Finite Group Databasebeta

← Group #264470

Character table — Group #264470

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68
size11111111222222224444444444444444444444444488888888161616161616161616161616161616163232
order12222222444444444488888888888888888888888822444444244444448888888844
χ111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111111111-1-111-1-11-1-1-11-1-1-1-1-1-1-11111-1-1
χ3111111111111111111111111111111111111111111-1-111-1-111-11-1-1-11-1-11111-1-1-1-1-1-1
χ4111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-111-1-111-1-1-1-1-1-1-1-111
χ511111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111-1-11-11111-1-111-1-1-1-1-1-11-1
χ611111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1111111-1-11-111-1-111-1-1-1-1-11
χ711111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1-111111-1-11111-11
χ811111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1111-1-1-1-1-1-11111111-1
χ9111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-111111111-1111-1111-1-1-1-111-1-1-1-1
χ10111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-111-1-111-1-1-1-1-1-1-1-1-1-1111111-1-111
χ11111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-111-1-11111-1-111-1-1-1-1-1-1-1-11111
χ12111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11-1111-1111111-1-111-1-1
χ13111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111111111-1-1-1-111-11-1-1-1-111-1-111-11
χ14111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111-1-11111-11-1-1-1-11111-1-1-1-1111-1
χ15111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-111-1-1-1-11-1-1-11111-1-11111-1-11-1
χ16111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-11111111-1-1-111-1-111-1-1-11
χ17222222222-2-222-22-2-2-22222-2-2-2-200000000000000002200-2-2002000-20000000000000
χ18222222222-2-222-22-2-2-22222-2-2-2-20000000000000000-2-2002200-200020000000000000
χ19222222222-2-222-22-2-2-2-2-2-2-2222200000000000000002200-2-200-200020000000000000
χ20222222222-2-222-22-2-2-2-2-2-2-222220000000000000000-2-20022002000-20000000000000
χ2122222222-222-2-22-22-2-2000000002222-2-2-2-200000000002200-2-202000-2000000000000
χ2222222222-222-2-22-22-2-2000000002222-2-2-2-20000000000-2-200220-20002000000000000
χ2322222222-222-2-22-22-2-200000000-2-2-2-2222200000000002200220-2000-2000000000000
χ2422222222-222-2-22-22-2-200000000-2-2-2-222220000000000-2-200-2-2020002000000000000
χ2522-22-2-2-2202-20020-20022−2−222−2−200002i2i−2i−2ii2i2i2i2−i2−i2−i2−i2002i−2i002-200000000i2−i22−2000000
χ2622-22-2-2-2202-20020-20022−2−222−2−200002i2i−2i−2ii2i2i2i2−i2−i2−i2−i200−2i2i00-2200000000−i2i2−22000000
χ2722-22-2-2-2202-20020-20022−2−222−2−20000−2i−2i2i2i−i2−i2−i2−i2i2i2i2i2002i−2i00-2200000000i2−i2−22000000
χ2822-22-2-2-2202-20020-20022−2−222−2−20000−2i−2i2i2i−i2−i2−i2−i2i2i2i2i200−2i2i002-200000000−i2i22−2000000
χ2922-22-2-2-2202-20020-200−2−222−2−22200002i2i−2i−2i−i2−i2−i2−i2i2i2i2i2002i−2i002-200000000−i2i2−22000000
χ3022-22-2-2-2202-20020-200−2−222−2−22200002i2i−2i−2i−i2−i2−i2−i2i2i2i2i200−2i2i00-2200000000i2−i22−2000000
χ3122-22-2-2-2202-20020-200−2−222−2−2220000−2i−2i2i2ii2i2i2i2−i2−i2−i2−i2002i−2i00-2200000000−i2i22−2000000
χ3222-22-2-2-2202-20020-200−2−222−2−2220000−2i−2i2i2ii2i2i2i2−i2−i2−i2−i200−2i2i002-200000000i2−i2−22000000
χ332-2-2-2-22222-2-2-2-22222-20000000022-2-22-22-20000000000000000002-2002-20000000000
χ342-2-2-2-22222-2-2-2-22222-20000000022-2-22-22-2000000000000000000-2200-220000000000
χ352-2-2-2-22222-2-2-2-22222-200000000-2-222-22-220000000000000000002-200-220000000000
χ362-2-2-2-22222-2-2-2-22222-200000000-2-222-22-22000000000000000000-22002-20000000000
χ372-2-2-2-2222-22222-2-2-22-200000000000000002i2i−2i−2i2i2i−2i−2i2-2002-200000000000000002i−2i00
χ382-2-2-2-2222-22222-2-2-22-200000000000000002i2i−2i−2i2i2i−2i−2i-2200-220000000000000000−2i2i00
χ392-2-2-2-2222-22222-2-2-22-20000000000000000−2i−2i2i2i−2i−2i2i2i2-2002-20000000000000000−2i2i00
χ402-2-2-2-2222-22222-2-2-22-20000000000000000−2i−2i2i2i−2i−2i2i2i-2200-2200000000000000002i−2i00
χ412-2-2-2-2222-2-2-2222-22-220000000022-2-2-22-22000000002-200-22000000000000002-20000
χ422-2-2-2-2222-2-2-2222-22-220000000022-2-2-22-2200000000-22002-200000000000000-220000
χ432-2-2-2-2222-2-2-2222-22-2200000000-2-2222-22-2000000002-200-2200000000000000-220000
χ442-2-2-2-2222-2-2-2222-22-2200000000-2-2222-22-200000000-22002-2000000000000002-20000
χ4544444444-4-4-4-4-4-4-4-44400000000000000000000000000000000000000000000000000
χ46444-4-44-4-4000000000022−2222−22000022−2222−2200002-22-22-22-200000000000000000000000000
χ47444-4-44-4-4000000000022−2222−220000−2222−22220000-22-22-22-2200000000000000000000000000
χ48444-4-44-4-40000000000−2222−2222000022−2222−220000-22-22-22-2200000000000000000000000000
χ49444-4-44-4-40000000000−2222−22220000−2222−222200002-22-22-22-200000000000000000000000000
χ5044-44-4-4-440-4400-404002222−22−22−22−222222000000000000000000000000000000000000000000
χ5144-44-4-4-440-4400-40400−22−2222222222−22−22000000000000000000000000000000000000000000
χ5244-4-44-44-44004-40-40004-4-440000000000000000000000000000000000000000000000
χ5344-4-44-44-44004-40-4000-444-40000000000000000000000000000000000000000000000
χ5444-4-44-44-4-400-440400000000000000000002i2−2i22i2−2i2−2i22i2−2i22i200000000000000000000000000
χ5544-4-44-44-4-400-44040000000000000000000−2i22i2−2i22i22i2−2i22i2−2i200000000000000000000000000
χ564-444-4-44-4400-440-4000000000000000000022−22−2222−222222−2200000000000000000000000000
χ574-444-4-44-4400-440-40000000000000000000−222222−2222−22−222200000000000000000000000000
χ584-444-4-44-4-4004-40400000004i−4i4i−4i000000000000000000000000000000000000000000
χ594-444-4-44-4-4004-4040000000−4i4i−4i4i000000000000000000000000000000000000000000
χ604-44-44-4-4404-400-4040000000000000000002222−22−22−22−22222200000000000000000000000000
χ614-44-44-4-4404-400-404000000000000000000−22−2222222222−22−2200000000000000000000000000
χ624-44-44-4-440-440040-4000000000000004i−4i−4i4i0000000000000000000000000000000000
χ634-44-44-4-440-440040-400000000000000−4i4i4i−4i0000000000000000000000000000000000
χ644-4-4444-4-4000000000000002i2−2i2−2i22i222−22−222200002i−2i−2i2i2i−2i−2i2i00000000000000000000000000
χ654-4-4444-4-4000000000000002i2−2i2−2i22i2−222222−220000−2i2i2i−2i−2i2i2i−2i00000000000000000000000000
χ664-4-4444-4-400000000000000−2i22i22i2−2i222−22−22220000−2i2i2i−2i−2i2i2i−2i00000000000000000000000000
χ674-4-4444-4-400000000000000−2i22i22i2−2i2−222222−2200002i−2i−2i2i2i−2i−2i2i00000000000000000000000000
χ684-4-4-4-4444444-4-4-44-4-4400000000000000000000000000000000000000000000000000

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