Finite Group Databasebeta

← Group #351242

Character table — Group #351242

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68
size11111111222222224444444444444444444444888888888888888888161616161616161632323232
order12222222444444444444444444444488888888224444888888888888888888882444
χ111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1
χ3111111111111111111111111111111-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-111-1-1
χ4111111111111111111111111111111-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-111
χ5111111111111111111111111-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1111111-1-1-1-1-1-111-1-111-1-11-11-1
χ6111111111111111111111111-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-111-1-111-11-11
χ7111111111111111111111111-1-1-1-111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1111-1-11
χ8111111111111111111111111-1-1-1-111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1111111-1-11111-1-1-111-1
χ91111111111111111-1-1-1-1-1-1-1-111111111111111-1-11-1-1111-1-1-1-111-1-1-1-111111111-1-1-1-1
χ101111111111111111-1-1-1-1-1-1-1-111111111111111-1-11-1-1111-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-11111
χ111111111111111111-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1-1-11-1-11-1-11111-1-111111111-1-1-1-1-1-111
χ121111111111111111-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1-1-11-1-11-1-11111-1-11111-1-1-1-1111111-1-1
χ131111111111111111-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-1-111-111-111-1-1-1-1-1-1111111-1-111-1-1-11-11
χ141111111111111111-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-1-111-111-111-1-1-1-1-1-11111-1-111-1-1111-11-1
χ151111111111111111-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-1111111-111-1-1-1111111-1-1-1-111-1-1-1-111-111-1
χ161111111111111111-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-1111111-111-1-1-1111111-1-1-1-1-1-11111-1-11-1-11
χ17222222222-2-222-2-222222-2-2-2-222-2-2-2-200000000222-2-2-2000000000000000000000000
χ18222222222-2-222-2-222222-2-2-2-2-2-222-2-200000000-2-2-2222000000000000000000000000
χ19222222222-2-222-2-22-2-2-2-2222222-2-2-2-200000000-2-2222-2000000000000000000000000
χ20222222222-2-222-2-22-2-2-2-22222-2-222-2-20000000022-2-2-22000000000000000000000000
χ2122222222-222-2-222-2000000002222-2-22222222200-200-2-2-20000-2-20000000000000000
χ2222222222-222-2-222-2000000002222-2-2-2-2-2-2-2-2-2-200-200-2220000220000000000000000
χ2322222222-222-2-222-200000000-2-2-2-2-2-22222-2-2-2-2002002-2-20000220000000000000000
χ2422222222-222-2-222-200000000-2-2-2-2-2-2-2-2-2-22222002002220000-2-20000000000000000
χ2522222222-2-2-2-2-2-2-2-20000000022-2-2220000000000-2002002i2i−2i−2i002i2i−2i−2i000000000000
χ2622222222-2-2-2-2-2-2-2-20000000022-2-2220000000000-200200−2i−2i2i2i00−2i−2i2i2i000000000000
χ2722222222-2-2-2-2-2-2-2-200000000-2-222220000000000200-2002i2i−2i−2i00−2i−2i2i2i000000000000
χ2822222222-2-2-2-2-2-2-2-200000000-2-222220000000000200-200−2i−2i2i2i002i2i−2i−2i000000000000
χ2922-22-2-22-222-2-2-22-222i2i−2i−2i2i2i−2i−2i00002-200002i2i−2i−2i0000000000002i−2i2-22-2000000000000
χ3022-22-2-22-222-2-2-22-222i2i−2i−2i2i2i−2i−2i00002-20000−2i−2i2i2i000000000000−2i2i-22-22000000000000
χ3122-22-2-22-222-2-2-22-22−2i−2i2i2i−2i−2i2i2i00002-200002i2i−2i−2i0000000000002i−2i-22-22000000000000
χ3222-22-2-22-222-2-2-22-22−2i−2i2i2i−2i−2i2i2i00002-20000−2i−2i2i2i000000000000−2i2i2-22-2000000000000
χ3322-22-2-22-22-22-2-2-2222i2i−2i−2i−2i−2i2i2i0000-222i2i−2i−2i00000000002i−2i2-22-2000000000000000000
χ3422-22-2-22-22-22-2-2-2222i2i−2i−2i−2i−2i2i2i0000-22−2i−2i2i2i0000000000−2i2i-22-22000000000000000000
χ3522-22-2-22-22-22-2-2-222−2i−2i2i2i2i2i−2i−2i0000-222i2i−2i−2i00000000002i−2i-22-22000000000000000000
χ3622-22-2-22-22-22-2-2-222−2i−2i2i2i2i2i−2i−2i0000-22−2i−2i2i2i0000000000−2i2i2-22-2000000000000000000
χ3722-22-2-22-2-22-2222-2-2000000000000-2200002i2i−2i−2i2-202-20002i−2i−2i2i−2i2i0000000000000000
χ3822-22-2-22-2-22-2222-2-2000000000000-2200002i2i−2i−2i-220-22000−2i2i2i−2i−2i2i0000000000000000
χ3922-22-2-22-2-22-2222-2-2000000000000-220000−2i−2i2i2i2-202-2000−2i2i2i−2i2i−2i0000000000000000
χ4022-22-2-22-2-22-2222-2-2000000000000-220000−2i−2i2i2i-220-220002i−2i−2i2i2i−2i0000000000000000
χ4122-22-2-22-2-2-2222-22-20000000000002-22i2i−2i−2i00002-20-220−2i2i000000−2i2i2i−2i000000000000
χ4222-22-2-22-2-2-2222-22-20000000000002-22i2i−2i−2i0000-2202-20−2i2i0000002i−2i−2i2i000000000000
χ4322-22-2-22-2-2-2222-22-20000000000002-2−2i−2i2i2i00002-20-2202i−2i0000002i−2i−2i2i000000000000
χ4422-22-2-22-2-2-2222-22-20000000000002-2−2i−2i2i2i0000-2202-202i−2i000000−2i2i2i−2i000000000000
χ45444-44-4-4-44004-400-44-44-4000000000000000000000000000000000000000000000000
χ46444-44-4-4-44004-400-4-44-44000000000000000000000000000000000000000000000000
χ47444-44-4-4-4-400-4400400004i−4i4i−4i00000000000000000000000000000000000000000000
χ48444-44-4-4-4-400-440040000−4i4i−4i4i00000000000000000000000000000000000000000000
χ4944-4-4-44-44400-4400-44i−4i−4i4i000000000000000000000000000000000000000000000000
χ5044-4-4-44-44400-4400-4−4i4i4i−4i000000000000000000000000000000000000000000000000
χ5144-4-4-44-44-4004-400400004-4-4400000000000000000000000000000000000000000000
χ5244-4-4-44-44-4004-40040000-444-400000000000000000000000000000000000000000000
χ534-444-4-4-4404400-4-4000000000000000000000000000000000000000002i2−2i20000000000
χ544-444-4-4-4404400-4-400000000000000000000000000000000000000000−2i22i20000000000
χ554-444-4-4-440-4-40044000000000000000000000000000000000000000000022−2200000000
χ564-444-4-4-440-4-400440000000000000000000000000000000000000000000−222200000000
χ574-44-4-444-40000000000000000004-4002i2−2i22i2−2i22i2−2i22i2−2i2000000000000000000000000000000
χ584-44-4-444-40000000000000000004-400−2i22i2−2i22i2−2i22i2−2i22i2000000000000000000000000000000
χ594-44-4-444-4000000000000000000-44002i2−2i22i2−2i2−2i22i2−2i22i2000000000000000000000000000000
χ604-44-4-444-4000000000000000000-4400−2i22i2−2i22i22i2−2i22i2−2i2000000000000000000000000000000
χ614-4-4444-4-404-400-44000000000000000000000000000000000000000000000002i2−2i20000
χ624-4-4444-4-404-400-4400000000000000000000000000000000000000000000000−2i22i20000
χ634-4-4444-4-40-44004-40000000000000000000000000000000000000000000002i2−2i2000000
χ644-4-4444-4-40-44004-4000000000000000000000000000000000000000000000−2i22i2000000
χ654-4-4-44-44400000000000000004-4000022−22−222222−22−2222000000000000000000000000000000
χ664-4-4-44-44400000000000000004-40000−222222−22−222222−22000000000000000000000000000000
χ674-4-4-44-4440000000000000000-44000022−22−2222−222222−22000000000000000000000000000000
χ684-4-4-44-4440000000000000000-440000−222222−2222−22−2222000000000000000000000000000000

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