Finite Group Databasebeta

← Group #314233

Character table — Group #314233

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68
size11111111222222224444444444444444444444444488888888161616161616161616161616161616163232
order12222222444444444488888888888888888888888822444444444444448888888844
χ111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111111111-1-1-1-111-111-1-1-1-1-111-1-111-1-1-1-1
χ3111111111111111111111111111111111111111111-1-11111-1-11-1-1-1-1-1-11-1-111-1-111-1-1
χ4111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-111
χ51111111111111111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-111111111-1111111-1-1-1-1-1-1-111-1-1
χ61111111111111111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-111111-1-1-1-11-1-111-1-1-1-111
χ71111111111111111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-111-1-1111111
χ81111111111111111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11-1-111111111111-1-1-1-1
χ9111111111111111111-1-1-1-11111-1-1-1-11111-1-1-1-1-1-1-1-1111111-1-111-1-1-111111-1-1-1-1-1-11-1
χ10111111111111111111-1-1-1-11111-1-1-1-11111-1-1-1-1-1-1-1-111-1-1-1-1-1-1-11-111-1-1-11111-1-111-11
χ11111111111111111111-1-1-1-11111-1-1-1-11111-1-1-1-1-1-1-1-1-1-11111111-1111-1-11-1-1-1-111-1-1-11
χ12111111111111111111-1-1-1-11111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-11-1-111-1-1-11111111-1
χ13111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111111111-1-1-11-1-1-111-1-1-11111-1-1-11
χ14111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-111-111-1-11-1-1-1-111111-1
χ15111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1111111-1-1111-1-1-11111-1-1-1-11-1
χ16111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1111-11-1-111111-1-1-1-111-11
χ17222222222-22-22-22-2-2-2000022220000-2-2-2-2000000000022-2-2002000000-20000000000
χ18222222222-22-22-22-2-2-2000022220000-2-2-2-20000000000-2-22200-200000020000000000
χ19222222222-22-22-22-2-2-20000-2-2-2-200002222000000000022-2-200-200000020000000000
χ20222222222-22-22-22-2-2-20000-2-2-2-2000022220000000000-2-222002000000-20000000000
χ2122222222-22-22-22-22-2-222220000-2-2-2-2000000000000220000220-2-2000000000000000
χ2222222222-22-22-22-22-2-222220000-2-2-2-2000000000000-2-20000-2-2022000000000000000
χ2322222222-22-22-22-22-2-2-2-2-2-200002222000000000000220000-2-20-22000000000000000
χ2422222222-22-22-22-22-2-2-2-2-2-200002222000000000000-2-200002202-2000000000000000
χ252-222-2-2-220-202020-20022-2-2i2i2−i2−i20000i2i2−i2−i2i2i2i2i2−i2−i2−i2−i22-200002-200000000i2−i200i2−i20000
χ262-222-2-2-220-202020-20022-2-2i2i2−i2−i20000i2i2−i2−i2i2i2i2i2−i2−i2−i2−i2-220000-2200000000−i2i200−i2i20000
χ272-222-2-2-220-202020-20022-2-2−i2−i2i2i20000−i2−i2i2i2−i2−i2−i2−i2i2i2i2i22-200002-200000000−i2i200−i2i20000
χ282-222-2-2-220-202020-20022-2-2−i2−i2i2i20000−i2−i2i2i2−i2−i2−i2−i2i2i2i2i2-220000-2200000000i2−i200i2−i20000
χ292-222-2-2-220-202020-200-2-222i2i2−i2−i20000i2i2−i2−i2−i2−i2−i2−i2i2i2i2i22-20000-2200000000i2−i200−i2i20000
χ302-222-2-2-220-202020-200-2-222i2i2−i2−i20000i2i2−i2−i2−i2−i2−i2−i2i2i2i2i2-2200002-200000000−i2i200i2−i20000
χ312-222-2-2-220-202020-200-2-222−i2−i2i2i20000−i2−i2i2i2i2i2i2i2−i2−i2−i2−i22-20000-2200000000−i2i200i2−i20000
χ322-222-2-2-220-202020-200-2-222−i2−i2i2i20000−i2−i2i2i2i2i2i2i2−i2−i2−i2−i2-2200002-200000000i2−i200−i2i20000
χ332-2-222-22-222-2-222-2-2-222i−2i2i−2i00002i2i−2i−2i000000000000002-22-200000000000000002i−2i00
χ342-2-222-22-222-2-222-2-2-222i−2i2i−2i00002i2i−2i−2i00000000000000-22-220000000000000000−2i2i00
χ352-2-222-22-222-2-222-2-2-22−2i2i−2i2i0000−2i−2i2i2i000000000000002-22-20000000000000000−2i2i00
χ362-2-222-22-222-2-222-2-2-22−2i2i−2i2i0000−2i−2i2i2i00000000000000-22-2200000000000000002i−2i00
χ372-2-222-22-22-2-222-2-222-200000000000000002i2i−2i−2i2i2i−2i−2i002-2-220000000000002i−2i000000
χ382-2-222-22-22-2-222-2-222-200000000000000002i2i−2i−2i2i2i−2i−2i00-222-2000000000000−2i2i000000
χ392-2-222-22-22-2-222-2-222-20000000000000000−2i−2i2i2i−2i−2i2i2i002-2-22000000000000−2i2i000000
χ402-2-222-22-22-2-222-2-222-20000000000000000−2i−2i2i2i−2i−2i2i2i00-222-20000000000002i−2i000000
χ412-2-222-22-2-222-2-222-22-22i−2i2i−2i0000−2i−2i2i2i000000000000000000000002i−2i2-200000000000
χ422-2-222-22-2-222-2-222-22-22i−2i2i−2i0000−2i−2i2i2i00000000000000000000000−2i2i-2200000000000
χ432-2-222-22-2-222-2-222-22-2−2i2i−2i2i00002i2i−2i−2i000000000000000000000002i−2i-2200000000000
χ442-2-222-22-2-222-2-222-22-2−2i2i−2i2i00002i2i−2i−2i00000000000000000000000−2i2i2-200000000000
χ4544444444-4-4-4-4-4-4-4-44400000000000000000000000000000000000000000000000000
χ46444-44-4-4-440-40-404000000000000000000022−2222−2222−2222−2200000000000000000000000000
χ47444-44-4-4-440-40-4040000000000000000000−2222−2222−2222−222200000000000000000000000000
χ48444-44-4-4-4-404040-400000004-44-4000000000000000000000000000000000000000000
χ49444-44-4-4-4-404040-40000000-44-44000000000000000000000000000000000000000000
χ5044-44-44-4-404040-40-40000000000000000002222−22−22−22−22222200000000000000000000000000
χ5144-44-44-4-404040-40-4000000000000000000−22−2222222222−22−2200000000000000000000000000
χ5244-44-44-4-40-40-40404004i−4i−4i4i0000000000000000000000000000000000000000000000
χ5344-44-44-4-40-40-4040400−4i4i4i−4i0000000000000000000000000000000000000000000000
χ5444-4-4-4-4440000000000000000002i2−2i22i2−2i22i2−2i22i2−2i22-2-22-222-200000000000000000000000000
χ5544-4-4-4-4440000000000000000002i2−2i22i2−2i2−2i22i2−2i22i2-222-22-2-2200000000000000000000000000
χ5644-4-4-4-444000000000000000000−2i22i2−2i22i22i2−2i22i2−2i2-222-22-2-2200000000000000000000000000
χ5744-4-4-4-444000000000000000000−2i22i2−2i22i2−2i22i2−2i22i22-2-22-222-200000000000000000000000000
χ584-444-4-4-44040-40-4040000002i22i2−2i2−2i20000−2i2−2i22i22i20000000000000000000000000000000000
χ594-444-4-4-44040-40-404000000−2i2−2i22i22i200002i22i2−2i2−2i20000000000000000000000000000000000
χ604-44-4-444-4000000000000002i2−2i2−2i22i222−22−222200002i−2i2i−2i−2i2i−2i2i00000000000000000000000000
χ614-44-4-444-4000000000000002i2−2i2−2i22i2−222222−220000−2i2i−2i2i2i−2i2i−2i00000000000000000000000000
χ624-44-4-444-400000000000000−2i22i22i2−2i222−22−22220000−2i2i−2i2i2i−2i2i−2i00000000000000000000000000
χ634-44-4-444-400000000000000−2i22i22i2−2i2−222222−2200002i−2i2i−2i−2i2i−2i2i00000000000000000000000000
χ644-4-444-44-4-4-444-4-444-4400000000000000000000000000000000000000000000000000
χ654-4-4-444-444040-40-400000000000000000002i2−2i2−2i22i22i2−2i2−2i22i200000000000000000000000000
χ664-4-4-444-444040-40-40000000000000000000−2i22i22i2−2i2−2i22i22i2−2i200000000000000000000000000
χ674-4-4-444-44-40-404040000000000000004-4-440000000000000000000000000000000000
χ684-4-4-444-44-40-40404000000000000000-444-40000000000000000000000000000000000

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