Finite Group Databasebeta

← Group #278305

Character table — Group #278305

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68
size1111222222222222444444444444444888888888888888888888888888881616161632323232
order12222244444488882244444444488884444888888888888888888888888844884488
χ111111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1
χ31111111111111111111111111111111-1-1-1-1111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1
χ41111111111111111111111111111111-1-1-1-111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111
χ51111111111111111-1-1-1-1111-1-1-1-111111111-1-11-1-111111111-1-1-1-1-1-1-1-11111-1-1-1-111-1-1
χ61111111111111111-1-1-1-1111-1-1-1-111111111-1-11-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-111
χ71111111111111111-1-1-1-1111-1-1-1-11111-1-1-1-1-1-11-1-111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-111
χ81111111111111111-1-1-1-1111-1-1-1-11111-1-1-1-1-1-11-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1111111-1-1
χ9111111111111-1-1-1-111111111111-1-1-1-11111-1-1-1-1-11111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1111-11-1
χ10111111111111-1-1-1-111111111111-1-1-1-11111-1-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1-1-1-1-111-11-11
χ11111111111111-1-1-1-111111111111-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1-1-1111111-1-1-11-11
χ12111111111111-1-1-1-111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-11111111111-1-11-11-1
χ13111111111111-1-1-1-1-1-1-1-1111-1-1-1-1-1-1-1-1111111-1111111-1-1-1-1-1-1-1-11111-1-1-1-111-1-11-1-11
χ14111111111111-1-1-1-1-1-1-1-1111-1-1-1-1-1-1-1-1111111-111-1-1-1-111111111-1-1-1-1-1-1-1-111-1-1-111-1
χ15111111111111-1-1-1-1-1-1-1-1111-1-1-1-1-1-1-1-1-1-1-1-111-1111111-1-1-1-1-1-1-1-111111111-1-111-111-1
χ16111111111111-1-1-1-1-1-1-1-1111-1-1-1-1-1-1-1-1-1-1-1-111-111-1-1-1-111111111-1-1-1-11111-1-1111-1-11
χ17222222222-2-2222222222-2-2-2-2-2-2-222-2-2000022-2-2-20000000000000000000000000000
χ18222222222-2-222222-2-2-2-2-2-2-2222222-2-20000-2-2-2220000000000000000000000000000
χ19222222222-2-22-2-2-2-22222-2-2-2-2-2-2-2-2-2220000-2-22220000000000000000000000000000
χ20222222222-2-22-2-2-2-2-2-2-2-2-2-2-22222-2-2220000222-2-20000000000000000000000000000
χ212222-2-22-2-2222000022-2-22-2-222-2-20000000000000000000000000000022-2-22-2000000
χ222222-2-22-2-2222000022-2-22-2-222-2-200000000000000000000000000000-2-222-22000000
χ232222-2-22-2-22220000-2-2222-2-2-2-2220000000000000000000000000000022-2-2-22000000
χ242222-2-22-2-22220000-2-2222-2-2-2-22200000000000000000000000000000-2-2222-2000000
χ252222-2-22-2-2-2-22000022-2-2-222-2-22200002i2i−2i−2i0000000000000000000000000002i−2i0000
χ262222-2-22-2-2-2-22000022-2-2-222-2-2220000−2i−2i2i2i000000000000000000000000000−2i2i0000
χ272222-2-22-2-2-2-220000-2-222-22222-2-200002i2i−2i−2i000000000000000000000000000−2i2i0000
χ282222-2-22-2-2-2-220000-2-222-22222-2-20000−2i−2i2i2i0000000000000000000000000002i−2i0000
χ292222-2-2-22222-222220000-22-20000-2-222000000-2000000000022-2-222-2-2000000000000
χ302222-2-2-22222-222220000-22-20000-2-222000000-20000000000-2-222-2-222000000000000
χ312222-2-2-22222-2-2-2-2-20000-22-2000022-2-20000002000000000022-2-2-2-222000000000000
χ322222-2-2-22222-2-2-2-2-20000-22-2000022-2-200000020000000000-2-22222-2-2000000000000
χ332222-2-2-222-2-2-2222200002-220000-2-2-2-20000002002i2i−2i−2i2i2i−2i−2i00000000000000000000
χ342222-2-2-222-2-2-2222200002-220000-2-2-2-2000000200−2i−2i2i2i−2i−2i2i2i00000000000000000000
χ352222-2-2-222-2-2-2-2-2-2-200002-2200002222000000-2002i2i−2i−2i−2i−2i2i2i00000000000000000000
χ362222-2-2-222-2-2-2-2-2-2-200002-2200002222000000-200−2i−2i2i2i2i2i−2i−2i00000000000000000000
χ3722-2-22-222-200-222-2-22-22-200000002-20000002-20002−22−22−22−22−22−22−22−2000000000000
χ3822-2-22-222-200-222-2-22-22-200000002-20000002-2000−22−22−22−22−22−22−22−22000000000000
χ3922-2-22-222-200-222-2-2-22-2200000002-2000000-220002−22−22−22−2−22−22−22−22000000000000
χ4022-2-22-222-200-222-2-2-22-2200000002-2000000-22000−22−22−22−222−22−22−22−2000000000000
χ4122-2-22-222-200-2-2-2222-22-20000000-22000000-220002−22−2−22−222−22−2−22−22000000000000
χ4222-2-22-222-200-2-2-2222-22-20000000-22000000-22000−22−222−22−2−22−222−22−2000000000000
χ4322-2-22-222-200-2-2-222-22-220000000-220000002-20002−22−2−22−22−22−222−22−2000000000000
χ4422-2-22-222-200-2-2-222-22-220000000-220000002-2000−22−222−22−22−22−2−22−22000000000000
χ4522-2-2-22-22-200222-2-200000002i−2i2i−2i-220000000002i−2ii2−i2−i2i2i2−i2−i2i22−2−222−2−22000000000000
χ4622-2-2-22-22-200222-2-200000002i−2i2i−2i-220000000002i−2i−i2i2i2−i2−i2i2i2−i2−222−2−222−2000000000000
χ4722-2-2-22-22-200222-2-20000000−2i2i−2i2i-22000000000−2i2ii2−i2−i2i2i2−i2−i2i2−222−2−222−2000000000000
χ4822-2-2-22-22-200222-2-20000000−2i2i−2i2i-22000000000−2i2i−i2i2i2−i2−i2i2i2−i22−2−222−2−22000000000000
χ4922-2-2-22-22-2002-2-22200000002i−2i2i−2i2-2000000000−2i2ii2−i2−i2i2−i2i2i2−i22−2−22−222−2000000000000
χ5022-2-2-22-22-2002-2-22200000002i−2i2i−2i2-2000000000−2i2i−i2i2i2−i2i2−i2−i2i2−222−22−2−22000000000000
χ5122-2-2-22-22-2002-2-2220000000−2i2i−2i2i2-20000000002i−2ii2−i2−i2i2−i2i2i2−i2−222−22−2−22000000000000
χ5222-2-2-22-22-2002-2-2220000000−2i2i−2i2i2-20000000002i−2i−i2i2i2−i2i2−i2−i2i22−2−22−222−2000000000000
χ53444444-4-4-444-400000000-4-44000000000000000000000000000000000000000000000
χ54444444-4-4-4-4-4-40000000044-4000000000000000000000000000000000000000000000
χ5544-4-44-4-4-44004000000000004i−4i−4i4i00000000000000000000000000000000000000000
χ5644-4-44-4-4-4400400000000000−4i4i4i−4i00000000000000000000000000000000000000000
χ5744-4-4-444-4400-400004-4-44000000000000000000000000000000000000000000000000
χ5844-4-4-444-4400-40000-444-4000000000000000000000000000000000000000000000000
χ594-44-4000004-402i2−2i22i2−2i200000000000002i2−2i22-22-2000000000000000000000002i2−2i200000000
χ604-44-4000004-402i2−2i22i2−2i200000000000002i2−2i2-22-2200000000000000000000000−2i22i200000000
χ614-44-4000004-40−2i22i2−2i22i20000000000000−2i22i22-22-200000000000000000000000−2i22i200000000
χ624-44-4000004-40−2i22i2−2i22i20000000000000−2i22i2-22-22000000000000000000000002i2−2i200000000
χ634-44-400000-4402i2−2i22i2−2i20000000000000−2i22i22i−2i−2i2i00000000000000000000022−220000000000
χ644-44-400000-4402i2−2i22i2−2i20000000000000−2i22i2−2i2i2i−2i000000000000000000000−22220000000000
χ654-44-400000-440−2i22i2−2i22i200000000000002i2−2i22i−2i−2i2i000000000000000000000−22220000000000
χ664-44-400000-440−2i22i2−2i22i200000000000002i2−2i2−2i2i2i−2i00000000000000000000022−220000000000
χ678-8-88000000004i2−4i2−4i24i20000000000000000000000000000000000000000000000000000
χ688-8-8800000000−4i24i24i2−4i20000000000000000000000000000000000000000000000000000

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