Finite Group Databasebeta

← Group #72284107

Character table — Group #72284107

Order 2048.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83
size112224444448888888888888888881616161616161616161616161616161616161616161616161616163232323232323232323232323232323232646464646464128128128128
order122442224444444448888888888882222444444444444444888888882224444488888888848161616164488
χ111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111111111111111111111-1-11111-1-11111111-1-1-1-1-1-1-1-1-1-1
χ31111111111111111111-1-1-1-1-1-1-1-1111-11111-1-1-11111-1-1-1-11111-1-1-1-1-1-11111-1-1-1-1111111-1-1-111-1-1-1-11-11-1
χ41111111111111111111-1-1-1-1-1-1-1-1111-11111-1-1-11111-1-1-1-11111-1-1-1-1-1-111-1-1-1-1-1-1-1-11111-1-1-1-1-11111-11-11
χ5111111111111-1-1111111111111111-1-111-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-11111111111-1-1-1-1-1-1-1111111-1-1-1-1
χ6111111111111-1-1111111111111111-1-111-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-111-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111
χ7111111111111-1-111111-1-1-1-1-1-1-1-111-1111-1-1111-1-1-1-111111111-1-1-1-1111111-1-1-1-111-1-1-1-111111-1-1-1-1-11-11
χ8111111111111-1-111111-1-1-1-1-1-1-1-111-1111-1-1111-1-1-1-111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1111-1-111111-11-1
χ911111-1-11111-1111-1-1111111-1-1-1-1111111-1-11-1-111-1-111-1-111-1-111-1-111-1-11111-1-1-1-111-1-11-1-1-1111-1-111-1-1
χ1011111-1-11111-1111-1-1111111-1-1-1-1111111-1-11-1-111-1-111-1-111-1-111-1-111-1-1-1-111-1-11111-1-11-1-11-1-1-111-1-111
χ1111111-1-11111-1111-1-111-1-1-1-11111111-111-1-1-11111-1-1-1-11111-1-1-1-111-1-1-1-111-1-111-1-111-1-1-111-11-1-1111-1-11
χ1211111-1-11111-1111-1-111-1-1-1-11111111-111-1-1-11111-1-1-1-11111-1-1-1-111-1-1-1-1-1-1-1-1111111-1-1-1111-111-1-1-111-1
χ1311111-1-11111-1-1-11-1-1111111-1-1-1-111-1-11111-111-1-111-1-11111-1-111-1-1-1-1-1-11111-1-1-1-1-1-111-111-1111-1-1-1-111
χ1411111-1-11111-1-1-11-1-1111111-1-1-1-111-1-11111-111-1-111-1-11111-1-111-1-1-1-1-1-1-1-111-1-111-1-111-1111-1-1-11111-1-1
χ1511111-1-11111-1-1-11-1-111-1-1-1-1111111-1111111-1-1-1-11111-1-111-1-1-1-11111-1-111-1-111-1-1-1-1111-1-1-11-1-111-111-1
χ1611111-1-11111-1-1-11-1-111-1-1-1-1111111-1111111-1-1-1-11111-1-111-1-1-1-11111-1-1-1-1-1-11111-1-1111-1-11-111-1-11-1-11
χ172222222222220022222222222222200-2-20000000000000-2-222222200-2-200-2-2-2-20000000000000000000
χ182222222222220022222-2-2-2-2-2-2-2-22200-2-20000000000000-2-222-2-2-2-200-2-20022220000000000000000000
χ1922222222222200222-2-200000000-2-2022-200222000022222-2-2-20000-2-22-2000000000000-2-2-20000000000
χ2022222222222200222-2-200000000-2-20-22-200-2-2-20000-2-2-2-22-2-2-20000222-20000000000002220000000000
χ2122222222222222222-2-200000000-2-220-222200022220000-22-2-2000000-2200000000-2-2-2-20000000000000
χ22222222222222-2-2222-2-200000000-2-2-20-22-2-2000-2-2-2-20000-22-2-2000000-220000000022220000000000000
χ2322222-2-22222-2002-2-2222222-2-2-2-22200-2-20000000000000-2-2-2-222-2-2002200-2-2220000000000000000000
χ2422222-2-22222-2002-2-222-2-2-2-222222200-2-20000000000000-2-2-2-2-2-22200220022-2-20000000000000000000
χ2522222-2-22222-2002-2-2-2-200000000-2-2022-2002-2-2000022-2-22-2220000-2-2-22000000000000-2220000000000
χ2622222-2-22222-2002-2-2-2-200000000-2-20-22-200-2220000-2-2222-222000022-220000000000002-2-20000000000
χ2722222-2-22222-2222-2-2-2-200000000-2-220-22-2-200022-2-20000-22220000002-200000000-2-2220000000000000
χ2822222-2-22222-2-2-22-2-2-2-200000000-2-2-20-2222000-2-2220000-22220000002-20000000022-2-20000000000000
χ29222-2-200-2222000-2002-2000022-2-22-2022-22-2-200002-22-200-2200002-2220000002-200002-2-2000000000000
χ30222-2-200-2222000-2002-2000022-2-22-20-22-2-2220000-22-2200-2200002-2-2-20000002-20000-222000000000000
χ31222-2-200-2222000-2002-20000-2-2222-2022-2-22-20000-222-200-220000-2222000000-220000-22-2000000000000
χ32222-2-200-2222000-2002-20000-2-2222-20-22-22-2200002-2-2200-220000-22-2-2000000-2200002-22000000000000
χ33222-2-200-2222000-200-2222-2-20000-2200-2-22-202-2002-2002-222002-2000000002-2000000-2202-20000000000
χ34222-2-200-2222000-200-2222-2-20000-2200-2-2-220-2200-2200-2222002-2000000002-20000002-20-220000000000
χ35222-2-200-2222000-200-22-2-2220000-2200-2-22-20-22002-200-222200-2200000000-22000000-220-220000000000
χ36222-2-200-2222000-200-22-2-2220000-2200-2-2-2202-200-22002-22200-2200000000-220000002-202-20000000000
χ37222-2-200-2222022-2002-2000022-2-22-2-20-220002-22-200002-22-200002-200000000-22002-2000-220000000000
χ38222-2-200-2222022-2002-20000-2-2222-2-20-22000-222-20000-222-20000-22000000002-2002-20002-20000000000
χ39222-2-200-2222022-200-2222-2-20000-22-222200-2002-2002-200-2-2002-200-2-20000-220000-22002000000000000
χ40222-2-200-2222022-200-22-2-2220000-22-2-222002002-200-2200-2-200-22002200002-20000-2200-2000000000000
χ41222-2-200-22220-2-2-2002-2000022-2-22-220-22000-22-220000-222-200002-200000000-2200-220002-20000000000
χ42222-2-200-22220-2-2-2002-20000-2-2222-220-220002-2-2200002-22-20000-22000000002-200-22000-220000000000
χ43222-2-200-22220-2-2-200-2222-2-20000-222-22200200-2200-2200-2-2002-200220000-2200002-200-2000000000000
χ44222-2-200-22220-2-2-200-22-2-2220000-22222200-200-22002-200-2-200-2200-2-200002-200002-2002000000000000
χ45444444444-4-4400-4-4-400000000000000000000000000000000000000000220000220000000-2-200000000
χ46444444444-4-4400-4-4-400000000000000000000000000000000000000000-2-20000-2-200000002200000000
χ474444444-4-400-4220000022222222002-20022-2-2-2-2-2-2-222220000-2-2-2-200000000000000000000000000000
χ484444444-4-400-42200000-2-2-2-2-2-2-2-200220022222-2-2-2-2-2-2-2-20000222200000000000000000000000000000
χ494444444-4-400-4-2-2000002222222200-2200-2-22222222-2-2-2-20000-2-2-2-200000000000000000000000000000
χ504444444-4-400-4-2-200000-2-2-2-2-2-2-2-200-2-200-2-2-2-2-2222222220000222200000000000000000000000000000
χ5144444-4-444-4-4-400-44400000000000000000000000000000000000000000220000-2-200000002-200000000
χ5244444-4-444-4-4-400-44400000000000000000000000000000000000000000-2-20000220000000-2200000000
χ5344444-4-4-4-400422000002222-2-2-2-2002-200-2-2-222-2-22222-2-20000-2-22200000000000000000000000000000
χ5444444-4-4-4-40042200000-2-2-2-22222002200-2-22-2-2-2-222-2-222000022-2-200000000000000000000000000000
χ5544444-4-4-4-4004-2-2000002222-2-2-2-200-2200222-2-222-2-2-2-2220000-2-22200000000000000000000000000000
χ5644444-4-4-4-4004-2-200000-2-2-2-2222200-2-20022-22222-2-222-2-2000022-2-200000000000000000000000000000
χ57444-4-4004-40002204-40022-2-222-2-200-2-2002-22-22-22-222-22-20000-22-2200000000000000000000000000000
χ58444-4-4004-40002204-400-2-222-2-22200-22002-2-22-2-22-22-22-2200002-22-200000000000000000000000000000
χ59444-4-4004-4000220-440022-2-2-2-22200-2-200-2222-2-222-22-2-220000-222-200000000000000000000000000000
χ60444-4-4004-4000220-4400-2-22222-2-200-2200-22-2-22-222-2-222-200002-2-2200000000000000000000000000000
χ61444-4-4004-4000-2-204-40022-2-222-2-2002200-22-22-22-22-2-22-220000-22-2200000000000000000000000000000
χ62444-4-4004-4000-2-204-400-2-222-2-222002-200-222-222-22-22-22-200002-22-200000000000000000000000000000
χ63444-4-4004-4000-2-20-440022-2-2-2-2220022002-2-2-222-2-22-222-20000-222-200000000000000000000000000000
χ64444-4-4004-4000-2-20-4400-2-22222-2-2002-2002-222-22-2-222-2-2200002-2-2200000000000000000000000000000
χ6544-4-444-40000000000222i2−2i22i2−2i22i2−2i22i2−2i2-2-200000000000000000002-2000000002-200002-2000000000i2−i2i2−i20000
χ6644-4-444-40000000000222i2−2i22i2−2i22i2−2i22i2−2i2-2-200000000000000000002-200000000-220000-22000000000−i2i2−i2i20000
χ6744-4-444-4000000000022−2i22i2−2i22i2−2i22i2−2i22i2-2-200000000000000000002-2000000002-200002-2000000000−i2i2−i2i20000
χ6844-4-444-4000000000022−2i22i2−2i22i2−2i22i2−2i22i2-2-200000000000000000002-200000000-220000-22000000000i2−i2i2−i20000
χ6944-4-44-440000000000222i2−2i22i2−2i2−2i22i2−2i22i2-2-20000000000000000000-22000000002-20000-22000000000i2−i2−i2i20000
χ7044-4-44-440000000000222i2−2i22i2−2i2−2i22i2−2i22i2-2-20000000000000000000-2200000000-2200002-2000000000−i2i2i2−i20000
χ7144-4-44-44000000000022−2i22i2−2i22i22i2−2i22i2−2i2-2-20000000000000000000-22000000002-20000-22000000000−i2i2i2−i20000
χ7244-4-44-44000000000022−2i22i2−2i22i22i2−2i22i2−2i2-2-20000000000000000000-2200000000-2200002-2000000000i2−i2−i2i20000
χ73888-8-800-88-8-8000800000000000000000000000000000000000000000000000000000000000000000000
χ7488-88-80000000000004-400004i2−4i2−4i24i2-44000000000000000000000000000000000000000000000000000000
χ7588-88-80000000000004-40000−4i24i24i2−4i2-44000000000000000000000000000000000000000000000000000000
χ7688-88-8000000000000-444i2−4i2−4i24i200004-4000000000000000000000000000000000000000000000000000000
χ7788-88-8000000000000-44−4i24i24i2−4i200004-4000000000000000000000000000000000000000000000000000000
χ7888-8-888-80000000000-4-400000000440000000000000000000-44000000000000000000000000000000000
χ7988-8-88-880000000000-4-4000000004400000000000000000004-4000000000000000000000000000000000
χ8016-1600000008-800000000000000000000000000000000000000000004i2−4i2000000000000000000000000000
χ8116-1600000008-80000000000000000000000000000000000000000000−4i24i2000000000000000000000000000
χ8216-160000000-8808i−8i000000000000000000000000000000000000000000000000000000000000000000000
χ8316-160000000-880−8i8i000000000000000000000000000000000000000000000000000000000000000000000

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