Finite Group Databasebeta

← Group #314239

Character table — Group #314239

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68
size11111111222222224444444444444444444444444488888888161616161616161616161616161616163232
order12222222444444444488888888888888888888888822224444444444448888888844
χ111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111111111-1-111-1-11-1-1-1-11-1-111-1-111-1-1-1-1
χ3111111111111111111111111111111111111111111-1-111-1-111-111-1-1-1-1-1-1-111-1-111-1-1
χ4111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-111-111-1-1-1-1-1-1-1-111
χ51111111111111111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-111111111-11111-111-1-1-1-111-1-1-1-1
χ61111111111111111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-111-1-111-1-1-1-1-1-1-1-1-1-1-1-111111111
χ71111111111111111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-111111-1-11-1-111-1-1-1-1-1-111
χ81111111111111111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11-1-1111111111-1-111-1-1
χ9111111111111111111-1-1-1-11111-1-1-1-11111-1-1-1-1-1-1-1-1111111-1-11-11111-1-1-1-111-1-1-1-1-11
χ10111111111111111111-1-1-1-11111-1-1-1-11111-1-1-1-1-1-1-1-111-1-1111111-1-1-1111-1-1-1-1-1-1111-1
χ11111111111111111111-1-1-1-11111-1-1-1-11111-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-11-1-1-111111111-1-11-1
χ12111111111111111111-1-1-1-11111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-111-11-111-1-1-111-1-11111-11
χ13111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111111111-1-1-1-1111-1-1-111-1-1-1-1111-1
χ14111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111-1-11111-11-1-1-1-1111111-1-1-1-1-11
χ15111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-111-1-1-1-11-11-1-1111-1-1-1-11111-11
χ16111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-11111-1111-1-1-1-11111-1-11-1
χ17222222222-22-22-22-2-2-2000022220000-2-2-2-2000000002200-2-200-200002000000000000
χ18222222222-22-22-22-2-2-2000022220000-2-2-2-200000000-2-200220020000-2000000000000
χ19222222222-22-22-22-2-2-20000-2-2-2-200002222000000002200-2-20020000-2000000000000
χ20222222222-22-22-22-2-2-20000-2-2-2-20000222200000000-2-2002200-200002000000000000
χ2122222222-22-22-22-22-2-222220000-2-2-2-2000000000000002200-2-202-2000000000000000
χ2222222222-22-22-22-22-2-222220000-2-2-2-200000000000000-2-200220-22000000000000000
χ2322222222-22-22-22-22-2-2-2-2-2-200002222000000000000002200220-2-2000000000000000
χ2422222222-22-22-22-22-2-2-2-2-2-20000222200000000000000-2-200-2-2022000000000000000
χ2522-2-2-222-222-2-222-2-2-222i2i−2i−2i00002i2i−2i−2i0000000000002-2002-2000000000000002i−2i0000
χ2622-2-2-222-222-2-222-2-2-222i2i−2i−2i00002i2i−2i−2i000000000000-2200-2200000000000000−2i2i0000
χ2722-2-2-222-222-2-222-2-2-22−2i−2i2i2i0000−2i−2i2i2i0000000000002-2002-200000000000000−2i2i0000
χ2822-2-2-222-222-2-222-2-2-22−2i−2i2i2i0000−2i−2i2i2i000000000000-2200-22000000000000002i−2i0000
χ2922-2-2-222-22-2-222-2-222-200000000000000002i2i2i2i−2i−2i−2i−2i2-200-2200000000002i−2i00000000
χ3022-2-2-222-22-2-222-2-222-200000000000000002i2i2i2i−2i−2i−2i−2i-22002-20000000000−2i2i00000000
χ3122-2-2-222-22-2-222-2-222-20000000000000000−2i−2i−2i−2i2i2i2i2i2-200-220000000000−2i2i00000000
χ3222-2-2-222-22-2-222-2-222-20000000000000000−2i−2i−2i−2i2i2i2i2i-22002-200000000002i−2i00000000
χ3322-2-2-222-2-222-2-222-22-22i2i−2i−2i0000−2i−2i2i2i000000000000000000000002-202i−2i0000000000
χ3422-2-2-222-2-222-2-222-22-22i2i−2i−2i0000−2i−2i2i2i00000000000000000000000-220−2i2i0000000000
χ3522-2-2-222-2-222-2-222-22-2−2i−2i2i2i00002i2i−2i−2i000000000000000000000002-20−2i2i0000000000
χ3622-2-2-222-2-222-2-222-22-2−2i−2i2i2i00002i2i−2i−2i00000000000000000000000-2202i−2i0000000000
χ372-22-222-2-20-202020-2000000i2i2−i2−i22i−2i2i−2ii2i2−i2−i222−2−222−2−2002-2002i−2i0000000000i2−i2002−200
χ382-22-222-2-20-202020-2000000i2i2−i2−i22i−2i2i−2ii2i2−i2−i222−2−222−2−200-2200−2i2i0000000000−i2i200−2200
χ392-22-222-2-20-202020-2000000i2i2−i2−i2−2i2i−2i2ii2i2−i2−i2−2−222−2−222002-200−2i2i0000000000i2−i200−2200
χ402-22-222-2-20-202020-2000000i2i2−i2−i2−2i2i−2i2ii2i2−i2−i2−2−222−2−22200-22002i−2i0000000000−i2i2002−200
χ412-22-222-2-20-202020-2000000−i2−i2i2i22i−2i2i−2i−i2−i2i2i2−2−222−2−222002-2002i−2i0000000000−i2i200−2200
χ422-22-222-2-20-202020-2000000−i2−i2i2i22i−2i2i−2i−i2−i2i2i2−2−222−2−22200-2200−2i2i0000000000i2−i2002−200
χ432-22-222-2-20-202020-2000000−i2−i2i2i2−2i2i−2i2i−i2−i2i2i222−2−222−2−2002-200−2i2i0000000000−i2i2002−200
χ442-22-222-2-20-202020-2000000−i2−i2i2i2−2i2i−2i2i−i2−i2i2i222−2−222−2−200-22002i−2i0000000000i2−i200−2200
χ4544444444-4-4-4-4-4-4-4-44400000000000000000000000000000000000000000000000000
χ464444-4-4-4-4000000000022−2222−220000000022−2222−222-22-22-22-200000000000000000000000000
χ474444-4-4-4-4000000000022−2222−2200000000−2222−2222-22-22-22-2200000000000000000000000000
χ484444-4-4-4-40000000000−2222−22220000000022−2222−22-22-22-22-2200000000000000000000000000
χ494444-4-4-4-40000000000−2222−222200000000−2222−22222-22-22-22-200000000000000000000000000
χ5044-4-44-4-4400000000002i2−2i2−2i22i222−2222−22000000002i−2i2i−2i−2i2i−2i2i00000000000000000000000000
χ5144-4-44-4-4400000000002i2−2i2−2i22i2−2222−222200000000−2i2i−2i2i2i−2i2i−2i00000000000000000000000000
χ5244-4-44-4-440000000000−2i22i22i2−2i222−2222−2200000000−2i2i−2i2i2i−2i2i−2i00000000000000000000000000
χ5344-4-44-4-440000000000−2i22i22i2−2i2−2222−2222000000002i−2i2i−2i−2i2i−2i2i00000000000000000000000000
χ5444-4-4-444-4-4-444-4-444-4400000000000000000000000000000000000000000000000000
χ554-44-444-4-4040-40-4040000002i22i2−2i2−2i20000−2i2−2i22i22i20000000000000000000000000000000000
χ564-44-444-4-4040-40-404000000−2i2−2i22i22i200002i22i2−2i2−2i20000000000000000000000000000000000
χ574-44-4-4-4444040-40-40000000000000004i−4i−4i4i0000000000000000000000000000000000
χ584-44-4-4-4444040-40-4000000000000000−4i4i4i−4i0000000000000000000000000000000000
χ594-44-4-4-444-40-40404000000000000000000022−22−222222−22−222200000000000000000000000000
χ604-44-4-4-444-40-404040000000000000000000−222222−22−222222−2200000000000000000000000000
χ614-4-444-44-440-40-40400000004i−4i−4i4i000000000000000000000000000000000000000000
χ624-4-444-44-440-40-4040000000−4i4i4i−4i000000000000000000000000000000000000000000
χ634-4-444-44-4-404040-400000000000000000002i2−2i2−2i22i2−2i22i22i2−2i200000000000000000000000000
χ644-4-444-44-4-404040-40000000000000000000−2i22i22i2−2i22i2−2i2−2i22i200000000000000000000000000
χ654-4-44-44-4404040-40-40000000000000000002i22i2−2i2−2i2−2i2−2i22i22i200000000000000000000000000
χ664-4-44-44-4404040-40-4000000000000000000−2i2−2i22i22i22i22i2−2i2−2i200000000000000000000000000
χ674-4-44-44-440-40-4040400000000004-4-4400000000000000000000000000000000000000
χ684-4-44-44-440-40-404040000000000-444-400000000000000000000000000000000000000

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