Finite Group Databasebeta

← Group #288391

Character table — Group #288391

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68
size11111111222222224444444444444444444444444488888888161616161616161616161616161616163232
order12222222444444444488888888888888888888888844444444224444448888888844
χ111111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1
χ3111111111111111111111111111111111111111111-1-1-1-11111-1-111-1-1-1-1-1-1-1-11111-1-1
χ4111111111111111111111111111111111111111111-1-1-1-1-1-1-1-111-1-111-1-1-1-1-1-1-1-1-1-111
χ51111111111111111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-111111111111111-1-111-1-1-1-1-1-1-1-1
χ61111111111111111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-111-1-1111111
χ71111111111111111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-111-1-111-1-111-1-1-1-111
χ81111111111111111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-11111-1-1111111-1-1
χ9111111111111111111-1-1-1-11111-1-1-1-11111-1-1-1-1-1-1-1-1111111-1-1111-1-1-111-1-1-1-111-1-11-1
χ10111111111111111111-1-1-1-11111-1-1-1-11111-1-1-1-1-1-1-1-11111-1-111-1-1-111111-1-1-1-1-1-111-11
χ11111111111111111111-1-1-1-11111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-11-111-1-1111111-1-1-11
χ12111111111111111111-1-1-1-11111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-11-1-1-1-11111-1-1111-1
χ13111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111111111-1-1111-1-1-1-1-1-1-111-1-111-11
χ14111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-111-1-1-1111-1-1-1-11111-1-11-1
χ15111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-111-1-1-1-11-1111111-1-1-1-1111-1
χ16111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-11111-11-1-11111-1-111-1-1-11
χ17222222222-2-22-222-2-2-222220000-2-2-2-20000000000000000222200-2-200000000000000
χ18222222222-2-22-222-2-2-222220000-2-2-2-20000000000000000-2-2-2-2002200000000000000
χ19222222222-2-22-222-2-2-2-2-2-2-200002222000000000000000022-2-200-2200000000000000
χ20222222222-2-22-222-2-2-2-2-2-2-2000022220000000000000000-2-222002-200000000000000
χ2122222222-222-22-2-22-2-2000022220000-2-2-2-20000000022-2-200000000002-20000000000
χ2222222222-222-22-2-22-2-2000022220000-2-2-2-200000000-2-2220000000000-220000000000
χ2322222222-222-22-2-22-2-20000-2-2-2-2000022220000000022-2-20000000000-220000000000
χ2422222222-222-22-2-22-2-20000-2-2-2-20000222200000000-2-22200000000002-20000000000
χ252-22-222-2-2-200202-200022-2-2i2i2−i2−i20000i2i2−i2−i2i2i2i2i2−i2−i2−i2−i200002-22-2000000000000i2−i2i2−i200
χ262-22-222-2-2-200202-200022-2-2i2i2−i2−i20000i2i2−i2−i2i2i2i2i2−i2−i2−i2−i20000-22-22000000000000−i2i2−i2i200
χ272-22-222-2-2-200202-200022-2-2−i2−i2i2i20000−i2−i2i2i2−i2−i2−i2−i2i2i2i2i200002-22-2000000000000−i2i2−i2i200
χ282-22-222-2-2-200202-200022-2-2−i2−i2i2i20000−i2−i2i2i2−i2−i2−i2−i2i2i2i2i20000-22-22000000000000i2−i2i2−i200
χ292-22-222-2-2-200202-2000-2-222i2i2−i2−i20000i2i2−i2−i2−i2−i2−i2−i2i2i2i2i200002-2-22000000000000i2−i2−i2i200
χ302-22-222-2-2-200202-2000-2-222i2i2−i2−i20000i2i2−i2−i2−i2−i2−i2−i2i2i2i2i20000-222-2000000000000−i2i2i2−i200
χ312-22-222-2-2-200202-2000-2-222−i2−i2i2i20000−i2−i2i2i2i2i2i2i2−i2−i2−i2−i200002-2-22000000000000−i2i2i2−i200
χ322-22-222-2-2-200202-2000-2-222−i2−i2i2i20000−i2−i2i2i2i2i2i2i2−i2−i2−i2−i20000-222-2000000000000i2−i2−i2i200
χ332-2-2-22-222222-2-22-2-2-22000000000000000022-2-222-2-22i−2i2i−2i000000000000002i−2i000000
χ342-2-2-22-222222-2-22-2-2-22000000000000000022-2-222-2-2−2i2i−2i2i00000000000000−2i2i000000
χ352-2-2-22-222222-2-22-2-2-220000000000000000-2-222-2-2222i−2i2i−2i00000000000000−2i2i000000
χ362-2-2-22-222222-2-22-2-2-220000000000000000-2-222-2-222−2i2i−2i2i000000000000002i−2i000000
χ372-2-2-22-222-2222-2-22-22-22-22-2000022-2-20000000000002i−2i−2i2i0000000000002i−2i00000000
χ382-2-2-22-222-2222-2-22-22-22-22-2000022-2-2000000000000−2i2i2i−2i000000000000−2i2i00000000
χ392-2-2-22-222-2222-2-22-22-2-22-220000-2-2220000000000002i−2i−2i2i000000000000−2i2i00000000
χ402-2-2-22-222-2222-2-22-22-2-22-220000-2-222000000000000−2i2i2i−2i0000000000002i−2i00000000
χ412-2-2-22-222-2-2-222-222-222-22-20000-2-222000000000000000000002-2002-2000000000000
χ422-2-2-22-222-2-2-222-222-222-22-20000-2-22200000000000000000000-2200-22000000000000
χ432-2-2-22-222-2-2-222-222-22-22-22000022-2-2000000000000000000002-200-22000000000000
χ442-2-2-22-222-2-2-222-222-22-22-22000022-2-200000000000000000000-22002-2000000000000
χ4544444444-4-4-4-4-4-4-4-44400000000000000000000000000000000000000000000000000
χ46444-4-4-44-404-40400-40000004-44-4000000000000000000000000000000000000000000
χ47444-4-4-44-404-40400-4000000-44-44000000000000000000000000000000000000000000
χ48444-4-4-44-40-440-40040000000000000000002i2−2i22i2−2i22i2−2i22i2−2i200000000000000000000000000
χ49444-4-4-44-40-440-4004000000000000000000−2i22i2−2i22i2−2i22i2−2i22i200000000000000000000000000
χ5044-444-4-4-440040-4-40004-4-440000000000000000000000000000000000000000000000
χ5144-444-4-4-440040-4-4000-444-40000000000000000000000000000000000000000000000
χ5244-444-4-4-4-400-404400000000000000000002i22i2−2i2−2i2−2i2−2i22i22i200000000000000000000000000
χ5344-444-4-4-4-400-40440000000000000000000−2i2−2i22i22i22i22i2−2i2−2i200000000000000000000000000
χ5444-4-4-44-440000000000000000002i2−2i22i2−2i22i2−2i22i2−2i22-2-22-222-200000000000000000000000000
χ5544-4-4-44-440000000000000000002i2−2i22i2−2i2−2i22i2−2i22i2-222-22-2-2200000000000000000000000000
χ5644-4-4-44-44000000000000000000−2i22i2−2i22i22i2−2i22i2−2i2-222-22-2-2200000000000000000000000000
χ5744-4-4-44-44000000000000000000−2i22i2−2i22i2−2i22i2−2i22i22-2-22-222-200000000000000000000000000
χ584-444-4-4-44000000000000002i2−2i2−2i22i22i2−2i2−2i22i200002-22-2-22-2200000000000000000000000000
χ594-444-4-4-44000000000000002i2−2i2−2i22i2−2i22i22i2−2i20000-22-222-22-200000000000000000000000000
χ604-444-4-4-4400000000000000−2i22i22i2−2i22i2−2i2−2i22i20000-22-222-22-200000000000000000000000000
χ614-444-4-4-4400000000000000−2i22i22i2−2i2−2i22i22i2−2i200002-22-2-22-2200000000000000000000000000
χ624-44-444-4-4400-40-4400000002i22i2−2i2−2i20000−2i2−2i22i22i20000000000000000000000000000000000
χ634-44-444-4-4400-40-440000000−2i2−2i22i22i200002i22i2−2i2−2i20000000000000000000000000000000000
χ644-4-44-444-404-40-4004000000000000004-4-440000000000000000000000000000000000
χ654-4-44-444-404-40-400400000000000000-444-40000000000000000000000000000000000
χ664-4-44-444-40-440400-40000000000000000002i2−2i2−2i22i22i2−2i2−2i22i200000000000000000000000000
χ674-4-44-444-40-440400-4000000000000000000−2i22i22i2−2i2−2i22i22i2−2i200000000000000000000000000
χ684-4-4-44-4444-4-4-444-444-400000000000000000000000000000000000000000000000000

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