Finite Group Databasebeta

← Group #10697834

Character table — Group #10697834

Order 768.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72
size1111222222222222224444444444448888888888888812121212121212121616161616161616161616162424242448484848
order122222344444444666446612121212121212128888121224242424242424244444444424446612121212121288884488
χ1111111111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1
χ311111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-1
χ411111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111
χ5111111111111111111111111111111-1-1-1-111-1-1-1-1-1-1-1-11111111111-1-11111-1-1-1-1-1-1-1-1-1-111
χ6111111111111111111111111111111-1-1-1-111-1-1-1-1-1-1-1-111111111-1-111-1-1-1-11111-1-1-1-111-1-1
χ7111111111111111111111111111111-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-11111-1-1-1-1111111-1-1
χ8111111111111111111111111111111-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-111111111-1-111
χ92222222222-2-2-2-22222-2-2222222-2-2-2-20000-2-2000000002222-2-2-2-200000000000000000000
χ102222222222-2-2-2-22222-2-2222222-2-2-2-20000-2-200000000-2-2-2-2222200000000000000000000
χ112222222-2-2-222-2-2-22222-222-2-2-2-2-2-22200002-20000000000000000002-2000022-2-200000000
χ122222222-2-2-222-2-2-22222-222-2-2-2-2-2-22200002-2000000000000000000-220000-2-22200000000
χ132222222-2-2-2-2-222-2222-2222-2-2-2-222-2-20000-22000000000000000000000000000000002-200
χ142222222-2-2-2-2-222-2222-2222-2-2-2-222-2-20000-2200000000000000000000000000000000-2200
χ15222222-122222222-1-1-122-1-1-1-1-1-1-1-1-1-12222-1-1-1-1-1-1-1-1-1-1000000002222-1-1-1-1-1-1-1-100000000
χ16222222-122222222-1-1-122-1-1-1-1-1-1-1-1-1-12222-1-1-1-1-1-1-1-1-1-100000000-2-2-2-21111111100000000
χ17222222-122222222-1-1-122-1-1-1-1-1-1-1-1-1-1-2-2-2-2-1-1111111110000000022-2-2-1-1-1-1111100000000
χ18222222-122222222-1-1-122-1-1-1-1-1-1-1-1-1-1-2-2-2-2-1-11111111100000000-2-2221111-1-1-1-100000000
χ19222222-1-2-2-222-2-2-2-1-1-12-2-1-1111111-1-10000-11−i3−i3−i3−i3i3i3i3i300000000002-2−i3i3−i3i3-1-11100000000
χ20222222-1-2-2-222-2-2-2-1-1-12-2-1-1111111-1-10000-11−i3−i3−i3−i3i3i3i3i30000000000-22i3−i3i3−i311-1-100000000
χ21222222-1-2-2-222-2-2-2-1-1-12-2-1-1111111-1-10000-11i3i3i3i3−i3−i3−i3−i300000000002-2i3−i3i3−i3-1-11100000000
χ22222222-1-2-2-222-2-2-2-1-1-12-2-1-1111111-1-10000-11i3i3i3i3−i3−i3−i3−i30000000000-22−i3i3−i3i311-1-100000000
χ232222-2-2222-22222-2222-2-2-2-222-2-222220000-2-200000000000000002-20022-2-2000000000000
χ242222-2-2222-22222-2222-2-2-2-222-2-222220000-2-20000000000000000-2200-2-222000000000000
χ252222-2-2222-2-2-2-2-2-222222-2-222-2-2-2-2-2-200002200000000000000000000000000000000002i−2i
χ262222-2-2222-2-2-2-2-2-222222-2-222-2-2-2-2-2-20000220000000000000000000000000000000000−2i2i
χ272222-2-22-2-2222-2-22222-22-2-2-2-222-2-22222-2-2-2222-2-222-2-20000000000000000000000000000
χ282222-2-22-2-2222-2-22222-22-2-2-2-222-2-222-2-222-22-2-222-2-2220000000000000000000000000000
χ292222-2-22-2-22-2-22222222-2-2-2-2-22222-2-200002-2000000000000000000000000000022-2-20000
χ302222-2-22-2-22-2-22222222-2-2-2-2-22222-2-200002-20000000000000000000000000000-2-2220000
χ312222-2-2-122-22222-2-1-1-1-2-211-1-111-1-1-1-1000011−i3−i3i3i3i3i3−i3−i3000000002-200-1-111−i3i3−i3i300000000
χ322222-2-2-122-22222-2-1-1-1-2-211-1-111-1-1-1-1000011−i3−i3i3i3i3i3−i3−i300000000-220011-1-1i3−i3i3−i300000000
χ332222-2-2-122-22222-2-1-1-1-2-211-1-111-1-1-1-1000011i3i3−i3−i3−i3−i3i3i3000000002-200-1-111i3−i3i3−i300000000
χ342222-2-2-122-22222-2-1-1-1-2-211-1-111-1-1-1-1000011i3i3−i3−i3−i3−i3i3i300000000-220011-1-1−i3i3−i3i300000000
χ352222-2-2-1-2-2222-2-22-1-1-1-221111-1-111-1-122-2-21-1-1-111-1-111000000000000−i3i3i3−i3−i3i3i3−i300000000
χ362222-2-2-1-2-2222-2-22-1-1-1-221111-1-111-1-122-2-21-1-1-111-1-111000000000000i3−i3−i3i3i3−i3−i3i300000000
χ372222-2-2-1-2-2222-2-22-1-1-1-221111-1-111-1-1-2-2221-111-1-111-1-1000000000000−i3i3i3−i3i3−i3−i3i300000000
χ382222-2-2-1-2-2222-2-22-1-1-1-221111-1-111-1-1-2-2221-111-1-111-1-1000000000000i3−i3−i3i3−i3i3i3−i300000000
χ392-22-22-222-2-200002-22-2002-22-22-20000−i2i2−i2i200−i2i2−i2i2−i2i2−i2i2000022-2-2000000000000−i2i2−i2i20000
χ402-22-22-222-2-200002-22-2002-22-22-20000−i2i2−i2i200−i2i2−i2i2−i2i2−i2i20000-2-222000000000000i2−i2i2−i20000
χ412-22-22-222-2-200002-22-2002-22-22-20000i2−i2i2−i200i2−i2i2−i2i2−i2i2−i2000022-2-2000000000000i2−i2i2−i20000
χ422-22-22-222-2-200002-22-2002-22-22-20000i2−i2i2−i200i2−i2i2−i2i2−i2i2−i20000-2-222000000000000−i2i2−i2i20000
χ432-22-2-222-22-200002-22-200-22-222-20000−i2i2i2−i200−i2i2i2−i2−i2i2i2−i222-2-20000000000000000−i2i2i2−i20000
χ442-22-2-222-22-200002-22-200-22-222-20000−i2i2i2−i200−i2i2i2−i2−i2i2i2−i2-2-2220000000000000000i2−i2−i2i20000
χ452-22-2-222-22-200002-22-200-22-222-20000i2−i2−i2i200i2−i2−i2i2i2−i2−i2i222-2-20000000000000000i2−i2−i2i20000
χ462-22-2-222-22-200002-22-200-22-222-20000i2−i2−i2i200i2−i2−i2i2i2−i2−i2i2-2-2220000000000000000−i2i2i2−i20000
χ47444444-2444-4-4-4-44-2-2-2-4-4-2-2-2-2-2-22222000022000000000000000000000000000000000000
χ48444444-2-4-4-4-4-444-4-2-2-2-44-2-22222-2-22200002-2000000000000000000000000000000000000
χ494444-4-4-244-4-4-4-4-4-4-2-2-24422-2-22222220000-2-2000000000000000000000000000000000000
χ504444-4-4-2-4-44-4-4444-2-2-24-42222-2-2-2-2220000-22000000000000000000000000000000000000
χ5144-4-40040004-40004-4-400000000004-4000000000000002-22-22-22-200000000000000000000
χ5244-4-40040004-40004-4-400000000004-400000000000000-22-22-22-2200000000000000000000
χ5344-4-4004000-440004-4-40000000000-44000000000000002-22-2-22-2200000000000000000000
χ5444-4-4004000-440004-4-40000000000-4400000000000000-22-222-22-200000000000000000000
χ554-44-44-44-4440000-4-44-4004-4-44-440000000000000000000000000000000000000000000000
χ564-44-44-4-24-4-4000042-2200-22-22-220000−2i22i2−2i22i200i2−i2i2−i2i2−i2i2−i20000000000000000000000000000
χ574-44-44-4-24-4-4000042-2200-22-22-2200002i2−2i22i2−2i200−i2i2−i2i2−i2i2−i2i20000000000000000000000000000
χ584-44-44-4-2-4440000-42-2200-222-22-200000000006−66−6−66−660000000000000000000000000000
χ594-44-44-4-2-4440000-42-2200-222-22-20000000000−66−666−66−60000000000000000000000000000
χ604-44-4-4444-440000-4-44-400-444-4-440000000000000000000000000000000000000000000000
χ614-44-4-44-24-440000-42-22002-2-222-200000000006−6−66−666−60000000000000000000000000000
χ624-44-4-44-24-440000-42-22002-2-222-20000000000−666−66−6−660000000000000000000000000000
χ634-44-4-44-2-44-4000042-22002-22-2-220000−2i22i22i2−2i200i2−i2−i2i2i2−i2−i2i20000000000000000000000000000
χ644-44-4-44-2-44-4000042-22002-22-2-2200002i2−2i2−2i22i200−i2i2i2−i2−i2i2i2−i20000000000000000000000000000
χ654-4-44004000004-40-4-44000000004-400000000000000002-2-222-2-2200000000000000000000
χ664-4-44004000004-40-4-44000000004-40000000000000000-222-2-222-200000000000000000000
χ674-4-4400400000-440-4-4400000000-4400000000000000002-2-22-222-200000000000000000000
χ684-4-4400400000-440-4-4400000000-440000000000000000-222-22-2-2200000000000000000000
χ6988-8-800-40008-8000-4440000000000-44000000000000000000000000000000000000000000
χ7088-8-800-4000-88000-44400000000004-4000000000000000000000000000000000000000000
χ718-8-8800-4000008-8044-400000000-4400000000000000000000000000000000000000000000
χ728-8-8800-400000-88044-4000000004-400000000000000000000000000000000000000000000

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