Finite Group Databasebeta

← Group #287375

Character table — Group #287375

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65
size1111111122222222222244444488888888888888888888888881616161616161616161616163232
order12222222444444444444444444488888888888888888888888844444444888844
χ111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111-1-1-1-111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1
χ31111111111111111111111111111111-1-1-1-111111111-1-1-1-11111-1-1-1-11111-1-1-1-1-1-1
χ41111111111111111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111
χ5111111111111111111111111111-1-1-1-111111111-1-1-1-111111111-1-1-1-1-1-1-1-11111-1-1
χ6111111111111111111111111111-1-1-1-11111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-11111-1-1-1-111
χ7111111111111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-111
χ8111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-1
χ9111111111-1-1-1-11111111-1-111-1-1-1111111-1-11111-1-1-1-111-1-1-1-1-1-11-11-111-1-111-1-11-1
χ10111111111-1-1-1-11111111-1-111-1-1-1111111-1-1-1-1-1-1-1-1-1-111-1-111111-11-1-1-111-1-111-11
χ11111111111-1-1-1-11111111-1-111-1-1-11111-1-1111111-1-1-1-1-1-111-1-1-1-1-11-1111-1-1-1-111-11
χ12111111111-1-1-1-11111111-1-111-1-1-11111-1-111-1-1-1-1-1-1-1-1-1-1111111-11-11-1-11111-1-11-1
χ13111111111-1-1-1-11111111-1-111-1-1-1-1-1-1-111-1-11111111111-1-1-1-1-1-1-11-11-1-11111-1-1-11
χ14111111111-1-1-1-11111111-1-111-1-1-1-1-1-1-111-1-1-1-1-1-1111111-1-11111-11-1111-1-1-1-1111-1
χ15111111111-1-1-1-11111111-1-111-1-1-1-1-1-1-1-1-11111111111-1-111-1-1-1-11-11-1-1-111-1-1111-1
χ16111111111-1-1-1-11111111-1-111-1-1-1-1-1-1-1-1-111-1-1-1-11111-1-11111111-11-111-1-111-1-1-11
χ172222222222222-222-2-22-222-2-2-2-2-20000222200000000-2-2-2-2000000000000000000
χ182222222222222-222-2-22-222-2-2-2-2-20000-2-2-2-2000000002222000000000000000000
χ19222222222-2-2-2-2-222-2-22-2-2-2-2-2222000022-2-200000000-2-222000000000000000000
χ20222222222-2-2-2-2-222-2-22-2-2-2-2-22220000-2-2220000000022-2-2000000000000000000
χ2122222222-222222-2-222-22-2-2-2-222-20000000000000000000000002-2-220000000000
χ2222222222-222222-2-222-22-2-2-2-222-2000000000000000000000000-222-20000000000
χ2322222222-22222-2-2-2-2-2-2-2-2-222-2-222i2i−2i−2i000000002i2i−2i−2i0000000000000000000000
χ2422222222-22222-2-2-2-2-2-2-2-2-222-2-22−2i−2i2i2i00000000−2i−2i2i2i0000000000000000000000
χ2522222222-2-2-2-2-22-2-222-2222-2-2-2-2200000000000000000000000022-2-20000000000
χ2622222222-2-2-2-2-22-2-222-2222-2-2-2-22000000000000000000000000-2-2220000000000
χ2722222222-2-2-2-2-2-2-2-2-2-2-2-2222222-22i2i−2i−2i00000000−2i−2i2i2i0000000000000000000000
χ2822222222-2-2-2-2-2-2-2-2-2-2-2-2222222-2−2i−2i2i2i000000002i2i−2i−2i0000000000000000000000
χ292222-2-2-2-2222-2-202-200-202-20000000002-22-222−2−20000000022−2−2000000002−22−200
χ302222-2-2-2-2222-2-202-200-202-20000000002-22-2−2−22200000000−2−22200000000−22−2200
χ312222-2-2-2-2222-2-202-200-202-2000000000-22-2222−2−20000000022−2−200000000−22−2200
χ322222-2-2-2-2222-2-202-200-202-2000000000-22-22−2−22200000000−2−222000000002−22−200
χ332222-2-2-2-22-2-22202-200-20-220000000002-2-2222−2−200000000−2−222000000002−2−2200
χ342222-2-2-2-22-2-22202-200-20-220000000002-2-22−2−2220000000022−2−200000000−222−200
χ352222-2-2-2-22-2-22202-200-20-22000000000-222-222−2−200000000−2−22200000000−222−200
χ362222-2-2-2-22-2-22202-200-20-22000000000-222-2−2−2220000000022−2−2000000002−2−2200
χ3722-2-22-22-220000-2-222-2-22002-2000000000002i−2i2i−2i2i−2i2i−2i000000000000002-2000000
χ3822-2-22-22-220000-2-222-2-22002-2000000000002i−2i2i−2i−2i2i−2i2i00000000000000-22000000
χ3922-2-22-22-220000-2-222-2-22002-200000000000−2i2i−2i2i2i−2i2i−2i00000000000000-22000000
χ4022-2-22-22-220000-2-222-2-22002-200000000000−2i2i−2i2i−2i2i−2i2i000000000000002-2000000
χ4122-2-22-22-2-2000022-2-222-2002-20000000000000002-2-2200002i−2i2i−2i00002i−2i00000000
χ4222-2-22-22-2-2000022-2-222-2002-20000000000000002-2-220000−2i2i−2i2i0000−2i2i00000000
χ4322-2-22-22-2-2000022-2-222-2002-2000000000000000-222-200002i−2i2i−2i0000−2i2i00000000
χ4422-2-22-22-2-2000022-2-222-2002-2000000000000000-222-20000−2i2i−2i2i00002i−2i00000000
χ454444-4-4-4-4-444-4-40-440040-440000000000000000000000000000000000000000000
χ464444-4-4-4-4-4-4-4440-4400404-40000000000000000000000000000000000000000000
χ4744-4-44-44-4400004-44-44-4-400-4400000000000000000000000000000000000000000
χ4844-4-44-44-4-40000-44-44-44400-4400000000000000000000000000000000000000000
χ4944-4-4-44-44400000-4-400400000000000000002i2−2i2−2i22i200000000000000000000000000
χ5044-4-4-44-44400000-4-40040000000000000000−2i22i22i2−2i200000000000000000000000000
χ5144-4-4-44-44-4000004400-400000000000000000000000000002i2−2i2−2i22i200000000000000
χ5244-4-4-44-44-4000004400-40000000000000000000000000000−2i22i22i2−2i200000000000000
χ534-44-44-4-4404i−4i4i−4i0000000000000000000000000000002i2−2i222−22000000000000000000
χ544-44-44-4-4404i−4i4i−4i000000000000000000000000000000−2i22i2−2222000000000000000000
χ554-44-44-4-440−4i4i−4i4i0000000000000000000000000000002i2−2i2−2222000000000000000000
χ564-44-44-4-440−4i4i−4i4i000000000000000000000000000000−2i22i222−22000000000000000000
χ574-44-4-444-404i−4i−4i4i400-4-40400004i−4i000000000000000000000000000000000000000
χ584-44-4-444-404i−4i−4i4i-400440-40000−4i4i000000000000000000000000000000000000000
χ594-44-4-444-40−4i4i4i−4i400-4-4040000−4i4i000000000000000000000000000000000000000
χ604-44-4-444-40−4i4i4i−4i-400440-400004i−4i000000000000000000000000000000000000000
χ614-4-44-4-444000004004-40-400000002i2−2i22i2−2i20000000000000000000000000000000000
χ624-4-44-4-444000004004-40-40000000−2i22i2−2i22i20000000000000000000000000000000000
χ634-4-44-4-44400000-400-4404000000022−22−22220000000000000000000000000000000000
χ644-4-44-4-44400000-400-44040000000−222222−220000000000000000000000000000000000
χ658-8-8888-8-8000000000000000000000000000000000000000000000000000000000

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