Finite Group Databasebeta

← Group #344207

Character table — Group #344207

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68
size11111111222222224444444444444444444444444488888888161616161616161616161616161616163232
order12222222444444444488888888888888888888888844444444444444448888888824
χ111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111111111-1-111-1-11-11-1-1-1-1-1-1-11111-1-1-1-1
χ3111111111111111111111111111111111111111111-1-111-1-111-11-11-1-1-1-111-1-1-1-111-1-1
χ4111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-111
χ511111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1111-111-1-111-1-1-1-1-1-11-1
χ611111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-111111-111-1-111-1-1-1-1-1-111-11
χ711111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-1-11-1-1-1-111111111-1-1-11
χ811111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1111-1-1-1-11111111-1
χ9111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-11111-1-111-1111-1-111-1-111-1-1-1-11-1
χ10111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-11-111-1-11111-1-111-11
χ11111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-111111111-1111-1-1-1-1-1-111-1-1-11
χ12111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-111-1-11-1-1-1-1-11111-1-111111-1
χ13111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-1-111-1-1-1-1-1-1-1-1-1111111
χ14111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111-1-1-1-111-1-111111111-1-111-1-1-1-1
χ15111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-11111-1-111-1-11111-1-111-1-111-1-1
χ16111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-111111-1-11-1-1-1-11111-1-1-1-111
χ17222222222-2-2222-2-2-2-22222-2-2-2-200000000000000002200-2-20020-2000000000000000
χ18222222222-2-2222-2-2-2-22222-2-2-2-20000000000000000-2-2002200-202000000000000000
χ19222222222-2-2222-2-2-2-2-2-2-2-22222000000000000000022002200-20-2000000000000000
χ20222222222-2-2222-2-2-2-2-2-2-2-222220000000000000000-2-200-2-200202000000000000000
χ2122222222-222-2-2-222-2-2000000002222-2-2-2-200000000002200220-20-200000000000000
χ2222222222-222-2-2-222-2-2000000002222-2-2-2-20000000000-2-200-2-2020200000000000000
χ2322222222-222-2-2-222-2-200000000-2-2-2-2222200000000002200-2-20-20200000000000000
χ2422222222-222-2-2-222-2-200000000-2-2-2-222220000000000-2-20022020-200000000000000
χ2522-22-2-22-22-2-2-22-2222-200000000000000002i2i2i2i−2i−2i−2i−2i0000000000002i−2i2-20000000000
χ2622-22-2-22-22-2-2-22-2222-200000000000000002i2i2i2i−2i−2i−2i−2i000000000000−2i2i-220000000000
χ2722-22-2-22-22-2-2-22-2222-20000000000000000−2i−2i−2i−2i2i2i2i2i0000000000002i−2i-220000000000
χ2822-22-2-22-22-2-2-22-2222-20000000000000000−2i−2i−2i−2i2i2i2i2i000000000000−2i2i2-20000000000
χ2922-2-22-2-22-20022-2000000002i2i−2i−2ii2i2−i2−i2i2i2−i2−i222−2−222−2−22i−2i002-20000000000002−2i2−i20000
χ3022-2-22-2-22-20022-2000000002i2i−2i−2ii2i2−i2−i2i2i2−i2−i222−2−222−2−2−2i2i00-22000000000000−22−i2i20000
χ3122-2-22-2-22-20022-2000000002i2i−2i−2i−i2−i2i2i2−i2−i2i2i2−2−222−2−2222i−2i002-2000000000000−22−i2i20000
χ3222-2-22-2-22-20022-2000000002i2i−2i−2i−i2−i2i2i2−i2−i2i2i2−2−222−2−222−2i2i00-220000000000002−2i2−i20000
χ3322-2-22-2-22-20022-200000000−2i−2i2i2ii2i2−i2−i2i2i2−i2−i2−2−222−2−2222i−2i00-220000000000002−2−i2i20000
χ3422-2-22-2-22-20022-200000000−2i−2i2i2ii2i2−i2−i2i2i2−i2−i2−2−222−2−222−2i2i002-2000000000000−22i2−i20000
χ3522-2-22-2-22-20022-200000000−2i−2i2i2i−i2−i2i2i2−i2−i2i2i222−2−222−2−22i−2i00-22000000000000−22i2−i20000
χ3622-2-22-2-22-20022-200000000−2i−2i2i2i−i2−i2i2i2−i2−i2i2i222−2−222−2−2−2i2i002-20000000000002−2−i2i20000
χ372-222-2-2-2202-20002-200i2i2−i2−i2i2−i2i2−i22i−2i2i−2i00002−22−22−22−2002i−2i002-2000000002−20000i2−i200
χ382-222-2-2-2202-20002-200i2i2−i2−i2i2−i2i2−i22i−2i2i−2i00002−22−22−22−200−2i2i00-2200000000−220000−i2i200
χ392-222-2-2-2202-20002-200i2i2−i2−i2i2−i2i2−i2−2i2i−2i2i0000−22−22−22−22002i−2i00-22000000002−20000−i2i200
χ402-222-2-2-2202-20002-200i2i2−i2−i2i2−i2i2−i2−2i2i−2i2i0000−22−22−22−2200−2i2i002-200000000−220000i2−i200
χ412-222-2-2-2202-20002-200−i2−i2i2i2−i2i2−i2i22i−2i2i−2i0000−22−22−22−22002i−2i002-200000000−220000−i2i200
χ422-222-2-2-2202-20002-200−i2−i2i2i2−i2i2−i2i22i−2i2i−2i0000−22−22−22−2200−2i2i00-22000000002−20000i2−i200
χ432-222-2-2-2202-20002-200−i2−i2i2i2−i2i2−i2i2−2i2i−2i2i00002−22−22−22−2002i−2i00-2200000000−220000i2−i200
χ442-222-2-2-2202-20002-200−i2−i2i2i2−i2i2−i2i2−2i2i−2i2i00002−22−22−22−200−2i2i002-2000000002−20000−i2i200
χ4544444444-4-4-4-4-4-4-4-44400000000000000000000000000000000000000000000000000
χ46444-4-44-4-44004-4-400004-44-40000000000000000000000000000000000000000000000
χ47444-4-44-4-44004-4-40000-44-440000000000000000000000000000000000000000000000
χ48444-4-44-4-4-400-444000000000000000000002i22i2−2i2−2i2−2i2−2i22i22i200000000000000000000000000
χ49444-4-44-4-4-400-44400000000000000000000−2i2−2i22i22i22i22i2−2i2−2i200000000000000000000000000
χ5044-44-4-44-4444-44-4-4-4-4400000000000000000000000000000000000000000000000000
χ5144-44-4-44-4-4444-44-4-44-400000000000000000000000000000000000000000000000000
χ5244-44-4-44-4-4-4-44-4444-4400000000000000000000000000000000000000000000000000
χ5344-4-44-4-44400-4-440000000000002i22i2−2i2−2i2−2i2−2i22i22i20000000000000000000000000000000000
χ5444-4-44-4-44400-4-44000000000000−2i2−2i22i22i22i22i2−2i2−2i20000000000000000000000000000000000
χ554-444-4-4-440-44000-44002i22i2−2i2−2i2−2i22i2−2i22i2000000000000000000000000000000000000000000
χ564-444-4-4-440-44000-4400−2i2−2i22i22i22i2−2i22i2−2i2000000000000000000000000000000000000000000
χ574-44-44-44-400000000002i2−2i2−2i22i20000000022−2222−222i−2i−2i2i−2i2i2i−2i00000000000000000000000000
χ584-44-44-44-400000000002i2−2i2−2i22i200000000−2222−2222−2i2i2i−2i2i−2i−2i2i00000000000000000000000000
χ594-44-44-44-40000000000−2i22i22i2−2i20000000022−2222−22−2i2i2i−2i2i−2i−2i2i00000000000000000000000000
χ604-44-44-44-40000000000−2i22i22i2−2i200000000−2222−22222i−2i−2i2i−2i2i2i−2i00000000000000000000000000
χ614-4-4444-4-404-4000-44000000000000004i−4i−4i4i0000000000000000000000000000000000
χ624-4-4444-4-404-4000-4400000000000000−4i4i4i−4i0000000000000000000000000000000000
χ634-4-4444-4-40-440004-40000000000000000002i2−2i22i2−2i2−2i22i2−2i22i200000000000000000000000000
χ644-4-4444-4-40-440004-4000000000000000000−2i22i2−2i22i22i2−2i22i2−2i200000000000000000000000000
χ654-4-4-4-44440000000000000022−22−222222−22−222200002-2-222-2-2200000000000000000000000000
χ664-4-4-4-44440000000000000022−22−2222−222222−220000-222-2-222-200000000000000000000000000
χ674-4-4-4-444400000000000000−222222−2222−22−22220000-222-2-222-200000000000000000000000000
χ684-4-4-4-444400000000000000−222222−22−222222−2200002-2-222-2-2200000000000000000000000000

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