Finite Group Databasebeta

← Group #365366

Character table — Group #365366

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92
size1111111122222222222222222222444444444444444444444444444488888888888888888888888888881616161616161616
order12222222222222224444444444442244444444444444444444444444224444444444444444448888888844448888
χ111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111111111111111111111-1-1-1-1-1-111-1-1-1-1-1-111-1-1-1-111111111-1-1-1-1-1-1-1-1
χ31111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ41111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-111111111
χ5111111111111111111111111111111-1-1-1-111-1-1-1-11111111111111111111111-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111
χ6111111111111111111111111111111-1-1-1-111-1-1-1-11111111111111111-1-1-1-1-1-1-1-1-1-11111-1-11111-1-1-1-1-1-1-1-11111-1-1-1-1
χ7111111111111111111111111111111-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111-1-111-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-1
χ8111111111111111111111111111111-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1111111111111-1-1-1-11111
χ911111111111-1-1-1-1111111-1-1-1-1111-1-11111-1-1111111111111-1-1-1-1-1-1-1-111-1-1-1-1-1-111-1-1-1-1-1-111111111-1-1-1-111-1-111-1-1
χ1011111111111-1-1-1-1111111-1-1-1-1111-1-11111-1-1111111111111-1-1-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1-1-1-1-11111-1-1-1-1-1-111-1-111
χ1111111111111-1-1-1-1111111-1-1-1-1111-1-11111-1-11111-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-111-1-1-1-1-1-11111-1-1-1-11111-1-111-1-111
χ1211111111111-1-1-1-1111111-1-1-1-1111-1-11111-1-11111-1-1-1-1-1-1-1-111111111-1-11111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1111111-1-111-1-1
χ1311111111111-1-1-1-1111111-1-1-1-1111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-111-1-1-1-11111111111-1-1-1-1-1-1-1-11111-1-11111-1-1
χ1411111111111-1-1-1-1111111-1-1-1-1111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1111111-1-1-1-1111111-1-1-1-111
χ1511111111111-1-1-1-1111111-1-1-1-1111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111-1-1-1-11111111111-1-1-1-11111-1-1-1-111-1-1-1-111
χ1611111111111-1-1-1-1111111-1-1-1-1111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1111111-1-1-1-1-1-11111111111-1-1-1-1-1-11111-1-1
χ171-111-11-1-11-1-111-1-1111-1-1-111-1-111-11-1ii−i−i1-1ii−i−i1111-1-1-1-11111-1-1-1-11-111-1-1i−i1-1ii−i−ii−iii−i−iii−i−iii−i−ii−ii−i1-11-1
χ181-111-11-1-11-1-111-1-1111-1-1-111-1-111-11-1ii−i−i1-1ii−i−i1111-1-1-1-11111-1-1-1-1-11-1-111i−i-11−i−iiii−i−i−iiiii−i−iii−i−i−ii−ii-11-11
χ191-111-11-1-11-1-111-1-1111-1-1-111-1-111-11-1ii−i−i1-1ii−i−i-1-1-1-11111-1-1-1-111111-111-1-1i−i1-1ii−i−ii−iii−i−i−i−iii−i−iii−ii−ii-11-11
χ201-111-11-1-11-1-111-1-1111-1-1-111-1-111-11-1ii−i−i1-1ii−i−i-1-1-1-11111-1-1-1-11111-11-1-111i−i-11−i−iiii−i−i−iii−i−iii−i−iiii−ii−i1-11-1
χ211-111-11-1-11-1-111-1-1111-1-1-111-1-111-11-1−i−iii1-1−i−iii1111-1-1-1-11111-1-1-1-11-111-1-1−ii1-1−i−iii−ii−i−iii−i−iii−i−iii−ii−ii1-11-1
χ221-111-11-1-11-1-111-1-1111-1-1-111-1-111-11-1−i−iii1-1−i−iii1111-1-1-1-11111-1-1-1-1-11-1-111−ii-11ii−i−i−iiii−i−i−i−iii−i−iiii−ii−i-11-11
χ231-111-11-1-11-1-111-1-1111-1-1-111-1-111-11-1−i−iii1-1−i−iii-1-1-1-11111-1-1-1-111111-111-1-1−ii1-1−i−iii−ii−i−iiiii−i−iii−i−ii−ii−i-11-11
χ241-111-11-1-11-1-111-1-1111-1-1-111-1-111-11-1−i−iii1-1−i−iii-1-1-1-11111-1-1-1-11111-11-1-111−ii-11ii−i−i−iiii−i−iii−i−iii−i−i−ii−ii1-11-1
χ251-111-11-1-11-1-1-1-111111-1-1-1-1-11111-1-11ii−i−i-11ii−i−i1111-1-1-1-1-1-1-1-111111-1-1-111−ii1-1−i−iii−iiii−i−iii−i−i−i−iiii−i−ii1-1-11
χ261-111-11-1-11-1-1-1-111111-1-1-1-1-11111-1-11ii−i−i-11ii−i−i1111-1-1-1-1-1-1-1-11111-1111-1-1−ii-11ii−i−i−ii−i−iiiii−i−i−i−iii−iii−i-111-1
χ271-111-11-1-11-1-1-1-111111-1-1-1-1-11111-1-11ii−i−i-11ii−i−i-1-1-1-111111111-1-1-1-11-1-1-111−ii1-1−i−iii−iiii−i−i−i−iiiii−i−i−iii−i-111-1
χ281-111-11-1-11-1-1-1-111111-1-1-1-1-11111-1-11ii−i−i-11ii−i−i-1-1-1-111111111-1-1-1-1-1111-1-1−ii-11ii−i−i−ii−i−iii−i−iiiii−i−ii−i−ii1-1-11
χ291-111-11-1-11-1-1-1-111111-1-1-1-1-11111-1-11−i−iii-11−i−iii1111-1-1-1-1-1-1-1-111111-1-1-111i−i1-1ii−i−ii−i−i−iii−i−iiiii−i−i−iii−i1-1-11
χ301-111-11-1-11-1-1-1-111111-1-1-1-1-11111-1-11−i−iii-11−i−iii1111-1-1-1-1-1-1-1-11111-1111-1-1i−i-11−i−iiii−iii−i−i−i−iiiii−i−ii−i−ii-111-1
χ311-111-11-1-11-1-1-1-111111-1-1-1-1-11111-1-11−i−iii-11−i−iii-1-1-1-111111111-1-1-1-11-1-1-111i−i1-1ii−i−ii−i−i−iiiii−i−i−i−iiii−i−ii-111-1
χ321-111-11-1-11-1-1-1-111111-1-1-1-1-11111-1-11−i−iii-11−i−iii-1-1-1-111111111-1-1-1-1-1111-1-1i−i-11−i−iiii−iii−i−iii−i−i−i−iii−iii−i1-1-11
χ332222222222222222-2-2-2-2-2-2-2-2-2-2-2-2220000-2-20000000000000000000000000000002-22-2002-22-20000000000000000
χ342222222222222222-2-2-2-2-2-2-2-2-2-2-2-2220000-2-2000000000000000000000000000000-22-2200-22-220000000000000000
χ3522222222222-2-2-2-22-2-2-2-2-22222-2-2-2-2-20000220000000000000000000000000000002-22-200-22-220000000000000000
χ3622222222222-2-2-2-22-2-2-2-2-22222-2-2-2-2-2000022000000000000000000000000000000-22-22002-22-20000000000000000
χ3722222222-2-2-22222-2222-2-22222-2-22-2-20000-2-200000000000000000000222-22-200-2-200000000000000000000000000
χ3822222222-2-2-22222-2222-2-22222-2-22-2-20000-2-200000000000000000000-2-2-22-22002200000000000000000000000000
χ3922222222-2-2-22222-2-2-2-222-2-2-2-222-2-2-2222222-2-2-2-2000000000000000000000022000000-2-200000000000000000000
χ4022222222-2-2-22222-2-2-2-222-2-2-2-222-2-2-2-2-2-2-22222220000000000000000000000-2-20000002200000000000000000000
χ4122222222-2-2-2-2-2-2-2-2222-2-2-2-2-2-2-2-22220000220000000000000000000022-22-2200-2-200000000000000000000000000
χ4222222222-2-2-2-2-2-2-2-2222-2-2-2-2-2-2-2-222200002200000000000000000000-2-22-22-2002200000000000000000000000000
χ4322222222-2-2-2-2-2-2-2-2-2-2-222222222-2222222-2-2-2-2-2-20000000000000000000000-2-20000002200000000000000000000
χ4422222222-2-2-2-2-2-2-2-2-2-2-222222222-222-2-2-2-2-2-22222000000000000000000000022000000-2-200000000000000000000
χ4522-2-2-222-222-20000-22-2-22-200002-22002i−2i2i−2i002i−2i2i−2i2i2i−2i−2i2i2i−2i−2i00000000000000000000000000002-22-2000000000000
χ4622-2-2-222-222-20000-22-2-22-200002-22002i−2i2i−2i002i−2i2i−2i−2i−2i2i2i−2i−2i2i2i0000000000000000000000000000-22-22000000000000
χ4722-2-2-222-222-20000-22-2-22-200002-2200−2i2i−2i2i00−2i2i−2i2i2i2i−2i−2i2i2i−2i−2i0000000000000000000000000000-22-22000000000000
χ4822-2-2-222-222-20000-22-2-22-200002-2200−2i2i−2i2i00−2i2i−2i2i−2i−2i2i2i−2i−2i2i2i00000000000000000000000000002-22-2000000000000
χ4922-2-2-222-2-2-2200002-2222-200002-2-2002i−2i2i−2i00−2i2i−2i2i0000000022-2-222-2-20000000000000000000000002i−2i2i−2i00000000
χ5022-2-2-222-2-2-2200002-2222-200002-2-2002i−2i2i−2i00−2i2i−2i2i00000000-2-222-2-222000000000000000000000000−2i2i−2i2i00000000
χ5122-2-2-222-2-2-2200002-2222-200002-2-200−2i2i−2i2i002i−2i2i−2i0000000022-2-222-2-2000000000000000000000000−2i2i−2i2i00000000
χ5222-2-2-222-2-2-2200002-2222-200002-2-200−2i2i−2i2i002i−2i2i−2i00000000-2-222-2-2220000000000000000000000002i−2i2i−2i00000000
χ532-222-22-2-22-2-222-2-22-2-2222-2-222-2-222-20000-220000000000000000000000000000002i−2i−2i2i002i−2i−2i2i0000000000000000
χ542-222-22-2-22-2-222-2-22-2-2222-2-222-2-222-20000-22000000000000000000000000000000−2i2i2i−2i00−2i2i2i−2i0000000000000000
χ552-222-22-2-22-2-2-2-2222-2-222222-2-2-2-22-2200002-20000000000000000000000000000002i−2i−2i2i00−2i2i2i−2i0000000000000000
χ562-222-22-2-22-2-2-2-2222-2-222222-2-2-2-22-2200002-2000000000000000000000000000000−2i2i2i−2i002i−2i−2i2i0000000000000000
χ572-222-22-2-2-22222-2-2-222-22222-2-2-2-2-2-220000-22000000000000000000002-22-2-2200-2200000000000000000000000000
χ582-222-22-2-2-22222-2-2-222-22222-2-2-2-2-2-220000-2200000000000000000000-22-222-2002-200000000000000000000000000
χ592-222-22-2-2-22222-2-2-2-2-22-2-2-2-222222-222i2i−2i−2i2-2−2i−2i2i2i00000000000000000000002i−2i000000−2i2i00000000000000000000
χ602-222-22-2-2-22222-2-2-2-2-22-2-2-2-222222-22−2i−2i2i2i2-22i2i−2i−2i0000000000000000000000−2i2i0000002i−2i00000000000000000000
χ612-222-22-2-2-222-2-222-222-222-2-222-2-2-22-200002-2000000000000000000002-2-222-200-2200000000000000000000000000
χ622-222-22-2-2-222-2-222-222-222-2-222-2-2-22-200002-200000000000000000000-222-2-22002-200000000000000000000000000
χ632-222-22-2-2-222-2-222-2-2-22-2-222-2-22222-22i2i−2i−2i-22−2i−2i2i2i0000000000000000000000−2i2i0000002i−2i00000000000000000000
χ642-222-22-2-2-222-2-222-2-2-22-2-222-2-22222-2−2i−2i2i2i-222i2i−2i−2i00000000000000000000002i−2i000000−2i2i00000000000000000000
χ652-2-2-222-222-220000-22-22-2200002-2-2002-2-22002-2-222i2i−2i−2i−2i−2i2i2i0000000000000000000000000000−2i2i2i−2i000000000000
χ662-2-2-222-222-220000-22-22-2200002-2-2002-2-22002-2-22−2i−2i2i2i2i2i−2i−2i00000000000000000000000000002i−2i−2i2i000000000000
χ672-2-2-222-222-220000-22-22-2200002-2-200-222-200-222-22i2i−2i−2i−2i−2i2i2i00000000000000000000000000002i−2i−2i2i000000000000
χ682-2-2-222-222-220000-22-22-2200002-2-200-222-200-222-2−2i−2i2i2i2i2i−2i−2i0000000000000000000000000000−2i2i2i−2i000000000000
χ692-2-2-222-22-22-200002-22-2-2200002-22002-2-2200-222-20000000022-2-2-2-2220000000000000000000000002-2-2200000000
χ702-2-2-222-22-22-200002-22-2-2200002-22002-2-2200-222-200000000-2-22222-2-2000000000000000000000000-222-200000000
χ712-2-2-222-22-22-200002-22-2-2200002-2200-222-2002-2-220000000022-2-2-2-222000000000000000000000000-222-200000000
χ722-2-2-222-22-22-200002-22-2-2200002-2200-222-2002-2-2200000000-2-22222-2-20000000000000000000000002-2-2200000000
χ73444-44-4-4-40004-44-400000000000000000000000002-22-22-22-22-22-22-22-2000000000000000000000000000000000000
χ74444-44-4-4-40004-44-40000000000000000000000000-22-22-22-22-22-22-22-22000000000000000000000000000000000000
χ75444-44-4-4-4000-44-4400000000000000000000000002-22-22-22-2-22-22-22-22000000000000000000000000000000000000
χ76444-44-4-4-4000-44-440000000000000000000000000-22-22-22-222-22-22-22-2000000000000000000000000000000000000
χ7744-44-4-4-4400000000000004i−4i4i−4i0000000000000002i−2i−2i2i2i−2i−2i2i2-2-222-2-22000000000000000000000000000000000000
χ7844-44-4-4-4400000000000004i−4i4i−4i000000000000000−2i2i2i−2i−2i2i2i−2i-222-2-222-2000000000000000000000000000000000000
χ7944-44-4-4-440000000000000−4i4i−4i4i0000000000000002i−2i−2i2i2i−2i−2i2i-222-2-222-2000000000000000000000000000000000000
χ8044-44-4-4-440000000000000−4i4i−4i4i000000000000000−2i2i2i−2i−2i2i2i−2i2-2-222-2-22000000000000000000000000000000000000
χ8144-4-4-444-444-40000-4-444-440000-44-40000000000000000000000000000000000000000000000000000000000000000
χ8244-4-4-444-4-4-44000044-4-4-440000-4440000000000000000000000000000000000000000000000000000000000000000
χ834-44-4-4-4440004-4-4400000000000000000000000002-22-2-22-222-22-2-22-22000000000000000000000000000000000000
χ844-44-4-4-4440004-4-440000000000000000000000000-22-222-22-2-22-222-22-2000000000000000000000000000000000000
χ854-44-4-4-444000-444-400000000000000000000000002-22-2-22-22-22-222-22-2000000000000000000000000000000000000
χ864-44-4-4-444000-444-40000000000000000000000000-22-222-22-22-22-2-22-22000000000000000000000000000000000000
χ874-4-444-44-400000000000004i−4i−4i4i0000000000000002i−2i−2i2i−2i2i2i−2i2-2-22-222-2000000000000000000000000000000000000
χ884-4-444-44-400000000000004i−4i−4i4i000000000000000−2i2i2i−2i2i−2i−2i2i-222-22-2-22000000000000000000000000000000000000
χ894-4-444-44-40000000000000−4i4i4i−4i0000000000000002i−2i−2i2i−2i2i2i−2i-222-22-2-22000000000000000000000000000000000000
χ904-4-444-44-40000000000000−4i4i4i−4i000000000000000−2i2i2i−2i2i−2i−2i2i2-2-22-222-2000000000000000000000000000000000000
χ914-4-4-444-444-440000-4-44-44-40000-4440000000000000000000000000000000000000000000000000000000000000000
χ924-4-4-444-44-44-4000044-444-40000-44-40000000000000000000000000000000000000000000000000000000000000000

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