Finite Group Databasebeta

← Group #289735

Character table — Group #289735

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68
size1111111122222222444444444444448888888888888888888888888888881616161632323232
order12222222444444444488888888888822444444444488888888888888888844882444
χ111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111-1-111-1-1-1-1-1-1-1-1-1-1111111-1-1-1-111111111-1-1-1-1
χ3111111111111111111111111111111-1-111-1-1111111111111-1-1-1-111111111-1-1-1-1-1-1-1-1
χ4111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-11111-1-1-1-11111
χ511111111111111111111111111-1-1-1-1111111-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-11-1-11
χ611111111111111111111111111-1-1-1-111-1-1111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-111-1-1-111-1
χ711111111111111111111111111-1-1-1-1-1-111-1-1-1-1-1-1111111-1-11111-1-1-1-1-1-1-1-1-1-111-111-1
χ811111111111111111111111111-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1111-1-11
χ9111111111111111111-1-1-1-1-1-1-1-11111111111111111-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-1-11-11
χ10111111111111111111-1-1-1-1-1-1-1-1111111-1-111-1-1-1-1-1-111111111111111-1-1-1-1-1-1-1-11-11-1
χ11111111111111111111-1-1-1-1-1-1-1-11111-1-111-1-1111111-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-111111-11-1
χ12111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-1-11111-1-1-1-11111-11-11
χ13111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-1-111-1-1-1-1-1-1-1-1-1-111111111-1-111-1-111
χ14111111111111111111-1-1-1-1-1-1-1-1-1-1-1-111-1-1111111-1-11111-1-1-1-1-1-1-1-1-1-11111-1-11111-1-1
χ15111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-111-1-1-1-1-1-111111111111111-1-111-1-1
χ16111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-11111-1-11111-1-1-1-1111111-1-1-1-111
χ172222222222-2-2-222-2-2-200000000222200220022-2-2-2-20000-2-200000000000000000000
χ182222222222-2-2-222-2-2-200000000222200-2-200-2-222220000-2-200000000000000000000
χ192222222222-2-2-222-2-2-200000000-2-2-2-2002200-2-222-2-200002200000000000000000000
χ202222222222-2-2-222-2-2-200000000-2-2-2-200-2-20022-2-22200002200000000000000000000
χ2122222222-2-2222-2-22-2-22222-2-2-2-200002200-2-20000000000000000000000002-2000000
χ2222222222-2-2222-2-22-2-22222-2-2-2-20000-2-20022000000000000000000000000-22000000
χ2322222222-2-2222-2-22-2-2-2-2-2-2222200002200-2-2000000000000000000000000-22000000
χ2422222222-2-2222-2-22-2-2-2-2-2-222220000-2-200220000000000000000000000002-2000000
χ2522-2-22-22-22-20002-2000i2i2−i2−i2i2i2−i2−i222-2-2002i−2i002i−2i000022−2−200000022−2−2i2i2−i2−i200000000
χ2622-2-22-22-22-20002-2000i2i2−i2−i2i2i2−i2−i222-2-200−2i2i00−2i2i0000−2−222000000−2−222i2i2−i2−i200000000
χ2722-2-22-22-22-20002-2000i2i2−i2−i2i2i2−i2−i2-2-222002i−2i00−2i2i000022−2−2000000−2−222−i2−i2i2i200000000
χ2822-2-22-22-22-20002-2000i2i2−i2−i2i2i2−i2−i2-2-22200−2i2i002i−2i0000−2−22200000022−2−2−i2−i2i2i200000000
χ2922-2-22-22-22-20002-2000−i2−i2i2i2−i2−i2i2i222-2-2002i−2i002i−2i0000−2−222000000−2−222−i2−i2i2i200000000
χ3022-2-22-22-22-20002-2000−i2−i2i2i2−i2−i2i2i222-2-200−2i2i00−2i2i000022−2−200000022−2−2−i2−i2i2i200000000
χ3122-2-22-22-22-20002-2000−i2−i2i2i2−i2−i2i2i2-2-222002i−2i00−2i2i0000−2−22200000022−2−2i2i2−i2−i200000000
χ3222-2-22-22-22-20002-2000−i2−i2i2i2−i2−i2i2i2-2-22200−2i2i002i−2i000022−2−2000000−2−222i2i2−i2−i200000000
χ332-2222-2-2-22-2000-22000i2−i2i2−i2i2−i2i2−i22i−2i2i−2i000000002-22i−2i2−22−2000000i2−i2i2−i22−22−200000000
χ342-2222-2-2-22-2000-22000i2−i2i2−i2i2−i2i2−i22i−2i2i−2i00000000-22−2i2i−22−22000000−i2i2−i2i22−22−200000000
χ352-2222-2-2-22-2000-22000i2−i2i2−i2i2−i2i2−i2−2i2i−2i2i000000002-2−2i2i−22−22000000i2−i2i2−i2−22−2200000000
χ362-2222-2-2-22-2000-22000i2−i2i2−i2i2−i2i2−i2−2i2i−2i2i00000000-222i−2i2−22−2000000−i2i2−i2i2−22−2200000000
χ372-2222-2-2-22-2000-22000−i2i2−i2i2−i2i2−i2i22i−2i2i−2i000000002-22i−2i−22−22000000−i2i2−i2i2−22−2200000000
χ382-2222-2-2-22-2000-22000−i2i2−i2i2−i2i2−i2i22i−2i2i−2i00000000-22−2i2i2−22−2000000i2−i2i2−i2−22−2200000000
χ392-2222-2-2-22-2000-22000−i2i2−i2i2−i2i2−i2i2−2i2i−2i2i000000002-2−2i2i2−22−2000000−i2i2−i2i22−22−200000000
χ402-2222-2-2-22-2000-22000−i2i2−i2i2−i2i2−i2i2−2i2i−2i2i00000000-222i−2i−22−22000000i2−i2i2−i22−22−200000000
χ412-2-2-222-22222-22-2-2-2-22000000002i−2i−2i2i0000000000002-2-222i−2i00002i−2i−2i2i000000000000
χ422-2-2-222-22222-22-2-2-2-22000000002i−2i−2i2i000000000000-222-22i−2i0000−2i2i2i−2i000000000000
χ432-2-2-222-22222-22-2-2-2-2200000000−2i2i2i−2i0000000000002-2-22−2i2i0000−2i2i2i−2i000000000000
χ442-2-2-222-22222-22-2-2-2-2200000000−2i2i2i−2i000000000000-222-2−2i2i00002i−2i−2i2i000000000000
χ452-2-2-222-2222-22-2-2-222-22-2-222-2-222i−2i−2i2i0000000000000000−2i2i00000000−2i2i2i−2i00000000
χ462-2-2-222-2222-22-2-2-222-22-2-222-2-22−2i2i2i−2i00000000000000002i−2i000000002i−2i−2i2i00000000
χ472-2-2-222-2222-22-2-2-222-2-222-2-222-22i−2i−2i2i0000000000000000−2i2i000000002i−2i−2i2i00000000
χ482-2-2-222-2222-22-2-2-222-2-222-2-222-2−2i2i2i−2i00000000000000002i−2i00000000−2i2i2i−2i00000000
χ492-2-2-222-22-2-2-22-2222-222-2-22-222-2000000000000000000000022-2-200000000002-20000
χ502-2-2-222-22-2-2-22-2222-222-2-22-222-20000000000000000000000-2-2220000000000-220000
χ512-2-2-222-22-2-2-22-2222-22-222-22-2-22000000000000000000000022-2-20000000000-220000
χ522-2-2-222-22-2-2-22-2222-22-222-22-2-220000000000000000000000-2-22200000000002-20000
χ5344444444-4-4-4-4-4-4-4-44400000000000000000000000000000000000000000000000000
χ5444-44-4-4-44004-4-40040000000000000000004i−4i00000000000000000000000000000000
χ5544-44-4-4-44004-4-4004000000000000000000−4i4i00000000000000000000000000000000
χ5644-44-4-4-4400-44400-4000000000000000000000000000000002i2−2i22i2−2i20000000000000000
χ5744-44-4-4-4400-44400-400000000000000000000000000000000−2i22i2−2i22i20000000000000000
χ5844-4-44-44-4-44000-440002i22i2−2i2−2i2−2i2−2i22i22i2000000000000000000000000000000000000000000
χ5944-4-44-44-4-44000-44000−2i2−2i22i22i22i22i2−2i2−2i2000000000000000000000000000000000000000000
χ604-4444-4-4-4-440004-40002i2−2i22i2−2i2−2i22i2−2i22i2000000000000000000000000000000000000000000
χ614-4444-4-4-4-440004-4000−2i22i2−2i22i22i2−2i22i2−2i2000000000000000000000000000000000000000000
χ624-44-4-4-4440044-400-4000000000000000000000000000000002i2−2i2−2i22i20000000000000000
χ634-44-4-4-4440044-400-400000000000000000000000000000000−2i22i22i2−2i20000000000000000
χ644-44-4-4-44400-4-44004000000000000004-4000000000000000000000000000000000000
χ654-44-4-4-44400-4-4400400000000000000-44000000000000000000000000000000000000
χ664-4-4-444-44-4-44-4444-44-400000000000000000000000000000000000000000000000000
χ67888-8-88-8-8000000000000000000000000000000000000000000000000000000000000
χ688-8-88-888-8000000000000000000000000000000000000000000000000000000000000

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