Finite Group Databasebeta

← Group #286168

Character table — Group #286168

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65
size1111111122222222222244444488888888888888888888888881616161616161616161616163232
order12222222444444444444224444488888888888888888888888844444444888844
χ111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1
χ3111111111111111111111111111111111-1-1-1-1-1-1-1-1111111111111-1-111-1-1-1-1-1-1-1-1
χ4111111111111111111111111111111111-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-111-1-111-1-1-1-111
χ5111111111111111111111111111-1-1-1-1-1-111111111-1-111111111-1-111-1-111-1-1-1-1-1-1
χ6111111111111111111111111111-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-111-1-111-1-1-1-1-1-111
χ7111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1111111
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
χ911111111-1-1-1-111111111-1-111-1-1-11111-1-11111-1-1-1-1-1-11111-1-1-1-11-1111-1-1-111-1-1-11
χ1011111111-1-1-1-111111111-1-111-1-1-11111-1-11111-1-1-1-1-1-1-1-1-1-11111-11-1-1-111111-1-11-1
χ1111111111-1-1-1-111111111-1-111-1-1-11111-1-1-1-1-1-11111-1-11111-1-1-1-11-1-1-11-111-1-1111-1
χ1211111111-1-1-1-111111111-1-111-1-1-11111-1-1-1-1-1-11111-1-1-1-1-1-11111-1111-11-1-1-1-111-11
χ1311111111-1-1-1-111111111-1-111-1-1-1-1-1-1-1111111-1-1-1-1111111-1-1-1-1-1111-11-1-1-1-1111-1
χ1411111111-1-1-1-111111111-1-111-1-1-1-1-1-1-1111111-1-1-1-111-1-1-1-111111-1-1-11-111-1-111-11
χ1511111111-1-1-1-111111111-1-111-1-1-1-1-1-1-111-1-1-1-11111111111-1-1-1-1-11-1-1-111111-1-1-11
χ1611111111-1-1-1-111111111-1-111-1-1-1-1-1-1-111-1-1-1-1111111-1-1-1-111111-1111-1-1-111-1-11-1
χ172222222222222-2-2-2222-2-2-2-2-222-20000000000000000000000002200-2-200000000
χ182222222222222-2-2-2222-2-2-2-2-222-2000000000000000000000000-2-2002200000000
χ19222222222222-2222-2-2-2222-2-2-2-2-222-2-22200000000-2-20000000000000000000000
χ20222222222222-2222-2-2-2222-2-2-2-2-2-2-222-2-200000000220000000000000000000000
χ21222222222222-2-2-2-2-2-2-2-2-2-222-2-2200000000000000002i2i−2i−2i2i2i−2i−2i00000000000000
χ22222222222222-2-2-2-2-2-2-2-2-2-222-2-220000000000000000−2i−2i2i2i−2i−2i2i2i00000000000000
χ2322222222-2-2-2-22-2-2-2222-222-2-2-2-220000000000000000000000002-200-2200000000
χ2422222222-2-2-2-22-2-2-2222-222-2-2-2-22000000000000000000000000-22002-200000000
χ2522222222-2-2-2-2-2222-2-2-22-2-2-2-222222-2-2-2-200000000220000000000000000000000
χ2622222222-2-2-2-2-2222-2-2-22-2-2-2-2222-2-2222200000000-2-20000000000000000000000
χ2722222222-2-2-2-2-2-2-2-2-2-2-2-2222222-200000000000000002i2i−2i−2i−2i−2i2i2i00000000000000
χ2822222222-2-2-2-2-2-2-2-2-2-2-2-2222222-20000000000000000−2i−2i2i2i2i2i−2i−2i00000000000000
χ292222-2-2-2-222-2-2022-2000-22-2000002-2002-222−2−222−2−20000000000000000002−22−200
χ302222-2-2-2-222-2-2022-2000-22-2000002-2002-2−2−222−2−222000000000000000000−22−2200
χ312222-2-2-2-222-2-2022-2000-22-200000-2200-2222−2−222−2−2000000000000000000−22−2200
χ322222-2-2-2-222-2-2022-2000-22-200000-2200-22−2−222−2−2220000000000000000002−22−200
χ332222-2-2-2-2-2-222022-2000-2-22000002-200-2222−2−2−2−2220000000000000000002−2−2200
χ342222-2-2-2-2-2-222022-2000-2-22000002-200-22−2−22222−2−2000000000000000000−222−200
χ352222-2-2-2-2-2-222022-2000-2-2200000-22002-222−2−2−2−222000000000000000000−222−200
χ362222-2-2-2-2-2-222022-2000-2-2200000-22002-2−2−22222−2−20000000000000000002−2−2200
χ372-2-222-22-2000022-2-22-2-22002-20000000002i−2i2i−2i00000000002-22-20000002i−2i000000
χ382-2-222-22-2000022-2-22-2-22002-20000000002i−2i2i−2i0000000000-22-22000000−2i2i000000
χ392-2-222-22-2000022-2-22-2-22002-2000000000−2i2i−2i2i00000000002-22-2000000−2i2i000000
χ402-2-222-22-2000022-2-22-2-22002-2000000000−2i2i−2i2i0000000000-22-220000002i−2i000000
χ412-2-222-22-20000-2-222-222-2002-200000000000002-22-20000002i−2i−2i2i002i−2i0000000000
χ422-2-222-22-20000-2-222-222-2002-200000000000002-22-2000000−2i2i2i−2i00−2i2i0000000000
χ432-2-222-22-20000-2-222-222-2002-20000000000000-22-220000002i−2i−2i2i00−2i2i0000000000
χ442-2-222-22-20000-2-222-222-2002-20000000000000-22-22000000−2i2i2i−2i002i−2i0000000000
χ454444-4-4-4-444-4-40-4-440004-440000000000000000000000000000000000000000000
χ464444-4-4-4-4-4-4440-4-4400044-40000000000000000000000000000000000000000000
χ4744-4-444-4-400004000-44-400000000000000000000000022−2222−22000000000000000000
χ4844-4-444-4-400004000-44-4000000000000000000000000−2222−2222000000000000000000
χ4944-4-444-4-40000-40004-440000000000000000000000002i2−2i2−2i22i2000000000000000000
χ5044-4-444-4-40000-40004-44000000000000000000000000−2i22i22i2−2i2000000000000000000
χ514-44-44-4-444i−4i4i−4i4000-4-44000004i−4i000000000000000000000000000000000000000
χ524-44-44-4-444i−4i4i−4i-400044-400000−4i4i000000000000000000000000000000000000000
χ534-44-44-4-44−4i4i−4i4i4000-4-4400000−4i4i000000000000000000000000000000000000000
χ544-44-44-4-44−4i4i−4i4i-400044-4000004i−4i000000000000000000000000000000000000000
χ554-44-4-444-44i−4i−4i4i000000000000000002i2−2i2000000000022−220000000000000000000000
χ564-44-4-444-44i−4i−4i4i00000000000000000−2i22i20000000000−22220000000000000000000000
χ574-44-4-444-4−4i4i4i−4i000000000000000002i2−2i20000000000−22220000000000000000000000
χ584-44-4-444-4−4i4i4i−4i00000000000000000−2i22i2000000000022−220000000000000000000000
χ594-4-444-44-400004-4444-4-4-400-4400000000000000000000000000000000000000000
χ604-4-444-44-40000-44-4-4-444400-4400000000000000000000000000000000000000000
χ614-4-44-44-44000004-44000-400000000000002i2−2i2−2i22i20000000000000000000000000000
χ624-4-44-44-44000004-44000-40000000000000−2i22i22i2−2i20000000000000000000000000000
χ634-4-44-44-4400000-44-400040000000000000000022−22−2222000000000000000000000000
χ644-4-44-44-4400000-44-4000400000000000000000−222222−22000000000000000000000000
χ6588-8-8-8-888000000000000000000000000000000000000000000000000000000000

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