Finite Group Databasebeta

← Group #368114

Character table — Group #368114

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92
size111111111111111122222222444444444444444444444444888888888888888888888888888888888888888816161616
order12222222222222224444444444444444444444444444444422224444444444444444444488888888888888884444
χ111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111111111111111111-1-1-1-11111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ3111111111111111111111111111111111111-1-1-1-1-1-1-1-11111111111-1-1-1-111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111
χ4111111111111111111111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-111-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-11111111111111111-1-1-1-1
χ51111111111111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-111-1-1
χ61111111111111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-111111111-1-111
χ71111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-11111111111-1-1
χ81111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-111111111111111111111-1-1-1-1-1-1-1-1-1-111
χ9111111111111111111111111-1-1-1-11111-1-1-1-11111111111111111-1-1-1-1-1-1-1-11111-1-1-1-111111111-1-1-1-11111-1-1-1-1-1-1-1-1
χ10111111111111111111111111-1-1-1-11111-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-111111111
χ11111111111111111111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-11111-1-1-1-1-1-111111111-1-1-1-11111-1-1-1-11111-1-1-1-1
χ12111111111111111111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-11111-1-1-1-1-1-11111-1-1-1-11111-1-1-1-11111-1-1-1-11111
χ13111111111111111111111111-1-1-1-1-1-1-1-1111111111111-1-1-1-11111-1-1-1-1-1-111-1-1-1-11111-1-1-1-11111-1-1-1-1-1-1-1-11111-1-111
χ14111111111111111111111111-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-111111111-1-1-1-111111111-1-1-1-111-1-1
χ15111111111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-11111-1-11111111111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-111
χ16111111111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111-1-1-1-111111111-1-1-1-1-1-1-1-1111111-1-1
χ171111-1-1-1-1-111-1-111-111-1-111-1-111-1-1ii−i−iii−i−i1111-1-1-1-1ii−i−i11-1-11-111-1-1i−iii−i−iii−i−iii−i−i11-1-111-1-1ii−i−iii−i−i1-1i−i
χ181111-1-1-1-1-111-1-111-111-1-111-1-111-1-1ii−i−iii−i−i1111-1-1-1-1ii−i−i-1-1111-111-1-1i−iii−i−iii−i−i−i−iii-1-111-1-111−i−iii−i−iii-11−ii
χ191111-1-1-1-1-111-1-111-111-1-111-1-111-1-1ii−i−iii−i−i-1-1-1-11111ii−i−i11-1-11-1-1-111i−i−i−iii−i−iiiii−i−i-1-111-1-111−i−iii−i−iii1-1i−i
χ201111-1-1-1-1-111-1-111-111-1-111-1-111-1-1ii−i−iii−i−i-1-1-1-11111ii−i−i-1-1111-1-1-111i−i−i−iii−i−iii−i−iii11-1-111-1-1ii−i−iii−i−i-11−ii
χ211111-1-1-1-1-111-1-111-111-1-111-1-111-1-1−i−iii−i−iii1111-1-1-1-1−i−iii11-1-11-111-1-1−ii−i−iii−i−iii−i−iii11-1-111-1-1−i−iii−i−iii1-1−ii
χ221111-1-1-1-1-111-1-111-111-1-111-1-111-1-1−i−iii−i−iii1111-1-1-1-1−i−iii-1-1111-111-1-1−ii−i−iii−i−iiiii−i−i-1-111-1-111ii−i−iii−i−i-11i−i
χ231111-1-1-1-1-111-1-111-111-1-111-1-111-1-1−i−iii−i−iii-1-1-1-11111−i−iii11-1-11-1-1-111−iiii−i−iii−i−i−i−iii-1-111-1-111ii−i−iii−i−i1-1−ii
χ241111-1-1-1-1-111-1-111-111-1-111-1-111-1-1−i−iii−i−iii-1-1-1-11111−i−iii-1-1111-1-1-111−iiii−i−iii−i−iii−i−i11-1-111-1-1−i−iii−i−iii-11i−i
χ251111-1-1-1-1-111-1-111-111-1-111-1-1-1-111ii−i−i−i−iii1111-1-1-1-1ii−i−i11-1-1-11-1-111−iiii−i−i−i−iiiii−i−i11-1-1-1-111ii−i−i−i−iii-11−ii
χ261111-1-1-1-1-111-1-111-111-1-111-1-1-1-111ii−i−i−i−iii1111-1-1-1-1ii−i−i-1-111-11-1-111−iiii−i−i−i−iii−i−iii-1-11111-1-1−i−iiiii−i−i1-1i−i
χ271111-1-1-1-1-111-1-111-111-1-111-1-1-1-111ii−i−i−i−iii-1-1-1-11111ii−i−i11-1-1-1111-1-1−ii−i−iiiii−i−iii−i−i-1-11111-1-1−i−iiiii−i−i-11−ii
χ281111-1-1-1-1-111-1-111-111-1-111-1-1-1-111ii−i−i−i−iii-1-1-1-11111ii−i−i-1-111-1111-1-1−ii−i−iiiii−i−i−i−iii11-1-1-1-111ii−i−i−i−iii1-1i−i
χ291111-1-1-1-1-111-1-111-111-1-111-1-1-1-111−i−iiiii−i−i1111-1-1-1-1−i−iii11-1-1-11-1-111i−i−i−iiiii−i−i−i−iii11-1-1-1-111−i−iiiii−i−i-11i−i
χ301111-1-1-1-1-111-1-111-111-1-111-1-1-1-111−i−iiiii−i−i1111-1-1-1-1−i−iii-1-111-11-1-111i−i−i−iiiii−i−iii−i−i-1-11111-1-1ii−i−i−i−iii1-1−ii
χ311111-1-1-1-1-111-1-111-111-1-111-1-1-1-111−i−iiiii−i−i-1-1-1-11111−i−iii11-1-1-1111-1-1i−iii−i−i−i−iii−i−iii-1-11111-1-1ii−i−i−i−iii-11i−i
χ321111-1-1-1-1-111-1-111-111-1-111-1-1-1-111−i−iiiii−i−i-1-1-1-11111−i−iii-1-111-1111-1-1i−iii−i−i−i−iiiii−i−i11-1-1-1-111−i−iiiii−i−i1-1−ii
χ332222222222222222-2-2-2-2-2-2-2-222222222222200000000-2-2-2-20000-2-20000-2-200000000000000000000000000000000
χ342222222222222222-2-2-2-2-2-2-2-22222-2-2-2-2-2-2-2-20000000022220000-2-200002200000000000000000000000000000000
χ352222222222222222-2-2-2-2-2-2-2-2-2-2-2-22222-2-2-2-200000000-2-2-2-200002200002200000000000000000000000000000000
χ362222222222222222-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-222220000000022220000220000-2-200000000000000000000000000000000
χ372222-2-2-2-2-222-2-222-2-2-222-2-22222-2-22i2i−2i−2i2i2i−2i−2i00000000−2i−2i2i2i0000-220000−2i2i00000000000000000000000000000000
χ382222-2-2-2-2-222-2-222-2-2-222-2-22222-2-2−2i−2i2i2i−2i−2i2i2i000000002i2i−2i−2i0000-2200002i−2i00000000000000000000000000000000
χ392222-2-2-2-2-222-2-222-2-2-222-2-222-2-2222i2i−2i−2i−2i−2i2i2i00000000−2i−2i2i2i00002-200002i−2i00000000000000000000000000000000
χ402222-2-2-2-2-222-2-222-2-2-222-2-222-2-222−2i−2i2i2i2i2i−2i−2i000000002i2i−2i−2i00002-20000−2i2i00000000000000000000000000000000
χ41222-22222-2-2-2-2-22-2-22-2222-2-2-200000000000022-2-222-2-200002-22-2000000000000000000002-22-20000000000000000
χ42222-22222-2-2-2-2-22-2-22-2222-2-2-200000000000022-2-222-2-20000-22-2200000000000000000000-22-220000000000000000
χ43222-22222-2-2-2-2-22-2-22-2222-2-2-2000000000000-2-222-2-22200002-22-200000000000000000000-22-220000000000000000
χ44222-22222-2-2-2-2-22-2-22-2222-2-2-2000000000000-2-222-2-2220000-22-22000000000000000000002-22-20000000000000000
χ45222-2-2-2-2-22-2-2222-222-2-2-22-22200000000000022-2-2-2-22200002-2-22000000000000000000002-2-220000000000000000
χ46222-2-2-2-2-22-2-2222-222-2-2-22-22200000000000022-2-2-2-2220000-222-200000000000000000000-222-20000000000000000
χ47222-2-2-2-2-22-2-2222-222-2-2-22-222000000000000-2-22222-2-200002-2-2200000000000000000000-222-20000000000000000
χ48222-2-2-2-2-22-2-2222-222-2-2-22-222000000000000-2-22222-2-20000-222-2000000000000000000002-2-220000000000000000
χ492-2-2222-2-22-222-22-2-2-2-22-2222-20000000000002-22-22-22-20000000000000000000000002i−2i2i−2i000000002i−2i2i−2i00000000
χ502-2-2222-2-22-222-22-2-2-2-22-2222-20000000000002-22-22-22-2000000000000000000000000−2i2i−2i2i00000000−2i2i−2i2i00000000
χ512-2-2222-2-22-222-22-2-2-2-22-2222-2000000000000-22-22-22-220000000000000000000000002i−2i2i−2i00000000−2i2i−2i2i00000000
χ522-2-2222-2-22-222-22-2-2-2-22-2222-2000000000000-22-22-22-22000000000000000000000000−2i2i−2i2i000000002i−2i2i−2i00000000
χ532-2-22-2-222-2-22-222-22-2-2-2222-220000000000002-22-2-22-220000000000000000000000002-2-22000000002-2-2200000000
χ542-2-22-2-222-2-22-222-22-2-2-2222-220000000000002-22-2-22-22000000000000000000000000-222-200000000-222-200000000
χ552-2-22-2-222-2-22-222-22-2-2-2222-22000000000000-22-222-22-20000000000000000000000002-2-2200000000-222-200000000
χ562-2-22-2-222-2-22-222-22-2-2-2222-22000000000000-22-222-22-2000000000000000000000000-222-2000000002-2-2200000000
χ572-2-2-222-2-2-22-2-222222-2-22-222-200002-22-20000000000002-22-20000002-22-20000002-22-2000000000000000000000000
χ582-2-2-222-2-2-22-2-222222-2-22-222-200002-22-20000000000002-22-2000000-22-22000000-22-22000000000000000000000000
χ592-2-2-222-2-2-22-2-222222-2-22-222-20000-22-22000000000000-22-220000002-22-2000000-22-22000000000000000000000000
χ602-2-2-222-2-2-22-2-222222-2-22-222-20000-22-22000000000000-22-22000000-22-220000002-22-2000000000000000000000000
χ612-2-2-222-2-2-22-2-22222-222-22-2-2200002-22-200002-2-222-2-22-22-220000000000002-22-20000000000000000000000000000
χ622-2-2-222-2-2-22-2-22222-222-22-2-2200002-22-20000-222-2-222-2-22-22000000000000-22-220000000000000000000000000000
χ632-2-2-222-2-2-22-2-22222-222-22-2-220000-22-2200002-2-222-2-222-22-2000000000000-22-220000000000000000000000000000
χ642-2-2-222-2-2-22-2-22222-222-22-2-220000-22-220000-222-2-222-22-22-20000000000002-22-20000000000000000000000000000
χ652-2-2-2-2-22222-22-222-22-22-2-22-2200002i−2i−2i2i0000000000002i−2i−2i2i0000002-2-220000002i−2i−2i2i000000000000000000000000
χ662-2-2-2-2-22222-22-222-22-22-2-22-2200002i−2i−2i2i0000000000002i−2i−2i2i000000-222-2000000−2i2i2i−2i000000000000000000000000
χ672-2-2-2-2-22222-22-222-22-22-2-22-220000−2i2i2i−2i000000000000−2i2i2i−2i0000002-2-22000000−2i2i2i−2i000000000000000000000000
χ682-2-2-2-2-22222-22-222-22-22-2-22-220000−2i2i2i−2i000000000000−2i2i2i−2i000000-222-20000002i−2i−2i2i000000000000000000000000
χ692-2-2-2-2-22222-22-222-2-22-222-22-200002i−2i−2i2i00002-2-22-222-2−2i2i2i−2i0000000000002i−2i−2i2i0000000000000000000000000000
χ702-2-2-2-2-22222-22-222-2-22-222-22-200002i−2i−2i2i0000-222-22-2-22−2i2i2i−2i000000000000−2i2i2i−2i0000000000000000000000000000
χ712-2-2-2-2-22222-22-222-2-22-222-22-20000−2i2i2i−2i00002-2-22-222-22i−2i−2i2i000000000000−2i2i2i−2i0000000000000000000000000000
χ722-2-2-2-2-22222-22-222-2-22-222-22-20000−2i2i2i−2i0000-222-22-2-222i−2i−2i2i0000000000002i−2i−2i2i0000000000000000000000000000
χ73444-44444-4-4-4-4-44-4-4-44-4-4-444400000000000000000000000000000000000000000000000000000000000000000000
χ74444-4-4-4-4-44-4-4444-44-4444-44-4-400000000000000000000000000000000000000000000000000000000000000000000
χ7544-444-44-444-4-4-4-4-4400000000000000004i−4i4i−4i00000000000000000000000000000000000000000000000000000000
χ7644-444-44-444-4-4-4-4-440000000000000000−4i4i−4i4i00000000000000000000000000000000000000000000000000000000
χ7744-44-44-44-44-444-4-4-400000000000000004-4-4400000000000000000000000000000000000000000000000000000000
χ7844-44-44-44-44-444-4-4-40000000000000000-444-400000000000000000000000000000000000000000000000000000000
χ7944-4-44-44-4-4-4444-44-4000000000000000000000000000000000000000000000000000000000000000000002i2−2i22i2−2i20000
χ8044-4-44-44-4-4-4444-44-400000000000000000000000000000000000000000000000000000000000000000000−2i22i2−2i22i20000
χ8144-4-4-44-444-44-4-4-4440000000000000000000000000000000000000000000000000000000000000000000022−22−22220000
χ8244-4-4-44-444-44-4-4-44400000000000000000000000000000000000000000000000000000000000000000000−222222−220000
χ834-4444-4-444-4-4-44-44-400000000000000000000000000000000000000000000000000000000000022−2222−22000000000000
χ844-4444-4-444-4-4-44-44-4000000000000000000000000000000000000000000000000000000000000−2222−2222000000000000
χ854-444-444-4-4-4-44-4-44400000000000000000000000000000000000000000000000000000000000022−22−2222000000000000
χ864-444-444-4-4-4-44-4-444000000000000000000000000000000000000000000000000000000000000−222222−22000000000000
χ874-44-44-4-44-4444-4-4-44000000004-44-40000000000000000000000000000000000000000000000000000000000000000
χ884-44-44-4-44-4444-4-4-4400000000-44-440000000000000000000000000000000000000000000000000000000000000000
χ894-44-4-444-4444-44-4-4-4000000004-4-440000000000000000000000000000000000000000000000000000000000000000
χ904-44-4-444-4444-44-4-4-400000000-444-40000000000000000000000000000000000000000000000000000000000000000
χ914-4-4444-4-44-444-44-4-444-44-4-4-4400000000000000000000000000000000000000000000000000000000000000000000
χ924-4-44-4-444-4-44-444-44444-4-4-44-400000000000000000000000000000000000000000000000000000000000000000000

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