Finite Group Databasebeta

← Group #267258

Character table — Group #267258

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65
size1111111122222222222244444488888888888888888888888881616161616161616161616163232
order12222222444444444444224444444444444888888888888888844448888888844
χ111111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-11111-1-1-1-1
χ311111111111111111111111111111111111-1-1-1-11111-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1
χ411111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-11111
χ5111111111111111111111111111-1-1-1-1-1-1-1-11111111111111111-1-1-1-111-1-1-1-111-1-1
χ6111111111111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1-1-11111-1-1-1-1-1-1-1-111
χ7111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1-1-1-1-11111-1-111
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
χ911111111-1-1-1-111111111-1-111-1-1-11111-1-1-1-111-1-1111111-1-1-1-1-1-111-1-11111-1-1-1-11-1
χ1011111111-1-1-1-111111111-1-111-1-1-11111-1-1-1-111-1-1-1-1-1-111-1-11111-1-111-1-111-1-111-11
χ1111111111-1-1-1-111111111-1-111-1-1-11111-1-1-1-1-1-1111111-1-111-1-1-1-111-1-1-1-1-1-11111-11
χ1211111111-1-1-1-111111111-1-111-1-1-11111-1-1-1-1-1-111-1-1-1-1-1-1111111-1-11111-1-111-1-11-1
χ1311111111-1-1-1-111111111-1-111-1-1-1-1-1-1-1111111-1-1111111-1-1-1-1-1-1-1-11111-1-111-1-1-11
χ1411111111-1-1-1-111111111-1-111-1-1-1-1-1-1-1111111-1-1-1-1-1-111-1-1111111-1-1-1-1-1-111111-1
χ1511111111-1-1-1-111111111-1-111-1-1-1-1-1-1-11111-1-1111111-1-111-1-1-1-1-1-111-1-111-1-1111-1
χ1611111111-1-1-1-111111111-1-111-1-1-1-1-1-1-11111-1-111-1-1-1-1-1-111111111-1-11111-1-1-1-1-11
χ172222222222222-2-222-2-22-2-2-2-222-222-2-222-2-2000000000000000000000000000000
χ182222222222222-2-222-2-22-2-2-2-222-2-2-222-2-222000000000000000000000000000000
χ19222222222222-222-2-222-222-2-2-2-2-20000000022220000-2-2-2-2000000000000000000
χ20222222222222-222-2-222-222-2-2-2-2-200000000-2-2-2-200002222000000000000000000
χ21222222222222-2-2-2-2-2-2-2-2-2-222-2-220000000000000000000000000000002i−2i2i−2i0000
χ22222222222222-2-2-2-2-2-2-2-2-2-222-2-22000000000000000000000000000000−2i2i−2i2i0000
χ2322222222-2-2-2-22-2-222-2-2222-2-2-2-2222-2-2-2-222000000000000000000000000000000
χ2422222222-2-2-2-22-2-222-2-2222-2-2-2-22-2-22222-2-2000000000000000000000000000000
χ2522222222-2-2-2-2-222-2-222-2-2-2-2-22220000000022-2-20000-2-222000000000000000000
χ2622222222-2-2-2-2-222-2-222-2-2-2-2-222200000000-2-222000022-2-2000000000000000000
χ2722222222-2-2-2-2-2-2-2-2-2-2-2-2222222-20000000000000000000000000000002i−2i−2i2i0000
χ2822222222-2-2-2-2-2-2-2-2-2-2-2-2222222-2000000000000000000000000000000−2i2i2i−2i0000
χ2922-2-222-2-222-2-20-2-2002202-200000000000002i−2i2i−2i22−2−2000022−2−20000i2−i20000i2−i200
χ3022-2-222-2-222-2-20-2-2002202-200000000000002i−2i2i−2i−2−2220000−2−2220000−i2i20000−i2i200
χ3122-2-222-2-222-2-20-2-2002202-20000000000000−2i2i−2i2i22−2−2000022−2−20000−i2i20000−i2i200
χ3222-2-222-2-222-2-20-2-2002202-20000000000000−2i2i−2i2i−2−2220000−2−2220000i2−i20000i2−i200
χ3322-2-222-2-2-2-2220-2-200220-2200000000000002i−2i−2i2i22−2−20000−2−2220000i2−i20000−i2i200
χ3422-2-222-2-2-2-2220-2-200220-2200000000000002i−2i−2i2i−2−222000022−2−20000−i2i20000i2−i200
χ3522-2-222-2-2-2-2220-2-200220-220000000000000−2i2i2i−2i22−2−20000−2−2220000−i2i20000i2−i200
χ3622-2-222-2-2-2-2220-2-200220-220000000000000−2i2i2i−2i−2−222000022−2−20000i2−i20000−i2i200
χ372-2-2-2-22220000-22-22-22-22002-20002-22-200000000000000002-22-2002-20000000000
χ382-2-2-2-22220000-22-22-22-22002-20002-22-20000000000000000-22-2200-220000000000
χ392-2-2-2-22220000-22-22-22-22002-2000-22-2200000000000000002-22-200-220000000000
χ402-2-2-2-22220000-22-22-22-22002-2000-22-220000000000000000-22-22002-20000000000
χ412-2-2-2-22220000-2-222-2-22200-220002-2-22000000002-22-2000000002-2000000000000
χ422-2-2-2-22220000-2-222-2-22200-220002-2-2200000000-22-2200000000-22000000000000
χ432-2-2-2-22220000-2-222-2-22200-22000-222-2000000002-22-200000000-22000000000000
χ442-2-2-2-22220000-2-222-2-22200-22000-222-200000000-22-22000000002-2000000000000
χ45444-4-4-44-400004004-400-400000000000004-4000000000000000000000000000000
χ46444-4-4-44-400004004-400-40000000000000-44000000000000000000000000000000
χ47444-4-4-44-40000-400-44004000000000004i−4i00000000000000000000000000000000
χ48444-4-4-44-40000-400-4400400000000000−4i4i00000000000000000000000000000000
χ4944-4-444-4-444-4-404400-4-40-440000000000000000000000000000000000000000000
χ5044-4-444-4-4-4-44404400-4-404-40000000000000000000000000000000000000000000
χ514-444-44-4-4000004-400-440000000000000000000022−22−22220000000000000000000000
χ524-444-44-4-4000004-400-4400000000000000000000−222222−220000000000000000000000
χ534-444-44-4-400000-44004-4000000000000000000000000000022−22−222200000000000000
χ544-444-44-4-400000-44004-40000000000000000000000000000−222222−2200000000000000
χ554-44-44-4-444i−4i4i−4i000000000000000000000000000000022−222i2−2i2000000000000000000
χ564-44-44-4-444i−4i4i−4i0000000000000000000000000000000−2222−2i22i2000000000000000000
χ574-44-44-4-44−4i4i−4i4i000000000000000000000000000000022−22−2i22i2000000000000000000
χ584-44-44-4-44−4i4i−4i4i0000000000000000000000000000000−22222i2−2i2000000000000000000
χ594-4-444-44-44i−4i−4i4i400-4-400400004i−4i000000000000000000000000000000000000000
χ604-4-444-44-44i−4i−4i4i-4004400-40000−4i4i000000000000000000000000000000000000000
χ614-4-444-44-4−4i4i4i−4i400-4-40040000−4i4i000000000000000000000000000000000000000
χ624-4-444-44-4−4i4i4i−4i-4004400-400004i−4i000000000000000000000000000000000000000
χ634-4-4-4-4444000044-4-444-4-400-4400000000000000000000000000000000000000000
χ644-4-4-4-444400004-44-44-44-4004-400000000000000000000000000000000000000000
χ6588-88-8-8-88000000000000000000000000000000000000000000000000000000000

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