Finite Group Databasebeta

← Group #337667

Character table — Group #337667

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65
size1111111122222222444444444488888888888888888888888888881616161616161616323232
order12222222444444444488888888222244444444888888888888888844448888224
χ111111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111-1-1-1-111-1-111-1-1-1-11111111111-11-1-111-1-1-1-1-1
χ311111111111111111111111111-1-1-1-11111-1-11111111111-1-1-1-111111-1-1-1-1-111-1-1-1
χ411111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-111-1-1-1-11111-1-111-1-1-1-1111
χ51111111111111111111111-1-1-1-11111111111-1-1-1-1111111-1-1-1-1-1-1-1-1-11-1-1-1-1-1-111-1
χ61111111111111111111111-1-1-1-11111-1-1-1-11111-1-1-1-1-1-111-1-1-1-1-1-1-1-11111-1-111-1-11
χ71111111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-11111111111-1-1-1-1-1-11111-1-1-1-11
χ81111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-1111111-1-1-1-11-1-1-1111111-1
χ9111111111111111111-1-1-1-1111111-1-11111111111-1-1-1-1-1-11111-1-1-1-11-1-1-1-1-1-1-11-11
χ10111111111111111111-1-1-1-1111111-1-1-1-1-1-111-1-1111111-1-11111-1-1-1-1-1-111-1-111-11-1
χ11111111111111111111-1-1-1-11111-1-1111111-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-11-1
χ12111111111111111111-1-1-1-11111-1-111-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-11-1-111111-11
χ13111111111111111111-1-1-1-1-1-1-1-111-1-1111111-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-11111111-1-1
χ14111111111111111111-1-1-1-1-1-1-1-111-1-1-1-1-1-11111-1-11111-1-1-1-1-1-111111-1-1-111-1-1-111
χ15111111111111111111-1-1-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-111111111-11-1-1-1-111-111
χ16111111111111111111-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-111-1-11111-1-1111111111111-1-1-1-11-1-1
χ17222222222-22-22-22-2-2-22222000022220000-2-200000000-2-2000000000-2000000000
χ18222222222-22-22-22-2-2-222220000-2-2-2-200002200000000-2-20000000002000000000
χ19222222222-22-22-22-2-2-2-2-2-2-2000022-2-20000-2-200000000220000000002000000000
χ20222222222-22-22-22-2-2-2-2-2-2-20000-2-2220000220000000022000000000-2000000000
χ2122222222-22-22-22-22-2-200002222000022-2-20022-2-200000000000000-20000000000
χ2222222222-22-22-22-22-2-2000022220000-2-22200-2-2-2-20000000000000020000000000
χ2322222222-22-22-22-22-2-20000-2-2-2-2000022-2-200-2-2220000000000000020000000000
χ2422222222-22-22-22-22-2-20000-2-2-2-20000-2-22200222200000000000000-20000000000
χ252222-2-2-2-2-202020-200022-2-2i2i2−i2−i22-22-200000000i2−i2000000i2i2−i2−i2i2i2−i2−i20000i2−i200000
χ262222-2-2-2-2-202020-200022-2-2i2i2−i2−i2-22-2200000000i2−i2000000−i2−i2i2i2i2i2−i2−i20000−i2i200000
χ272222-2-2-2-2-202020-200022-2-2−i2−i2i2i22-22-200000000−i2i2000000−i2−i2i2i2−i2−i2i2i20000−i2i200000
χ282222-2-2-2-2-202020-200022-2-2−i2−i2i2i2-22-2200000000−i2i2000000i2i2−i2−i2−i2−i2i2i20000i2−i200000
χ292222-2-2-2-2-202020-2000-2-222i2i2−i2−i22-2-2200000000i2−i2000000i2i2−i2−i2−i2−i2i2i20000−i2i200000
χ302222-2-2-2-2-202020-2000-2-222i2i2−i2−i2-222-200000000i2−i2000000−i2−i2i2i2−i2−i2i2i20000i2−i200000
χ312222-2-2-2-2-202020-2000-2-222−i2−i2i2i22-2-2200000000−i2i2000000−i2−i2i2i2i2i2−i2−i20000i2−i200000
χ322222-2-2-2-2-202020-2000-2-222−i2−i2i2i2-222-200000000−i2i2000000i2i2−i2−i2i2i2−i2−i20000−i2i200000
χ3322-2-2-222-222-2-222-2-22-2000000000000000000000022-2-2002i−2i2i−2i0000002i−2i0000000
χ3422-2-2-222-222-2-222-2-22-2000000000000000000000022-2-200−2i2i−2i2i000000−2i2i0000000
χ3522-2-2-222-222-2-222-2-22-20000000000000000000000-2-222002i−2i2i−2i000000−2i2i0000000
χ3622-2-2-222-222-2-222-2-22-20000000000000000000000-2-22200−2i2i−2i2i0000002i−2i0000000
χ372-22-222-2-202020-20-2002−22−22i−2i2i−2i00002-200002i−2i002−22−22−20000i2−i2i2−i2000000i2−i2000
χ382-22-222-2-202020-20-2002−22−22i−2i2i−2i0000-220000−2i2i00−22−222−20000i2−i2i2−i2000000−i2i2000
χ392-22-222-2-202020-20-2002−22−2−2i2i−2i2i00002-20000−2i2i002−22−22−20000−i2i2−i2i2000000−i2i2000
χ402-22-222-2-202020-20-2002−22−2−2i2i−2i2i0000-2200002i−2i00−22−222−20000−i2i2−i2i2000000i2−i2000
χ412-22-222-2-202020-20-200−22−222i−2i2i−2i00002-200002i−2i00−22−22−220000−i2i2−i2i2000000−i2i2000
χ422-22-222-2-202020-20-200−22−222i−2i2i−2i0000-220000−2i2i002−22−2−220000−i2i2−i2i2000000i2−i2000
χ432-22-222-2-202020-20-200−22−22−2i2i−2i2i00002-20000−2i2i00−22−22−220000i2−i2i2−i2000000i2−i2000
χ442-22-222-2-202020-20-200−22−22−2i2i−2i2i0000-2200002i−2i002−22−2−220000i2−i2i2−i2000000−i2i2000
χ4544444444-4-4-4-4-4-4-4-44400000000000000000000000000000000000000000000000
χ464444-4-4-4-440-40-40400000002i22i2−2i2−2i2000000000000−2i22i20000000000000000000000000
χ474444-4-4-4-440-40-4040000000−2i2−2i22i22i20000000000002i2−2i20000000000000000000000000
χ4844-4-44-4-444040-40-400000000000000000004i−4i00000000000000000000000000000
χ4944-4-44-4-444040-40-40000000000000000000−4i4i00000000000000000000000000000
χ5044-4-44-4-44-40-40404000000000000000000000000000000022−22−2222000000000000000
χ5144-4-44-4-44-40-404040000000000000000000000000000000−222222−22000000000000000
χ5244-4-4-444-44-4-444-4-44-4400000000000000000000000000000000000000000000000
χ5344-4-4-444-4-444-4-444-4-4400000000000000000000000000000000000000000000000
χ5444-4-4-444-4-4-444-4-4444-400000000000000000000000000000000000000000000000
χ554-44-444-4-40-40-404040022−2222−220000000000000000000000−22220000000000000000000
χ564-44-444-4-40-40-4040400−2222−2222000000000000000000000022−220000000000000000000
χ574-44-4-4-444000000000022−22−222222−22−22220000000000000000000000002-2-2200000000000
χ584-44-4-4-444000000000022−22−2222−222222−22000000000000000000000000-222-200000000000
χ594-44-4-4-4440000000000−222222−2222−22−2222000000000000000000000000-222-200000000000
χ604-44-4-4-4440000000000−222222−22−222222−220000000000000000000000002-2-2200000000000
χ614-4-44-44-44040-40-40400000000000000000000000022−22−2222000000000000000000000
χ624-4-44-44-44040-40-404000000000000000000000000−222222−22000000000000000000000
χ634-4-44-44-440-404040-400000000000000004-40000000000000000000000000000000
χ644-4-44-44-440-404040-40000000000000000-440000000000000000000000000000000
χ658-8-888-88-8000000000000000000000000000000000000000000000000000000000

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