Finite Group Databasebeta

← Group #287017

Character table — Group #287017

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65
size1111111122222222444444444444888888888888888888888881616161616161616161616163232
order12222222444444444444444488884444488888888888888888844444488888844
χ111111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111111111-1-1-1-11111-1-1-1-111-1-1-1-1-1-111-1-1-1-1
χ311111111111111111111111111111-1-1-1-111-1-1-1-1111111111111-1-1-1-1-1-111-1-111-1-1
χ411111111111111111111111111111-1-1-1-111-1-1-1-1-1-1-1-11111-1-1-1-1-1-11111-1-1-1-1-1-111
χ5111111111111111111111111-1-1-1-111111-1-1-1-1-1-11111-1-1-1-1111111-1-1-1-1-1-1-1-1-1-111
χ6111111111111111111111111-1-1-1-111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-111-1-1
χ7111111111111111111111111-1-1-1-11-1-1-1-1-1-111111111-1-1-1-11111-1-11111-1-111-1-1-1-1
χ8111111111111111111111111-1-1-1-11-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111
χ91111111111111111-1-1-1-1-1-1111111-11111-1-11111111111-1-1-1-1-1-1-1-111-1-111-1-1-1-1-11
χ101111111111111111-1-1-1-1-1-1111111-11111-1-11111-1-1-1-111-1-11111-1-1-1-111-1-1-1-1111-1
χ111111111111111111-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1111111-1-1-1-1-1-111-1-1111111-1-11-1
χ121111111111111111-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-111111111-1-1-1-11111-11
χ131111111111111111-1-1-1-1-1-111-1-1-1-1-1111111-1-1-1-11111-1-111-1-1-1-1-1-1-1-111-1-11111-11
χ141111111111111111-1-1-1-1-1-111-1-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1111111-1-111-1-11111-1-11-1
χ151111111111111111-1-1-1-1-1-111-1-1-1-1-1-1-1-1-11111111111-1-111-1-1-1-11111-1-1-1-1-1-1111-1
χ161111111111111111-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1111111-1-1-1-1-1-111111111-1-11111-1-1-1-1-11
χ17222222222-222-2-22-222-2-222-2-20000-222-2-20000000000000000002-2000000000000
χ18222222222-222-2-22-222-2-222-2-20000-2-2-222000000000000000000-22000000000000
χ19222222222-222-2-22-2-2-222-2-2-2-20000222-2-2000000000000000000-22000000000000
χ20222222222-222-2-22-2-2-222-2-2-2-200002-2-2220000000000000000002-2000000000000
χ2122222222-22-2-222-222222-2-2-2-22222-20000-2-200000000-2-222000000000000000000
χ2222222222-22-2-222-222222-2-2-2-2-2-2-2-2-20000220000000022-2-2000000000000000000
χ2322222222-22-2-222-22-2-2-2-222-2-22222200002200000000-2-2-2-2000000000000000000
χ2422222222-22-2-222-22-2-2-2-222-2-2-2-2-2-220000-2-2000000002222000000000000000000
χ2522222222-2-2-2-2-2-2-2-222-2-2-2-222000020000002i2i−2i−2i000000000000000000002i−2i0000
χ2622222222-2-2-2-2-2-2-2-222-2-2-2-22200002000000−2i−2i2i2i00000000000000000000−2i2i0000
χ2722222222-2-2-2-2-2-2-2-2-2-22222220000-20000002i2i−2i−2i00000000000000000000−2i2i0000
χ2822222222-2-2-2-2-2-2-2-2-2-22222220000-2000000−2i−2i2i2i000000000000000000002i−2i0000
χ2922-2-2-22-222-22-22-2-220000002-2000000000002i−2i2i−2i000000002i2i−2i−2i00002-200000000
χ3022-2-2-22-222-22-22-2-220000002-2000000000002i−2i2i−2i00000000−2i−2i2i2i0000-2200000000
χ3122-2-2-22-222-22-22-2-220000002-200000000000−2i2i−2i2i000000002i2i−2i−2i0000-2200000000
χ3222-2-2-22-222-22-22-2-220000002-200000000000−2i2i−2i2i00000000−2i−2i2i2i00002-200000000
χ3322-2-2-22-22-22-22-222-20000002-2000000000002-2-222i2i−2i−2i00000000002i−2i0000000000
χ3422-2-2-22-22-22-22-222-20000002-2000000000002-2-22−2i−2i2i2i0000000000−2i2i0000000000
χ3522-2-2-22-22-22-22-222-20000002-200000000000-222-22i2i−2i−2i0000000000−2i2i0000000000
χ3622-2-2-22-22-22-22-222-20000002-200000000000-222-2−2i−2i2i2i00000000002i−2i0000000000
χ372-22-2-222-20200-2-2022i−2i2i−2i00002i2i−2i−2i00000000000i2−i2i2−i2002-22−22−20000002−200i2−i200
χ382-22-2-222-20200-2-2022i−2i2i−2i00002i2i−2i−2i00000000000−i2i2−i2i2002-2−22−22000000−2200−i2i200
χ392-22-2-222-20200-2-2022i−2i2i−2i0000−2i−2i2i2i00000000000i2−i2i2−i200-222−22−2000000−2200−i2i200
χ402-22-2-222-20200-2-2022i−2i2i−2i0000−2i−2i2i2i00000000000−i2i2−i2i200-22−22−220000002−200i2−i200
χ412-22-2-222-20200-2-202−2i2i−2i2i00002i2i−2i−2i00000000000i2−i2i2−i200-22−22−220000002−200−i2i200
χ422-22-2-222-20200-2-202−2i2i−2i2i00002i2i−2i−2i00000000000−i2i2−i2i200-222−22−2000000−2200i2−i200
χ432-22-2-222-20200-2-202−2i2i−2i2i0000−2i−2i2i2i00000000000i2−i2i2−i2002-2−22−22000000−2200i2−i200
χ442-22-2-222-20200-2-202−2i2i−2i2i0000−2i−2i2i2i00000000000−i2i2−i2i2002-22−22−20000002−200−i2i200
χ454444-4-4-4-440-4-400400000000022−2222−2200000000000000022−2200000000000000000000
χ464444-4-4-4-440-4-4004000000000−2222−2222000000000000000−222200000000000000000000
χ474444-4-4-4-4-404400-400000000022−2222−22000000000000000−222200000000000000000000
χ484444-4-4-4-4-404400-4000000000−2222−222200000000000000022−2200000000000000000000
χ4944-4-44-44-440-4400-400000000000000004-400000000000000000000000000000000
χ5044-4-44-44-440-4400-40000000000000000-4400000000000000000000000000000000
χ5144-4-44-44-4-404-4004000000000000004i−4i0000000000000000000000000000000000
χ5244-4-44-44-4-404-400400000000000000−4i4i0000000000000000000000000000000000
χ5344-4-4-44-44444-4-44-4-4000000-4400000000000000000000000000000000000000000
χ5444-4-4-44-44-4-4-444-444000000-4400000000000000000000000000000000000000000
χ554-44-44-4-440000000000004i−4i002i2−2i2−2i22i20000022−22000000000000000000000000000000
χ564-44-44-4-440000000000004i−4i00−2i22i22i2−2i200000−2222000000000000000000000000000000
χ574-44-44-4-44000000000000−4i4i002i2−2i2−2i22i200000−2222000000000000000000000000000000
χ584-44-44-4-44000000000000−4i4i00−2i22i22i2−2i20000022−22000000000000000000000000000000
χ594-44-4-444-40-400440-44i−4i−4i4i000000000000000000000000000000000000000000000
χ604-44-4-444-40-400440-4−4i4i4i−4i000000000000000000000000000000000000000000000
χ614-4-4444-4-404004-40-40000000000000000000000022−22−22220000000000000000000000
χ624-4-4444-4-404004-40-400000000000000000000000−222222−220000000000000000000000
χ634-4-4444-4-40-400-440400000000000000000000000000000002i2−2i2−2i22i200000000000000
χ644-4-4444-4-40-400-44040000000000000000000000000000000−2i22i22i2−2i200000000000000
χ658-8-88-8-888000000000000000000000000000000000000000000000000000000000

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