Finite Group Databasebeta

← Group #308508

Character table — Group #308508

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65
size11111111222222224444444444888888888888888888888888161616161616161616161616161632
order12222222444444444444448888444444444488888888888888224444448888884
χ111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111-1-1-1-1111111-1-1-1-1-1-1-1-111111-1-1-1-1-1-1-1-1
χ31111111111111111111111111111-1-1-1-1-1-11111111111111111-1-1-1-1-1-1-11-1-111-1-1-1
χ41111111111111111111111111111-1-1-1-1-1-1-1-1-1-1111111-1-1-1-1-1-111-1-1-1-1-1-111-1-1111
χ51111111111111111111111-1-1-1-11111-1-1111111-1-1-1-1-1-111-1-1-1-11111-1-1-1111-1-1-1-1-1
χ61111111111111111111111-1-1-1-11111-1-111-1-1-1-1-1-1-1-1-1-1-1-11111-1-111-1-1-1-1-1-111111
χ71111111111111111111111-1-1-1-111-1-111-1-11111-1-1-1-1-1-111-1-1-1-1-1-1-1-11111-1-1-1-1111
χ81111111111111111111111-1-1-1-111-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1111-11111-1-1-1
χ911111111111111111-1-1-1-111111-1-111111111-1-111-1-1-1-1-1-1-1-1-1-111-1-11-1-11-1-111-1-11
χ1011111111111111111-1-1-1-111111-1-1111111-1-11111-1-1-1-1111111-1-1-1-11-1-1-111-1-111-1
χ1111111111111111111-1-1-1-111111-1-1-1-1-1-1-1-111-1-111-1-1-1-1-1-1-1-1-1-1-1-111-1111111111-1
χ1211111111111111111-1-1-1-111111-1-1-1-1-1-1-1-1-1-11111-1-1-1-11111111111-111-1-1-1-1-1-1-11
χ1311111111111111111-1-1-1-11-1-1-1-1-1-111-1-11111-1-1-1-11111-1-1111111-1-1-1111-1-1-1-111-1
χ1411111111111111111-1-1-1-11-1-1-1-1-1-111-1-111-1-111-1-1111111-1-1-1-1-1-1-1-1-111-11111-1-11
χ1511111111111111111-1-1-1-11-1-1-1-1-1-1-1-111-1-111-1-1-1-11111-1-11111-1-1111-1-1111-1-1-1-11
χ1611111111111111111-1-1-1-11-1-1-1-1-1-1-1-111-1-1-1-111-1-1111111-1-1-1-111111-1-1-1-1-11111-1
χ172222222222-2-2-222-2-20000-22222002222-2-20000-2-200000000000000-20000000000
χ182222222222-2-2-222-2-20000-2222200-2-2-2-2220000-2-20000000000000020000000000
χ192222222222-2-2-222-2-20000-2-2-2-2-20022-2-2-2-20000220000000000000020000000000
χ202222222222-2-2-222-2-20000-2-2-2-2-200-2-2222200002200000000000000-20000000000
χ2122222222-2-2222-2-22-22222-20000-2-200000022-2-20000002200000000000-20000000
χ2222222222-2-2222-2-22-22222-20000-2-2000000-2-222000000-2-20000000000020000000
χ2322222222-2-2222-2-22-2-2-2-2-2-20000220000002222000000-2-200000000000-20000000
χ2422222222-2-2222-2-22-2-2-2-2-2-2000022000000-2-2-2-2000000220000000000020000000
χ252-2222-2-2-2222-22-2-2-2222-2-2-200002-200000000000000000000002-20000002-200000
χ262-2222-2-2-2222-22-2-2-2222-2-2-200002-20000000000000000000000-22000000-2200000
χ272-2222-2-2-2222-22-2-2-22-2-222-20000-2200000000000000000000002-2000000-2200000
χ282-2222-2-2-2222-22-2-2-22-2-222-20000-220000000000000000000000-220000002-200000
χ292-2222-2-2-2-2-22-2222-2-222-2-220000-222i−2i002i−2i0000000000000000002i−2i00000000000
χ302-2222-2-2-2-2-22-2222-2-222-2-220000-22−2i2i00−2i2i000000000000000000−2i2i00000000000
χ312-2222-2-2-2-2-22-2222-2-2-2-222200002-22i−2i002i−2i000000000000000000−2i2i00000000000
χ322-2222-2-2-2-2-22-2222-2-2-2-222200002-2−2i2i00−2i2i0000000000000000002i−2i00000000000
χ332-2222-2-2-2-2-2-22-222220000-20000002i−2i00−2i2i00000022-2-2000000000002i−2i00000000
χ342-2222-2-2-2-2-2-22-222220000-20000002i−2i00−2i2i000000-2-22200000000000−2i2i00000000
χ352-2222-2-2-2-2-2-22-222220000-2000000−2i2i002i−2i00000022-2-200000000000−2i2i00000000
χ362-2222-2-2-2-2-2-22-222220000-2000000−2i2i002i−2i000000-2-222000000000002i−2i00000000
χ372-2-22-222-20022-200-202i−2i2i−2i022−2−2000000002-2002−2i2−i2i2−i22i−2ii2i2−i2−i200000000002−2000
χ382-2-22-222-20022-200-202i−2i2i−2i022−2−200000000-22002−2i2−i2i2−i2−2i2i−i2−i2i2i20000000000−22000
χ392-2-22-222-20022-200-202i−2i2i−2i0−2−222000000002-200−22−i2i2−i2i22i−2i−i2−i2i2i20000000000−22000
χ402-2-22-222-20022-200-202i−2i2i−2i0−2−22200000000-2200−22−i2i2−i2i2−2i2ii2i2−i2−i200000000002−2000
χ412-2-22-222-20022-200-20−2i2i−2i2i022−2−2000000002-2002−2−i2i2−i2i2−2i2i−i2−i2i2i200000000002−2000
χ422-2-22-222-20022-200-20−2i2i−2i2i022−2−200000000-22002−2−i2i2−i2i22i−2ii2i2−i2−i20000000000−22000
χ432-2-22-222-20022-200-20−2i2i−2i2i0−2−222000000002-200−22i2−i2i2−i2−2i2ii2i2−i2−i20000000000−22000
χ442-2-22-222-20022-200-20−2i2i−2i2i0−2−22200000000-2200−22i2−i2i2−i22i−2i−i2−i2i2i200000000002−2000
χ4544444444-4-4-4-4-4-4-4-44000040000000000000000000000000000000000000000000
χ46444-4-44-4-44-40004-40000000000000004-4000000000000000000000000000000000
χ47444-4-44-4-44-40004-4000000000000000-44000000000000000000000000000000000
χ48444-4-44-4-4-44000-440000000000000000000000000000000000000000000000022−220
χ49444-4-44-4-4-44000-4400000000000000000000000000000000000000000000000−22220
χ5044-44-4-4-44004-4-400404i−4i−4i4i00000000000000000000000000000000000000000000
χ5144-44-4-4-44004-4-40040−4i4i4i−4i00000000000000000000000000000000000000000000
χ5244-44-4-4-4400-44400-40000000000000000000000002i2−2i2−2i22i2000000000000000000000
χ5344-44-4-4-4400-44400-4000000000000000000000000−2i22i22i2−2i2000000000000000000000
χ5444-4-44-44-40000000000000022−2222−2200000000002i2−2i2000000002i−2i2i−2i000000000000000
χ5544-4-44-44-40000000000000022−2222−220000000000−2i22i200000000−2i2i−2i2i000000000000000
χ5644-4-44-44-400000000000000−2222−222200000000002i2−2i200000000−2i2i−2i2i000000000000000
χ5744-4-44-44-400000000000000−2222−22220000000000−2i22i2000000002i−2i2i−2i000000000000000
χ584-4444-4-4-444-44-4-4-44-4000040000000000000000000000000000000000000000000
χ594-44-4-4-4444-4000-44000000000000000000000000000000022−22−2222000000000000000
χ604-44-4-4-4444-4000-440000000000000000000000000000000−222222−22000000000000000
χ614-44-4-4-444-440004-400000004-4-44000000000000000000000000000000000000000
χ624-44-4-4-444-440004-40000000-444-4000000000000000000000000000000000000000
χ634-4-44-444-400-4-440040000002222−22−22000000000000−22220000000000000000000000000
χ644-4-44-444-400-4-44004000000−22−22222200000000000022−220000000000000000000000000
χ658-8-8-888-88000000000000000000000000000000000000000000000000000000000

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