Finite Group Databasebeta

← Group #293767

Character table — Group #293767

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68
size11111111222222224444444444444444444444444488888888161616161616161616161616161616163232
order12222222444444444444444444888888888888888822444444244444448888888844
χ111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111111111-1-111-1-1-11-1-1-1-11-11111-1-1-1-1-1-1
χ3111111111111111111111111111111111111111111-1-111-1-1111-1-1-1-1-1-11-1-1-1-11111-1-1
χ4111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-111
χ511111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111111111-1-1-1-1-1-1-1-1-1-1
χ611111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-111-1-1-11-1-1-1-11-1-1-1-1-1111111
χ711111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1111-1-1-1-1-1-111111-1-1-1-111
χ811111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-111111111-1-1
χ91111111111111111-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-11111-1-111-11-1-111-1-111-1-111-1-11-1
χ101111111111111111-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-111-1-1-1-1-1-11111-1-1-1111-1-1-1-111-11
χ111111111111111111-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-1111111-1-111-1-11-1-1-11111-1-1-11
χ121111111111111111-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-1-1-111-1-11-1-1-11111-1-111-1-1111-1
χ131111111111111111-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1111111111111-1-111-11-1-111-1-1-1-111-1-111-11
χ141111111111111111-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-11111-1-1-11-1-11111-1-11-1
χ151111111111111111-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-111111111-1-1111111-1-111-1-11-111-1-1-1-1111-1
χ161111111111111111-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-111111111-1-1-1-111-1-11-1-1-1111111-1-111-1-1-11
χ172222222222-2-222-2-22222-2-2-2-2-2-20000000000000000002200-2-2-200000020000000000
χ182222222222-2-222-2-22222-2-2-2-2-2-2000000000000000000-2-200222000000-20000000000
χ192222222222-2-222-2-2-2-2-2-22222-2-20000000000000000002200-2-22000000-20000000000
χ202222222222-2-222-2-2-2-2-2-22222-2-2000000000000000000-2-20022-200000020000000000
χ2122222222-2-222-2-22222-2-222-2-2-2-200000000000000002200-2-2000-20000200000000000
χ2222222222-2-222-2-22222-2-222-2-2-2-20000000000000000-2-2002200020000-200000000000
χ2322222222-2-222-2-222-2-222-2-222-2-20000000000000000220022000-20000-200000000000
χ2422222222-2-222-2-222-2-222-2-222-2-20000000000000000-2-200-2-200020000200000000000
χ2522222222-2-2-2-2-2-2-2-222-2-2-2-22222000000000000000000000000002-22-2000000000000
χ2622222222-2-2-2-2-2-2-2-222-2-2-2-2222200000000000000000000000000-22-22000000000000
χ2722222222-2-2-2-2-2-2-2-2-2-22222-2-222000000000000000000000000002-2-22000000000000
χ2822222222-2-2-2-2-2-2-2-2-2-22222-2-22200000000000000000000000000-222-2000000000000
χ2922-2-22-2-22002-2002-2002i−2i002i−2i002222−2−2−2−2i2i2i2i2−i2−i2−i2−i22-2002i−2i00000000002−2i2−i2000000
χ3022-2-22-2-22002-2002-2002i−2i002i−2i002222−2−2−2−2i2i2i2i2−i2−i2−i2−i2-2200−2i2i0000000000−22−i2i2000000
χ3122-2-22-2-22002-2002-2002i−2i002i−2i00−2−2−2−22222−i2−i2−i2−i2i2i2i2i22-2002i−2i0000000000−22−i2i2000000
χ3222-2-22-2-22002-2002-2002i−2i002i−2i00−2−2−2−22222−i2−i2−i2−i2i2i2i2i2-2200−2i2i00000000002−2i2−i2000000
χ3322-2-22-2-22002-2002-200−2i2i00−2i2i002222−2−2−2−2−i2−i2−i2−i2i2i2i2i22-200−2i2i00000000002−2−i2i2000000
χ3422-2-22-2-22002-2002-200−2i2i00−2i2i002222−2−2−2−2−i2−i2−i2−i2i2i2i2i2-22002i−2i0000000000−22i2−i2000000
χ3522-2-22-2-22002-2002-200−2i2i00−2i2i00−2−2−2−22222i2i2i2i2−i2−i2−i2−i22-200−2i2i0000000000−22i2−i2000000
χ3622-2-22-2-22002-2002-200−2i2i00−2i2i00−2−2−2−22222i2i2i2i2−i2−i2−i2−i2-22002i−2i00000000002−2−i2i2000000
χ372-22-2-22-22222-2-2-2-22000000002-22i2i−2i−2i2i2i−2i−2i00000000002i−2i002i−2i0000000000002-20000
χ382-22-2-22-22222-2-2-2-22000000002-22i2i−2i−2i2i2i−2i−2i0000000000−2i2i00−2i2i000000000000-220000
χ392-22-2-22-22222-2-2-2-22000000002-2−2i−2i2i2i−2i−2i2i2i00000000002i−2i002i−2i000000000000-220000
χ402-22-2-22-22222-2-2-2-22000000002-2−2i−2i2i2i−2i−2i2i2i0000000000−2i2i00−2i2i0000000000002-20000
χ412-22-2-22-2222-22-2-22-200000000-22000000002i2i−2i−2i2i2i−2i−2i002i−2i00−2i2i000000000000002-200
χ422-22-2-22-2222-22-2-22-200000000-22000000002i2i−2i−2i2i2i−2i−2i00−2i2i002i−2i00000000000000-2200
χ432-22-2-22-2222-22-2-22-200000000-2200000000−2i−2i2i2i−2i−2i2i2i002i−2i00−2i2i00000000000000-2200
χ442-22-2-22-2222-22-2-22-200000000-2200000000−2i−2i2i2i−2i−2i2i2i00−2i2i002i−2i000000000000002-200
χ454444-4-4-4-44-4004-40000000000000000000022−2222−2222−2222−2200000000000000000000000000
χ464444-4-4-4-44-4004-400000000000000000000−2222−2222−2222−222200000000000000000000000000
χ474444-4-4-4-4-4400-4400000000000022−2222−2222−2222−220000000000000000000000000000000000
χ484444-4-4-4-4-4400-44000000000000−2222−2222−2222−22220000000000000000000000000000000000
χ4944-4-44-4-4400-4400-44004i−4i00−4i4i00000000000000000000000000000000000000000000
χ5044-4-44-4-4400-4400-4400−4i4i004i−4i00000000000000000000000000000000000000000000
χ5144-4-4-444-40000000000004i−4i00002-22-2-22-222i−2i2i−2i−2i2i−2i2i00000000000000000000000000
χ5244-4-4-444-40000000000004i−4i0000-22-222-22-2−2i2i−2i2i2i−2i2i−2i00000000000000000000000000
χ5344-4-4-444-4000000000000−4i4i00002-22-2-22-22−2i2i−2i2i2i−2i2i−2i00000000000000000000000000
χ5444-4-4-444-4000000000000−4i4i0000-22-222-22-22i−2i2i−2i−2i2i−2i2i00000000000000000000000000
χ554-44-44-44-44-400-44000000000000000000002i2−2i2−2i22i22i2−2i2−2i22i200000000000000000000000000
χ564-44-44-44-44-400-4400000000000000000000−2i22i22i2−2i2−2i22i22i2−2i200000000000000000000000000
χ574-44-44-44-4-44004-40000000000002i2−2i2−2i22i22i2−2i2−2i22i20000000000000000000000000000000000
χ584-44-44-44-4-44004-4000000000000−2i22i22i2−2i2−2i22i22i2−2i20000000000000000000000000000000000
χ594-44-4-44-44-4-44-444-4400000000-44000000000000000000000000000000000000000000
χ604-44-4-44-44-4-4-44444-4000000004-4000000000000000000000000000000000000000000
χ614-4-4444-4-4000000004i−4i000000002i−2i−2i2i−2i2i2i−2i2-2-22-222-200000000000000000000000000
χ624-4-4444-4-4000000004i−4i00000000−2i2i2i−2i2i−2i−2i2i-222-22-2-2200000000000000000000000000
χ634-4-4444-4-400000000−4i4i000000002i−2i−2i2i−2i2i2i−2i-222-22-2-2200000000000000000000000000
χ644-4-4444-4-400000000−4i4i00000000−2i2i2i−2i2i−2i−2i2i2-2-22-222-200000000000000000000000000
χ654-4-44-4-444004400-4-400000000002i22i2−2i2−2i2−2i2−2i22i22i20000000000000000000000000000000000
χ664-4-44-4-444004400-4-40000000000−2i2−2i22i22i22i22i2−2i2−2i20000000000000000000000000000000000
χ674-4-44-4-44400-4-400440000000000000000002222−22−22−22−22222200000000000000000000000000
χ684-4-44-4-44400-4-40044000000000000000000−22−2222222222−22−2200000000000000000000000000

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