Finite Group Databasebeta

← Group #258718

Character table — Group #258718

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65
size111111112222222244444444888888888888888888888888816161616161616161616161616161616
order12222222444444444444444444444444488888888888888882244444444448888
χ111111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111-1-111-1-1-1-1-1-1
χ3111111111111111111111111111-1-111-1-111111111-1-1-1-1-1-1-1-11-1-11-1-111-1-111-1-1-1-1
χ4111111111111111111111111111-1-111-1-1-1-1-1-1-1-1-1-1111111111-1-11-1-1-1-1-1-1-1-11111
χ5111111111111111111111111-1-1111-1-1111111111111111111-111-1-1-1-1-1-1-1-1-1-1-1-1-1
χ6111111111111111111111111-1-1111-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-111-1-1111111
χ7111111111111111111111111-1-11-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-111-1-111-1-11111
χ8111111111111111111111111-1-11-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-111111111-1-1-1-1
χ911111111111111111-1-1-1-1-1-1111-11111-1-11111-1-1-1-11111-1-1-1-1-1-11-1-1-11111-1-111-1-1
χ1011111111111111111-1-1-1-1-1-1111-11111-1-1-1-1-1-11111-1-1-1-11111-1-11-1-1-1-1-11111-1-111
χ1111111111111111111-1-1-1-1-1-1111-1-1-111111111-1-1-1-1-1-1-1-11111-11-1-11111-1-1-1-1-1-111
χ1211111111111111111-1-1-1-1-1-1111-1-1-11111-1-1-1-111111111-1-1-1-1-11-1-111-1-1-1-11111-1-1
χ1311111111111111111-1-1-1-1-1-11-1-1-111-1-1-1-11111-1-1-1-11111-1-1-1-11-11111-1-1-1-111-1-111
χ1411111111111111111-1-1-1-1-1-11-1-1-111-1-1-1-1-1-1-1-11111-1-1-1-111111-1111111-1-1-1-111-1-1
χ1511111111111111111-1-1-1-1-1-11-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1111111-11-1-1-1-1111111-1-1
χ1611111111111111111-1-1-1-1-1-11-1-1-1-1-1-1-111-1-1-1-111111111-1-1-1-111-11-1-11111-1-1-1-111
χ172222222222-2-222-2-2-222-2-222-200-222002200000000000000000-2-20000000000000
χ182222222222-2-222-2-2-222-2-222-200-2-2-200-2-200000000000000000220000000000000
χ192222222222-2-222-2-2-2-2-222-2-2-20022200-2-2000000000000000002-20000000000000
χ202222222222-2-222-2-2-2-2-222-2-2-2002-2-2002200000000000000000-220000000000000
χ2122222222-2-222-2-222-222-2-2-2-2-222200-2-2000000000000000000-2002000000000000
χ2222222222-2-222-2-222-222-2-2-2-2-2-2-220022000000000000000000200-2000000000000
χ2322222222-2-222-2-222-2-2-22222-222-200-2-2000000000000000000200-2000000000000
χ2422222222-2-222-2-222-2-2-22222-2-2-2-20022000000000000000000-2002000000000000
χ2522222222-2-2-2-2-2-2-2-222222-2-2200-2000000000000000000000000002-2002-2000000
χ2622222222-2-2-2-2-2-2-2-222222-2-2200-200000000000000000000000000-2200-22000000
χ2722222222-2-2-2-2-2-2-2-22-2-2-2-2222002000000000000000000000000002-200-22000000
χ2822222222-2-2-2-2-2-2-2-22-2-2-2-222200200000000000000000000000000-22002-2000000
χ2922-22-2-22-2222-2-2-22-2-200000022i−2i0002i−2i0022-2-20000000000000000002i−2i00000000
χ3022-22-2-22-2222-2-2-22-2-200000022i−2i0002i−2i00-2-222000000000000000000−2i2i00000000
χ3122-22-2-22-2222-2-2-22-2-20000002−2i2i000−2i2i0022-2-2000000000000000000−2i2i00000000
χ3222-22-2-22-2222-2-2-22-2-20000002−2i2i000−2i2i00-2-2220000000000000000002i−2i00000000
χ3322-22-2-22-2-2-22-2222-22000000-22i−2i000−2i2i0000002i2i−2i−2i0000000000000000002-20000
χ3422-22-2-22-2-2-22-2222-22000000-22i−2i000−2i2i000000−2i−2i2i2i000000000000000000-220000
χ3522-22-2-22-2-2-22-2222-22000000-2−2i2i0002i−2i0000002i2i−2i−2i000000000000000000-220000
χ3622-22-2-22-2-2-22-2222-22000000-2−2i2i0002i−2i000000−2i−2i2i2i0000000000000000002-20000
χ372-2-2222-2-22-2002-20002i−2i002i−2i00002-2002i−2ii2−i2i2−i22−22−2i2i2−i2−i222−2−20000000000000000
χ382-2-2222-2-22-2002-20002i−2i002i−2i00002-2002i−2i−i2i2−i2i2−22−22−i2−i2i2i2−2−2220000000000000000
χ392-2-2222-2-22-2002-20002i−2i002i−2i0000-2200−2i2ii2−i2i2−i22−22−2−i2−i2i2i2−2−2220000000000000000
χ402-2-2222-2-22-2002-20002i−2i002i−2i0000-2200−2i2i−i2i2−i2i2−22−22i2i2−i2−i222−2−20000000000000000
χ412-2-2222-2-22-2002-2000−2i2i00−2i2i00002-200−2i2ii2−i2i2−i2−22−22i2i2−i2−i2−2−2220000000000000000
χ422-2-2222-2-22-2002-2000−2i2i00−2i2i00002-200−2i2i−i2i2−i2i22−22−2−i2−i2i2i222−2−20000000000000000
χ432-2-2222-2-22-2002-2000−2i2i00−2i2i0000-22002i−2ii2−i2i2−i2−22−22−i2−i2i2i222−2−20000000000000000
χ442-2-2222-2-22-2002-2000−2i2i00−2i2i0000-22002i−2i−i2i2−i2i22−22−2i2i2−i2−i2−2−2220000000000000000
χ4544-44-4-44-444-44-4-4-444000000-400000000000000000000000000000000000000000
χ4644-44-4-44-4-4-4-4444-44-4000000400000000000000000000000000000000000000000
χ4744-4-44-4-44000000000004i−4i000000000000000000002-22-22i−2i2i−2i0000000000000000
χ4844-4-44-4-44000000000004i−4i00000000000000000000-22-22−2i2i−2i2i0000000000000000
χ4944-4-44-4-4400000000000−4i4i000000000000000000002-22-2−2i2i−2i2i0000000000000000
χ5044-4-44-4-4400000000000−4i4i00000000000000000000-22-222i−2i2i−2i0000000000000000
χ514-444-4-4-444-400-4400000000000000000002i2−2i2−2i22i20000000000000000000000000000
χ524-444-4-4-444-400-440000000000000000000−2i22i22i2−2i20000000000000000000000000000
χ534-444-4-4-44-44004-4000000000000000000000002i2−2i2−2i22i2000000000000000000000000
χ544-444-4-4-44-44004-400000000000000000000000−2i22i22i2−2i2000000000000000000000000
χ554-44-44-44-4004-400-44000000000000000000000000000002i2−2i2−2i22i20000000000000000
χ564-44-44-44-4004-400-4400000000000000000000000000000−2i22i22i2−2i20000000000000000
χ574-44-44-44-400-44004-400000000000000000000000002i2−2i2−2i22i200000000000000000000
χ584-44-44-44-400-44004-40000000000000000000000000−2i22i22i2−2i200000000000000000000
χ594-4-4444-4-4-4400-440004i−4i00−4i4i000000000000000000000000000000000000000000
χ604-4-4444-4-4-4400-44000−4i4i004i−4i000000000000000000000000000000000000000000
χ614-4-4-4-4444004400-4-4000000000000000000000000000000000000000000000002i2−2i2
χ624-4-4-4-4444004400-4-400000000000000000000000000000000000000000000000−2i22i2
χ634-4-4-4-444400-4-4004400000000000000000000000000000000000000000000022−2200
χ644-4-4-4-444400-4-40044000000000000000000000000000000000000000000000−222200
χ65888-8-88-8-8000000000000000000000000000000000000000000000000000000000

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