Finite Group Databasebeta

← Group #10697073

Character table — Group #10697073

Order 768.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72
size1111222222222222224444444444448888888888888812121212121212121616161616161616161616162424242448484848
order122222344444444666446612121212121212128888121224242424242424248888888824446612121212121288884488
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
χ5111111111111111111111111111111-1-1-1-111-1-1-1-1-1-1-1-1111111111-1-111111-1-1-1-1-1-1-1-1-1-111
χ6111111111111111111111111111111-1-1-1-111-1-1-1-1-1-1-1-111111111-111-1-1-1-1-11111-1-1-1-111-1-1
χ7111111111111111111111111111111-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11-1-111111-1-1-1-1111111-1-1
χ8111111111111111111111111111111-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-1-111111111-1-111
χ9222222222-2-2-2-2-2-22222-222-2-2-2-222-2-20000-2200000000000000000000000000000000002i−2i
χ10222222222-2-2-2-2-2-22222-222-2-2-2-222-2-20000-220000000000000000000000000000000000−2i2i
χ112222222-2-2222-2-22222-2-222-2-222-2-22222-2-2-2-22222-2-2-2-20000000000000000000000000000
χ122222222-2-2222-2-22222-2-222-2-222-2-222-2-222-2-2-2-2-2-222220000000000000000000000000000
χ132222222-2-2-2-2-222-2222-222222-2-2-2-2-2-200002-2000000000000000000000000000000002-200
χ142222222-2-2-2-2-222-2222-222222-2-2-2-2-2-200002-200000000000000000000000000000000-2200
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
χ17222222-122222222-1-1-122-1-1-1-1-1-1-1-1-1-1-2-2-2-2-1-111111111000000002-2-22-1-1-1-1111100000000
χ18222222-122222222-1-1-122-1-1-1-1-1-1-1-1-1-1-2-2-2-2-1-11111111100000000-222-21111-1-1-1-100000000
χ19222222-1-2-2222-2-22-1-1-1-2-2-1-111-1-111-1-122-2-211-1-1-1-11111000000000000−i3i3−i3i3−i3−i3i3i300000000
χ20222222-1-2-2222-2-22-1-1-1-2-2-1-111-1-111-1-122-2-211-1-1-1-11111000000000000i3−i3i3−i3i3i3−i3−i300000000
χ21222222-1-2-2222-2-22-1-1-1-2-2-1-111-1-111-1-1-2-222111111-1-1-1-1000000000000−i3i3−i3i3i3i3−i3−i300000000
χ22222222-1-2-2222-2-22-1-1-1-2-2-1-111-1-111-1-1-2-222111111-1-1-1-1000000000000i3−i3i3−i3−i3−i3i3i300000000
χ232222-2-22222-2-2-2-22222-22-2-2-2-22222-2-200002-2000000002222-2-2-2-200000000000000000000
χ242222-2-22222-2-2-2-22222-22-2-2-2-22222-2-200002-200000000-2-2-2-2222200000000000000000000
χ252222-2-2222-22222-2222-2-2-2-222-2-222220000-2-20000000000000000200-222-2-2000000000000
χ262222-2-2222-22222-2222-2-2-2-222-2-222220000-2-20000000000000000-2002-2-222000000000000
χ272222-2-22-2-22-2-22222222-2-2-22222-2-2-2-20000-22000000000000000000000000000022-2-20000
χ282222-2-22-2-22-2-22222222-2-2-22222-2-2-2-20000-220000000000000000000000000000-2-2220000
χ292222-2-22-2-2-222-2-2-222222-2-2-2-2-2-2-2-222000022000000000000000002-2000002-22-200000000
χ302222-2-22-2-2-222-2-2-222222-2-2-2-2-2-2-2-22200002200000000000000000-2200000-22-2200000000
χ312222-2-2-122-22222-2-1-1-1-2-211-1-111-1-1-1-1000011−i3−i3i3i3−i3−i3i3i300000000200-2-1-111−i3i3i3−i300000000
χ322222-2-2-122-22222-2-1-1-1-2-211-1-111-1-1-1-1000011−i3−i3i3i3−i3−i3i3i300000000-200211-1-1i3−i3−i3i300000000
χ332222-2-2-122-22222-2-1-1-1-2-211-1-111-1-1-1-1000011i3i3−i3−i3i3i3−i3−i300000000200-2-1-111i3−i3−i3i300000000
χ342222-2-2-122-22222-2-1-1-1-2-211-1-111-1-1-1-1000011i3i3−i3−i3i3i3−i3−i300000000-200211-1-1−i3i3i3−i300000000
χ352222-2-2-1-2-2-222-2-2-2-1-1-12211111111-1-10000-1-1−i3−i3i3i3i3i3−i3−i30000000002-20−i3i3i3−i3-11-1100000000
χ362222-2-2-1-2-2-222-2-2-2-1-1-12211111111-1-10000-1-1−i3−i3i3i3i3i3−i3−i3000000000-220i3−i3−i3i31-11-100000000
χ372222-2-2-1-2-2-222-2-2-2-1-1-12211111111-1-10000-1-1i3i3−i3−i3−i3−i3i3i30000000002-20i3−i3−i3i3-11-1100000000
χ382222-2-2-1-2-2-222-2-2-2-1-1-12211111111-1-10000-1-1i3i3−i3−i3−i3−i3i3i3000000000-220−i3i3i3−i31-11-100000000
χ392-2-222-220022-200-2-22-2002-2002-2002-2002i−2i0000002i−2i2i−2i−i2−i2i2i2−i2−i2i2i20000000000002−22−20000
χ402-2-222-220022-200-2-22-2002-2002-2002-2002i−2i0000002i−2i2i−2ii2i2−i2−i2i2i2−i2−i2000000000000−22−220000
χ412-2-222-220022-200-2-22-2002-2002-2002-200−2i2i000000−2i2i−2i2i−i2−i2i2i2−i2−i2i2i2000000000000−22−220000
χ422-2-222-220022-200-2-22-2002-2002-2002-200−2i2i000000−2i2i−2i2ii2i2−i2−i2i2i2−i2−i20000000000002−22−20000
χ432-2-22-222002-2200-2-22-200-22002-200-222i−2i00002i−2i2i−2i0000−i2−i2i2i2i2i2−i2−i20000000000002−2−220000
χ442-2-22-222002-2200-2-22-200-22002-200-222i−2i00002i−2i2i−2i0000i2i2−i2−i2−i2−i2i2i2000000000000−222−20000
χ452-2-22-222002-2200-2-22-200-22002-200-22−2i2i0000−2i2i−2i2i0000−i2−i2i2i2i2i2−i2−i2000000000000−222−20000
χ462-2-22-222002-2200-2-22-200-22002-200-22−2i2i0000−2i2i−2i2i0000i2i2−i2−i2−i2−i2i2i20000000000002−2−220000
χ47444444-244-4-4-4-4-4-4-2-2-24-4-2-22222-2-22200002-2000000000000000000000000000000000000
χ48444444-2-4-4-4-4-444-4-2-2-2-44-2-2-2-22222220000-22000000000000000000000000000000000000
χ494444-4-4-2444-4-4-4-44-2-2-2-442222-2-2-2-2220000-22000000000000000000000000000000000000
χ504444-4-4-2-4-44-4-4444-2-2-24-422-2-2-2-2222200002-2000000000000000000000000000000000000
χ5144-4-4004000004-404-4-400004-4000000000000000000002-22-22-22-200000000000000000000
χ5244-4-4004000004-404-4-400004-400000000000000000000-22-22-22-2200000000000000000000
χ5344-4-400400000-4404-4-40000-44000000000000000000002-22-2-22-2200000000000000000000
χ5444-4-400400000-4404-4-40000-4400000000000000000000-22-222-22-200000000000000000000
χ554-44-40044-4000000-4-44000000004-400000000000000000000−2i22i22i2−2i200000000000000000000
χ564-44-40044-4000000-4-44000000004-4000000000000000000002i2−2i2−2i22i200000000000000000000
χ574-44-4004-44000000-4-4400000000-440000000000000000−2i22i22i2−2i2000000000000000000000000
χ584-44-4004-44000000-4-4400000000-4400000000000000002i2−2i2−2i22i2000000000000000000000000
χ594-4-444-4400-4-44004-44-4004-400-4400-44000000000000000000000000000000000000000000
χ604-4-444-4-20044-400-42-2200-2200-2200-22004i−4i000000−2i2i−2i2i0000000000000000000000000000
χ614-4-444-4-20044-400-42-2200-2200-2200-2200−4i4i0000002i−2i2i−2i0000000000000000000000000000
χ624-4-444-4-200-4-440042-2200-22002-2002-200000023−23−232300000000000000000000000000000000
χ634-4-444-4-200-4-440042-2200-22002-2002-2000000−232323−2300000000000000000000000000000000
χ644-4-44-44400-44-4004-44-400-4400-44004-4000000000000000000000000000000000000000000
χ654-4-44-44-2004-4400-42-22002-200-22002-24i−4i0000−2i2i−2i2i00000000000000000000000000000000
χ664-4-44-44-2004-4400-42-22002-200-22002-2−4i4i00002i−2i2i−2i00000000000000000000000000000000
χ674-4-44-44-200-44-40042-22002-2002-200-22000000000023−23−23230000000000000000000000000000
χ684-4-44-44-200-44-40042-22002-2002-200-220000000000−232323−230000000000000000000000000000
χ6988-8-800-4000008-80-4440000-44000000000000000000000000000000000000000000000000
χ7088-8-800-400000-880-44400004-4000000000000000000000000000000000000000000000000
χ718-88-800-48-800000044-400000000-4400000000000000000000000000000000000000000000
χ728-88-800-4-8800000044-4000000004-400000000000000000000000000000000000000000000

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