Finite Group Databasebeta

← Group #307441

Character table — Group #307441

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62
size111111112222222244444444448888888888888888888816161616161616161616161616163232
order12222222444444444444448888224444888888888888884444444488888844
χ111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111-1-1-1-11111-1-1-1-111111-1-11-1-1-1-1-1-1-1-1
χ311111111111111111111111111-1-1-1-11111111111111111-1-1-1-1-111-111-1-1-1-1-1-1
χ411111111111111111111111111-1-1-1-11111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111
χ51111111111111111111111-1-1-1-111-1-111-1-11111-1-1-1-1-1-1-1-1111-1-111-1-1-111-1-11-1
χ61111111111111111111111-1-1-1-111-1-111-1-1-1-1-1-1-1-1-1-11111111-1-1-1-1-111-1-111-11
χ71111111111111111111111-1-1-1-1-1-11111-1-11111-1-1-1-1-1-1-1-1-1-1-111111-1-1-1-111-11
χ81111111111111111111111-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-11111-1-1-111-1-111111-1-11-1
χ91111111111111111-1-1-1-11111111111-1-1111111-1-1-1-111111-1-1-1-1-1-11-1-11111-1-1
χ101111111111111111-1-1-1-11111111111-1-111-1-1-1-1-1-1-1-1-1-1-1-11-1-1-1-111111-1-1-1-111
χ111111111111111111-1-1-1-1111111-1-1-1-1-1-1111111-1-1-1-11111-11111-1-1-1-1-1-1-1-1-111
χ121111111111111111-1-1-1-1111111-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1111111-1111111-1-1
χ131111111111111111-1-1-1-111-1-1-1-111-1-1-1-1-1-111111111-1-1-1-11-1-111-1-1-11111-1-1-11
χ141111111111111111-1-1-1-111-1-1-1-111-1-1-1-1-1-1-1-1-1-1111111111-1-11111-1-1-1-1-1111-1
χ151111111111111111-1-1-1-111-1-1-1-1-1-111-1-1-1-111111111-1-1-1-1-111-1-1-1-1111-1-1111-1
χ161111111111111111-1-1-1-111-1-1-1-1-1-111-1-1-1-1-1-1-1-111111111-111-1-1111-1-111-1-1-11
χ17222222222-222-2-22-20000-2-22222222200-2-2000000000000-2000000-200000000
χ18222222222-222-2-22-20000-2-22222-2-2-2-200-2-20000000000002000000200000000
χ19222222222-222-2-22-20000-2-2-2-2-2-222-2-20022000000000000-2000000200000000
χ20222222222-222-2-22-20000-2-2-2-2-2-2-2-22200220000000000002000000-200000000
χ2122222222-22-2-222-222222-2-200000000-2-20022-2-200000000000002-2000000000
χ2222222222-22-2-222-222222-2-200000000-2-200-2-2220000000000000-22000000000
χ2322222222-22-2-222-22-2-2-2-2-2-200000000220022-2-20000000000000-22000000000
χ2422222222-22-2-222-22-2-2-2-2-2-2000000002200-2-22200000000000002-2000000000
χ252222-2-2-2-2202-200-2000000022-2-22-22-200002−22−2000022−2−200000000002−22−200
χ262222-2-2-2-2202-200-2000000022-2-22-22-20000−22−220000−2−2220000000000−22−2200
χ272222-2-2-2-2202-200-2000000022-2-2-22-2200002−22−2000022−2−20000000000−22−2200
χ282222-2-2-2-2202-200-2000000022-2-2-22-220000−22−220000−2−22200000000002−22−200
χ292222-2-2-2-2202-200-20000000-2-2222-2-2200002−22−20000−2−22200000000002−2−2200
χ302222-2-2-2-2202-200-20000000-2-2222-2-220000−22−22000022−2−20000000000−222−200
χ312222-2-2-2-2202-200-20000000-2-222-222-200002−22−20000−2−2220000000000−222−200
χ322222-2-2-2-2202-200-20000000-2-222-222-20000−22−22000022−2−200000000002−2−2200
χ332-2-222-2-222-2-2-2222-22i2i−2i−2i2-2000000002i−2i00000000002i−2i2i−2i000000002-2000000
χ342-2-222-2-222-2-2-2222-22i2i−2i−2i2-2000000002i−2i0000000000−2i2i−2i2i00000000-22000000
χ352-2-222-2-222-2-2-2222-2−2i−2i2i2i2-200000000−2i2i00000000002i−2i2i−2i00000000-22000000
χ362-2-222-2-222-2-2-2222-2−2i−2i2i2i2-200000000−2i2i0000000000−2i2i−2i2i000000002-2000000
χ372-2-222-2-22-2222-2-2-2200002-22-22-20000002-200000000000002i−2i2i−2i00000000000
χ382-2-222-2-22-2222-2-2-2200002-22-22-20000002-20000000000000−2i2i−2i2i00000000000
χ392-2-222-2-22-2222-2-2-2200002-2-22-22000000-2200000000000002i−2i−2i2i00000000000
χ402-2-222-2-22-2222-2-2-2200002-2-22-22000000-220000000000000−2i2i2i−2i00000000000
χ412-2-222-2-22-2-22222-2-22i2i−2i−2i-222-22-20000−2i2i-2200002i2i−2i−2i00000000000000000000
χ422-2-222-2-22-2-22222-2-22i2i−2i−2i-22-22-220000−2i2i2-20000−2i−2i2i2i00000000000000000000
χ432-2-222-2-22-2-22222-2-2−2i−2i2i2i-222-22-200002i−2i-220000−2i−2i2i2i00000000000000000000
χ442-2-222-2-22-2-22222-2-2−2i−2i2i2i-22-22-2200002i−2i2-200002i2i−2i−2i00000000000000000000
χ4544444444-4-4-4-4-4-4-4-40000440000000000000000000000000000000000000000
χ464444-4-4-4-4-40-44004000000000000000000022−22−2222000000000000000000000000
χ474444-4-4-4-4-40-440040000000000000000000−222222−22000000000000000000000000
χ4844-4-444-4-404004-40-4000000000000000000000022−2222−2200000000000000000000
χ4944-4-444-4-404004-40-40000000000000000000000−2222−222200000000000000000000
χ5044-4-444-4-40-400-44044i−4i4i−4i000000000000000000000000000000000000000000
χ5144-4-444-4-40-400-4404−4i4i−4i4i000000000000000000000000000000000000000000
χ524-44-44-44-40400-440-44-4-44000000000000000000000000000000000000000000
χ534-44-44-44-40400-440-4-444-4000000000000000000000000000000000000000000
χ544-44-44-44-40-4004-40400000000000000000000002i2−2i2−2i22i200000000000000000000
χ554-44-44-44-40-4004-4040000000000000000000000−2i22i22i2−2i200000000000000000000
χ564-4-444-4-4444-4-4-4-4440000-440000000000000000000000000000000000000000
χ574-4-44-444-440-4400-40000000000000000000000000002i2−2i2−2i22i20000000000000000
χ584-4-44-444-440-4400-4000000000000000000000000000−2i22i22i2−2i20000000000000000
χ594-4-44-444-4-404-400400000004-4-44000000000000000000000000000000000000
χ604-4-44-444-4-404-40040000000-444-4000000000000000000000000000000000000
χ6188-8-8-8-888000000000000000000000000000000000000000000000000000000
χ628-88-8-88-88000000000000000000000000000000000000000000000000000000

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