Finite Group Databasebeta

← Group #133293

Character table — Group #133293

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44
size11112222444448888888888161616161616161616161616161616161632323232
order12222222222222222224444244444444444444444444
χ111111111111111111111111111111111111111111111
χ211111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1
χ311111111111111111111111-11-1-1-1-1-1-1-111111111-1-1-1-1
χ411111111111111111111111-11-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111
χ51111111111111-1-1-1-11111-1-11-11-1-111-1-11111-1-1-1-111-1-1
χ61111111111111-1-1-1-11111-1-11-11-1-111-1-1-1-1-1-11111-1-111
χ71111111111111-1-1-1-11111-1-1-1-1-111-1-1111111-1-1-1-1-1-111
χ81111111111111-1-1-1-11111-1-1-1-1-111-1-111-1-1-1-1111111-1-1
χ9111111111-1-1-1-111-1-1-1-111111-1111-1-1-1-1ii−i−iii−i−ii−ii−i
χ10111111111-1-1-1-111-1-1-1-111111-1111-1-1-1-1−i−iii−i−iii−ii−ii
χ11111111111-1-1-1-111-1-1-1-11111-1-1-1-1-11111ii−i−iii−i−i−ii−ii
χ12111111111-1-1-1-111-1-1-1-11111-1-1-1-1-11111−i−iii−i−iiii−ii−i
χ13111111111-1-1-1-1-1-111-1-111-1-1111-1-1-1-111ii−i−i−i−iiii−i−ii
χ14111111111-1-1-1-1-1-111-1-111-1-1111-1-1-1-111−i−iiiii−i−i−iii−i
χ15111111111-1-1-1-1-1-111-1-111-1-1-11-11111-1-1ii−i−i−i−iii−iii−i
χ16111111111-1-1-1-1-1-111-1-111-1-1-11-11111-1-1−i−iiiii−i−ii−i−ii
χ1722222222222222222-2-2-2-2-2-20-20000000000000000000
χ182222222222222-2-2-2-2-2-2-2-222020000000000000000000
χ19222222222-2-2-2-222-2-222-2-2-2-2020000000000000000000
χ20222222222-2-2-2-2-2-22222-2-2220-20000000000000000000
χ212222-2-222-22-22-200002-22-2000002-2002-2000000000000
χ222222-2-222-22-22-200002-22-200000-2200-22000000000000
χ232222-2-222-22-22-20000-22-220020-2002-200000000000000
χ242222-2-222-22-22-20000-22-2200-20200-2200000000000000
χ252222-2-222-2-22-2200002-2-220020-200-2200000000000000
χ262222-2-222-2-22-2200002-2-2200-202002-200000000000000
χ272222-2-222-2-22-220000-222-2000002-200-22000000000000
χ282222-2-222-2-22-220000-222-200000-22002-2000000000000
χ29444444-4-4-400004-400000000000000000000000000000
χ30444444-4-4-40000-4400000000000000000000000000000
χ314444-4-4-4-440000000000004-4000000000000000000000
χ324444-4-4-4-44000000000000-44000000000000000000000
χ3344-4-4004-40040-4000000000000000000000002i−2i2i−2i0000
χ3444-4-4004-40040-400000000000000000000000−2i2i−2i2i0000
χ3544-4-4004-400-404000000000000000000000002-2-220000
χ3644-4-4004-400-40400000000000000000000000-222-20000
χ3744-4-400-44040-4000000000000000000002i−2i2i−2i00000000
χ3844-4-400-44040-400000000000000000000−2i2i−2i2i00000000
χ3944-4-400-440-404000000000000000000002-2-2200000000
χ4044-4-400-440-40400000000000000000000-222-200000000
χ418-88-8000000000004-4000000000000000000000000000
χ428-88-800000000000-44000000000000000000000000000
χ438-8-888-800000000000000000000000000000000000000
χ448-8-88-8800000000000000000000000000000000000000

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