Finite Group Databasebeta

← Group #376233

Character table — Group #376233

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92
size1111111122222222222222222222444444444444444444444444444488888888888888888888888888881616161616161616
order12222222222222222222444444444444444444444444444444444444222244444444444444444444444444444444
χ111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111111111111111111111-1-1-1-111-1-1-1-111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1
χ31111111111111111111111111111111111111111-1-1-1-111111111-1-1-1-111-1-1-1-111-1-1-1-111-1-111-1-1-1-1-1-1-1-1-1-11111-1-1-1-1
χ41111111111111111111111111111111111111111-1-1-1-111111111-1-1-1-1-1-111-1-1-1-111-1-1-1-111-1-111-1-1-1-1-1-1-1-1-1-1-1-11111
χ511111111111111111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ611111111111111111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-11111-1-1-1-111-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111
χ711111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-111-1-1-1-111-1-111-1-111111111-1-1-1-11111
χ811111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-111-1-1-1-111-1-111111111111111-1-1-1-1
χ911111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-1111111-1-1-1-111-1-1-1-1-1-111-1-1111111-1-1-1-111-1-111-1-1
χ1011111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-11111-1-111-1-1-1-111-1-111-1-111-1-11111-1-1-1-1-1-111-1-111
χ1111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-1-111
χ1211111111111111111111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-11111111111-1-1-1-11111-1-11111-1-1
χ1311111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111111111-1-1-1-111-1-1-1-1-1-111-1-111-1-1-1-11111-1-111-1-111
χ1411111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111111111-1-111-1-1-1-111-1-111-1-111-1-1-1-1-1-1111111-1-111-1-1
χ1511111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-11111-1-1
χ1611111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-111-1-1-1-111111111111111-1-1-1-111-1-1-1-111
χ171-111-11-1-1111-1-1-1111-1-1-1iiii−i−i−i−iii−i−i1111-1-1-1-1ii−i−iiiii−i−i−i−iii−i−i1-11-11-11-11-11-1i−ii−ii−ii−iii−i−i11-1-11-1i−ii−i1-1
χ181-111-11-1-1111-1-1-1111-1-1-1iiii−i−i−i−iii−i−i1111-1-1-1-1ii−i−iiiii−i−i−i−iii−i−i-11-111-1-11-111-1−ii−ii−ii−iiii−i−i11-1-1-11−ii−ii-11
χ191-111-11-1-1111-1-1-1111-1-1-1iiii−i−i−i−iii−i−i1111-1-1-1-1−i−iiiiiii−i−i−i−i−i−iii1-1-11-111-1-11-11i−i−iii−i−ii−i−iii-1-1111-1i−i−ii-11
χ201-111-11-1-1111-1-1-1111-1-1-1iiii−i−i−i−iii−i−i1111-1-1-1-1−i−iiiiiii−i−i−i−i−i−iii-111-1-11-111-1-11−iii−i−iii−i−i−iii-1-111-11−iii−i1-1
χ211-111-11-1-1111-1-1-1111-1-1-1iiii−i−i−i−iii−i−i-1-1-1-11111ii−i−i−i−i−i−iiiiiii−i−i1-11-11-11-11-11-1i−ii−ii−ii−i−i−iii-1-111-11−ii−ii-11
χ221-111-11-1-1111-1-1-1111-1-1-1iiii−i−i−i−iii−i−i-1-1-1-11111ii−i−i−i−i−i−iiiiiii−i−i-11-111-1-11-111-1−ii−ii−ii−ii−i−iii-1-1111-1i−ii−i1-1
χ231-111-11-1-1111-1-1-1111-1-1-1iiii−i−i−i−iii−i−i-1-1-1-11111−i−iii−i−i−i−iiiii−i−iii1-1-11-111-1-11-11i−i−iii−i−iiii−i−i11-1-1-11−iii−i1-1
χ241-111-11-1-1111-1-1-1111-1-1-1iiii−i−i−i−iii−i−i-1-1-1-11111−i−iii−i−i−i−iiiii−i−iii-111-1-11-111-1-11−iii−i−iii−iii−i−i11-1-11-1i−i−ii-11
χ251-111-11-1-1111-1-1-1111-1-1-1−i−i−i−iiiii−i−iii1111-1-1-1-1ii−i−i−i−i−i−iiiiiii−i−i1-1-11-111-1-11-11−iii−i−iii−iii−i−i-1-1111-1−iii−i-11
χ261-111-11-1-1111-1-1-1111-1-1-1−i−i−i−iiiii−i−iii1111-1-1-1-1ii−i−i−i−i−i−iiiiiii−i−i-111-1-11-111-1-11i−i−iii−i−iiii−i−i-1-111-11i−i−ii1-1
χ271-111-11-1-1111-1-1-1111-1-1-1−i−i−i−iiiii−i−iii1111-1-1-1-1−i−iii−i−i−i−iiiii−i−iii1-11-11-11-11-11-1−ii−ii−ii−ii−i−iii11-1-11-1−ii−ii1-1
χ281-111-11-1-1111-1-1-1111-1-1-1−i−i−i−iiiii−i−iii1111-1-1-1-1−i−iii−i−i−i−iiiii−i−iii-11-111-1-11-111-1i−ii−ii−ii−i−i−iii11-1-1-11i−ii−i-11
χ291-111-11-1-1111-1-1-1111-1-1-1−i−i−i−iiiii−i−iii-1-1-1-11111ii−i−iiiii−i−i−i−iii−i−i1-1-11-111-1-11-11−iii−i−iii−i−i−iii11-1-1-11i−i−ii1-1
χ301-111-11-1-1111-1-1-1111-1-1-1−i−i−i−iiiii−i−iii-1-1-1-11111ii−i−iiiii−i−i−i−iii−i−i-111-1-11-111-1-11i−i−iii−i−ii−i−iii11-1-11-1−iii−i-11
χ311-111-11-1-1111-1-1-1111-1-1-1−i−i−i−iiiii−i−iii-1-1-1-11111−i−iiiiiii−i−i−i−i−i−iii1-11-11-11-11-11-1−ii−ii−ii−iiii−i−i-1-111-11i−ii−i-11
χ321-111-11-1-1111-1-1-1111-1-1-1−i−i−i−iiiii−i−iii-1-1-1-11111−i−iiiiiii−i−i−i−i−i−iii-11-111-1-11-111-1i−ii−ii−ii−iii−i−i-1-1111-1−ii−ii1-1
χ33222222222-2-22-2-22-2-22-2-222222222-2-2-2-200000000222200000000-2-2-2-20000220000-2-2000000000000000000000000
χ34222222222-2-22-2-22-2-22-2-222222222-2-2-2-200000000-2-2-2-20000000022220000-2-2000022000000000000000000000000
χ35222222222-2-22-2-22-2-22-2-2-2-2-2-2-2-2-2-2222200000000222200000000-2-2-2-20000-2-2000022000000000000000000000000
χ36222222222-2-22-2-22-2-22-2-2-2-2-2-2-2-2-2-2222200000000-2-2-2-20000000022220000220000-2-2000000000000000000000000
χ3722222222-22-2-22-2-22-2-22-222-2-222-2-22-22-200000000000000000000000000220000-2-200002200-2-20000000000000000
χ3822222222-22-2-22-2-22-2-22-222-2-222-2-22-22-200000000000000000000000000-2-20000220000-2-200220000000000000000
χ3922222222-22-2-22-2-22-2-22-2-2-222-2-222-22-2200000000000000000000000000220000-2-20000-2-200220000000000000000
χ4022222222-22-2-22-2-22-2-22-2-2-222-2-222-22-2200000000000000000000000000-2-200002200002200-2-20000000000000000
χ4122222222-2-22-2-22-2-22-2-2222-2-222-2-2-22-22000000000000000000000000220000-2-200002200-2-2000000000000000000
χ4222222222-2-22-2-22-2-22-2-2222-2-222-2-2-22-22000000000000000000000000-2-20000220000-2-20022000000000000000000
χ4322222222-2-22-2-22-2-22-2-22-2-222-2-2222-22-2000000000000000000000000220000-2-20000-2-20022000000000000000000
χ4422222222-2-22-2-22-2-22-2-22-2-222-2-2222-22-2000000000000000000000000-2-200002200002200-2-2000000000000000000
χ4522-222-2-2-2-222-2-2-22-2-22220000000000002i2i−2i−2i2i2i−2i−2i2i−2i2i−2i000000002i−2i2i−2i000000000000000000002-22-2000000000000
χ4622-222-2-2-2-222-2-2-22-2-22220000000000002i2i−2i−2i2i2i−2i−2i−2i2i−2i2i00000000−2i2i−2i2i00000000000000000000-22-22000000000000
χ4722-222-2-2-2-222-2-2-22-2-2222000000000000−2i−2i2i2i−2i−2i2i2i2i−2i2i−2i000000002i−2i2i−2i00000000000000000000-22-22000000000000
χ4822-222-2-2-2-222-2-2-22-2-2222000000000000−2i−2i2i2i−2i−2i2i2i−2i2i−2i2i00000000−2i2i−2i2i000000000000000000002-22-2000000000000
χ4922-222-2-2-2-2-2-2-2222222-2-2000000000000000000002i−2i2i−2i2i2i−2i−2i2i2i−2i−2i−2i2i−2i2i0000000000000000000000002-22-200000000
χ5022-222-2-2-2-2-2-2-2222222-2-2000000000000000000002i−2i2i−2i−2i−2i2i2i−2i−2i2i2i−2i2i−2i2i000000000000000000000000-22-2200000000
χ5122-222-2-2-2-2-2-2-2222222-2-200000000000000000000−2i2i−2i2i2i2i−2i−2i2i2i−2i−2i2i−2i2i−2i000000000000000000000000-22-2200000000
χ5222-222-2-2-2-2-2-2-2222222-2-200000000000000000000−2i2i−2i2i−2i−2i2i2i−2i−2i2i2i2i−2i2i−2i0000000000000000000000002-22-200000000
χ532-222-22-2-22-2-2-2222-2-2-2222i2i2i2i−2i−2i−2i−2i−2i−2i2i2i000000002i2i−2i−2i00000000−2i−2i2i2i00002-20000-22000000000000000000000000
χ542-222-22-2-22-2-2-2222-2-2-2222i2i2i2i−2i−2i−2i−2i−2i−2i2i2i00000000−2i−2i2i2i000000002i2i−2i−2i0000-2200002-2000000000000000000000000
χ552-222-22-2-22-2-2-2222-2-2-222−2i−2i−2i−2i2i2i2i2i2i2i−2i−2i000000002i2i−2i−2i00000000−2i−2i2i2i0000-2200002-2000000000000000000000000
χ562-222-22-2-22-2-2-2222-2-2-222−2i−2i−2i−2i2i2i2i2i2i2i−2i−2i00000000−2i−2i2i2i000000002i2i−2i−2i00002-20000-22000000000000000000000000
χ572-222-22-2-2-22-22-22-22-22-222i2i−2i−2i−2i−2i2i2i2i−2i−2i2i000000000000000000000000002-20000-2200002i−2i00−2i2i0000000000000000
χ582-222-22-2-2-22-22-22-22-22-222i2i−2i−2i−2i−2i2i2i2i−2i−2i2i00000000000000000000000000-2200002-20000−2i2i002i−2i0000000000000000
χ592-222-22-2-2-22-22-22-22-22-22−2i−2i2i2i2i2i−2i−2i−2i2i2i−2i000000000000000000000000002-20000-220000−2i2i002i−2i0000000000000000
χ602-222-22-2-2-22-22-22-22-22-22−2i−2i2i2i2i2i−2i−2i−2i2i2i−2i00000000000000000000000000-2200002-200002i−2i00−2i2i0000000000000000
χ612-222-22-2-2-2-2222-2-2-2222-22i2i−2i−2i−2i−2i2i2i−2i2i2i−2i0000000000000000000000002-20000-2200002i−2i00−2i2i000000000000000000
χ622-222-22-2-2-2-2222-2-2-2222-22i2i−2i−2i−2i−2i2i2i−2i2i2i−2i000000000000000000000000-2200002-20000−2i2i002i−2i000000000000000000
χ632-222-22-2-2-2-2222-2-2-2222-2−2i−2i2i2i2i2i−2i−2i2i−2i−2i2i0000000000000000000000002-20000-220000−2i2i002i−2i000000000000000000
χ642-222-22-2-2-2-2222-2-2-2222-2−2i−2i2i2i2i2i−2i−2i2i−2i−2i2i000000000000000000000000-2200002-200002i−2i00−2i2i000000000000000000
χ652-2-22-2-222-2222222-2-2-2-2-20000000000002i2i−2i−2i−2i−2i2i2i2-2-22000000002-2-2200000000000000000000−2i2i2i−2i000000000000
χ662-2-22-2-222-2222222-2-2-2-2-20000000000002i2i−2i−2i−2i−2i2i2i-222-200000000-222-2000000000000000000002i−2i−2i2i000000000000
χ672-2-22-2-222-2222222-2-2-2-2-2000000000000−2i−2i2i2i2i2i−2i−2i2-2-22000000002-2-22000000000000000000002i−2i−2i2i000000000000
χ682-2-22-2-222-2222222-2-2-2-2-2000000000000−2i−2i2i2i2i2i−2i−2i-222-200000000-222-200000000000000000000−2i2i2i−2i000000000000
χ692-2-22-2-222-2-2-22-2-2222-222000000000000000000002-2-2222-2-2-2-222-222-20000000000000000000000002-2-2200000000
χ702-2-22-2-222-2-2-22-2-2222-222000000000000000000002-2-22-2-22222-2-2-222-2000000000000000000000000-222-200000000
χ712-2-22-2-222-2-2-22-2-2222-22200000000000000000000-222-222-2-2-2-2222-2-22000000000000000000000000-222-200000000
χ722-2-22-2-222-2-2-22-2-2222-22200000000000000000000-222-2-2-22222-2-22-2-220000000000000000000000002-2-2200000000
χ73444-4-4-4-440000000000004i−4i004i−4i0000002i−2i2i−2i2i−2i2i−2i00002-22-22-22-20000000000000000000000000000000000000000
χ74444-4-4-4-440000000000004i−4i004i−4i000000−2i2i−2i2i−2i2i−2i2i0000-22-22-22-220000000000000000000000000000000000000000
χ75444-4-4-4-44000000000000−4i4i00−4i4i0000002i−2i2i−2i2i−2i2i−2i0000-22-22-22-220000000000000000000000000000000000000000
χ76444-4-4-4-44000000000000−4i4i00−4i4i000000−2i2i−2i2i−2i2i−2i2i00002-22-22-22-20000000000000000000000000000000000000000
χ7744-444-4-4-444-44-44-4-44-44-4000000000000000000000000000000000000000000000000000000000000000000000000
χ7844-444-4-4-44-4444-4-44-4-4-44000000000000000000000000000000000000000000000000000000000000000000000000
χ7944-4-4-444-4000000000000004i−4i004i−4i00002-2-222-2-2200002i−2i−2i2i2i−2i−2i2i0000000000000000000000000000000000000000
χ8044-4-4-444-4000000000000004i−4i004i−4i0000-222-2-222-20000−2i2i2i−2i−2i2i2i−2i0000000000000000000000000000000000000000
χ8144-4-4-444-400000000000000−4i4i00−4i4i00002-2-222-2-220000−2i2i2i−2i−2i2i2i−2i0000000000000000000000000000000000000000
χ8244-4-4-444-400000000000000−4i4i00−4i4i0000-222-2-222-200002i−2i−2i2i2i−2i−2i2i0000000000000000000000000000000000000000
χ834-44-44-44-40000000000004-400-440000002i−2i2i−2i−2i2i−2i2i0000−2i2i−2i2i2i−2i2i−2i0000000000000000000000000000000000000000
χ844-44-44-44-40000000000004-400-44000000−2i2i−2i2i2i−2i2i−2i00002i−2i2i−2i−2i2i−2i2i0000000000000000000000000000000000000000
χ854-44-44-44-4000000000000-44004-40000002i−2i2i−2i−2i2i−2i2i00002i−2i2i−2i−2i2i−2i2i0000000000000000000000000000000000000000
χ864-44-44-44-4000000000000-44004-4000000−2i2i−2i2i2i−2i2i−2i0000−2i2i−2i2i2i−2i2i−2i0000000000000000000000000000000000000000
χ874-4-44-4-44444-4-44-4-4-444-44000000000000000000000000000000000000000000000000000000000000000000000000
χ884-4-44-4-4444-44-4-44-44-444-4000000000000000000000000000000000000000000000000000000000000000000000000
χ894-4-4-444-44000000000000004-400-4400002-2-22-222-200002-2-22-222-20000000000000000000000000000000000000000
χ904-4-4-444-44000000000000004-400-440000-222-22-2-220000-222-22-2-220000000000000000000000000000000000000000
χ914-4-4-444-4400000000000000-44004-400002-2-22-222-20000-222-22-2-220000000000000000000000000000000000000000
χ924-4-4-444-4400000000000000-44004-40000-222-22-2-2200002-2-22-222-20000000000000000000000000000000000000000

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