Finite Group Databasebeta

← Group #324846

Character table — Group #324846

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68
size1111111122222222444444444444448888888888888888888888888888881616161632323232
order12222222444444444444448888888844444444448888888888888888888888882444
χ111111111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111111111111-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-1
χ31111111111111111111111111111111-1-1-1-11-1-1-1-1111111111111-1-1-1-1-1-1-1-11111-1-1-1-1
χ41111111111111111111111111111111-1-1-1-11-1-1-1-111-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-11111
χ51111111111111111111111-1-1-1-1-1-1-1-11111111111-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111
χ61111111111111111111111-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1
χ71111111111111111111111-1-1-1-1-1-1-1-11-1-1-1-11-1-1-1-1-1-111111111-1-111111111-1-1-1-111-1-1
χ81111111111111111111111-1-1-1-1-1-1-1-11-1-1-1-11-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-111
χ9111111111111111111-1-1-1-111111111-111-1-1-111-1-1-1-11111-1-1-1-1-1-11111-1-1-1-111-1-11-11-1
χ10111111111111111111-1-1-1-111111111-111-1-1-111-1-1-1-1-1-1-1-11111-1-11111-1-1-1-1-1-111-11-11
χ11111111111111111111-1-1-1-111111111-1-1-111-1-1-111-1-11111-1-1-1-1-1-1-1-1-1-1111111-1-1-11-11
χ12111111111111111111-1-1-1-111111111-1-1-111-1-1-111-1-1-1-1-1-11111-1-1-1-1-1-11111-1-1111-11-1
χ13111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-111-1-1111111-1-1-1-111-1-1-1-11111-1-111-111-1
χ14111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-111-1-111-1-1-1-1111111-1-1-1-1111111-1-11-1-11
χ15111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-111111111-1-1-1-1111111-1-1-1-1-1-1111-1-11
χ16111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-11111-1-1-1-11111111111-1-1-1-111-1-1-111-1
χ172222222222-2-2-222-2-2-2222200000000-22222-2-2-2-2-20000000000000000000000000000
χ182222222222-2-2-222-2-2-2222200000000-2-2-2-2-2-222220000000000000000000000000000
χ192222222222-2-2-222-2-2-2-2-2-2-200000000222-2-22-2-2220000000000000000000000000000
χ202222222222-2-2-222-2-2-2-2-2-2-2000000002-2-222222-2-20000000000000000000000000000
χ2122222222-2-2222-2-22-2-222-2-22222-2-2-2-2-20000200002200000000-2-20000000000000000
χ2222222222-2-2222-2-22-2-222-2-2-2-2-2-22222-2000020000-2-200000000220000000000000000
χ2322222222-2-2222-2-22-2-2-2-2222222-2-2-2-220000-20000-2-200000000220000000000000000
χ2422222222-2-2222-2-22-2-2-2-222-2-2-2-2222220000-200002200000000-2-20000000000000000
χ2522222222-2-2-2-2-2-2-2-22222-2-20000000020000-200000000000000002i2i−2i−2i2i2i−2i−2i00000000
χ2622222222-2-2-2-2-2-2-2-22222-2-20000000020000-20000000000000000−2i−2i2i2i−2i−2i2i2i00000000
χ2722222222-2-2-2-2-2-2-2-222-2-22200000000-20000200000000000000002i2i−2i−2i−2i−2i2i2i00000000
χ2822222222-2-2-2-2-2-2-2-222-2-22200000000-2000020000000000000000−2i−2i2i2i2i2i−2i−2i00000000
χ29222-2-22-2-22-22-2-22-222-200002i2i−2i−2i2i2i−2i−2i000000000000000022-2-20000000000002i−2i0000
χ30222-2-22-2-22-22-2-22-222-200002i2i−2i−2i2i2i−2i−2i0000000000000000-2-222000000000000−2i2i0000
χ31222-2-22-2-22-22-2-22-222-20000−2i−2i2i2i−2i−2i2i2i000000000000000022-2-2000000000000−2i2i0000
χ32222-2-22-2-22-22-2-22-222-20000−2i−2i2i2i−2i−2i2i2i0000000000000000-2-2220000000000002i−2i0000
χ33222-2-22-2-2-222-2-2-222-2200002i2i−2i−2i−2i−2i2i2i00000000000022-2-2000000000000002i−2i000000
χ34222-2-22-2-2-222-2-2-222-2200002i2i−2i−2i−2i−2i2i2i000000000000-2-22200000000000000−2i2i000000
χ35222-2-22-2-2-222-2-2-222-220000−2i−2i2i2i2i2i−2i−2i00000000000022-2-200000000000000−2i2i000000
χ36222-2-22-2-2-222-2-2-222-220000−2i−2i2i2i2i2i−2i−2i000000000000-2-222000000000000002i−2i000000
χ3722-22-2-22-22-2000-220002i−2i2i−2ii2−i2i2−i2i2−i2i2−i20000002i−2i2-22−2000000002−22−22−2i2−i2i2−i200000000
χ3822-22-2-22-22-2000-220002i−2i2i−2ii2−i2i2−i2i2−i2i2−i2000000−2i2i-222−2000000002−2−22−22−i2i2−i2i200000000
χ3922-22-2-22-22-2000-220002i−2i2i−2i−i2i2−i2i2−i2i2−i2i20000002i−2i2-2−2200000000−22−22−22−i2i2−i2i200000000
χ4022-22-2-22-22-2000-220002i−2i2i−2i−i2i2−i2i2−i2i2−i2i2000000−2i2i-22−2200000000−222−22−2i2−i2i2−i200000000
χ4122-22-2-22-22-2000-22000−2i2i−2i2ii2−i2i2−i2i2−i2i2−i20000002i−2i-22−2200000000−222−22−2−i2i2−i2i200000000
χ4222-22-2-22-22-2000-22000−2i2i−2i2ii2−i2i2−i2i2−i2i2−i2000000−2i2i2-2−2200000000−22−22−22i2−i2i2−i200000000
χ4322-22-2-22-22-2000-22000−2i2i−2i2i−i2i2−i2i2−i2i2−i2i20000002i−2i-222−2000000002−2−22−22i2−i2i2−i200000000
χ4422-22-2-22-22-2000-22000−2i2i−2i2i−i2i2−i2i2−i2i2−i2i2000000−2i2i2-22−2000000002−22−22−2−i2i2−i2i200000000
χ4522-22-2-22-2-220002-20002i−2i−2i2ii2−i2i2−i2−i2i2−i2i202-22i−2i000002−200000000−22i2−i2−i2i2−222−200000000
χ4622-22-2-22-2-220002-20002i−2i−2i2ii2−i2i2−i2−i2i2−i2i20-22−2i2i000002−200000000−22−i2i2i2−i22−2−2200000000
χ4722-22-2-22-2-220002-20002i−2i−2i2i−i2i2−i2i2i2−i2i2−i202-22i−2i00000−22000000002−2−i2i2i2−i22−2−2200000000
χ4822-22-2-22-2-220002-20002i−2i−2i2i−i2i2−i2i2i2−i2i2−i20-22−2i2i00000−22000000002−2i2−i2−i2i2−222−200000000
χ4922-22-2-22-2-220002-2000−2i2i2i−2ii2−i2i2−i2−i2i2−i2i202-2−2i2i00000−22000000002−2i2−i2−i2i22−2−2200000000
χ5022-22-2-22-2-220002-2000−2i2i2i−2ii2−i2i2−i2−i2i2−i2i20-222i−2i00000−22000000002−2−i2i2i2−i2−222−200000000
χ5122-22-2-22-2-220002-2000−2i2i2i−2i−i2i2−i2i2i2−i2i2−i202-2−2i2i000002−200000000−22−i2i2i2−i2−222−200000000
χ5222-22-2-22-2-220002-2000−2i2i2i−2i−i2i2−i2i2i2−i2i2−i20-222i−2i000002−200000000−22i2−i2−i2i22−2−2200000000
χ53444-4-44-4-44-4-4444-4-4-4400000000000000000000000000000000000000000000000000
χ54444-4-44-4-4-44-444-44-44-400000000000000000000000000000000000000000000000000
χ5544-4-44-4-4444000-4-4000000022−22−222222−22−222200000000000000000000000000000000000000
χ5644-4-44-4-4444000-4-40000000−222222−22−222222−2200000000000000000000000000000000000000
χ5744-4-44-4-44-4-400044000000022−22−2222−222222−2200000000000000000000000000000000000000
χ5844-4-44-4-44-4-4000440000000−222222−2222−22−222200000000000000000000000000000000000000
χ594-4-44-44-440044-400-40000000000000000000000000000002i2−2i22i2−2i2000000000000000000
χ604-4-44-44-440044-400-4000000000000000000000000000000−2i22i2−2i22i2000000000000000000
χ614-4-44-44-4400-4-440040000000000000000000000000022−2222−220000000000000000000000
χ624-4-44-44-4400-4-4400400000000000000000000000000−2222−22220000000000000000000000
χ634-4-4-4444-4004-4400-40000000000000000000000000000002i2−2i2−2i22i2000000000000000000
χ644-4-4-4444-4004-4400-4000000000000000000000000000000−2i22i22i2−2i2000000000000000000
χ654-4-4-4444-400-44-40040000000000000000000000000022−22−22220000000000000000000000
χ664-4-4-4444-400-44-400400000000000000000000000000−222222−220000000000000000000000
χ678-8888-8-8-8000000000000000000000000000000000000000000000000000000000000
χ688-88-8-8-888000000000000000000000000000000000000000000000000000000000000

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