Finite Group Databasebeta

← Group #363313

Character table — Group #363313

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92
size1111111111111111222222224444444444444444444444444444444488888888888888888888888888881616161616161616
order12222222222222224444444444444444444444448888888888888888444444444444444444448888888844444444
χ111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1
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
χ41111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111
χ51111111111111111111111111111-1-1-1-11111-1-1-1-11111111111111111-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1
χ61111111111111111111111111111-1-1-1-11111-1-1-1-11111111111111111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-11111
χ71111111111111111111111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-111111111-1-1-1-11111
χ81111111111111111111111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111111111111111-1-1-1-1
χ9111111111111111111111111-1-1-1-11111-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1-1-11111-1-1-1-111-1-111-1-1
χ10111111111111111111111111-1-1-1-11111-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-111111111-1-1-1-1-1-111-1-111
χ11111111111111111111111111-1-1-1-11111-1-1-1-11111-1-1-1-1-1-1-1-111111111-1-1-1-11111-1-1-1-11111-1-1-1-1-1-1-1-11111-1-111-1-111
χ12111111111111111111111111-1-1-1-11111-1-1-1-11111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1-1-1111111-1-111-1-1
χ13111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-11111-1-1-1-1111111-1-1-1-111
χ14111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-11111-1-1-1-111111111-1-1-1-1-1-1-1-11111-1-11111-1-1
χ15111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-11111-1-1
χ16111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-111111111-1-1-1-11111-1-1-1-111-1-1-1-111
χ171-1-1-1-1111-1-1-1-111111111-1-1-1-111-1-111-1-111-1-111-1-1iiii−i−i−i−iiiii−i−i−i−i1-11-111-1-111-1-111-1-111-1-1ii−i−iii−i−ii−ii−ii−ii−i
χ181-1-1-1-1111-1-1-1-111111111-1-1-1-111-1-111-1-111-1-111-1-1iiii−i−i−i−iiiii−i−i−i−i1-11-1-1-111-1-111-1-111-1-111ii−i−iii−i−i−ii−ii−ii−ii
χ191-1-1-1-1111-1-1-1-111111111-1-1-1-111-1-111-1-111-1-111-1-1−i−i−i−iiiii−i−i−i−iiiii1-11-111-1-111-1-111-1-111-1-1−i−iii−i−iii−ii−ii−ii−ii
χ201-1-1-1-1111-1-1-1-111111111-1-1-1-111-1-111-1-111-1-111-1-1−i−i−i−iiiii−i−i−i−iiiii1-11-1-1-111-1-111-1-111-1-111−i−iii−i−iiii−ii−ii−ii−i
χ211-1-1-1-1111-1-1-1-111111111-1-1-1-111-1-1-1-11111-1-1-1-111iiii−i−i−i−iiiii−i−i−i−i-11-1111-1-111-1-1-1-111-1-111−i−iii−i−iiii−ii−i−ii−ii
χ221-1-1-1-1111-1-1-1-111111111-1-1-1-111-1-1-1-11111-1-1-1-111iiii−i−i−i−iiiii−i−i−i−i-11-11-1-111-1-11111-1-111-1-1−i−iii−i−iii−ii−iii−ii−i
χ231-1-1-1-1111-1-1-1-111111111-1-1-1-111-1-1-1-11111-1-1-1-111−i−i−i−iiiii−i−i−i−iiiii-11-1111-1-111-1-1-1-111-1-111ii−i−iii−i−i−ii−iii−ii−i
χ241-1-1-1-1111-1-1-1-111111111-1-1-1-111-1-1-1-11111-1-1-1-111−i−i−i−iiiii−i−i−i−iiiii-11-11-1-111-1-11111-1-111-1-1ii−i−iii−i−ii−ii−i−ii−ii
χ251-1-1-1-1111-1-1-1-111111111-1-1-1-1-1-11111-1-1-1-11111-1-1iiii−i−i−i−i−i−i−i−iiiii-11-1111-1-1-1-11111-1-1-1-111ii−i−i−i−iiii−i−iii−i−ii
χ261-1-1-1-1111-1-1-1-111111111-1-1-1-1-1-11111-1-1-1-11111-1-1iiii−i−i−i−i−i−i−i−iiiii-11-11-1-11111-1-1-1-11111-1-1ii−i−i−i−iii−iii−i−iii−i
χ271-1-1-1-1111-1-1-1-111111111-1-1-1-1-1-11111-1-1-1-11111-1-1−i−i−i−iiiiiiiii−i−i−i−i-11-1111-1-1-1-11111-1-1-1-111−i−iiiii−i−i−iii−i−iii−i
χ281-1-1-1-1111-1-1-1-111111111-1-1-1-1-1-11111-1-1-1-11111-1-1−i−i−i−iiiiiiiii−i−i−i−i-11-11-1-11111-1-1-1-11111-1-1−i−iiiii−i−ii−i−iii−i−ii
χ291-1-1-1-1111-1-1-1-111111111-1-1-1-1-1-111-1-111-1-111-1-111iiii−i−i−i−i−i−i−i−iiiii1-11-111-1-1-1-111-1-11111-1-1−i−iiiii−i−ii−i−ii−iii−i
χ301-1-1-1-1111-1-1-1-111111111-1-1-1-1-1-111-1-111-1-111-1-111iiii−i−i−i−i−i−i−i−iiiii1-11-1-1-11111-1-111-1-1-1-111−i−iiiii−i−i−iii−ii−i−ii
χ311-1-1-1-1111-1-1-1-111111111-1-1-1-1-1-111-1-111-1-111-1-111−i−i−i−iiiiiiiii−i−i−i−i1-11-111-1-1-1-111-1-11111-1-1ii−i−i−i−iii−iii−ii−i−ii
χ321-1-1-1-1111-1-1-1-111111111-1-1-1-1-1-111-1-111-1-111-1-111−i−i−i−iiiiiiiii−i−i−i−i1-11-1-1-11111-1-111-1-1-1-111ii−i−i−i−iiii−i−ii−iii−i
χ332222222222222222-2-2-2-2-2-2-2-222222222-2-2-2-2-2-2-2-2000000000000000022-2-200000000000000000000000000000000
χ342222222222222222-2-2-2-2-2-2-2-22222-2-2-2-2-2-2-2-222220000000000000000-2-22200000000000000000000000000000000
χ352222222222222222-2-2-2-2-2-2-2-2-2-2-2-222222222-2-2-2-20000000000000000-2-22200000000000000000000000000000000
χ362222222222222222-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-222222222000000000000000022-2-200000000000000000000000000000000
χ37222-2-22-2-222-2-222-2-222-2-22-22-200002i−2i2i−2i00002i−2i2i−2i000000002i2i−2i−2i2i2i−2i−2i0000000000000000000000002-22-200000000
χ38222-2-22-2-222-2-222-2-222-2-22-22-200002i−2i2i−2i00002i−2i2i−2i00000000−2i−2i2i2i−2i−2i2i2i000000000000000000000000-22-2200000000
χ39222-2-22-2-222-2-222-2-222-2-22-22-20000−2i2i−2i2i0000−2i2i−2i2i000000002i2i−2i−2i2i2i−2i−2i000000000000000000000000-22-2200000000
χ40222-2-22-2-222-2-222-2-222-2-22-22-20000−2i2i−2i2i0000−2i2i−2i2i00000000−2i−2i2i2i−2i−2i2i2i0000000000000000000000002-22-200000000
χ41222-2-22-2-222-2-222-2-2-2-222-22-2200002i−2i2i−2i0000−2i2i−2i2i2i2i−2i−2i2i2i−2i−2i00000000000000000000000000002-22-2000000000000
χ42222-2-22-2-222-2-222-2-2-2-222-22-2200002i−2i2i−2i0000−2i2i−2i2i−2i−2i2i2i−2i−2i2i2i0000000000000000000000000000-22-22000000000000
χ43222-2-22-2-222-2-222-2-2-2-222-22-220000−2i2i−2i2i00002i−2i2i−2i2i2i−2i−2i2i2i−2i−2i0000000000000000000000000000-22-22000000000000
χ44222-2-22-2-222-2-222-2-2-2-222-22-220000−2i2i−2i2i00002i−2i2i−2i−2i−2i2i2i−2i−2i2i2i00000000000000000000000000002-22-2000000000000
χ4522-22-2-22-22-22-22-22-22-22-22-2-222i−2i2i−2i00002i−2i2i−2i000000000000000000000000000000002-22-22i−2i2i−2i0000000000000000
χ4622-22-2-22-22-22-22-22-22-22-22-2-222i−2i2i−2i00002i−2i2i−2i00000000000000000000000000000000-22-22−2i2i−2i2i0000000000000000
χ4722-22-2-22-22-22-22-22-22-22-22-2-22−2i2i−2i2i0000−2i2i−2i2i000000000000000000000000000000002-22-2−2i2i−2i2i0000000000000000
χ4822-22-2-22-22-22-22-22-22-22-22-2-22−2i2i−2i2i0000−2i2i−2i2i00000000000000000000000000000000-22-222i−2i2i−2i0000000000000000
χ4922-22-2-22-22-22-22-22-2-22-22-222-22i−2i2i−2i0000−2i2i−2i2i0000000000000000000000002-22-22i−2i2i−2i000000000000000000000000
χ5022-22-2-22-22-22-22-22-2-22-22-222-22i−2i2i−2i0000−2i2i−2i2i000000000000000000000000-22-22−2i2i−2i2i000000000000000000000000
χ5122-22-2-22-22-22-22-22-2-22-22-222-2−2i2i−2i2i00002i−2i2i−2i0000000000000000000000002-22-2−2i2i−2i2i000000000000000000000000
χ5222-22-2-22-22-22-22-22-2-22-22-222-2−2i2i−2i2i00002i−2i2i−2i000000000000000000000000-22-222i−2i2i−2i000000000000000000000000
χ532-22-22-22-2-22-222-22-22-22-2-222-22i−2i−2i2i00002i−2i−2i2i000000000000000000000000000000002-2-222i−2i−2i2i0000000000000000
χ542-22-22-22-2-22-222-22-22-22-2-222-22i−2i−2i2i00002i−2i−2i2i00000000000000000000000000000000-222-2−2i2i2i−2i0000000000000000
χ552-22-22-22-2-22-222-22-22-22-2-222-2−2i2i2i−2i0000−2i2i2i−2i000000000000000000000000000000002-2-22−2i2i2i−2i0000000000000000
χ562-22-22-22-2-22-222-22-22-22-2-222-2−2i2i2i−2i0000−2i2i2i−2i00000000000000000000000000000000-222-22i−2i−2i2i0000000000000000
χ572-22-22-22-2-22-222-22-2-22-222-2-222i−2i−2i2i0000−2i2i2i−2i0000000000000000000000002-2-222i−2i−2i2i000000000000000000000000
χ582-22-22-22-2-22-222-22-2-22-222-2-222i−2i−2i2i0000−2i2i2i−2i000000000000000000000000-222-2−2i2i2i−2i000000000000000000000000
χ592-22-22-22-2-22-222-22-2-22-222-2-22−2i2i2i−2i00002i−2i−2i2i0000000000000000000000002-2-22−2i2i2i−2i000000000000000000000000
χ602-22-22-22-2-22-222-22-2-22-222-2-22−2i2i2i−2i00002i−2i−2i2i000000000000000000000000-222-22i−2i−2i2i000000000000000000000000
χ612-2-2222-2-2-2-22222-2-222-2-2-22-2200002i−2i−2i2i00002i−2i−2i2i0000000022-2-2-2-222000000000000000000000000−2i2i2i−2i00000000
χ622-2-2222-2-2-2-22222-2-222-2-2-22-2200002i−2i−2i2i00002i−2i−2i2i00000000-2-22222-2-20000000000000000000000002i−2i−2i2i00000000
χ632-2-2222-2-2-2-22222-2-222-2-2-22-220000−2i2i2i−2i0000−2i2i2i−2i0000000022-2-2-2-2220000000000000000000000002i−2i−2i2i00000000
χ642-2-2222-2-2-2-22222-2-222-2-2-22-220000−2i2i2i−2i0000−2i2i2i−2i00000000-2-22222-2-2000000000000000000000000−2i2i2i−2i00000000
χ652-2-2222-2-2-2-22222-2-2-2-2222-22-200002i−2i−2i2i0000−2i2i2i−2i22-2-2-2-2220000000000000000000000000000−2i2i2i−2i000000000000
χ662-2-2222-2-2-2-22222-2-2-2-2222-22-200002i−2i−2i2i0000−2i2i2i−2i-2-22222-2-200000000000000000000000000002i−2i−2i2i000000000000
χ672-2-2222-2-2-2-22222-2-2-2-2222-22-20000−2i2i2i−2i00002i−2i−2i2i22-2-2-2-22200000000000000000000000000002i−2i−2i2i000000000000
χ682-2-2222-2-2-2-22222-2-2-2-2222-22-20000−2i2i2i−2i00002i−2i−2i2i-2-22222-2-20000000000000000000000000000−2i2i2i−2i000000000000
χ692-2-2-2-2222-2-2-2-22222-2-2-2-2222222-2-222-2-2-2-222-2-22200000000000000002-2-2200000000000000000000000000000000
χ702-2-2-2-2222-2-2-2-22222-2-2-2-2222222-2-2-2-222-2-22222-2-20000000000000000-222-200000000000000000000000000000000
χ712-2-2-2-2222-2-2-2-22222-2-2-2-22222-2-22222-2-222-2-2-2-2220000000000000000-222-200000000000000000000000000000000
χ722-2-2-2-2222-2-2-2-22222-2-2-2-22222-2-222-2-22222-2-222-2-200000000000000002-2-2200000000000000000000000000000000
χ734444-4-444-4-4-44-44-4-400000000000000000000000022−2222−2222−2222−2200000000000000000000000000000000000000000000
χ744444-4-444-4-4-44-44-4-4000000000000000000000000−2222−2222−2222−222200000000000000000000000000000000000000000000
χ75444-44-4-4-4-4-44-4-44440000000000000000000000002i2−2i2−2i22i22i2−2i2−2i22i200000000000000000000000000000000000000000000
χ76444-44-4-4-4-4-44-4-4444000000000000000000000000−2i22i22i2−2i2−2i22i22i2−2i200000000000000000000000000000000000000000000
χ7744-44444-4-44-4-4-4-4-440000000000000000000000000000000022−2222−2222−2222−22000000000000000000000000000000000000
χ7844-44444-4-44-4-4-4-4-4400000000000000000000000000000000−2222−2222−2222−2222000000000000000000000000000000000000
χ7944-4-44-4-444-4-444-4-444-4-4444-4-400000000000000000000000000000000000000000000000000000000000000000000
χ8044-4-44-4-444-4-444-4-44-444-4-4-44400000000000000000000000000000000000000000000000000000000000000000000
χ8144-4-4-44-44-4444-4-44-4000000000000000000000000000000002i2−2i2−2i22i22i2−2i2−2i22i2000000000000000000000000000000000000
χ8244-4-4-44-44-4444-4-44-400000000000000000000000000000000−2i22i22i2−2i2−2i22i22i2−2i2000000000000000000000000000000000000
χ834-44444-444-4-4-4-4-44-40000000000000000000000000000000022−22−2222−222222−22000000000000000000000000000000000000
χ844-44444-444-4-4-4-4-44-400000000000000000000000000000000−222222−2222−22−2222000000000000000000000000000000000000
χ854-444-4-4-44-444-44-4-444-4-44-4-44400000000000000000000000000000000000000000000000000000000000000000000
χ864-444-4-4-44-444-44-4-44-444-444-4-400000000000000000000000000000000000000000000000000000000000000000000
χ874-44-4-444-44-444-4-4-44000000000000000000000000000000002i2−2i22i2−2i2−2i22i2−2i22i2000000000000000000000000000000000000
χ884-44-4-444-44-444-4-4-4400000000000000000000000000000000−2i22i2−2i22i22i2−2i22i2−2i2000000000000000000000000000000000000
χ894-4-44-4-4-4-444-44-444400000000000000000000000022−22−2222−222222−2200000000000000000000000000000000000000000000
χ904-4-44-4-4-4-444-44-4444000000000000000000000000−222222−2222−22−222200000000000000000000000000000000000000000000
χ914-4-4-44-444444-4-44-4-40000000000000000000000002i2−2i22i2−2i2−2i22i2−2i22i200000000000000000000000000000000000000000000
χ924-4-4-44-444444-4-44-4-4000000000000000000000000−2i22i2−2i22i22i2−2i22i2−2i200000000000000000000000000000000000000000000

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