Finite Group Databasebeta

← Group #342102

Character table — Group #342102

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68
size11111111222222224444444444444444444444444488888888161616161616161616161616161616163232
order12222222444444444488888888888888888888888844444444244444448888888844
χ111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111111111-1-111-1-1-1-1-111-1-1-111-1-1-1-111-1-1
χ3111111111111111111111111111111111111111111-1-111-1-1111-1-1-1-11-1-1-1-11111-1-1-1-1
χ4111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-111-1-1-111-1-1-1-1-1-1-1-111
χ511111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111-1-11-1-111-111-1-111-1-1-1-1-11
χ611111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-11111-111111-1-1-1-1-1-111-1-11-1
χ711111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-1111-1-1-1-1-11111-1-1111-1
χ811111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-1-111111-1-11111-11
χ9111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-11111-1-111111-111-1-1-1-1-1-1-1-111-11
χ10111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-11-111-1-11111111-1
χ11111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-11111111-1-11-111111-1-1-1-1-1-11-1
χ12111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1111-1-1-1-1111111-1-1-11
χ13111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-11-1-1-11-1-1-111-1-111-1-111
χ14111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111-1-1-1-111-111-111111111-1-1-1-1-1-1
χ15111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-11111-1-11111-1-111-1-1-1-11111-1-1
χ16111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-11111-1-1-11-11-1-1-1-111-1-11111
χ17222222222-2-22-2-222-2-2000000002222-2-2-2-200000000002200-2-2-200002000000000000
χ18222222222-2-22-2-222-2-2000000002222-2-2-2-20000000000-2-2002220000-2000000000000
χ19222222222-2-22-2-222-2-200000000-2-2-2-222220000000000220022-20000-2000000000000
χ20222222222-2-22-2-222-2-200000000-2-2-2-222220000000000-2-200-2-2200002000000000000
χ2122222222-222-222-2-2-2-22222-2-2-2-2000000000000000022002200000-2-20000000000000
χ2222222222-222-222-2-2-2-22222-2-2-2-20000000000000000-2-200-2-200000220000000000000
χ2322222222-222-222-2-2-2-2-2-2-2-2222200000000000000002200-2-2000002-20000000000000
χ2422222222-222-222-2-2-2-2-2-2-2-222220000000000000000-2-2002200000-220000000000000
χ252-22-2-222-2200-200-2200i2i2−i2−i2i2i2−i2−i2000022-2-2i2i2i2i2−i2−i2−i2−i2002i−2i002i−2i00000000002−22−20000
χ262-22-2-222-2200-200-2200i2i2−i2−i2i2i2−i2−i2000022-2-2i2i2i2i2−i2−i2−i2−i200−2i2i00−2i2i0000000000−22−220000
χ272-22-2-222-2200-200-2200i2i2−i2−i2i2i2−i2−i20000-2-222−i2−i2−i2−i2i2i2i2i2002i−2i00−2i2i00000000002−2−220000
χ282-22-2-222-2200-200-2200i2i2−i2−i2i2i2−i2−i20000-2-222−i2−i2−i2−i2i2i2i2i200−2i2i002i−2i0000000000−222−20000
χ292-22-2-222-2200-200-2200−i2−i2i2i2−i2−i2i2i2000022-2-2−i2−i2−i2−i2i2i2i2i2002i−2i002i−2i0000000000−22−220000
χ302-22-2-222-2200-200-2200−i2−i2i2i2−i2−i2i2i2000022-2-2−i2−i2−i2−i2i2i2i2i200−2i2i00−2i2i00000000002−22−20000
χ312-22-2-222-2200-200-2200−i2−i2i2i2−i2−i2i2i20000-2-222i2i2i2i2−i2−i2−i2−i2002i−2i00−2i2i0000000000−222−20000
χ322-22-2-222-2200-200-2200−i2−i2i2i2−i2−i2i2i20000-2-222i2i2i2i2−i2−i2−i2−i200−2i2i002i−2i00000000002−2−220000
χ332-2-2222-2-202-202-200002-22-20000i2i2−i2−i2i2−i2i2−i2i2i2−i2−i2i2i2−i2−i22i−2i002i−2i00000000002−200002−200
χ342-2-2222-2-202-202-200002-22-20000i2i2−i2−i2i2−i2i2−i2i2i2−i2−i2i2i2−i2−i2−2i2i00−2i2i0000000000−220000−2200
χ352-2-2222-2-202-202-200002-22-20000−i2−i2i2i2−i2i2−i2i2−i2−i2i2i2−i2−i2i2i22i−2i002i−2i0000000000−220000−2200
χ362-2-2222-2-202-202-200002-22-20000−i2−i2i2i2−i2i2−i2i2−i2−i2i2i2−i2−i2i2i2−2i2i00−2i2i00000000002−200002−200
χ372-2-2222-2-202-202-20000-22-220000i2i2−i2−i2i2−i2i2−i2−i2−i2i2i2−i2−i2i2i22i−2i00−2i2i0000000000−2200002−200
χ382-2-2222-2-202-202-20000-22-220000i2i2−i2−i2i2−i2i2−i2−i2−i2i2i2−i2−i2i2i2−2i2i002i−2i00000000002−20000−2200
χ392-2-2222-2-202-202-20000-22-220000−i2−i2i2i2−i2i2−i2i2i2i2−i2−i2i2i2−i2−i22i−2i00−2i2i00000000002−20000−2200
χ402-2-2222-2-202-202-20000-22-220000−i2−i2i2i2−i2i2−i2i2i2i2−i2−i2i2i2−i2−i2−2i2i002i−2i0000000000−2200002−200
χ412-2-2-22-222222-2-2-22-22-200000000000000002i−2i2i−2i2i−2i2i−2i0000000002i−2i0002-20000000000
χ422-2-2-22-222222-2-2-22-22-200000000000000002i−2i2i−2i2i−2i2i−2i000000000−2i2i000-220000000000
χ432-2-2-22-222222-2-2-22-22-20000000000000000−2i2i−2i2i−2i2i−2i2i0000000002i−2i000-220000000000
χ442-2-2-22-222222-2-2-22-22-20000000000000000−2i2i−2i2i−2i2i−2i2i000000000−2i2i0002-20000000000
χ4544444444-4-4-4-4-4-4-4-44400000000000000000000000000000000000000000000000000
χ46444-44-4-4-404-40-440000000000000000000022−22−222222−22−222200000000000000000000000000
χ47444-44-4-4-404-40-4400000000000000000000−222222−22−222222−2200000000000000000000000000
χ48444-44-4-4-40-4404-4000000004-44-4000000000000000000000000000000000000000000
χ49444-44-4-4-40-4404-400000000-44-44000000000000000000000000000000000000000000
χ5044-44-4-44-4400400-4-400000000000000000022−2222−22−2222−222200000000000000000000000000
χ5144-44-4-44-4400400-4-4000000000000000000−2222−222222−2222−2200000000000000000000000000
χ5244-44-4-44-4-400-4004400000000004i−4i4i−4i00000000000000000000000000000000000000
χ5344-44-4-44-4-400-400440000000000−4i4i−4i4i00000000000000000000000000000000000000
χ5444-4-4-44-4400000000002i2−2i2−2i22i2000000002i2−2i2−2i22i2-2-22222-2-200000000000000000000000000
χ5544-4-4-44-4400000000002i2−2i2−2i22i200000000−2i22i22i2−2i222-2-2-2-22200000000000000000000000000
χ5644-4-4-44-440000000000−2i22i22i2−2i2000000002i2−2i2−2i22i222-2-2-2-22200000000000000000000000000
χ5744-4-4-44-440000000000−2i22i22i2−2i200000000−2i22i22i2−2i2-2-22222-2-200000000000000000000000000
χ584-444-4-4-44000000000000002i2−2i2−2i22i222−22−222200002i−2i−2i2i−2i2i2i−2i00000000000000000000000000
χ594-444-4-4-44000000000000002i2−2i2−2i22i2−222222−220000−2i2i2i−2i2i−2i−2i2i00000000000000000000000000
χ604-444-4-4-4400000000000000−2i22i22i2−2i222−22−22220000−2i2i2i−2i2i−2i−2i2i00000000000000000000000000
χ614-444-4-4-4400000000000000−2i22i22i2−2i2−222222−2200002i−2i−2i2i−2i2i2i−2i00000000000000000000000000
χ624-44-4-444-4-4004004-4002i22i2−2i2−2i2−2i2−2i22i22i2000000000000000000000000000000000000000000
χ634-44-4-444-4-4004004-400−2i2−2i22i22i22i22i2−2i2−2i2000000000000000000000000000000000000000000
χ644-4-4444-4-40-440-440000000000002i22i2−2i2−2i2−2i22i2−2i22i20000000000000000000000000000000000
χ654-4-4444-4-40-440-44000000000000−2i2−2i22i22i22i2−2i22i2−2i20000000000000000000000000000000000
χ664-4-4-44-4444-4-4-4444-4-4400000000000000000000000000000000000000000000000000
χ674-4-4-44-444-4444-4-4-44-4400000000000000000000000000000000000000000000000000
χ684-4-4-44-444-4-4-4444-444-400000000000000000000000000000000000000000000000000

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