Finite Group Databasebeta

← Group #314271

Character table — Group #314271

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68
size11111111222222224444444444444444444444444488888888161616161616161616161616161616163232
order12222222444444444488888888888888888888888822444444224444448888888844
χ111111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111111111-1-1-1-1-1-11-1-11-1-111-1-111-1-1-1-1
χ3111111111111111111111111111111111111111111-1-1-1-11111-1-1-111-1-1-1-1-111-1-111-1-1
χ4111111111111111111111111111111111111111111-1-1-1-1-1-1-1-111-1-1-1-111-1-1-1-1-1-1-1-111
χ51111111111111111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-11111111111-111-111-1-1-1-111-1-1-1-1
χ61111111111111111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111
χ71111111111111111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-11111-1-111-1-1-1-1-1-111
χ81111111111111111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111-1-11111111-1-111-1-1
χ9111111111111111111-1-1-1-11111-1-1-1-11111-1-1-1-1-1-1-1-1111111-1-1111-111-1-1-1-111-1-1-1-1-11
χ10111111111111111111-1-1-1-11111-1-1-1-11111-1-1-1-1-1-1-1-11111-1-111-1-111-1111-1-1-1-1-1-1111-1
χ11111111111111111111-1-1-1-11111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-11-111111111-1-11-1
χ12111111111111111111-1-1-1-11111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-11-1-1-1-111-1-11111-11
χ13111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111111111-1-111-1-11-1-1-111-1-1-1-1111-1
χ14111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-111-1-1-11-1-1111111-1-1-1-1-11
χ15111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-111-1-1-1-11-11111-1-1-1-11111-11
χ16111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1111111-11-1-1-1-11111-1-11-1
χ17222222222-22-22-22-2-2-2000022220000-2-2-2-20000000022-2-2000000-2002000000000000
χ18222222222-22-22-22-2-2-2000022220000-2-2-2-200000000-2-222000000200-2000000000000
χ19222222222-22-22-22-2-2-20000-2-2-2-2000022220000000022-2-2000000200-2000000000000
χ20222222222-22-22-22-2-2-20000-2-2-2-20000222200000000-2-222000000-2002000000000000
χ2122222222-22-22-22-22-2-222220000-2-2-2-2000000000000000022-2-20002-20000000000000
χ2222222222-22-22-22-22-2-222220000-2-2-2-20000000000000000-2-222000-220000000000000
χ2322222222-22-22-22-22-2-2-2-2-2-20000222200000000000000002222000-2-20000000000000
χ2422222222-22-22-22-22-2-2-2-2-2-2000022220000000000000000-2-2-2-2000220000000000000
χ2522-2-2-222-222-2-222-2-2-222i2i−2i−2i00002i2i−2i−2i0000000000002-22-200000000000000002i−2i0000
χ2622-2-2-222-222-2-222-2-2-222i2i−2i−2i00002i2i−2i−2i000000000000-22-220000000000000000−2i2i0000
χ2722-2-2-222-222-2-222-2-2-22−2i−2i2i2i0000−2i−2i2i2i0000000000002-22-20000000000000000−2i2i0000
χ2822-2-2-222-222-2-222-2-2-22−2i−2i2i2i0000−2i−2i2i2i000000000000-22-2200000000000000002i−2i0000
χ2922-2-2-222-22-2-222-2-222-200000000000000002i2i2i2i−2i−2i−2i−2i2-2-220000000000002i−2i00000000
χ3022-2-2-222-22-2-222-2-222-200000000000000002i2i2i2i−2i−2i−2i−2i-222-2000000000000−2i2i00000000
χ3122-2-2-222-22-2-222-2-222-20000000000000000−2i−2i−2i−2i2i2i2i2i2-2-22000000000000−2i2i00000000
χ3222-2-2-222-22-2-222-2-222-20000000000000000−2i−2i−2i−2i2i2i2i2i-222-20000000000002i−2i00000000
χ3322-2-2-222-2-222-2-222-22-22i2i−2i−2i0000−2i−2i2i2i000000000000000000002-200002i−2i0000000000
χ3422-2-2-222-2-222-2-222-22-22i2i−2i−2i0000−2i−2i2i2i00000000000000000000-220000−2i2i0000000000
χ3522-2-2-222-2-222-2-222-22-2−2i−2i2i2i00002i2i−2i−2i000000000000000000002-20000−2i2i0000000000
χ3622-2-2-222-2-222-2-222-22-2−2i−2i2i2i00002i2i−2i−2i00000000000000000000-2200002i−2i0000000000
χ372-22-222-2-20-202020-2000000i2i2−i2−i22i−2i2i−2ii2i2−i2−i222−2−222−2−200002-22i−2i0000000000i2−i2002−200
χ382-22-222-2-20-202020-2000000i2i2−i2−i22i−2i2i−2ii2i2−i2−i222−2−222−2−20000-22−2i2i0000000000−i2i200−2200
χ392-22-222-2-20-202020-2000000i2i2−i2−i2−2i2i−2i2ii2i2−i2−i2−2−222−2−22200002-2−2i2i0000000000i2−i200−2200
χ402-22-222-2-20-202020-2000000i2i2−i2−i2−2i2i−2i2ii2i2−i2−i2−2−222−2−2220000-222i−2i0000000000−i2i2002−200
χ412-22-222-2-20-202020-2000000−i2−i2i2i22i−2i2i−2i−i2−i2i2i2−2−222−2−22200002-22i−2i0000000000−i2i200−2200
χ422-22-222-2-20-202020-2000000−i2−i2i2i22i−2i2i−2i−i2−i2i2i2−2−222−2−2220000-22−2i2i0000000000i2−i2002−200
χ432-22-222-2-20-202020-2000000−i2−i2i2i2−2i2i−2i2i−i2−i2i2i222−2−222−2−200002-2−2i2i0000000000−i2i2002−200
χ442-22-222-2-20-202020-2000000−i2−i2i2i2−2i2i−2i2i−i2−i2i2i222−2−222−2−20000-222i−2i0000000000i2−i200−2200
χ4544444444-4-4-4-4-4-4-4-44400000000000000000000000000000000000000000000000000
χ46444-4-4-4-4440-40-40400000000000000000002i2−2i22i2−2i22i2−2i22i2−2i200000000000000000000000000
χ47444-4-4-4-4440-40-4040000000000000000000−2i22i2−2i22i2−2i22i2−2i22i200000000000000000000000000
χ48444-4-4-4-44-404040-40000000000000004i−4i4i−4i0000000000000000000000000000000000
χ49444-4-4-4-44-404040-4000000000000000−4i4i−4i4i0000000000000000000000000000000000
χ5044-444-4-4-44040-40-4000000000000000000022−2222−22−2222−222200000000000000000000000000
χ5144-444-4-4-44040-40-40000000000000000000−2222−222222−2222−2200000000000000000000000000
χ5244-444-4-4-4-40-4040400000004i−4i4i−4i000000000000000000000000000000000000000000
χ5344-444-4-4-4-40-404040000000−4i4i−4i4i000000000000000000000000000000000000000000
χ5444-4-4-444-4-4-444-4-444-4400000000000000000000000000000000000000000000000000
χ554-444-4-44-400000000002i2−2i22i2−2i20000000022−22−22222i−2i−2i2i2i−2i−2i2i00000000000000000000000000
χ564-444-4-44-400000000002i2−2i22i2−2i200000000−222222−22−2i2i2i−2i−2i2i2i−2i00000000000000000000000000
χ574-444-4-44-40000000000−2i22i2−2i22i20000000022−22−2222−2i2i2i−2i−2i2i2i−2i00000000000000000000000000
χ584-444-4-44-40000000000−2i22i2−2i22i200000000−222222−222i−2i−2i2i2i−2i−2i2i00000000000000000000000000
χ594-44-444-4-4040-40-4040000002i22i2−2i2−2i20000−2i2−2i22i22i20000000000000000000000000000000000
χ604-44-444-4-4040-40-404000000−2i2−2i22i22i200002i22i2−2i2−2i20000000000000000000000000000000000
χ614-4-44-44-4404040-40-40000000000000000002i22i2−2i2−2i2−2i2−2i22i22i200000000000000000000000000
χ624-4-44-44-4404040-40-4000000000000000000−2i2−2i22i22i22i22i2−2i2−2i200000000000000000000000000
χ634-4-44-44-440-40-4040400000000004-4-4400000000000000000000000000000000000000
χ644-4-44-44-440-40-404040000000000-444-400000000000000000000000000000000000000
χ654-4-4-44-444000000000022−22−222222−22−2222000000002-2-22-222-200000000000000000000000000
χ664-4-4-44-444000000000022−22−2222−222222−2200000000-222-22-2-2200000000000000000000000000
χ674-4-4-44-4440000000000−222222−2222−22−222200000000-222-22-2-2200000000000000000000000000
χ684-4-4-44-4440000000000−222222−22−222222−22000000002-2-22-222-200000000000000000000000000

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