Finite Group Databasebeta

← Group #305720

Character table — Group #305720

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65
size11111111222222224444444444888888888888888888888888161616161616161616161616161632
order12222222444444444444448888444444444488888888888888224444448888884
χ111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111-1-111-1-1111111-1-1-1-1-1-1111-1-1-111-1-1-1-1-1-1-1
χ31111111111111111111111111111-1-1-1-111-1-111111111111111-1-1-11-1-1-1-111-1-1-1-1-1
χ41111111111111111111111111111-1-1-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1-1-111-1-1-1-111111
χ51111111111111111111111-1-1-1-11111-1-1111111-1-1-1-1-1-111-1-1-1-111-1111-1-1-1-111-1-1-1
χ61111111111111111111111-1-1-1-11111-1-1-1-111-1-1-1-1-1-1-1-1-1-1111111-1-1-1-1-1-111-1-1111
χ71111111111111111111111-1-1-1-111-1-11111-1-111-1-1-1-1-1-111-1-1-1-1-1-111-1-111-1-1-1-1111
χ81111111111111111111111-1-1-1-111-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-11-111111111-1-1-1
χ911111111111111111-1-1-1-111111-1-111111111-1-111-1-1-1-1-1-1-1-1-1-1-1-11111-1-111-1-1-1-11
χ1011111111111111111-1-1-1-111111-1-11111-1-1111111-1-1-1-1111111-1-11-1-1-1-1-1-1-11111-1
χ1111111111111111111-1-1-1-111111-1-1-1-1-1-111-1-1-1-111-1-1-1-1-1-1-1-1-1-111-11-1-111111111-1
χ1211111111111111111-1-1-1-111111-1-1-1-1-1-1-1-1-1-11111-1-1-1-111111111-1-11111-1-1-1-1-1-11
χ1311111111111111111-1-1-1-11-1-1-1-1-1-111-1-11111-1-1-1-11111-1-11111-1-1-111111-1-1-1-111-1
χ1411111111111111111-1-1-1-11-1-1-1-1-1-111-1-1-1-11111-1-1111111-1-1-1-1-1-1-1-1-1-1111111-1-11
χ1511111111111111111-1-1-1-11-1-1-1-1-1-1-1-11111-1-1-1-1-1-11111-1-111111111-1-1-1-1-1-111-1-11
χ1611111111111111111-1-1-1-11-1-1-1-1-1-1-1-111-1-1-1-111-1-1111111-1-1-1-1111-111-1-111-1-111-1
χ172222222222-2-22-2-22-22222-20000-2-20000220022000000-2-20000000-200000000000
χ182222222222-2-22-2-22-22222-20000-2-20000-2-200-2-2000000220000000200000000000
χ192222222222-2-22-2-22-2-2-2-2-2-200002200002200-2-2000000220000000-200000000000
χ202222222222-2-22-2-22-2-2-2-2-2-20000220000-2-20022000000-2-20000000200000000000
χ2122222222-2-222-222-2-20000-222220022-2-200-2-200-2-20000000000002000000000000
χ2222222222-2-222-222-2-20000-2222200-2-222002200-2-2000000000000-2000000000000
χ2322222222-2-222-222-2-20000-2-2-2-2-200222200-2-20022000000000000-2000000000000
χ2422222222-2-222-222-2-20000-2-2-2-2-200-2-2-2-2002200220000000000002000000000000
χ252-222-22-2-22222-2-2-2-2222-2-2-200002-22-200002-2000000000000002-20000000000000
χ262-222-22-2-22222-2-2-2-2222-2-2-200002-2-220000-2200000000000000-220000000000000
χ272-222-22-2-22222-2-2-2-22-2-222-20000-222-200002-200000000000000-220000000000000
χ282-222-22-2-22222-2-2-2-22-2-222-20000-22-220000-22000000000000002-20000000000000
χ292-222-22-2-222-2-2-222-2-222-2-220000-22000000000000000000000000002i−2i00002i−2i000
χ302-222-22-2-222-2-2-222-2-222-2-220000-2200000000000000000000000000−2i2i0000−2i2i000
χ312-222-22-2-222-2-2-222-2-2-2-222200002-2000000000000000000000000002i−2i0000−2i2i000
χ322-222-22-2-222-2-2-222-2-2-2-222200002-200000000000000000000000000−2i2i00002i−2i000
χ332-222-22-2-2-2-2222-2-22-2000020000002-20000-2200002i2i−2i−2i0000000000002i−2i0000000
χ342-222-22-2-2-2-2222-2-22-2000020000002-20000-220000−2i−2i2i2i000000000000−2i2i0000000
χ352-222-22-2-2-2-2222-2-22-200002000000-2200002-200002i2i−2i−2i000000000000−2i2i0000000
χ362-222-22-2-2-2-2222-2-22-200002000000-2200002-20000−2i−2i2i2i0000000000002i−2i0000000
χ372-22-2-2-2222-200200-202i−2i2i−2i022−2−20000002i−2i002-22−2i2−i2i2−i20022−2−200000000i2−i200000
χ382-22-2-2-2222-200200-202i−2i2i−2i022−2−2000000−2i2i00-222−2i2−i2i2−i200−2−22200000000−i2i200000
χ392-22-2-2-2222-200200-202i−2i2i−2i0−2−2220000002i−2i002-2−22−i2i2−i2i200−2−22200000000−i2i200000
χ402-22-2-2-2222-200200-202i−2i2i−2i0−2−222000000−2i2i00-22−22−i2i2−i2i20022−2−200000000i2−i200000
χ412-22-2-2-2222-200200-20−2i2i−2i2i022−2−20000002i−2i00-222−2−i2i2−i2i200−2−22200000000i2−i200000
χ422-22-2-2-2222-200200-20−2i2i−2i2i022−2−2000000−2i2i002-22−2−i2i2−i2i20022−2−200000000−i2i200000
χ432-22-2-2-2222-200200-20−2i2i−2i2i0−2−2220000002i−2i00-22−22i2−i2i2−i20022−2−200000000−i2i200000
χ442-22-2-2-2222-200200-20−2i2i−2i2i0−2−222000000−2i2i002-2−22i2−i2i2−i200−2−22200000000i2−i200000
χ4544444444-4-4-4-4-4-4-4-44000040000000000000000000000000000000000000000000
χ46444-44-4-4-44-400-400404i−4i−4i4i00000000000000000000000000000000000000000000
χ47444-44-4-4-44-400-40040−4i4i4i−4i00000000000000000000000000000000000000000000
χ48444-44-4-4-4-4400400-400000000000000000000000022−22−2222000000000000000000000
χ49444-44-4-4-4-4400400-4000000000000000000000000−222222−22000000000000000000000
χ5044-44-4-4-44004-404-40000000000000004i−4i000000000000000000000000000000000
χ5144-44-4-4-44004-404-4000000000000000−4i4i000000000000000000000000000000000
χ5244-44-4-4-4400-440-44000000000000000000000000000000000000000000000002i2−2i20
χ5344-44-4-4-4400-440-4400000000000000000000000000000000000000000000000−2i22i20
χ5444-4-4-444-4000000000000002i2−2i22i2−2i200000000000000000022−222i−2i2i−2i000000000000000
χ5544-4-4-444-4000000000000002i2−2i22i2−2i2000000000000000000−2222−2i2i−2i2i000000000000000
χ5644-4-4-444-400000000000000−2i22i2−2i22i200000000000000000022−22−2i2i−2i2i000000000000000
χ5744-4-4-444-400000000000000−2i22i2−2i22i2000000000000000000−22222i−2i2i−2i000000000000000
χ584-444-44-4-4-4-4-4-4444440000-40000000000000000000000000000000000000000000
χ594-44-4-4-444-4400-40040000002222−22−22000000000000−22220000000000000000000000000
χ604-44-4-4-444-4400-4004000000−22−22222200000000000022−220000000000000000000000000
χ614-4-444-44-4004-40-4400000004i−4i−4i4i000000000000000000000000000000000000000
χ624-4-444-44-4004-40-440000000−4i4i4i−4i000000000000000000000000000000000000000
χ634-4-444-44-400-4404-400000000000000000000000000000002i2−2i2−2i22i2000000000000000
χ644-4-444-44-400-4404-40000000000000000000000000000000−2i22i22i2−2i2000000000000000
χ658-8-8-888-88000000000000000000000000000000000000000000000000000000000

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