Finite Group Databasebeta

← Group #229677

Character table — Group #229677

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92
size1111111111111111222222224444444444444444444444444444444488888888888888888888888888881616161616161616
order12222222444444444444444444448888888888888888888888888888224444444444448888888888888844888888
χ111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111111111111111111111-1-111-1-1-1-1-1-1-1-1-1-111-1-1-1-111111111-1-1-1-1-1-1-1-1
χ31111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-11111-1-1-1-1
χ41111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-11111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111
χ51111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-111-1-11111
χ61111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-111-1-111111111-1-111111111-1-1-1-1-1-111-1-1-1-1
χ71111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111111111111111-1-1-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1
χ81111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1111111
χ9111111111111111111111111-1-1-1-111111111-1-1-1-1111111111111111111-1-1111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1
χ10111111111111111111111111-1-1-1-111111111-1-1-1-11111111111111111-1-1-1-1-1-1-1-1-1-11111-1-11111-1-1-1-1-1-1-1-111-1-1-1-111
χ11111111111111111111111111-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-111-1-1-1-11111-1-1-1-1-1-111111111-1-111-1-111
χ12111111111111111111111111-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-111111111111111-1-111-1-1
χ13111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-111-1-111-1-1-1-11111111111-1-1-1-11111-1-1-1-111-1-1
χ14111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-111-1-1-1-1-1-1-1-111111111-1-111
χ15111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-11111111111-1-1111111-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-111
χ16111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1111111-1-1-1-11111-1-1-1-1111111-1-1
χ1711111111-1-1-1-1-1-1-1-111-1-1-1-11111-1-1ii−i−iii−i−iii−i−iiiii−i−i−i−i1111-1-1-1-1111-1-1-111-1-111-1-1i−iii−i−iii−i−i11-1-11-1i−ii−ii−i
χ1811111111-1-1-1-1-1-1-1-111-1-1-1-11111-1-1ii−i−iii−i−iii−i−iiiii−i−i−i−i1111-1-1-1-1-1-11-111-1-111-1-111i−i−i−iiiii−i−i11-1-1-11−ii−ii−ii
χ1911111111-1-1-1-1-1-1-1-111-1-1-1-11111-1-1ii−i−iii−i−iii−i−i−i−i−i−iiiii-1-1-1-11111111-1-1-1-1-111-1-111i−iii−i−i−i−iii-1-1111-1i−i−ii−ii
χ2011111111-1-1-1-1-1-1-1-111-1-1-1-11111-1-1ii−i−iii−i−iii−i−i−i−i−i−iiiii-1-1-1-11111-1-11-11111-1-111-1-1i−i−i−iii−i−iii-1-111-11−iii−ii−i
χ2111111111-1-1-1-1-1-1-1-111-1-1-1-11111-1-1−i−iii−i−iii−i−iiiiiii−i−i−i−i-1-1-1-11111111-1-1-1-1-111-1-111−ii−i−iiiii−i−i-1-1111-1−iii−ii−i
χ2211111111-1-1-1-1-1-1-1-111-1-1-1-11111-1-1−i−iii−i−iii−i−iiiiiii−i−i−i−i-1-1-1-11111-1-11-11111-1-111-1-1−iiii−i−iii−i−i-1-111-11i−i−ii−ii
χ2311111111-1-1-1-1-1-1-1-111-1-1-1-11111-1-1−i−iii−i−iii−i−iii−i−i−i−iiiii1111-1-1-1-1111-1-1-111-1-111-1-1−ii−i−iii−i−iii11-1-11-1−ii−ii−ii
χ2411111111-1-1-1-1-1-1-1-111-1-1-1-11111-1-1−i−iii−i−iii−i−iii−i−i−i−iiiii1111-1-1-1-1-1-11-111-1-111-1-111−iiii−i−i−i−iii11-1-1-11i−ii−ii−i
χ2511111111-1-1-1-1-1-1-1-111-1-1-1-111-1-111ii−i−iii−i−i−i−iiiiiii−i−i−i−i1111-1-1-1-111-11-1-111-1-1-1-111−ii−i−iii−i−iii-1-111-11i−ii−i−ii
χ2611111111-1-1-1-1-1-1-1-111-1-1-1-111-1-111ii−i−iii−i−i−i−iiiiiii−i−i−i−i1111-1-1-1-1-1-1-1111-1-11111-1-1−iiii−i−i−i−iii-1-1111-1−ii−iii−i
χ2711111111-1-1-1-1-1-1-1-111-1-1-1-111-1-111ii−i−iii−i−i−i−iii−i−i−i−iiiii-1-1-1-1111111-11-1-1-1-11111-1-1−ii−i−iiiii−i−i11-1-1-11i−i−iii−i
χ2811111111-1-1-1-1-1-1-1-111-1-1-1-111-1-111ii−i−iii−i−i−i−iii−i−i−i−iiiii-1-1-1-11111-1-1-111111-1-1-1-111−iiii−i−iii−i−i11-1-11-1−iii−i−ii
χ2911111111-1-1-1-1-1-1-1-111-1-1-1-111-1-111−i−iii−i−iiiii−i−iiiii−i−i−i−i-1-1-1-1111111-11-1-1-1-11111-1-1i−iii−i−i−i−iii11-1-1-11−iii−i−ii
χ3011111111-1-1-1-1-1-1-1-111-1-1-1-111-1-111−i−iii−i−iiiii−i−iiiii−i−i−i−i-1-1-1-11111-1-1-111111-1-1-1-111i−i−i−iii−i−iii11-1-11-1i−i−iii−i
χ3111111111-1-1-1-1-1-1-1-111-1-1-1-111-1-111−i−iii−i−iiiii−i−i−i−i−i−iiiii1111-1-1-1-111-11-1-111-1-1-1-111i−iii−i−iii−i−i-1-111-11−ii−iii−i
χ3211111111-1-1-1-1-1-1-1-111-1-1-1-111-1-111−i−iii−i−iiiii−i−i−i−i−i−iiiii1111-1-1-1-1-1-1-1111-1-11111-1-1i−i−i−iiiii−i−i-1-1111-1i−ii−i−ii
χ332222222222222222-2-2-2-2-2-2-2-222222222-2-2-2-22222000000000000000000-2-20000000000-2-200000000000000000000
χ342222222222222222-2-2-2-2-2-2-2-22222-2-2-2-22222-2-2-2-2000000000000000000-2-200000000002200000000000000000000
χ352222222222222222-2-2-2-2-2-2-2-2-2-2-2-22222-2-2-2-2-2-2-2-20000000000000000002200000000002200000000000000000000
χ362222222222222222-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-222222222000000000000000000220000000000-2-200000000000000000000
χ3722222222-2-2-2-2-2-2-2-2-2-22222-2-222-2-22i2i−2i−2i−2i−2i2i2i2i2i−2i−2i000000000000000000-220000000000−2i2i00000000000000000000
χ3822222222-2-2-2-2-2-2-2-2-2-22222-2-222-2-2−2i−2i2i2i2i2i−2i−2i−2i−2i2i2i000000000000000000-2200000000002i−2i00000000000000000000
χ3922222222-2-2-2-2-2-2-2-2-2-22222-2-2-2-2222i2i−2i−2i−2i−2i2i2i−2i−2i2i2i0000000000000000002-200000000002i−2i00000000000000000000
χ4022222222-2-2-2-2-2-2-2-2-2-22222-2-2-2-222−2i−2i2i2i2i2i−2i−2i2i2i−2i−2i0000000000000000002-20000000000−2i2i00000000000000000000
χ4122-22-2-22-22i−2i2i−2i2i−2i2i−2i2-22i2i−2i−2i2-200000000000000000000000022-2-22i2i−2i−2i2-2002i−2i2-22i−2i00000000000000000000000000
χ4222-22-2-22-22i−2i2i−2i2i−2i2i−2i2-22i2i−2i−2i2-200000000000000000000000022-2-22i2i−2i−2i-2200−2i2i-22−2i2i00000000000000000000000000
χ4322-22-2-22-22i−2i2i−2i2i−2i2i−2i2-22i2i−2i−2i2-2000000000000000000000000-2-222−2i−2i2i2i2-2002i−2i-22−2i2i00000000000000000000000000
χ4422-22-2-22-22i−2i2i−2i2i−2i2i−2i2-22i2i−2i−2i2-2000000000000000000000000-2-222−2i−2i2i2i-2200−2i2i2-22i−2i00000000000000000000000000
χ4522-22-2-22-2−2i2i−2i2i−2i2i−2i2i2-2−2i−2i2i2i2-200000000000000000000000022-2-2−2i−2i2i2i2-200−2i2i2-2−2i2i00000000000000000000000000
χ4622-22-2-22-2−2i2i−2i2i−2i2i−2i2i2-2−2i−2i2i2i2-200000000000000000000000022-2-2−2i−2i2i2i-22002i−2i-222i−2i00000000000000000000000000
χ4722-22-2-22-2−2i2i−2i2i−2i2i−2i2i2-2−2i−2i2i2i2-2000000000000000000000000-2-2222i2i−2i−2i2-200−2i2i-222i−2i00000000000000000000000000
χ4822-22-2-22-2−2i2i−2i2i−2i2i−2i2i2-2−2i−2i2i2i2-2000000000000000000000000-2-2222i2i−2i−2i-22002i−2i2-2−2i2i00000000000000000000000000
χ492-2-2222-2-222-2-2-2-222000000002i−2i2i−2i2i−2i2i−2i00002-22-2i2i2−i2−i2i2i2−i2−i22−22−22−22−2000000000000000000002−22−2i2−i2i2−i200000000
χ502-2-2222-2-222-2-2-2-222000000002i−2i2i−2i2i−2i2i−2i00002-22-2−i2−i2i2i2−i2−i2i2i2−22−22−22−2200000000000000000000−22−22−i2i2−i2i200000000
χ512-2-2222-2-222-2-2-2-222000000002i−2i2i−2i−2i2i−2i2i0000-22-22i2i2−i2−i2i2i2−i2−i2−22−22−22−22000000000000000000002−22−2−i2i2−i2i200000000
χ522-2-2222-2-222-2-2-2-222000000002i−2i2i−2i−2i2i−2i2i0000-22-22−i2−i2i2i2−i2−i2i2i22−22−22−22−200000000000000000000−22−22i2−i2i2−i200000000
χ532-2-2222-2-222-2-2-2-22200000000−2i2i−2i2i2i−2i2i−2i0000-22-22i2i2−i2−i2i2i2−i2−i22−22−22−22−200000000000000000000−22−22−i2i2−i2i200000000
χ542-2-2222-2-222-2-2-2-22200000000−2i2i−2i2i2i−2i2i−2i0000-22-22−i2−i2i2i2−i2−i2i2i2−22−22−22−22000000000000000000002−22−2i2−i2i2−i200000000
χ552-2-2222-2-222-2-2-2-22200000000−2i2i−2i2i−2i2i−2i2i00002-22-2i2i2−i2−i2i2i2−i2−i2−22−22−22−2200000000000000000000−22−22i2−i2i2−i200000000
χ562-2-2222-2-222-2-2-2-22200000000−2i2i−2i2i−2i2i−2i2i00002-22-2−i2−i2i2i2−i2−i2i2i22−22−22−22−2000000000000000000002−22−2−i2i2−i2i200000000
χ572-2-2222-2-2-2-22222-2-2000000002i−2i−2i2i2-2-220000−2i2i2i−2i22−2−2−2−2222−22−2−22−2200000000000000000000−i2i2i2−i2i2−i2−i2i200000000
χ582-2-2222-2-2-2-22222-2-2000000002i−2i−2i2i2-2-220000−2i2i2i−2i−2−22222−2−2−22−222−22−200000000000000000000i2−i2−i2i2−i2i2i2−i200000000
χ592-2-2222-2-2-2-22222-2-2000000002i−2i−2i2i-222-200002i−2i−2i2i22−2−2−2−222−22−222−22−200000000000000000000−i2i2i2−i2−i2i2i2−i200000000
χ602-2-2222-2-2-2-22222-2-2000000002i−2i−2i2i-222-200002i−2i−2i2i−2−22222−2−22−22−2−22−2200000000000000000000i2−i2−i2i2i2−i2−i2i200000000
χ612-2-2222-2-2-2-22222-2-200000000−2i2i2i−2i2-2-2200002i−2i−2i2i22−2−2−2−2222−22−2−22−2200000000000000000000i2−i2−i2i2−i2i2i2−i200000000
χ622-2-2222-2-2-2-22222-2-200000000−2i2i2i−2i2-2-2200002i−2i−2i2i−2−22222−2−2−22−222−22−200000000000000000000−i2i2i2−i2i2−i2−i2i200000000
χ632-2-2222-2-2-2-22222-2-200000000−2i2i2i−2i-222-20000−2i2i2i−2i22−2−2−2−222−22−222−22−200000000000000000000i2−i2−i2i2i2−i2−i2i200000000
χ642-2-2222-2-2-2-22222-2-200000000−2i2i2i−2i-222-20000−2i2i2i−2i−2−22222−2−22−22−2−22−2200000000000000000000−i2i2i2−i2−i2i2i2−i200000000
χ652-2-2-22-2222222-2-2-2-2-2-22-22-22200000000000000002i−2i2i−2i2i−2i2i−2i0000000000000000002-22-2002i−2i2i−2i0000000000000000
χ662-2-2-22-2222222-2-2-2-2-2-22-22-22200000000000000002i−2i2i−2i2i−2i2i−2i000000000000000000-22-2200−2i2i−2i2i0000000000000000
χ672-2-2-22-2222222-2-2-2-2-2-22-22-2220000000000000000−2i2i−2i2i−2i2i−2i2i0000000000000000002-22-200−2i2i−2i2i0000000000000000
χ682-2-2-22-2222222-2-2-2-2-2-22-22-2220000000000000000−2i2i−2i2i−2i2i−2i2i000000000000000000-22-22002i−2i2i−2i0000000000000000
χ692-2-2-22-222-2-2-2-22222-2-2-22-222200000000000000002-22-2-22-220000000000000000002-2-22002-2-220000000000000000
χ702-2-2-22-222-2-2-2-22222-2-2-22-222200000000000000002-22-2-22-22000000000000000000-222-200-222-20000000000000000
χ712-2-2-22-222-2-2-2-22222-2-2-22-22220000000000000000-22-222-22-20000000000000000002-2-2200-222-20000000000000000
χ722-2-2-22-222-2-2-2-22222-2-2-22-22220000000000000000-22-222-22-2000000000000000000-222-2002-2-220000000000000000
χ73444-44-4-4-444-4-444-4-400000000000000000000000022−22−222222−22−222200000000000000000000000000000000000000000000
χ74444-44-4-4-444-4-444-4-4000000000000000000000000−222222−22−222222−2200000000000000000000000000000000000000000000
χ75444-44-4-4-4-4-444-4-4440000000000000000000000002i2−2i2−2i22i2−2i22i22i2−2i200000000000000000000000000000000000000000000
χ76444-44-4-4-4-4-444-4-444000000000000000000000000−2i22i22i2−2i22i2−2i2−2i22i200000000000000000000000000000000000000000000
χ7744-44-4-44-44i−4i4i−4i4i−4i4i−4i-44−4i−4i4i4i-4400000000000000000000000000000000000000000000000000000000000000000000
χ7844-44-4-44-4−4i4i−4i4i−4i4i−4i4i-444i4i−4i−4i-4400000000000000000000000000000000000000000000000000000000000000000000
χ7944-4-4-44-444i−4i−4i4i4i−4i−4i4i00000000000000004ζ3−4ζ34ζ−4ζ00000000000000000000000000000000000000000000000000000000
χ8044-4-4-44-444i−4i−4i4i4i−4i−4i4i0000000000000000−4ζ34ζ3−4ζ4ζ00000000000000000000000000000000000000000000000000000000
χ8144-4-4-44-44−4i4i4i−4i−4i4i4i−4i00000000000000004ζ−4ζ4ζ3−4ζ300000000000000000000000000000000000000000000000000000000
χ8244-4-4-44-44−4i4i4i−4i−4i4i4i−4i0000000000000000−4ζ4ζ−4ζ34ζ300000000000000000000000000000000000000000000000000000000
χ834-444-4-4-444i−4i−4i4i−4i4i4i−4i0000000000000000000000000000000022−22−22222i2−2i2−2i22i2000000000000000000000000000000000000
χ844-444-4-4-444i−4i−4i4i−4i4i4i−4i00000000000000000000000000000000−222222−22−2i22i22i2−2i2000000000000000000000000000000000000
χ854-444-4-4-44−4i4i4i−4i4i−4i−4i4i0000000000000000000000000000000022−22−2222−2i22i22i2−2i2000000000000000000000000000000000000
χ864-444-4-4-44−4i4i4i−4i4i−4i−4i4i00000000000000000000000000000000−222222−222i2−2i2−2i22i2000000000000000000000000000000000000
χ874-44-4-444-44i−4i4i−4i−4i4i−4i4i4-4−4i4i4i−4i-4400000000000000000000000000000000000000000000000000000000000000000000
χ884-44-4-444-44i−4i4i−4i−4i4i−4i4i-444i−4i−4i4i4-400000000000000000000000000000000000000000000000000000000000000000000
χ894-44-4-444-4−4i4i−4i4i4i−4i4i−4i4-44i−4i−4i4i-4400000000000000000000000000000000000000000000000000000000000000000000
χ904-44-4-444-4−4i4i−4i4i4i−4i4i−4i-44−4i4i4i−4i4-400000000000000000000000000000000000000000000000000000000000000000000
χ914-4-4-44-4444444-4-4-4-444-44-44-4-400000000000000000000000000000000000000000000000000000000000000000000
χ924-4-4-44-444-4-4-4-44444444-44-4-4-400000000000000000000000000000000000000000000000000000000000000000000

Here ζ is a primitive root of unity of order 8 (ζ8 = 1); i = ζ2.