Finite Group Databasebeta

← Group #287386

Character table — Group #287386

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65
size1111111122222222222244444488888888888888888888888881616161616161616161616163232
order12222222444444444444444444488888888888888888888888822444444888844
χ111111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111111111-1-1-1-11111-1-1-1-1-1-11111-1-1-1-1-1-1-1-1
χ311111111111111111111111111111111111-1-1-1-11111-1-1-1-11111-1-1-1-1-1-1-1-11111-1-1
χ411111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-111-1-1-1-111
χ5111111111111111111111111111-1-1-1-1-1-1-1-1111111111111111111-1-1-1-111-1-1-1-1-1-1
χ6111111111111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1111111
χ7111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-11111-1-11111-1-1-1-1-1-111
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
χ9111111111-1-1-1-11111111-1-111-1-1-11111-1-1-1-1111111-1-1-1-1-1-111-1-11-111-1-11-111-1-11-1
χ10111111111-1-1-1-11111111-1-111-1-1-11111-1-1-1-11111-1-111-1-1-1-1-1-111-1111-1-1-11-1-111-11
χ11111111111-1-1-1-11111111-1-111-1-1-11111-1-1-1-1-1-1-1-111-1-1111111-1-1-11-1-111-1111-1-1-11
χ12111111111-1-1-1-11111111-1-111-1-1-11111-1-1-1-1-1-1-1-1-1-1111111-1-1111-1-1-1111-1-1-1111-1
χ13111111111-1-1-1-11111111-1-111-1-1-1-1-1-1-11111111111-1-1-1-1-1-111-1-11-1-1-1111-1-1-111-11
χ14111111111-1-1-1-11111111-1-111-1-1-1-1-1-1-111111111-1-111-1-1-1-1-1-111-11-1-111-1111-1-11-1
χ15111111111-1-1-1-11111111-1-111-1-1-1-1-1-1-11111-1-1-1-111-1-1111111-1-1-1111-1-1-11-1-1111-1
χ16111111111-1-1-1-11111111-1-111-1-1-1-1-1-1-11111-1-1-1-1-1-1111111-1-1111-111-1-11-111-1-1-11
χ172222222222222-222-2-22-222-2-2-2-2-2000000000000000000000000220000-2-2000000
χ182222222222222-222-2-22-222-2-2-2-2-2000000000000000000000000-2-2000022000000
χ19222222222-2-2-2-2-222-2-22-2-2-2-2-22220000000000000000000000002-20000-22000000
χ20222222222-2-2-2-2-222-2-22-2-2-2-2-2222000000000000000000000000-2200002-2000000
χ2122222222-222222-2-222-22-2-2-2-222-200000000000022220000-2-2-2-200000000000000
χ2222222222-222222-2-222-22-2-2-2-222-2000000000000-2-2-2-20000222200000000000000
χ2322222222-22222-2-2-2-2-2-2-2-2-222-2-22000000002i2i−2i−2i00002i2i−2i−2i000000000000000000
χ2422222222-22222-2-2-2-2-2-2-2-2-222-2-2200000000−2i−2i2i2i0000−2i−2i2i2i000000000000000000
χ2522222222-2-2-2-2-22-2-222-2222-2-2-2-2200000000000022-2-20000-2-22200000000000000
χ2622222222-2-2-2-2-22-2-222-2222-2-2-2-22000000000000-2-222000022-2-200000000000000
χ2722222222-2-2-2-2-2-2-2-2-2-2-2-2222222-2000000002i2i−2i−2i0000−2i−2i2i2i000000000000000000
χ2822222222-2-2-2-2-2-2-2-2-2-2-2-2222222-200000000−2i−2i2i2i00002i2i−2i−2i000000000000000000
χ2922-2-222-2-220000-22-22-2-22002-200000002i2i−2i−2i000000002-22-20000002i−2i0000000000
χ3022-2-222-2-220000-22-22-2-22002-200000002i2i−2i−2i00000000-22-22000000−2i2i0000000000
χ3122-2-222-2-220000-22-22-2-22002-20000000−2i−2i2i2i000000002-22-2000000−2i2i0000000000
χ3222-2-222-2-220000-22-22-2-22002-20000000−2i−2i2i2i00000000-22-220000002i−2i0000000000
χ3322-2-222-2-2-200002-22-222-2002-20002i2i−2i−2i0000000000002i−2i−2i2i000000002-200000000
χ3422-2-222-2-2-200002-22-222-2002-20002i2i−2i−2i000000000000−2i2i2i−2i00000000-2200000000
χ3522-2-222-2-2-200002-22-222-2002-2000−2i−2i2i2i0000000000002i−2i−2i2i00000000-2200000000
χ3622-2-222-2-2-200002-22-222-2002-2000−2i−2i2i2i000000000000−2i2i2i−2i000000002-200000000
χ372-22-22-2-22022-2-22002-20-200002-202−22−22−22−20000000000002i−2i2i−2i00000000i2−i2i2−i200
χ382-22-22-2-22022-2-22002-20-200002-202−22−22−22−2000000000000−2i2i−2i2i00000000−i2i2−i2i200
χ392-22-22-2-22022-2-22002-20-200002-20−22−22−22−220000000000002i−2i2i−2i00000000−i2i2−i2i200
χ402-22-22-2-22022-2-22002-20-200002-20−22−22−22−22000000000000−2i2i−2i2i00000000i2−i2i2−i200
χ412-22-22-2-220-2-2222002-20-20000-2202−22−2−22−220000000000002i−2i−2i2i00000000i2−i2−i2i200
χ422-22-22-2-220-2-2222002-20-20000-2202−22−2−22−22000000000000−2i2i2i−2i00000000−i2i2i2−i200
χ432-22-22-2-220-2-2222002-20-20000-220−22−222−22−20000000000002i−2i−2i2i00000000−i2i2i2−i200
χ442-22-22-2-220-2-2222002-20-20000-220−22−222−22−2000000000000−2i2i2i−2i00000000i2−i2−i2i200
χ454444-4-4-4-444-44-40-4-400404-40000000000000000000000000000000000000000000
χ464444-4-4-4-44-44-440-4-40040-440000000000000000000000000000000000000000000
χ474444-4-4-4-4-44-44-404400-40-440000000000000000000000000000000000000000000
χ484444-4-4-4-4-4-44-4404400-404-40000000000000000000000000000000000000000000
χ4944-4-444-4-44000044-4-44-4-400-4400000000000000000000000000000000000000000
χ5044-4-444-4-4-40000-4-444-44400-4400000000000000000000000000000000000000000
χ5144-4-4-4-444400000-4400-400000000000000002i2−2i22i2−2i200000000000000000000000000
χ5244-4-4-4-444400000-4400-40000000000000000−2i22i2−2i22i200000000000000000000000000
χ5344-4-4-4-444-4000004-4004000000000000000022−22−222200000000000000000000000000
χ5444-4-4-4-444-4000004-40040000000000000000−222222−2200000000000000000000000000
χ554-44-44-4-44044-4-4-400-44040000-44000000000000000000000000000000000000000
χ564-44-44-4-440-4-444-400-440400004-4000000000000000000000000000000000000000
χ574-44-4-444-404-4-44000000000000000000000000002i2−2i22i2−2i20000000000000000000000
χ584-44-4-444-404-4-4400000000000000000000000000−2i22i2−2i22i20000000000000000000000
χ594-44-4-444-40-444-4000000000000000000000000002i2−2i2−2i22i20000000000000000000000
χ604-44-4-444-40-444-400000000000000000000000000−2i22i22i2−2i20000000000000000000000
χ614-4-444-44-400000400-4-40400000002i2−2i2−2i22i20000000000000000000000000000000000
χ624-4-444-44-400000400-4-4040000000−2i22i22i2−2i20000000000000000000000000000000000
χ634-4-444-44-400000-400440-4000000000002i2−2i2−2i22i2000000000000000000000000000000
χ644-4-444-44-400000-400440-400000000000−2i22i22i2−2i2000000000000000000000000000000
χ658-8-88-88-88000000000000000000000000000000000000000000000000000000000

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