Finite Group Databasebeta

← Group #101148

Character table — Group #101148

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68
size111111112222222244444444444444888888888888888888888816161616161616161616161616161616
order12222222222244444444444444444422444488888888888888884444444488888888
χ111111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ3111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1
χ4111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111
χ51111111111111111-1-1-1-1-1-1-1-1111111-1-1-1-11111111111-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1-1-1
χ61111111111111111-1-1-1-1-1-1-1-1111111-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-11111
χ71111111111111111-1-1-1-1-1-1-1-1111111-1-1-1-111-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-11111
χ81111111111111111-1-1-1-1-1-1-1-1111111-1-1-1-111-1-1-1-1-1-1-1-111111111-1-1-1-111111111-1-1-1-1
χ9111111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-111-1-111iiii−i−i−i−iiiii−i−i−i−i11-1-111-1-1ii−i−iii−i−i
χ10111111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-111-1-111iiii−i−i−i−iiiii−i−i−i−i-1-111-1-111−i−iii−i−iii
χ11111111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-111-1-111−i−i−i−iiiii−i−i−i−iiiii11-1-111-1-1−i−iii−i−iii
χ12111111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-111-1-111−i−i−i−iiiii−i−i−i−iiiii-1-111-1-111ii−i−iii−i−i
χ13111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-11111iiii−i−i−i−i−i−i−i−iiiii11-1-1-1-111ii−i−i−i−iii
χ14111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-11111iiii−i−i−i−i−i−i−i−iiiii-1-11111-1-1−i−iiiii−i−i
χ15111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-11111−i−i−i−iiiiiiiii−i−i−i−i11-1-1-1-111−i−iiiii−i−i
χ16111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-11111−i−i−i−iiiiiiiii−i−i−i−i-1-11111-1-1ii−i−i−i−iii
χ1722222222222222222222222222-2-2-2-2-2-2-2-2-2-200000000000000000000000000000000
χ182222222222222222-2-2-2-2-2-2-2-222-2-2-2-22222-2-200000000000000000000000000000000
χ19222222222222-2-2-2-22222-2-2-2-2-2-22222-2-222-2-200000000000000000000000000000000
χ20222222222222-2-2-2-2-2-2-2-22222-2-2222222-2-2-2-200000000000000000000000000000000
χ2122222222-2-2-2-2222200000000-2-222-2-200002-20000000022-2-222-2-20000000000000000
χ2222222222-2-2-2-2222200000000-2-222-2-200002-200000000-2-222-2-2220000000000000000
χ2322222222-2-2-2-2222200000000-2-2-2-2220000-2222-2-222-2-2000000000000000000000000
χ2422222222-2-2-2-2222200000000-2-2-2-2220000-22-2-222-2-222000000000000000000000000
χ2522222222-2-2-2-2-2-2-2-2000000002222-2-20000-222i2i−2i−2i−2i−2i2i2i000000000000000000000000
χ2622222222-2-2-2-2-2-2-2-2000000002222-2-20000-22−2i−2i2i2i2i2i−2i−2i000000000000000000000000
χ2722222222-2-2-2-2-2-2-2-20000000022-2-22200002-2000000002i2i−2i−2i−2i−2i2i2i0000000000000000
χ2822222222-2-2-2-2-2-2-2-20000000022-2-22200002-200000000−2i−2i2i2i2i2i−2i−2i0000000000000000
χ2922-2-2-222-22-22-2000000002i2i−2i−2i002i−2i2i−2i2-200001+i−1−i1+i−1−i1−i−1+i1−i−1+i1+i−1−i1+i−1−i1−i−1+i1−i−1+i0000000000000000
χ3022-2-2-222-22-22-2000000002i2i−2i−2i002i−2i2i−2i2-20000−1−i1+i−1−i1+i−1+i1−i−1+i1−i−1−i1+i−1−i1+i−1+i1−i−1+i1−i0000000000000000
χ3122-2-2-222-22-22-2000000002i2i−2i−2i00−2i2i−2i2i-2200001−i−1+i1−i−1+i1+i−1−i1+i−1−i−1+i1−i−1+i1−i−1−i1+i−1−i1+i0000000000000000
χ3222-2-2-222-22-22-2000000002i2i−2i−2i00−2i2i−2i2i-220000−1+i1−i−1+i1−i−1−i1+i−1−i1+i1−i−1+i1−i−1+i1+i−1−i1+i−1−i0000000000000000
χ3322-2-2-222-22-22-200000000−2i−2i2i2i002i−2i2i−2i-2200001+i−1−i1+i−1−i1−i−1+i1−i−1+i−1−i1+i−1−i1+i−1+i1−i−1+i1−i0000000000000000
χ3422-2-2-222-22-22-200000000−2i−2i2i2i002i−2i2i−2i-220000−1−i1+i−1−i1+i−1+i1−i−1+i1−i1+i−1−i1+i−1−i1−i−1+i1−i−1+i0000000000000000
χ3522-2-2-222-22-22-200000000−2i−2i2i2i00−2i2i−2i2i2-200001−i−1+i1−i−1+i1+i−1−i1+i−1−i1−i−1+i1−i−1+i1+i−1−i1+i−1−i0000000000000000
χ3622-2-2-222-22-22-200000000−2i−2i2i2i00−2i2i−2i2i2-20000−1+i1−i−1+i1−i−1−i1+i−1−i1+i−1+i1−i−1+i1−i−1−i1+i−1−i1+i0000000000000000
χ3722-2-2-222-2-22-2200002i2i−2i−2i0000002i−2i−2i2i002-2001−i−1+i−1+i1−i1+i−1−i−1−i1+i1+i−1−i−1−i1+i1−i−1+i−1+i1−i0000000000000000
χ3822-2-2-222-2-22-2200002i2i−2i−2i0000002i−2i−2i2i002-200−1+i1−i1−i−1+i−1−i1+i1+i−1−i−1−i1+i1+i−1−i−1+i1−i1−i−1+i0000000000000000
χ3922-2-2-222-2-22-2200002i2i−2i−2i000000−2i2i2i−2i00-22001+i−1−i−1−i1+i1−i−1+i−1+i1−i−1+i1−i1−i−1+i−1−i1+i1+i−1−i0000000000000000
χ4022-2-2-222-2-22-2200002i2i−2i−2i000000−2i2i2i−2i00-2200−1−i1+i1+i−1−i−1+i1−i1−i−1+i1−i−1+i−1+i1−i1+i−1−i−1−i1+i0000000000000000
χ4122-2-2-222-2-22-220000−2i−2i2i2i0000002i−2i−2i2i00-22001−i−1+i−1+i1−i1+i−1−i−1−i1+i−1−i1+i1+i−1−i−1+i1−i1−i−1+i0000000000000000
χ4222-2-2-222-2-22-220000−2i−2i2i2i0000002i−2i−2i2i00-2200−1+i1−i1−i−1+i−1−i1+i1+i−1−i1+i−1−i−1−i1+i1−i−1+i−1+i1−i0000000000000000
χ4322-2-2-222-2-22-220000−2i−2i2i2i000000−2i2i2i−2i002-2001+i−1−i−1−i1+i1−i−1+i−1+i1−i1−i−1+i−1+i1−i1+i−1−i−1−i1+i0000000000000000
χ4422-2-2-222-2-22-220000−2i−2i2i2i000000−2i2i2i−2i002-200−1−i1+i1+i−1−i−1+i1−i1−i−1+i−1+i1−i1−i−1+i−1−i1+i1+i−1−i0000000000000000
χ452-222-22-2-22-2-222i2i−2i−2i2i−2i2i−2i2-22-22i−2i00000000000000000000000000000000001+i−1−i1−i−1+i1−i−1+i1+i−1−i
χ462-222-22-2-22-2-222i2i−2i−2i2i−2i2i−2i2-22-22i−2i0000000000000000000000000000000000−1−i1+i−1+i1−i−1+i1−i−1−i1+i
χ472-222-22-2-22-2-222i2i−2i−2i−2i2i−2i2i-22-222i−2i00000000000000000000000000000000001+i−1−i1−i−1+i−1+i1−i−1−i1+i
χ482-222-22-2-22-2-222i2i−2i−2i−2i2i−2i2i-22-222i−2i0000000000000000000000000000000000−1−i1+i−1+i1−i1−i−1+i1+i−1−i
χ492-222-22-2-22-2-22−2i−2i2i2i2i−2i2i−2i-22-22−2i2i00000000000000000000000000000000001−i−1+i1+i−1−i−1−i1+i−1+i1−i
χ502-222-22-2-22-2-22−2i−2i2i2i2i−2i2i−2i-22-22−2i2i0000000000000000000000000000000000−1+i1−i−1−i1+i1+i−1−i1−i−1+i
χ512-222-22-2-22-2-22−2i−2i2i2i−2i2i−2i2i2-22-2−2i2i00000000000000000000000000000000001−i−1+i1+i−1−i1+i−1−i1−i−1+i
χ522-222-22-2-22-2-22−2i−2i2i2i−2i2i−2i2i2-22-2−2i2i0000000000000000000000000000000000−1+i1−i−1−i1+i−1−i1+i−1+i1−i
χ53444-4-4-4-4400004i−4i4i−4i0000000000000000000000000000000000002i−2i2-2000000000000
χ54444-4-4-4-4400004i−4i4i−4i000000000000000000000000000000000000−2i2i-22000000000000
χ55444-4-4-4-440000−4i4i−4i4i0000000000000000000000000000000000002i−2i-22000000000000
χ56444-4-4-4-440000−4i4i−4i4i000000000000000000000000000000000000−2i2i2-2000000000000
χ574-444-44-4-4-444-44i4i−4i−4i00000000−4i4i000000000000000000000000000000000000000000
χ584-444-44-4-4-444-4−4i−4i4i4i000000004i−4i000000000000000000000000000000000000000000
χ594-44-44-44-400004-4-4400000000000000000000000000000000000000002i−2i2i−2i00000000
χ604-44-44-44-400004-4-440000000000000000000000000000000000000000−2i2i−2i2i00000000
χ614-44-44-44-40000-444-400000000000000000000000000000000000000002i−2i−2i2i00000000
χ624-44-44-44-40000-444-40000000000000000000000000000000000000000−2i2i2i−2i00000000
χ634-4-4-444-4444-4-4000000004i−4i−4i4i00000000000000000000000000000000000000000000
χ644-4-4-444-4444-4-400000000−4i4i4i−4i00000000000000000000000000000000000000000000
χ654-4-4-444-44-4-44400004-4-44000000000000000000000000000000000000000000000000
χ664-4-4-444-44-4-4440000-444-4000000000000000000000000000000000000000000000000
χ6788-888-8-8-8000000000000000000000000000000000000000000000000000000000000
χ688-8-88-8-888000000000000000000000000000000000000000000000000000000000000

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