Finite Group Databasebeta

← Group #369173

Character table — Group #369173

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92
size1111111122222222222222222222222222224444444444444444888888888888888888888888888888881616161616161616
order12222222222244444444888888888888888844444444888888882222444444444444888888888888888822444444
χ111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1
χ31111111111111111111111111111111111111111111111111111-1-1-1-111111111-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ41111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111
χ51111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-111111111-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-111
χ61111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1-1-111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-11111-1-1
χ71111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-11111-1-1-1-111111111-1-11111-1-1
χ81111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-111111111111111-1-1-1-111
χ911111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1111111-1-11111111111-1-1-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1-1-1
χ1011111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1-1-111-1-1111111111111-1-1-1-1-1-1-1-11111
χ1111111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-11111111111-1-111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-11111
χ1211111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-111-1-1-1-1-1-1-1-1-1-11111111111-1-1-1-111111111-1-1-1-1
χ1311111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-111-1-11111-1-1-1-111-1-1-1-1-1-11111-1-1-1-1111111-1-111-1-1
χ1411111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-111-1-1-1-1-1-1111111-1-11111-1-1-1-1-1-1-1-11111-1-111-1-111
χ1511111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1111111-1-1-1-1-1-111-1-1-1-111111111-1-1-1-1-1-111-1-111
χ1611111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-111-1-1-1-11111-1-1111111-1-1-1-11111-1-1-1-111-1-111-1-1
χ17111-1-1-1-1111-1-111-1-111-1-11111-1-1-1-1iiii−i−i−i−iiiii−i−i−i−i11-1-1ii−i−i1-11-111-1-1ii−i−i1-11-111-1-1ii−i−iii−i−iii−i−i1-1i−ii−i1-1
χ18111-1-1-1-1111-1-111-1-111-1-11111-1-1-1-1iiii−i−i−i−iiiii−i−i−i−i11-1-1ii−i−i1-11-1-1-111−i−iii1-11-1-1-111−i−iiiii−i−iii−i−i-11−ii−ii-11
χ19111-1-1-1-1111-1-111-1-111-1-11111-1-1-1-1iiii−i−i−i−iiiii−i−i−i−i11-1-1ii−i−i-11-1111-1-1ii−i−i-11-1111-1-1ii−i−i−i−iii−i−iii-11−ii−ii-11
χ20111-1-1-1-1111-1-111-1-111-1-11111-1-1-1-1iiii−i−i−i−iiiii−i−i−i−i11-1-1ii−i−i-11-11-1-111−i−iii-11-11-1-111−i−iii−i−iii−i−iii1-1i−ii−i1-1
χ21111-1-1-1-1111-1-111-1-111-1-11111-1-1-1-1−i−i−i−iiiii−i−i−i−iiiii11-1-1−i−iii1-11-111-1-1−i−iii1-11-111-1-1−i−iii−i−iii−i−iii1-1−ii−ii1-1
χ22111-1-1-1-1111-1-111-1-111-1-11111-1-1-1-1−i−i−i−iiiii−i−i−i−iiiii11-1-1−i−iii1-11-1-1-111ii−i−i1-11-1-1-111ii−i−i−i−iii−i−iii-11i−ii−i-11
χ23111-1-1-1-1111-1-111-1-111-1-11111-1-1-1-1−i−i−i−iiiii−i−i−i−iiiii11-1-1−i−iii-11-1111-1-1−i−iii-11-1111-1-1−i−iiiii−i−iii−i−i-11i−ii−i-11
χ24111-1-1-1-1111-1-111-1-111-1-11111-1-1-1-1−i−i−i−iiiii−i−i−i−iiiii11-1-1−i−iii-11-11-1-111ii−i−i-11-11-1-111ii−i−iii−i−iii−i−i1-1−ii−ii1-1
χ25111-1-1-1-1111-1-111-1-111-1-1-1-1-1-11111iiii−i−i−i−i−i−i−i−iiiii-1-111ii−i−i1-1-1111-1-1ii−i−i1-1-11-1-111−i−iiiii−i−i−i−iii1-1i−i−ii-11
χ26111-1-1-1-1111-1-111-1-111-1-1-1-1-1-11111iiii−i−i−i−i−i−i−i−iiiii-1-111ii−i−i1-1-11-1-111−i−iii1-1-1111-1-1ii−i−iii−i−i−i−iii-11−iii−i1-1
χ27111-1-1-1-1111-1-111-1-111-1-1-1-1-1-11111iiii−i−i−i−i−i−i−i−iiiii-1-111ii−i−i-111-111-1-1ii−i−i-111-1-1-111−i−iii−i−iiiii−i−i-11−iii−i1-1
χ28111-1-1-1-1111-1-111-1-111-1-1-1-1-1-11111iiii−i−i−i−i−i−i−i−iiiii-1-111ii−i−i-111-1-1-111−i−iii-111-111-1-1ii−i−i−i−iiiii−i−i1-1i−i−ii-11
χ29111-1-1-1-1111-1-111-1-111-1-1-1-1-1-11111−i−i−i−iiiiiiiii−i−i−i−i-1-111−i−iii1-1-1111-1-1−i−iii1-1-11-1-111ii−i−i−i−iiiii−i−i1-1−iii−i-11
χ30111-1-1-1-1111-1-111-1-111-1-1-1-1-1-11111−i−i−i−iiiiiiiii−i−i−i−i-1-111−i−iii1-1-11-1-111ii−i−i1-1-1111-1-1−i−iii−i−iiiii−i−i-11i−i−ii1-1
χ31111-1-1-1-1111-1-111-1-111-1-1-1-1-1-11111−i−i−i−iiiiiiiii−i−i−i−i-1-111−i−iii-111-111-1-1−i−iii-111-1-1-111ii−i−iii−i−i−i−iii-11i−i−ii1-1
χ32111-1-1-1-1111-1-111-1-111-1-1-1-1-1-11111−i−i−i−iiiiiiiii−i−i−i−i-1-111−i−iii-111-1-1-111ii−i−i-111-111-1-1−i−iiiii−i−i−i−iii1-1−iii−i-11
χ3322222222-2-2-2-2222-2-2-2-220000000022222222000000000000-2-2-2-200002-22-22-22-20000000000000000000000000000
χ3422222222-2-2-2-2222-2-2-2-220000000022222222000000000000-2-2-2-20000-22-22-22-220000000000000000000000000000
χ3522222222-2-2-2-2222-2-2-2-2200000000-2-2-2-2-2-2-2-2000000000000222200002-22-2-22-220000000000000000000000000000
χ3622222222-2-2-2-2222-2-2-2-2200000000-2-2-2-2-2-2-2-200000000000022220000-22-222-22-20000000000000000000000000000
χ3722222222-2-2-2-2-2-2-22222-2222222220000000000000000-2-2-2-2000022-2-200000000-2-222000000000000000000000000
χ3822222222-2-2-2-2-2-2-22222-2222222220000000000000000-2-2-2-20000-2-2220000000022-2-2000000000000000000000000
χ3922222222-2-2-2-2-2-2-22222-2-2-2-2-2-2-2-2-2000000000000000022220000222200000000-2-2-2-2000000000000000000000000
χ4022222222-2-2-2-2-2-2-22222-2-2-2-2-2-2-2-2-2000000000000000022220000-2-2-2-2000000002222000000000000000000000000
χ41222-2-2-2-22-2-22222-22-2-22-2000000002i2i2i2i−2i−2i−2i−2i000000000000−2i−2i2i2i00002-2-222i−2i−2i2i0000000000000000000000000000
χ42222-2-2-2-22-2-22222-22-2-22-2000000002i2i2i2i−2i−2i−2i−2i000000000000−2i−2i2i2i0000-222-2−2i2i2i−2i0000000000000000000000000000
χ43222-2-2-2-22-2-22222-22-2-22-200000000−2i−2i−2i−2i2i2i2i2i0000000000002i2i−2i−2i00002-2-22−2i2i2i−2i0000000000000000000000000000
χ44222-2-2-2-22-2-22222-22-2-22-200000000−2i−2i−2i−2i2i2i2i2i0000000000002i2i−2i−2i0000-222-22i−2i−2i2i0000000000000000000000000000
χ45222-2-2-2-22-2-222-2-22-222-222222-2-2-2-20000000000000000-2-22200002-2-2200000000-222-2000000000000000000000000
χ46222-2-2-2-22-2-222-2-22-222-222222-2-2-2-20000000000000000-2-2220000-222-2000000002-2-22000000000000000000000000
χ47222-2-2-2-22-2-222-2-22-222-22-2-2-2-22222000000000000000022-2-200002-22-200000000-22-22000000000000000000000000
χ48222-2-2-2-22-2-222-2-22-222-22-2-2-2-22222000000000000000022-2-20000-22-22000000002-22-2000000000000000000000000
χ492-2-222-2-222-22-22-22-22-22-222-2-222-2-22i2i−2i−2i2i2i−2i−2i2i2i−2i−2i2i2i−2i−2i2-22-22i−2i2i−2i0000000000000000000000000000000000000000
χ502-2-222-2-222-22-22-22-22-22-222-2-222-2-2−2i−2i2i2i−2i−2i2i2i−2i−2i2i2i−2i−2i2i2i2-22-2−2i2i−2i2i0000000000000000000000000000000000000000
χ512-2-222-2-222-22-22-22-22-22-2-2-222-2-2222i2i−2i−2i2i2i−2i−2i−2i−2i2i2i−2i−2i2i2i-22-222i−2i2i−2i0000000000000000000000000000000000000000
χ522-2-222-2-222-22-22-22-22-22-2-2-222-2-222−2i−2i2i2i−2i−2i2i2i2i2i−2i−2i2i2i−2i−2i-22-22−2i2i−2i2i0000000000000000000000000000000000000000
χ532-2-222-2-22-22-222-222-22-2-2000000002i2i−2i−2i2i2i−2i−2i000000000000−2i2i−2i2i00000000000000002-22-22i−2i2i−2i0000000000000000
χ542-2-222-2-22-22-222-222-22-2-2000000002i2i−2i−2i2i2i−2i−2i000000000000−2i2i−2i2i0000000000000000-22-22−2i2i−2i2i0000000000000000
χ552-2-222-2-22-22-222-222-22-2-200000000−2i−2i2i2i−2i−2i2i2i0000000000002i−2i2i−2i00000000000000002-22-2−2i2i−2i2i0000000000000000
χ562-2-222-2-22-22-222-222-22-2-200000000−2i−2i2i2i−2i−2i2i2i0000000000002i−2i2i−2i0000000000000000-22-222i−2i2i−2i0000000000000000
χ572-2-222-2-22-22-22-22-2-22-22222-2-222-2-20000000000000000-22-2200000000000000000000000000002-22-22-22-200000000
χ582-2-222-2-22-22-22-22-2-22-22222-2-222-2-20000000000000000-22-220000000000000000000000000000-22-22-22-2200000000
χ592-2-222-2-22-22-22-22-2-22-222-2-222-2-22200000000000000002-22-200000000000000000000000000002-22-2-22-2200000000
χ602-2-222-2-22-22-22-22-2-22-222-2-222-2-22200000000000000002-22-20000000000000000000000000000-22-222-22-200000000
χ612-2-2-2-22222-2-222-2-222-2-2222-2-2-2-22222-2-2-2-22222-2-2-2-2222-2-222-2-220000000000000000000000000000000000000000
χ622-2-2-2-22222-2-222-2-222-2-2222-2-2-2-222-2-22222-2-2-2-22222-2-22-2-22-222-20000000000000000000000000000000000000000
χ632-2-2-2-22222-2-222-2-222-2-22-2-22222-2-222-2-2-2-222-2-22222-2-2-222-22-2-220000000000000000000000000000000000000000
χ642-2-2-2-22222-2-222-2-222-2-22-2-22222-2-2-2-22222-2-222-2-2-2-222-222-2-222-20000000000000000000000000000000000000000
χ652-2-2-2-2222-222-22-2-2-2-22220000000022-2-2-2-222000000000000-222-200000000000000002-2-222-2-220000000000000000
χ662-2-2-2-2222-222-22-2-2-2-22220000000022-2-2-2-222000000000000-222-20000000000000000-222-2-222-20000000000000000
χ672-2-2-2-2222-222-22-2-2-2-222200000000-2-22222-2-20000000000002-2-2200000000000000002-2-22-222-20000000000000000
χ682-2-2-2-2222-222-22-2-2-2-222200000000-2-22222-2-20000000000002-2-220000000000000000-222-22-2-220000000000000000
χ692-2-2-2-2222-222-2-22222-2-2-222-2-2-2-2220000000000000000-222-200000000000000000000000000002i−2i−2i2i2i−2i−2i2i00000000
χ702-2-2-2-2222-222-2-22222-2-2-222-2-2-2-2220000000000000000-222-20000000000000000000000000000−2i2i2i−2i−2i2i2i−2i00000000
χ712-2-2-2-2222-222-2-22222-2-2-2-2-22222-2-200000000000000002-2-2200000000000000000000000000002i−2i−2i2i−2i2i2i−2i00000000
χ722-2-2-2-2222-222-2-22222-2-2-2-2-22222-2-200000000000000002-2-220000000000000000000000000000−2i2i2i−2i2i−2i−2i2i00000000
χ73444444444444-4-4-4-4-4-4-4-4000000000000000000000000000000000000000000000000000000000000000000000000
χ74444-4-4-4-4444-4-4-4-444-4-444000000000000000000000000000000000000000000000000000000000000000000000000
χ7544-44-44-4-40000000000002i2−2i22i2−2i22i2−2i22i2−2i22i2−2i22i2−2i22i2−2i22i2−2i22-22-22-22-2000000000000000000000000000000000000000000000000
χ7644-44-44-4-40000000000002i2−2i22i2−2i22i2−2i22i2−2i2−2i22i2−2i22i2−2i22i2−2i22i2-22-22-22-22000000000000000000000000000000000000000000000000
χ7744-44-44-4-4000000000000−2i22i2−2i22i2−2i22i2−2i22i22i2−2i22i2−2i22i2−2i22i2−2i2-22-22-22-22000000000000000000000000000000000000000000000000
χ7844-44-44-4-4000000000000−2i22i2−2i22i2−2i22i2−2i22i2−2i22i2−2i22i2−2i22i2−2i22i22-22-22-22-2000000000000000000000000000000000000000000000000
χ7944-4-44-44-40000000000002i2−2i22i2−2i2−2i22i2−2i22i222−2222−22−2222−2222−2i2i−2i2i2i−2i2i−2i000000000000000000000000000000000000000000000000
χ8044-4-44-44-40000000000002i2−2i22i2−2i2−2i22i2−2i22i2−2222−222222−2222−222i−2i2i−2i−2i2i−2i2i000000000000000000000000000000000000000000000000
χ8144-4-44-44-4000000000000−2i22i2−2i22i22i2−2i22i2−2i222−2222−22−2222−22222i−2i2i−2i−2i2i−2i2i000000000000000000000000000000000000000000000000
χ8244-4-44-44-4000000000000−2i22i2−2i22i22i2−2i22i2−2i2−2222−222222−2222−22−2i2i−2i2i2i−2i2i−2i000000000000000000000000000000000000000000000000
χ834-444-4-44-40000000000002i2−2i2−2i22i22i2−2i2−2i22i222−22−222222−22−2222−2i2i2i−2i−2i2i2i−2i000000000000000000000000000000000000000000000000
χ844-444-4-44-40000000000002i2−2i2−2i22i22i2−2i2−2i22i2−222222−22−222222−222i−2i−2i2i2i−2i−2i2i000000000000000000000000000000000000000000000000
χ854-444-4-44-4000000000000−2i22i22i2−2i2−2i22i22i2−2i222−22−222222−22−22222i−2i−2i2i2i−2i−2i2i000000000000000000000000000000000000000000000000
χ864-444-4-44-4000000000000−2i22i22i2−2i2−2i22i22i2−2i2−222222−22−222222−22−2i2i2i−2i−2i2i2i−2i000000000000000000000000000000000000000000000000
χ874-44-444-4-40000000000002i2−2i2−2i22i2−2i22i22i2−2i22i2−2i2−2i22i2−2i22i22i2−2i22-2-22-222-2000000000000000000000000000000000000000000000000
χ884-44-444-4-40000000000002i2−2i2−2i22i2−2i22i22i2−2i2−2i22i22i2−2i22i2−2i2−2i22i2-222-22-2-22000000000000000000000000000000000000000000000000
χ894-44-444-4-4000000000000−2i22i22i2−2i22i2−2i2−2i22i22i2−2i2−2i22i2−2i22i22i2−2i2-222-22-2-22000000000000000000000000000000000000000000000000
χ904-44-444-4-4000000000000−2i22i22i2−2i22i2−2i2−2i22i2−2i22i22i2−2i22i2−2i2−2i22i22-2-22-222-2000000000000000000000000000000000000000000000000
χ914-4-444-4-444-44-4-44-44-44-44000000000000000000000000000000000000000000000000000000000000000000000000
χ924-4-4-4-44444-4-44-444-4-444-4000000000000000000000000000000000000000000000000000000000000000000000000

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