Finite Group Databasebeta

← Group #72324300

Character table — Group #72324300

Order 4096.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88
size11222444444888888888888161616161616161616163232323232323232323232323232323232323232323232323232323232323264646464128128128128128128128128128128128128128128128128128128128128
order1222222222222222222222222224444442222244444444444444444444444444444444444444888888888888
χ11111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ3111111111111111111111111111111111111-1-111-1-111111111-1-1-1-11111111111-1-1-1-1-1-1-1-111-1-111-1-11111-1-1-1-1
χ4111111111111111111111111111111111111-1-111-1-111111111-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-111-1-111-1-1-1-11111
χ51111111111111111111111111111111111-1-111-1-1111111-1-1-1-11111-1-1-1-1-1-1-1-1111111-1-1-1-111111111-1-1-1-1-1-1-1-1
χ61111111111111111111111111111111111-1-111-1-1111111-1-1-1-11111-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-111111111
χ71111111111111111111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-1111111-1-111-1-1-1-1-1-11111
χ81111111111111111111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-11111-1-111-1-1111111-1-1-1-1
χ91111111111111111111111111-1-11111-1-11111-1111-1-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-111-1-111-1-1i−ii−ii−ii−iii−i−iii−i−i
χ101111111111111111111111111-1-11111-1-11111-1111-1-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-111-1-111-1-1−ii−ii−ii−ii−i−iii−i−iii
χ111111111111111111111111111-1-11111-1-1111-1111-11-1-1-1-11111-1-111-1-1-1-1-1-1-1-1-1-1-1-111-1-111i−i−iii−i−iiii−i−i−i−iii
χ121111111111111111111111111-1-11111-1-1111-1111-11-1-1-1-11111-1-111-1-1-1-1-1-1-1-1-1-1-1-111-1-111−iii−i−iii−i−i−iiiii−i−i
χ131111111111111111111111111-1-11111-1-11-1-11-1-1-11-1-1-1-1-1-1-1-1-111-1-111111111-1-111-1-1-1-111i−ii−ii−ii−i−i−iii−i−iii
χ141111111111111111111111111-1-11111-1-11-1-11-1-1-11-1-1-1-1-1-1-1-1-111-1-111111111-1-111-1-1-1-111−ii−ii−ii−iiii−i−iii−i−i
χ151111111111111111111111111-1-11111-1-11-1-1-11-1-1-11-1-1-1-1-1-1-1-1-1-11111111111-1-1-1-11111-1-1i−i−iii−i−ii−i−iiiii−i−i
χ161111111111111111111111111-1-11111-1-11-1-1-11-1-1-11-1-1-1-1-1-1-1-1-1-11111111111-1-1-1-11111-1-1−iii−i−iii−iii−i−i−i−iii
χ172222222222222222222-2-2-2-22222-2-2-2-222-200000000-22-2-20000000000000000-2200000000002200-2-200000000
χ182222222222222222222-2-2-2-22222-2-2-2-222-200000000-22-2-20000000000000000-220000000000-2-2002200000000
χ192222222222222222222-2-2-2-222-2-2-2-2-2-2-2-2-2000000002-22200000000000000002-200000000002i−2i00−2i2i00000000
χ202222222222222222222-2-2-2-222-2-2-2-2-2-2-2-2-2000000002-22200000000000000002-20000000000−2i2i002i−2i00000000
χ21222222222222222-2-2-2-22222-2-22222-2-222-200220022-2-2220000222200000000-2-2-2-2-2-200000000000000000000
χ22222222222222222-2-2-2-22222-2-22222-2-222-200-2-200-2-2-2-2220000-2-2-2-200000000-2-2222200000000000000000000
χ23222222222222222-2-2-2-22222-2-2-2-222-2-2-2-2-2002-2002-222-2-2000022-2-20000000022-2-22200000000000000000000
χ24222222222222222-2-2-2-22222-2-2-2-222-2-2-2-2-200-2200-2222-2-20000-2-222000000002222-2-200000000000000000000
χ25222222222222222-2-2-2-2-2-2-2-2-2-222-2-222222000000002-2-2-200000000000000002-2000000002200-2-20000000000
χ26222222222222222-2-2-2-2-2-2-2-2-2-222-2-222222000000002-2-2-200000000000000002-200000000-2-200220000000000
χ27222222222222222-2-2-2-2-2-2-2-2-2-2-2-2-2-222-2-2200000000-22220000000000000000-22000000002i−2i00−2i2i0000000000
χ28222222222222222-2-2-2-2-2-2-2-2-2-2-2-2-2-222-2-2200000000-22220000000000000000-2200000000−2i2i002i−2i0000000000
χ29222222-2-22222-2-2-222222222-2-22-2-2-2-2-22-22000000002-22-20000000000000000-2200002-22-20000000000000000
χ30222222-2-22222-2-2-222222222-2-22-2-2-2-2-22-22000000002-22-20000000000000000-220000-22-220000000000000000
χ31222222-2-22222-2-2-222222222-2-2-22-2-2-2-2-22200000000-22-2200000000000000002-200002-2-220000000000000000
χ32222222-2-22222-2-2-222222222-2-2-22-2-2-2-2-22200000000-22-2200000000000000002-20000-222-20000000000000000
χ33222222-2-22222-2-2-22222-2-2-2-2-2-22-222222-2-200000000-2-2-2200000000000000002200000000000000002-22-20000
χ34222222-2-22222-2-2-22222-2-2-2-2-2-22-222222-2-200000000-2-2-220000000000000000220000000000000000-22-220000
χ35222222-2-22222-2-2-22222-2-2-2-2-2-2-222222-22-200000000222-20000000000000000-2-200000000000000002i−2i−2i2i0000
χ36222222-2-22222-2-2-22222-2-2-2-2-2-2-222222-22-200000000222-20000000000000000-2-20000000000000000−2i2i2i−2i0000
χ37222222-2-22222-2-2-2-2-2-2-22222222-2-2-2222-2-222002200-222-2-2-2-2-200002222-2-2-2-22-2000000000000000000000000
χ38222222-2-22222-2-2-2-2-2-2-22222222-2-2-2222-2-2-2-200-2-200-222-222220000-2-2-2-222222-2000000000000000000000000
χ39222222-2-22222-2-2-2-2-2-2-2222222-22-2-222-22-2220022002-2-22-2-2-2-20000-2-2-2-22222-22000000000000000000000000
χ40222222-2-22222-2-2-2-2-2-2-2222222-22-2-222-22-2-2-200-2-2002-2-22222200002222-2-2-2-2-22000000000000000000000000
χ41222222-2-22222-2-2-2-2-2-2-2-2-2-2-2222-222-2-22-220000000022-220000000000000000-2-2000000000000000000002i−2i2i−2i
χ42222222-2-22222-2-2-2-2-2-2-2-2-2-2-2222-222-2-22-220000000022-220000000000000000-2-200000000000000000000−2i2i−2i2i
χ43222222-2-22222-2-2-2-2-2-2-2-2-2-2-222-2222-2-2-22200000000-2-22-2000000000000000022000000000000000000002-2-22
χ44222222-2-22222-2-2-2-2-2-2-2-2-2-2-222-2222-2-2-22200000000-2-22-200000000000000002200000000000000000000-222-2
χ4544444444-4-44-44-4-40000000000440000-4-402200-2-200000022-2-2000022-2-222-2-200000000000000000000000000
χ4644444444-4-44-44-4-40000000000440000-4-40-2-20022000000-2-2220000-2-222-2-22200000000000000000000000000
χ4744444444-4-44-44-4-40000000000-4-400004402200-2-200000022-2-20000-2-222-2-22200000000000000000000000000
χ4844444444-4-44-44-4-40000000000-4-40000440-2-20022000000-2-222000022-2-222-2-200000000000000000000000000
χ49444444-4-4-4-44-4-44400000000004-40000-4402200-2-2000000-2-222000022-2-2-2-22200000000000000000000000000
χ50444444-4-4-4-44-4-44400000000004-40000-440-2-2002200000022-2-20000-2-22222-2-200000000000000000000000000
χ51444444-4-4-4-44-4-4440000000000-4400004-402200-2-2000000-2-2220000-2-22222-2-200000000000000000000000000
χ52444444-4-4-4-44-4-4440000000000-4400004-40-2-2002200000022-2-2000022-2-2-2-22200000000000000000000000000
χ5344444-44444-4-4-44-4000044-4-400004-400000000400040000000000-4-40000000000000000000000000000000000
χ5444444-44444-4-4-44-4000044-4-400004-400000000-4000-40000000000440000000000000000000000000000000000
χ5544444-44444-4-4-44-40000-4-4440000-44000000040004000000000-4-4000000000000000000000000000000000000
χ5644444-44444-4-4-44-40000-4-4440000-440000000-4000-400000000044000000000000000000000000000000000000
χ5744444-4-4-444-4-44-44000044-4-40000-4400000000000000000000000000000000000004-400000000000000000000
χ5844444-4-4-444-4-44-44000044-4-40000-440000000000000000000000000000000000000-4400000000000000000000
χ5944444-4-4-444-4-44-440000-4-44400004-4000000000000000000000000000000000004-40000000000000000000000
χ6044444-4-4-444-4-44-440000-4-44400004-400000000000000000000000000000000000-440000000000000000000000
χ6188888-888-8-8-88-8-880000000000000000000000000000000000000000000000000000000000000000000000000
χ6288888-8-8-8-8-8-8888-80000000000000000000000000000000000000000000000000000000000000000000000000
χ6388-88-80008-8000000000008-8000000000000004000-400000000004-40000000000000000000000000000000000
χ6488-88-80008-8000000000008-800000000000000-400040000000000-440000000000000000000000000000000000
χ6588-88-80008-800000000000-88000000000000004000-40000000000-440000000000000000000000000000000000
χ6688-88-80008-800000000000-8800000000000000-4000400000000004-40000000000000000000000000000000000
χ6788-88-8000-880000000008-80000000000000004000-40000000004-4000000000000000000000000000000000000
χ6888-88-8000-880000000008-8000000000000000-40004000000000-44000000000000000000000000000000000000
χ6988-88-8000-88000000000-880000000000000004000-4000000000-44000000000000000000000000000000000000
χ7088-88-8000-88000000000-88000000000000000-400040000000004-4000000000000000000000000000000000000
χ7188-8-8808-8000000044-4-400004-400000000000004-4000000004-400000000000000000000000000000000000000
χ7288-8-8808-8000000044-4-400004-40000000000000-4400000000-4400000000000000000000000000000000000000
χ7388-8-8808-80000000-4-4440000-440000000004-400000000004-40000000000000000000000000000000000000000
χ7488-8-8808-80000000-4-4440000-44000000000-440000000000-440000000000000000000000000000000000000000
χ7588-8-880-88000000044-4-40000-440000000004-40000000000-440000000000000000000000000000000000000000
χ7688-8-880-88000000044-4-40000-44000000000-4400000000004-40000000000000000000000000000000000000000
χ7788-8-880-880000000-4-44400004-400000000000004-400000000-4400000000000000000000000000000000000000
χ7888-8-880-880000000-4-44400004-40000000000000-44000000004-400000000000000000000000000000000000000
χ79161616-16-160000000000000000000000008-8000000000000000000000000000000000000000000000000000000000
χ80161616-16-16000000000000000000000000-88000000000000000000000000000000000000000000000000000000000
χ8116-1600080000-80000008-800000000000000000000000000000000000004i−4i004i−4i00000000000000000000000000
χ8216-1600080000-80000008-80000000000000000000000000000000000000−4i4i00−4i4i00000000000000000000000000
χ8316-1600080000-8000000-8800000000000000000000000000000000000004i−4i00−4i4i00000000000000000000000000
χ8416-1600080000-8000000-880000000000000000000000000000000000000−4i4i004i−4i00000000000000000000000000
χ8516-16000-80000800008-800000000000000000000000000000000000004-4004-40000000000000000000000000000
χ8616-16000-80000800008-80000000000000000000000000000000000000-4400-440000000000000000000000000000
χ8716-16000-8000080000-8800000000000000000000000000000000000004-400-440000000000000000000000000000
χ8816-16000-8000080000-880000000000000000000000000000000000000-44004-40000000000000000000000000000

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