Finite Group Databasebeta

← Group #211441

Character table — Group #211441

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92
size1111111122222222222222222222222222224444444444444444888888888888888888888888888888881616161616161616
order12222222444444444444444444448888888844448888888888882244444488888888888888888888888844444444
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
χ31111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-11111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1
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
χ51111111111111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-11111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1
χ61111111111111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-11111
χ71111111111111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-111111111-1-1-1-11111
χ81111111111111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111111111111111-1-1-1-1
χ911111111-1-1-1-1-1-1-1-1-1-1-1-11111111111111111-1-1111111-1-1-1-1-1-1-1-111-1-111-1-11111-1-1-1-11111-1-1-1-11111-1-1-1-111-1-111-1-1
χ1011111111-1-1-1-1-1-1-1-1-1-1-1-11111111111111111-1-1111111-1-1-1-1-1-1-1-111-1-111-1-1-1-1-1-11111-1-1-1-111111111-1-1-1-1-1-111-1-111
χ1111111111-1-1-1-1-1-1-1-1-1-1-1-11111111111111111-1-1111111-1-1-1-1-1-1-1-1-1-111-1-1111111-1-1-1-11111-1-1-1-1-1-1-1-11111-1-111-1-111
χ1211111111-1-1-1-1-1-1-1-1-1-1-1-11111111111111111-1-1111111-1-1-1-1-1-1-1-1-1-111-1-111-1-1-1-11111-1-1-1-11111-1-1-1-1111111-1-111-1-1
χ1311111111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-111-1-1-1-11111111111-1-111-1-11111-1-1-1-1-1-1-1-11111-1-1-1-1111111-1-1-1-111
χ1411111111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-111-1-1-1-11111111111-1-111-1-1-1-1-1-111111111-1-1-1-1-1-1-1-11111-1-11111-1-1
χ1511111111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-111-1-1-1-111111111-1-111-1-1111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-11111-1-1
χ1611111111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-111-1-1-1-111111111-1-111-1-111-1-1-1-111111111-1-1-1-11111-1-1-1-111-1-1-1-111
χ1711-1-11-11-1ii−i−iii−i−iii−i−i1-111-1-11-1iiii−i−i−i−ii−i1-1ii−i−i11-1-111-1-11-1i−i1-1i−i11-1-1ii−i−iii−i−i11-1-1ii−i−i11-1-11-1i−ii−i1-1
χ1811-1-11-11-1ii−i−iii−i−iii−i−i1-111-1-11-1iiii−i−i−i−ii−i1-1ii−i−i11-1-111-1-11-1i−i1-1i−i-1-111−i−iii−i−iii-1-111ii−i−i11-1-1-11−ii−ii-11
χ1911-1-11-11-1ii−i−iii−i−iii−i−i1-111-1-11-1iiii−i−i−i−ii−i1-1ii−i−i11-1-111-1-1-11−ii-11−ii11-1-1ii−i−iii−i−i11-1-1−i−iii-1-111-11−ii−ii-11
χ2011-1-11-11-1ii−i−iii−i−iii−i−i1-111-1-11-1iiii−i−i−i−ii−i1-1ii−i−i11-1-111-1-1-11−ii-11−ii-1-111−i−iii−i−iii-1-111−i−iii-1-1111-1i−ii−i1-1
χ2111-1-11-11-1ii−i−iii−i−iii−i−i1-111-1-11-1−i−i−i−iiiiii−i1-1−i−iii-1-111-1-1111-1i−i1-1i−i11-1-1ii−i−i−i−iii-1-111−i−iii-1-1111-1i−i−ii-11
χ2211-1-11-11-1ii−i−iii−i−iii−i−i1-111-1-11-1−i−i−i−iiiiii−i1-1−i−iii-1-111-1-1111-1i−i1-1i−i-1-111−i−iiiii−i−i11-1-1−i−iii-1-111-11−iii−i1-1
χ2311-1-11-11-1ii−i−iii−i−iii−i−i1-111-1-11-1−i−i−i−iiiiii−i1-1−i−iii-1-111-1-111-11−ii-11−ii11-1-1ii−i−i−i−iii-1-111ii−i−i11-1-1-11−iii−i1-1
χ2411-1-11-11-1ii−i−iii−i−iii−i−i1-111-1-11-1−i−i−i−iiiiii−i1-1−i−iii-1-111-1-111-11−ii-11−ii-1-111−i−iiiii−i−i11-1-1ii−i−i11-1-11-1i−i−ii-11
χ2511-1-11-11-1−i−iii−i−iii−i−iii1-111-1-11-1iiii−i−i−i−i−ii1-1ii−i−i-1-111-1-1111-1−ii1-1−ii11-1-1−i−iiiii−i−i-1-111ii−i−i-1-1111-1−iii−i-11
χ2611-1-11-11-1−i−iii−i−iii−i−iii1-111-1-11-1iiii−i−i−i−i−ii1-1ii−i−i-1-111-1-1111-1−ii1-1−ii-1-111ii−i−i−i−iii11-1-1ii−i−i-1-111-11i−i−ii1-1
χ2711-1-11-11-1−i−iii−i−iii−i−iii1-111-1-11-1iiii−i−i−i−i−ii1-1ii−i−i-1-111-1-111-11i−i-11i−i11-1-1−i−iiiii−i−i-1-111−i−iii11-1-1-11i−i−ii1-1
χ2811-1-11-11-1−i−iii−i−iii−i−iii1-111-1-11-1iiii−i−i−i−i−ii1-1ii−i−i-1-111-1-111-11i−i-11i−i-1-111ii−i−i−i−iii11-1-1−i−iii11-1-11-1−iii−i-11
χ2911-1-11-11-1−i−iii−i−iii−i−iii1-111-1-11-1−i−i−i−iiiii−ii1-1−i−iii11-1-111-1-11-1−ii1-1−ii11-1-1−i−iii−i−iii11-1-1−i−iii11-1-11-1−ii−ii1-1
χ3011-1-11-11-1−i−iii−i−iii−i−iii1-111-1-11-1−i−i−i−iiiii−ii1-1−i−iii11-1-111-1-11-1−ii1-1−ii-1-111ii−i−iii−i−i-1-111−i−iii11-1-1-11i−ii−i-11
χ3111-1-11-11-1−i−iii−i−iii−i−iii1-111-1-11-1−i−i−i−iiiii−ii1-1−i−iii11-1-111-1-1-11i−i-11i−i11-1-1−i−iii−i−iii11-1-1ii−i−i-1-111-11i−ii−i-11
χ3211-1-11-11-1−i−iii−i−iii−i−iii1-111-1-11-1−i−i−i−iiiii−ii1-1−i−iii11-1-111-1-1-11i−i-11i−i-1-111ii−i−iii−i−i-1-111ii−i−i-1-1111-1−ii−ii1-1
χ332222222222222222-2-2-2-2-2-2-2-2-2-2-2-200000000-2-2220000000000000000000000000000000000002i−2i2i−2i2i−2i2i−2i00000000
χ342222222222222222-2-2-2-2-2-2-2-2-2-2-2-200000000-2-222000000000000000000000000000000000000−2i2i−2i2i−2i2i−2i2i00000000
χ35222222222222-2-2-2-2222222-2-2-2-22222222222-2-2-2-2-2-2-2-2-2-2-2-222220000000000000000000000000000000000000000
χ36222222222222-2-2-2-2222222-2-2-2-222-2-2-2-2-2-2-2-2-2-2-2-222222222-2-2-2-20000000000000000000000000000000000000000
χ37222222222222-2-2-2-2-2-2-2-2-2-22222-2-20000000022-2-200000000000022-2-2-2-22200000000000000000000000000000000
χ38222222222222-2-2-2-2-2-2-2-2-2-22222-2-20000000022-2-2000000000000-2-22222-2-200000000000000000000000000000000
χ3922222222-2-2-2-222222222-2-22222-2-200000000-2-2-2-20000000000002222-2-2-2-200000000000000000000000000000000
χ4022222222-2-2-2-222222222-2-22222-2-200000000-2-2-2-2000000000000-2-2-2-2222200000000000000000000000000000000
χ4122222222-2-2-2-22222-2-2-2-222-2-2-2-2222222222222-2-2-2-2-2-22222-2-2-2-20000000000000000000000000000000000000000
χ4222222222-2-2-2-22222-2-2-2-222-2-2-2-222-2-2-2-2-2-2-2-222-2-22222-2-2-2-222220000000000000000000000000000000000000000
χ4322222222-2-2-2-2-2-2-2-22222-2-2-2-2-2-2-2-20000000022220000000000000000000000000000000000002i−2i2i−2i−2i2i−2i2i00000000
χ4422222222-2-2-2-2-2-2-2-22222-2-2-2-2-2-2-2-2000000002222000000000000000000000000000000000000−2i2i−2i2i2i−2i2i−2i00000000
χ4522-2-22-22-22i2i−2i−2i2i2i−2i−2i−2i−2i2i2i-22-2-222-2200000000−2i2i2-20000000000000000000000000000000000002-2-22−2i2i2i−2i00000000
χ4622-2-22-22-22i2i−2i−2i2i2i−2i−2i−2i−2i2i2i-22-2-222-2200000000−2i2i2-2000000000000000000000000000000000000-222-22i−2i−2i2i00000000
χ4722-2-22-22-22i2i−2i−2i−2i−2i2i2i2i2i−2i−2i2-2-2-2222-22i2i2i2i−2i−2i−2i−2i−2i2i-22−2i−2i2i2i-2-22222-2-20000000000000000000000000000000000000000
χ4822-2-22-22-22i2i−2i−2i−2i−2i2i2i2i2i−2i−2i2-2-2-2222-2−2i−2i−2i−2i2i2i2i2i−2i2i-222i2i−2i−2i22-2-2-2-2220000000000000000000000000000000000000000
χ4922-2-22-22-22i2i−2i−2i−2i−2i2i2i−2i−2i2i2i-2222-2-2-22000000002i−2i-220000000000002-2−2i2i-222i−2i00000000000000000000000000000000
χ5022-2-22-22-22i2i−2i−2i−2i−2i2i2i−2i−2i2i2i-2222-2-2-22000000002i−2i-22000000000000-222i−2i2-2−2i2i00000000000000000000000000000000
χ5122-2-22-22-2−2i−2i2i2i2i2i−2i−2i2i2i−2i−2i-2222-2-2-2200000000−2i2i-220000000000002-22i−2i-22−2i2i00000000000000000000000000000000
χ5222-2-22-22-2−2i−2i2i2i2i2i−2i−2i2i2i−2i−2i-2222-2-2-2200000000−2i2i-22000000000000-22−2i2i2-22i−2i00000000000000000000000000000000
χ5322-2-22-22-2−2i−2i2i2i2i2i−2i−2i−2i−2i2i2i2-2-2-2222-22i2i2i2i−2i−2i−2i−2i2i−2i-22−2i−2i2i2i22-2-2-2-2220000000000000000000000000000000000000000
χ5422-2-22-22-2−2i−2i2i2i2i2i−2i−2i−2i−2i2i2i2-2-2-2222-2−2i−2i−2i−2i2i2i2i2i2i−2i-222i2i−2i−2i-2-22222-2-20000000000000000000000000000000000000000
χ5522-2-22-22-2−2i−2i2i2i−2i−2i2i2i2i2i−2i−2i-22-2-222-22000000002i−2i2-20000000000000000000000000000000000002-2-222i−2i−2i2i00000000
χ5622-2-22-22-2−2i−2i2i2i−2i−2i2i2i2i2i−2i−2i-22-2-222-22000000002i−2i2-2000000000000000000000000000000000000-222-2−2i2i2i−2i00000000
χ572-22-2-222-22i−2i2i−2i00002i−2i2i−2i2-20000-2222-2-222-2-20000000000002i−2i2i−2i00000000i2−i2i2−i22−22−2i2−i2i2−i22−22−20000000000000000
χ582-22-2-222-22i−2i2i−2i00002i−2i2i−2i2-20000-2222-2-222-2-20000000000002i−2i2i−2i00000000−i2i2−i2i2−22−22−i2i2−i2i2−22−220000000000000000
χ592-22-2-222-22i−2i2i−2i00002i−2i2i−2i2-20000-22-2-222-2-222000000000000−2i2i−2i2i00000000i2−i2i2−i22−22−2−i2i2−i2i2−22−220000000000000000
χ602-22-2-222-22i−2i2i−2i00002i−2i2i−2i2-20000-22-2-222-2-222000000000000−2i2i−2i2i00000000−i2i2−i2i2−22−22i2−i2i2−i22−22−20000000000000000
χ612-22-2-222-2−2i2i−2i2i0000−2i2i−2i2i2-20000-2222-2-222-2-2000000000000−2i2i−2i2i00000000i2−i2i2−i2−22−22i2−i2i2−i2−22−220000000000000000
χ622-22-2-222-2−2i2i−2i2i0000−2i2i−2i2i2-20000-2222-2-222-2-2000000000000−2i2i−2i2i00000000−i2i2−i2i22−22−2−i2i2−i2i22−22−20000000000000000
χ632-22-2-222-2−2i2i−2i2i0000−2i2i−2i2i2-20000-22-2-222-2-2220000000000002i−2i2i−2i00000000i2−i2i2−i2−22−22−i2i2−i2i22−22−20000000000000000
χ642-22-2-222-2−2i2i−2i2i0000−2i2i−2i2i2-20000-22-2-222-2-2220000000000002i−2i2i−2i00000000−i2i2−i2i22−22−2i2−i2i2−i2−22−220000000000000000
χ652-2-22-2-2222-2-2200002-2-22220000-2-22i2i−2i−2i−2i−2i2i2i000000000000−2i2i2i−2i00000000i2−i2−i2i2−i2i2i2−i2−222−2−222−20000000000000000
χ662-2-22-2-2222-2-2200002-2-22220000-2-22i2i−2i−2i−2i−2i2i2i000000000000−2i2i2i−2i00000000−i2i2i2−i2i2−i2−i2i22−2−222−2−220000000000000000
χ672-2-22-2-2222-2-2200002-2-22220000-2-2−2i−2i2i2i2i2i−2i−2i0000000000002i−2i−2i2i00000000i2−i2−i2i2−i2i2i2−i22−2−222−2−220000000000000000
χ682-2-22-2-2222-2-2200002-2-22220000-2-2−2i−2i2i2i2i2i−2i−2i0000000000002i−2i−2i2i00000000−i2i2i2−i2i2−i2−i2i2−222−2−222−20000000000000000
χ692-2-22-2-222-222-20000-222-2220000-2-22i2i−2i−2i−2i−2i2i2i0000000000002i−2i−2i2i00000000i2−i2−i2i2i2−i2−i2i2−222−22−2−220000000000000000
χ702-2-22-2-222-222-20000-222-2220000-2-22i2i−2i−2i−2i−2i2i2i0000000000002i−2i−2i2i00000000−i2i2i2−i2−i2i2i2−i22−2−22−222−20000000000000000
χ712-2-22-2-222-222-20000-222-2220000-2-2−2i−2i2i2i2i2i−2i−2i000000000000−2i2i2i−2i00000000i2−i2−i2i2i2−i2−i2i22−2−22−222−20000000000000000
χ722-2-22-2-222-222-20000-222-2220000-2-2−2i−2i2i2i2i2i−2i−2i000000000000−2i2i2i−2i00000000−i2i2i2−i2−i2i2i2−i2−222−22−2−220000000000000000
χ734444-4-4-4-4000000000000004-44-40022−2222−2222−2222−22000022−2222−22000000000000000000000000000000000000000000000000
χ744444-4-4-4-4000000000000004-44-400−2222−2222−2222−22220000−2222−2222000000000000000000000000000000000000000000000000
χ754444-4-4-4-400000000000000-44-440022−2222−2222−2222−220000−2222−2222000000000000000000000000000000000000000000000000
χ764444-4-4-4-400000000000000-44-4400−2222−2222−2222−2222000022−2222−22000000000000000000000000000000000000000000000000
χ7744-4-4-44-44000000000000004-4-44002i2−2i22i2−2i2−2i22i2−2i22i200002i2−2i2−2i22i2000000000000000000000000000000000000000000000000
χ7844-4-4-44-44000000000000004-4-4400−2i22i2−2i22i22i2−2i22i2−2i20000−2i22i22i2−2i2000000000000000000000000000000000000000000000000
χ7944-4-4-44-4400000000000000-444-4002i2−2i22i2−2i2−2i22i2−2i22i20000−2i22i22i2−2i2000000000000000000000000000000000000000000000000
χ8044-4-4-44-4400000000000000-444-400−2i22i2−2i22i22i2−2i22i2−2i200002i2−2i2−2i22i2000000000000000000000000000000000000000000000000
χ814-44-44-4-4400004i−4i4i−4i00000000000022−22−222222−22−2222000000002i2−2i22i2−2i200000000000000000000000000000000000000000000
χ824-44-44-4-4400004i−4i4i−4i000000000000−222222−22−222222−2200000000−2i22i2−2i22i200000000000000000000000000000000000000000000
χ834-44-44-4-440000−4i4i−4i4i00000000000022−22−222222−22−222200000000−2i22i2−2i22i200000000000000000000000000000000000000000000
χ844-44-44-4-440000−4i4i−4i4i000000000000−222222−22−222222−22000000002i2−2i22i2−2i200000000000000000000000000000000000000000000
χ854-44-4-444-44i−4i4i−4i0000−4i4i−4i4i-4400004-40000000000000000000000000000000000000000000000000000000000000000
χ864-44-4-444-4−4i4i−4i4i00004i−4i4i−4i-4400004-40000000000000000000000000000000000000000000000000000000000000000
χ874-4-4444-4-400004-4-440000000000002i2−2i2−2i22i2−2i22i22i2−2i200000000−2i22i22i2−2i200000000000000000000000000000000000000000000
χ884-4-4444-4-400004-4-44000000000000−2i22i22i2−2i22i2−2i2−2i22i2000000002i2−2i2−2i22i200000000000000000000000000000000000000000000
χ894-4-4444-4-40000-444-40000000000002i2−2i2−2i22i2−2i22i22i2−2i2000000002i2−2i2−2i22i200000000000000000000000000000000000000000000
χ904-4-4444-4-40000-444-4000000000000−2i22i22i2−2i22i2−2i2−2i22i200000000−2i22i22i2−2i200000000000000000000000000000000000000000000
χ914-4-44-4-4444-4-440000-444-4-4-40000440000000000000000000000000000000000000000000000000000000000000000
χ924-4-44-4-444-444-400004-4-44-4-40000440000000000000000000000000000000000000000000000000000000000000000

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