Finite Group Databasebeta

← Group #72343338

Character table — Group #72343338

Order 1024.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58
size112224444444444448888888881616161616161616323232323232323232323232323232323232323232323232
order12244244444888888888881616161688161616161616222444888888161616163232323232323232
χ11111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111111-1-111-1-11111-1-1-1-1-1-1-1-1-1-1-1-1
χ31111111111111111111111111111111111-1-111-1-111-1-1-1-11111-1-1-1-1-1-1-1-1
χ41111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111
χ5111111111111111111-1-1-1-11111-1-111-1-1-1-111111111-1-1-1-1-1-1-1-11111-1-1-1-1
χ6111111111111111111-1-1-1-11111-1-111-1-1-1-111-1-111-1-1-1-1-1-11111-1-1-1-11111
χ7111111111111111111-1-1-1-11111-1-111-1-1-1-1-1-111-1-1111111-1-1-1-1-1-1-1-11111
χ8111111111111111111-1-1-1-11111-1-111-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-1
χ91111111-1-1-1-1-111-1-1-11ii−i−i11-1-1i−i1-1ii−i−i1-1111-1-1-1ii−i−iii−i−i11-1-1ii−i−i
χ101111111-1-1-1-1-111-1-1-11ii−i−i11-1-1i−i1-1ii−i−i1-1-1-11-111ii−i−i−i−iii-1-111−i−iii
χ111111111-1-1-1-1-111-1-1-11ii−i−i11-1-1i−i1-1ii−i−i-1111-11-1-1−i−iiiii−i−i-1-111−i−iii
χ121111111-1-1-1-1-111-1-1-11ii−i−i11-1-1i−i1-1ii−i−i-11-1-1-1111−i−iii−i−iii11-1-1ii−i−i
χ131111111-1-1-1-1-111-1-1-11−i−iii11-1-1−ii1-1−i−iii1-1111-1-1-1−i−iii−i−iii11-1-1−i−iii
χ141111111-1-1-1-1-111-1-1-11−i−iii11-1-1−ii1-1−i−iii1-1-1-11-111−i−iiiii−i−i-1-111ii−i−i
χ151111111-1-1-1-1-111-1-1-11−i−iii11-1-1−ii1-1−i−iii-1111-11-1-1ii−i−i−i−iii-1-111ii−i−i
χ161111111-1-1-1-1-111-1-1-11−i−iii11-1-1−ii1-1−i−iii-11-1-1-1111ii−i−iii−i−i11-1-1−i−iii
χ172222222222222222222222-2-2-2-222-2-2-2-2-2-2000000000000000000000000
χ18222222222222222222-2-2-2-2-2-2-2-2-2-2-2-22222000000000000000000000000
χ192222222-2-2-2-2-222-2-2-222i2i−2i−2i-2-2222i−2i-22−2i−2i2i2i000000000000000000000000
χ202222222-2-2-2-2-222-2-2-22−2i−2i2i2i-2-222−2i2i-222i2i−2i−2i000000000000000000000000
χ2122222-2-222-2-2222-2-22-20000222200-2-200002200-2-2000000000000000000
χ2222222-2-222-2-2222-2-22-20000222200-2-20000-2-20022000000000000000000
χ2322222-2-222-2-2222-2-22-20000-2-2-2-200220000000000002i−2i2i−2i000000000000
χ2422222-2-222-2-2222-2-22-20000-2-2-2-20022000000000000−2i2i−2i2i000000000000
χ2522222-2-222-2-2-2-2-222-222i2i−2i−2i0000−2i2i00000000000000000000002−22−2i2−i2i2−i2
χ2622222-2-222-2-2-2-2-222-222i2i−2i−2i0000−2i2i0000000000000000000000−22−22−i2i2−i2i2
χ2722222-2-222-2-2-2-2-222-22−2i−2i2i2i00002i−2i00000000000000000000002−22−2−i2i2−i2i2
χ2822222-2-222-2-2-2-2-222-22−2i−2i2i2i00002i−2i0000000000000000000000−22−22i2−i2i2−i2
χ2922222-2-2-2-2222-2-2-2-22222220000-2-200000000000000000000002−2−222−2−22
χ3022222-2-2-2-2222-2-2-2-22222220000-2-20000000000000000000000−222−2−222−2
χ3122222-2-2-2-2222-2-2-2-222-2-2-2-200002200000000000000000000002−2−22−222−2
χ3222222-2-2-2-2222-2-2-2-222-2-2-2-20000220000000000000000000000−222−22−2−22
χ3322222-2-2-2-222-22222-2-2000022-2-200-2200002-200-22000000000000000000
χ3422222-2-2-2-222-22222-2-2000022-2-200-220000-22002-2000000000000000000
χ3522222-2-2-2-222-22222-2-20000-2-222002-20000000000002-2-22000000000000
χ3622222-2-2-2-222-22222-2-20000-2-222002-2000000000000-222-2000000000000
χ3744444444444-4-4-4-4-4-4-40000000000000000000000000000000000000000
χ384444444-4-4-4-44-4-4444-40000000000000000000000000000000000000000
χ3944-44-400004i−4i04-44i−4i000000000000000000002-2002i−2i0000000000000000
χ4044-44-400004i−4i04-44i−4i00000000000000000000-2200−2i2i0000000000000000
χ4144-44-400004i−4i0-44−4i4i0000000000000000000000000000002ζ−2ζ2ζ3−2ζ300000000
χ4244-44-400004i−4i0-44−4i4i000000000000000000000000000000−2ζ2ζ−2ζ32ζ300000000
χ4344-44-40000−4i4i04-4−4i4i000000000000000000002-200−2i2i0000000000000000
χ4444-44-40000−4i4i04-4−4i4i00000000000000000000-22002i−2i0000000000000000
χ4544-44-40000−4i4i0-444i−4i0000000000000000000000000000002ζ3−2ζ32ζ−2ζ00000000
χ4644-44-40000−4i4i0-444i−4i000000000000000000000000000000−2ζ32ζ3−2ζ2ζ00000000
χ4744-4-4400000040000-402i2−2i22i2−2i222−2222−2200002i−2i2i−2i000000000000000000000000
χ4844-4-4400000040000-402i2−2i22i2−2i2−2222−22220000−2i2i−2i2i000000000000000000000000
χ4944-4-4400000040000-40−2i22i2−2i22i222−2222−220000−2i2i−2i2i000000000000000000000000
χ5044-4-4400000040000-40−2i22i2−2i22i2−2222−222200002i−2i2i−2i000000000000000000000000
χ5144-4-44000000-400004022−22−222222−22−222200002-2-22000000000000000000000000
χ5244-4-44000000-400004022−22−2222−222222−220000-222-2000000000000000000000000
χ5344-4-44000000-4000040−222222−2222−22−22220000-222-2000000000000000000000000
χ5444-4-44000000-4000040−222222−22−222222−2200002-2-22000000000000000000000000
χ55888-8-88-8000000000000000000000000000000000000000000000000000
χ56888-8-8-88000000000000000000000000000000000000000000000000000
χ5716-16000008-80000000000000000000000000000000000000000000000000
χ5816-1600000-880000000000000000000000000000000000000000000000000

Here ζ is a primitive root of unity of order 8 (ζ8 = 1); i = ζ2.