000000000000000000
χ6988-8-8800-88000000000000000000000000000040-40000000000000000000000000000000000
χ7088-8-8800-880000000000000000000000000000-4040000000000000000000000000000000000
χ7116-160000000800-80000000000000000004i−4i4i−4i000000000000000000000000000000000000000
χ7216-160000000800-8000000000000000000−4i4i−4i4i000000000000000000000000000000000000000
χ7316-160000000-80080000000000000000004-4-44000000000000000000000000000000000000000
χ7416-160000000-8008000000000000000000-444-4000000000000000000000000000000000000000

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