Finite Group Databasebeta

← Group #72324325

Character table — Group #72324325

Order 2048.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59
size112224444888881616161616161616161616161616161616163232323232323232326464646464646464646464646464128128128128
order12222222222222222224444444444444444444444444444444488888888
χ111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1
χ311111111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1-1-111111111-1-1-1-1
χ411111111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-11111
χ511111111111111111-1-1111-111111111-11-1-1-1-1-1-1-1-11-111-1-1ii−i−iii−i−iii−i−i
χ611111111111111111-1-1111-111111111-11-1-1-1-1-1-1-1-11-111-1-1−i−iii−i−iii−i−iii
χ711111111111111111-1-1111-1-1-1-1-1-1-1-1-1-11-1-11111-1-11-1-1-111ii−i−iii−i−i−i−iii
χ811111111111111111-1-1111-1-1-1-1-1-1-1-1-1-11-1-11111-1-11-1-1-111−i−iii−i−iiiii−i−i
χ91111111111111111-11-111-1111111111-1-11-1-1-1-1-1-1-1-11-1-111i−ii−ii−ii−ii−ii−i
χ101111111111111111-11-111-1111111111-1-11-1-1-1-1-1-1-1-11-1-111−ii−ii−ii−ii−ii−ii
χ111111111111111111-11-111-11-1-1-1-1-1-1-1-1-1-11-11111-1-1-1111-1-1i−ii−ii−ii−i−ii−ii
χ121111111111111111-11-111-11-1-1-1-1-1-1-1-1-1-11-11111-1-1-1111-1-1−ii−ii−ii−iii−ii−i
χ131111111111111111-1-1111-1-1111111111-1-11111111-1-1-1-1-1-11-1-111-1-111-1-11
χ141111111111111111-1-1111-1-1111111111-1-11111111-1-1-1-1-1-1-111-1-111-1-111-1
χ151111111111111111-1-1111-1-1-1-1-1-1-1-1-1-11-1-11-1-1-1-111-1-111111-1-111-1-11-111-1
χ161111111111111111-1-1111-1-1-1-1-1-1-1-1-1-11-1-11-1-1-1-111-1-11111-111-1-111-11-1-11
χ1722222222222222-2-2222-2-2220000000022220000-2-2-2-20000000000000000
χ1822222222222222-2-22-2-2-2-22-200000000-22-2-2000022-220000000000000000
χ1922222222222222-2-2-22-2-2-2-2200000000-2-22-20000222-20000000000000000
χ2022222222222222-2-2-2-22-2-2-2-2000000002-2-220000-2-2220000000000000000
χ212222222222-2-2-2-222002-2-20000000000200-20000-2200000002200-2-200000
χ222222222222-2-2-2-222002-2-20000000000200-20000-220000000-2-2002200000
χ232222222222-2-2-2-22200-2-2-20000000000-200200002-200000002i−2i00−2i2i00000
χ242222222222-2-2-2-22200-2-2-20000000000-200200002-20000000−2i2i002i−2i00000
χ252222222222-2-2-2-2-2-2002220000000000200-200002-20000002002-200-20000
χ262222222222-2-2-2-2-2-2002220000000000200-200002-2000000-200-220020000
χ272222222222-2-2-2-2-2-200-2220000000000-20020000-220000002i00−2i−2i002i0000
χ282222222222-2-2-2-2-2-200-2220000000000-20020000-22000000−2i002i2i00−2i0000
χ29444444-4-44-400000000400002222-2-2-2-2-400022-2-200000000000000000000
χ30444444-4-44-40000000040000-2-2-2-22222-4000-2-22200000000000000000000
χ31444444-4-44-400000000-400002222-2-2-2-24000-2-22200000000000000000000
χ32444444-4-44-400000000-40000-2-2-2-22222400022-2-200000000000000000000
χ3344444-444-4-44-44-40004000040000000000-40000000000000000000000000
χ3444444-444-4-44-44-4000-40000-4000000000040000000000000000000000000
χ3544444-444-4-4-44-44004000040000000000-400000000000000000000000000
χ3644444-444-4-4-44-4400-40000-40000000000400000000000000000000000000
χ3744-44-404-400040-40040000-402i2i−2i−2i2i2i−2i−2i0000000000002i−2i00000000000000
χ3844-44-404-400040-40040000-40−2i−2i2i2i−2i−2i2i2i000000000000−2i2i00000000000000
χ3944-44-404-400040-400-40000402i2i−2i−2i2i2i−2i−2i000000000000−2i2i00000000000000
χ4044-44-404-400040-400-4000040−2i−2i2i2i−2i−2i2i2i0000000000002i−2i00000000000000
χ4144-44-40-440040-4000040000-42i2i−2i−2i−2i−2i2i2i000000000000002i−2i000000000000
χ4244-44-40-440040-4000040000-4−2i−2i2i2i2i2i−2i−2i00000000000000−2i2i000000000000
χ4344-44-40-440040-40000-4000042i2i−2i−2i−2i−2i2i2i00000000000000−2i2i000000000000
χ4444-44-40-440040-40000-400004−2i−2i2i2i2i2i−2i−2i000000000000002i−2i000000000000
χ4588888-8-8-8-880000000000000000000000000000000000000000000000000
χ46888-8-8000000000000004-40000004i−4i4i−4i0000000000000000000000000000
χ47888-8-8000000000000004-4000000−4i4i−4i4i0000000000000000000000000000
χ48888-8-800000000000000-44004i−4i4i−4i00000000000000000000000000000000
χ49888-8-800000000000000-4400−4i4i−4i4i00000000000000000000000000000000
χ5088-88-808-8000-808000000000000000000000000000000000000000000000
χ5188-88-80-8800-8080000000000000000000000000000000000000000000000
χ5288-8-880000000004-4000000000004-4-440000000000000000000000000000
χ5388-8-880000000004-400000000000-444-40000000000000000000000000000
χ5488-8-88000000000-4400000004-4-4400000000000000000000000000000000
χ5588-8-88000000000-440000000-444-400000000000000000000000000000000
χ5616-16000800-800000000000000000000000000004i−4i00000000000000000000
χ5716-16000800-80000000000000000000000000000−4i4i00000000000000000000
χ5816-16000-8008000000000000000000000000004-40000000000000000000000
χ5916-16000-800800000000000000000000000000-440000000000000000000000

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