Finite Group Databasebeta

← Group #291681

Character table — Group #291681

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65
size11111111222222224444444488888888888888888888888888888161616161616161616163232
order12222222444444442244444444444444444448888888888888888244444888844
χ111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1
χ3111111111111111111111111111-1-1-1-1-1-111-1-111111111111111111-11-1-1-1-1-1-1-1-1-1
χ4111111111111111111111111111-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11-11-1-1-1111111
χ51111111111111111111111111-1-111-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-1-11-11-1-1-1-1-1-111
χ61111111111111111111111111-1-111-1-1-1-1-1-111-1-1-1-1-1-1-1-111111111-11-11-1-11111-1-1
χ71111111111111111111111111-1-1-1-11111-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1
χ81111111111111111111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-111-1-1-1-111
χ91111111111111111-1-1-1-1-1-111-11111-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1-1-1-1-1111111-1-11-1
χ101111111111111111-1-1-1-1-1-111-11111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-11111-1-11111-1-111-11
χ111111111111111111-1-1-1-1-1-111-111-1-11111-1-1111111-1-1-1-11111-1-1-1-1-111-1-1-1-1-111-11
χ121111111111111111-1-1-1-1-1-111-111-1-11111-1-111-1-1-1-11111-1-1-1-11111-111-1-1-111-1-11-1
χ131111111111111111-1-1-1-1-1-111-1-1-111111111-1-11111-1-1-1-1-1-1-1-111111-1-11-1-1-1-1111-1
χ141111111111111111-1-1-1-1-1-111-1-1-111111111-1-1-1-1-1-111111111-1-1-1-11-1-11-1-111-1-1-11
χ151111111111111111-1-1-1-1-1-111-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1111111-1-11111-1-1-11
χ161111111111111111-1-1-1-1-1-111-1-1-1-1-1-1-1-1-11111-1-1-1-111111111-1-1-1-111-1-111-1-1111-1
χ172222222222-2-2-222-222-2-2-2-2-2-2222000000-2-200000000000000000020-2000000000
χ182222222222-2-2-222-222-2-2-2-2-2-22-2-200000022000000000000000000-202000000000
χ192222222222-2-2-222-2-2-22222-2-2-22200000022000000000000000000-20-2000000000
χ202222222222-2-2-222-2-2-22222-2-2-2-2-2000000-2-2000000000000000000202000000000
χ2122222222-2-2222-2-2222-2-222-2-2-20022000000-2-20000000000000000020-200000000
χ2222222222-2-2222-2-2222-2-222-2-2-200-2-20000002200000000000000000-20200000000
χ2322222222-2-2222-2-22-2-222-2-2-2-2200220000002200000000000000000-20-200000000
χ2422222222-2-2222-2-22-2-222-2-2-2-2200-2-2000000-2-20000000000000000020200000000
χ2522222222-2-2-2-2-2-2-2-22222-2-222-2000022-2-20000000000000000000000002-2000000
χ2622222222-2-2-2-2-2-2-2-22222-2-222-20000-2-222000000000000000000000000-22000000
χ2722222222-2-2-2-2-2-2-2-2-2-2-2-222222000022-2-2000000000000000000000000-22000000
χ2822222222-2-2-2-2-2-2-2-2-2-2-2-2222220000-2-2220000000000000000000000002-2000000
χ292-222-2-22-2222-2-2-2-220000002-2000002i−2i2i−2i0000000022-2-2000000000000002i−2i0000
χ302-222-2-22-2222-2-2-2-220000002-2000002i−2i2i−2i00000000-2-22200000000000000−2i2i0000
χ312-222-2-22-2222-2-2-2-220000002-200000−2i2i−2i2i0000000022-2-200000000000000−2i2i0000
χ322-222-2-22-2222-2-2-2-220000002-200000−2i2i−2i2i00000000-2-222000000000000002i−2i0000
χ332-222-2-22-2-2-2-22222-20000002-2000002i−2i−2i2i00002i2i−2i−2i000000000000000000002-200
χ342-222-2-22-2-2-2-22222-20000002-2000002i−2i−2i2i0000−2i−2i2i2i00000000000000000000-2200
χ352-222-2-22-2-2-2-22222-20000002-200000−2i2i2i−2i00002i2i−2i−2i00000000000000000000-2200
χ362-222-2-22-2-2-2-22222-20000002-200000−2i2i2i−2i0000−2i−2i2i2i000000000000000000002-200
χ372-22-22-2-222-20002-20002i−2i2i−2i0002-20000002i−2i00i2−i2i2−i22−22−2i2i2−i2−i222−2−2000000000000
χ382-22-22-2-222-20002-20002i−2i2i−2i0002-20000002i−2i00−i2i2−i2i2−22−22−i2−i2i2i2−2−222000000000000
χ392-22-22-2-222-20002-20002i−2i2i−2i000-22000000−2i2i00i2−i2i2−i22−22−2−i2−i2i2i2−2−222000000000000
χ402-22-22-2-222-20002-20002i−2i2i−2i000-22000000−2i2i00−i2i2−i2i2−22−22i2i2−i2−i222−2−2000000000000
χ412-22-22-2-222-20002-2000−2i2i−2i2i0002-2000000−2i2i00i2−i2i2−i2−22−22i2i2−i2−i2−2−222000000000000
χ422-22-22-2-222-20002-2000−2i2i−2i2i0002-2000000−2i2i00−i2i2−i2i22−22−2−i2−i2i2i222−2−2000000000000
χ432-22-22-2-222-20002-2000−2i2i−2i2i000-220000002i−2i00i2−i2i2−i2−22−22−i2−i2i2i222−2−2000000000000
χ442-22-22-2-222-20002-2000−2i2i−2i2i000-220000002i−2i00−i2i2−i2i22−22−2i2i2−i2−i2−2−222000000000000
χ45444-4-44-4-44-4000-440000000000000000000000000022−22−222200000000000000000000
χ46444-4-44-4-44-4000-4400000000000000000000000000−222222−2200000000000000000000
χ47444-4-44-4-4-440004-4000000000000000000000022−22−2222000000000000000000000000
χ48444-4-44-4-4-440004-40000000000000000000000−222222−22000000000000000000000000
χ4944-444-4-4-4000000004-40000000000000000000000000002-22-22-22-2000000000000
χ5044-444-4-4-4000000004-4000000000000000000000000000-22-22-22-22000000000000
χ5144-444-4-4-400000000-440000000000000000000000000002-22-2-22-22000000000000
χ5244-444-4-4-400000000-44000000000000000000000000000-22-222-22-2000000000000
χ5344-4-4-4-4440044-400-4000000000004i−4i000000000000000000000000000000000000
χ5444-4-4-4-4440044-400-400000000000−4i4i000000000000000000000000000000000000
χ5544-4-4-4-44400-4-4400400000000000000000004-40000000000000000000000000000
χ5644-4-4-4-44400-4-440040000000000000000000-440000000000000000000000000000
χ574-444-4-44-444-444-4-4-4000000-4400000000000000000000000000000000000000000
χ584-444-4-44-4-4-44-4-4444000000-4400000000000000000000000000000000000000000
χ594-44-44-4-44-44000-440004i−4i−4i4i0000000000000000000000000000000000000000000
χ604-44-44-4-44-44000-44000−4i4i4i−4i0000000000000000000000000000000000000000000
χ614-4-4-4444-4004-4400-4000000000000000000000000000002i2−2i2−2i22i20000000000000000
χ624-4-4-4444-4004-4400-400000000000000000000000000000−2i22i22i2−2i20000000000000000
χ634-4-4-4444-400-44-400400000000000000000000000000000000022−22−2222000000000000
χ644-4-4-4444-400-44-4004000000000000000000000000000000000−222222−22000000000000
χ658-8-88-88-88000000000000000000000000000000000000000000000000000000000

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