Finite Group Databasebeta

← Group #371080

Character table — Group #371080

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92
size11111111111111112222222244444444444444448888888888888888888888888888888888888888888888888888
order12222222222222224444444444444444444444444444444444444444444444444444444444448888888888888888
χ111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ311111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ411111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111111111
χ511111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1
χ611111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1-1-1-1-1-1-111111111
χ711111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-111111111
χ811111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-111111111111111111111-1-1-1-1-1-1-1-1
χ9111111111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-11111-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-11111-1-1-1-1
χ10111111111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-11111-1-1-1-11111-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-11111
χ11111111111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1-1-1-1-1-1-111111111-1-1-1-11111-1-1-1-11111
χ12111111111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1111111111111-1-1-1-11111-1-1-1-11111-1-1-1-1
χ13111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-11111-1-1-1-111111111-1-1-1-11111-1-1-1-1-1-1-1-11111
χ14111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-111111111-1-1-1-111111111-1-1-1-1
χ15111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1111111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1
χ16111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-111111111-1-1-1-11111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-11111
χ1711-1-111-1-1-1111-11-1-111-1-111-1-11111-1-1-1-1ii−i−iii−i−iii−i−i11-1-111-1-1ii−i−i11-1-111-1-1ii−i−iii−i−iii−i−i11-1-111-1-1ii−i−iii−i−i
χ1811-1-111-1-1-1111-11-1-111-1-111-1-11111-1-1-1-1ii−i−iii−i−iii−i−i11-1-111-1-1ii−i−i-1-111-1-111−i−iiiii−i−i−i−iii-1-111-1-111−i−iii−i−iii
χ1911-1-111-1-1-1111-11-1-111-1-111-1-11111-1-1-1-1ii−i−iii−i−iii−i−i-1-111-1-111−i−iii11-1-111-1-1ii−i−i−i−iiiii−i−i-1-111-1-111−i−iii−i−iii
χ2011-1-111-1-1-1111-11-1-111-1-111-1-11111-1-1-1-1ii−i−iii−i−iii−i−i-1-111-1-111−i−iii-1-111-1-111−i−iii−i−iii−i−iii11-1-111-1-1ii−i−iii−i−i
χ2111-1-111-1-1-1111-11-1-111-1-111-1-11111-1-1-1-1−i−iii−i−iii−i−iii11-1-111-1-1−i−iii11-1-111-1-1−i−iii−i−iii−i−iii11-1-111-1-1−i−iii−i−iii
χ2211-1-111-1-1-1111-11-1-111-1-111-1-11111-1-1-1-1−i−iii−i−iii−i−iii11-1-111-1-1−i−iii-1-111-1-111ii−i−i−i−iiiii−i−i-1-111-1-111ii−i−iii−i−i
χ2311-1-111-1-1-1111-11-1-111-1-111-1-11111-1-1-1-1−i−iii−i−iii−i−iii-1-111-1-111ii−i−i11-1-111-1-1−i−iiiii−i−i−i−iii-1-111-1-111ii−i−iii−i−i
χ2411-1-111-1-1-1111-11-1-111-1-111-1-11111-1-1-1-1−i−iii−i−iii−i−iii-1-111-1-111ii−i−i-1-111-1-111ii−i−iii−i−iii−i−i11-1-111-1-1−i−iii−i−iii
χ2511-1-111-1-1-1111-11-1-111-1-111-1-1-1-1-1-11111ii−i−iii−i−i−i−iii11-1-1-1-111ii−i−i11-1-1-1-111−i−iii−i−iiiii−i−i11-1-1-1-111ii−i−i−i−iii
χ2611-1-111-1-1-1111-11-1-111-1-111-1-1-1-1-1-11111ii−i−iii−i−i−i−iii11-1-1-1-111ii−i−i-1-11111-1-1ii−i−i−i−iii−i−iii-1-11111-1-1−i−iiiii−i−i
χ2711-1-111-1-1-1111-11-1-111-1-111-1-1-1-1-1-11111ii−i−iii−i−i−i−iii-1-11111-1-1−i−iii11-1-1-1-111−i−iiiii−i−iii−i−i-1-11111-1-1−i−iiiii−i−i
χ2811-1-111-1-1-1111-11-1-111-1-111-1-1-1-1-1-11111ii−i−iii−i−i−i−iii-1-11111-1-1−i−iii-1-11111-1-1ii−i−iii−i−i−i−iii11-1-1-1-111ii−i−i−i−iii
χ2911-1-111-1-1-1111-11-1-111-1-111-1-1-1-1-1-11111−i−iii−i−iiiii−i−i11-1-1-1-111−i−iii11-1-1-1-111ii−i−iii−i−i−i−iii11-1-1-1-111−i−iiiii−i−i
χ3011-1-111-1-1-1111-11-1-111-1-111-1-1-1-1-1-11111−i−iii−i−iiiii−i−i11-1-1-1-111−i−iii-1-11111-1-1−i−iiiii−i−iii−i−i-1-11111-1-1ii−i−i−i−iii
χ3111-1-111-1-1-1111-11-1-111-1-111-1-1-1-1-1-11111−i−iii−i−iiiii−i−i-1-11111-1-1ii−i−i11-1-1-1-111ii−i−i−i−iii−i−iii-1-11111-1-1ii−i−i−i−iii
χ3211-1-111-1-1-1111-11-1-111-1-111-1-1-1-1-1-11111−i−iii−i−iiiii−i−i-1-11111-1-1ii−i−i-1-11111-1-1−i−iii−i−iiiii−i−i11-1-1-1-111−i−iiiii−i−i
χ332222222222222222-2-2-2-2-2-2-2-222-2-222-2-22222-2-2-2-22-22-2000000000000000000000000000000000000000000000000
χ342222222222222222-2-2-2-2-2-2-2-222-2-222-2-2-2-2-2-22222-22-22000000000000000000000000000000000000000000000000
χ352222222222222222-2-2-2-2-2-2-2-2-2-222-2-2222222-2-2-2-2-22-22000000000000000000000000000000000000000000000000
χ362222222222222222-2-2-2-2-2-2-2-2-2-222-2-222-2-2-2-222222-22-2000000000000000000000000000000000000000000000000
χ37222-2-2-222-22-2-2-22-222-22-22-22-22i−2i2i−2i2i−2i2i−2i000000000000000000000000000000002i−2i2i−2i00002-22-20000000000000000
χ38222-2-2-222-22-2-2-22-222-22-22-22-22i−2i2i−2i2i−2i2i−2i00000000000000000000000000000000−2i2i−2i2i0000-22-220000000000000000
χ39222-2-2-222-22-2-2-22-222-22-22-22-2−2i2i−2i2i−2i2i−2i2i000000000000000000000000000000002i−2i2i−2i0000-22-220000000000000000
χ40222-2-2-222-22-2-2-22-222-22-22-22-2−2i2i−2i2i−2i2i−2i2i00000000000000000000000000000000−2i2i−2i2i00002-22-20000000000000000
χ41222-2-2-222-22-2-2-22-22-22-22-22-222i−2i−2i2i2i−2i−2i2i0000000000000000000000002i−2i2i−2i2-22-20000000000000000000000000000
χ42222-2-2-222-22-2-2-22-22-22-22-22-222i−2i−2i2i2i−2i−2i2i000000000000000000000000−2i2i−2i2i-22-220000000000000000000000000000
χ43222-2-2-222-22-2-2-22-22-22-22-22-22−2i2i2i−2i−2i2i2i−2i0000000000000000000000002i−2i2i−2i-22-220000000000000000000000000000
χ44222-2-2-222-22-2-2-22-22-22-22-22-22−2i2i2i−2i−2i2i2i−2i000000000000000000000000−2i2i−2i2i2-22-20000000000000000000000000000
χ4522-22-2-2-2-222-2-2222-22-2-222-2-222i−2i2i−2i−2i2i−2i2i000000000000000000000000000000002-2-220000−2i2i2i−2i0000000000000000
χ4622-22-2-2-2-222-2-2222-22-2-222-2-222i−2i2i−2i−2i2i−2i2i00000000000000000000000000000000-222-200002i−2i−2i2i0000000000000000
χ4722-22-2-2-2-222-2-2222-22-2-222-2-22−2i2i−2i2i2i−2i2i−2i000000000000000000000000000000002-2-2200002i−2i−2i2i0000000000000000
χ4822-22-2-2-2-222-2-2222-22-2-222-2-22−2i2i−2i2i2i−2i2i−2i00000000000000000000000000000000-222-20000−2i2i2i−2i0000000000000000
χ4922-22-2-2-2-222-2-2222-2-222-2-222-22i−2i−2i2i−2i2i2i−2i0000000000000000000000002i−2i−2i2i2-2-220000000000000000000000000000
χ5022-22-2-2-2-222-2-2222-2-222-2-222-22i−2i−2i2i−2i2i2i−2i000000000000000000000000−2i2i2i−2i-222-20000000000000000000000000000
χ5122-22-2-2-2-222-2-2222-2-222-2-222-2−2i2i2i−2i2i−2i−2i2i0000000000000000000000002i−2i−2i2i-222-20000000000000000000000000000
χ5222-22-2-2-2-222-2-2222-2-222-2-222-2−2i2i2i−2i2i−2i−2i2i000000000000000000000000−2i2i2i−2i2-2-220000000000000000000000000000
χ5322-2-222-2-2-2222-22-2-2-2-222-2-22222-2-2-2-2222i2i−2i−2i−2i−2i2i2i2i−2i−2i2i000000000000000000000000000000000000000000000000
χ5422-2-222-2-2-2222-22-2-2-2-222-2-22222-2-2-2-222−2i−2i2i2i2i2i−2i−2i−2i2i2i−2i000000000000000000000000000000000000000000000000
χ5522-2-222-2-2-2222-22-2-2-2-222-2-222-2-22222-2-22i2i−2i−2i−2i−2i2i2i−2i2i2i−2i000000000000000000000000000000000000000000000000
χ5622-2-222-2-2-2222-22-2-2-2-222-2-222-2-22222-2-2−2i−2i2i2i2i2i−2i−2i2i−2i−2i2i000000000000000000000000000000000000000000000000
χ572-22222-2-2-2-2-2-222-222-2-22-222-2000000002i−2i2i−2i2i−2i2i−2i00002i−2i2i−2i00002-22-2000000000000000000000000000000000000
χ582-22222-2-2-2-2-2-222-222-2-22-222-2000000002i−2i2i−2i2i−2i2i−2i0000−2i2i−2i2i0000-22-22000000000000000000000000000000000000
χ592-22222-2-2-2-2-2-222-222-2-22-222-200000000−2i2i−2i2i−2i2i−2i2i00002i−2i2i−2i0000-22-22000000000000000000000000000000000000
χ602-22222-2-2-2-2-2-222-222-2-22-222-200000000−2i2i−2i2i−2i2i−2i2i0000−2i2i−2i2i00002-22-2000000000000000000000000000000000000
χ612-22222-2-2-2-2-2-222-22-222-22-2-22000000002i−2i2i−2i−2i2i−2i2i000000002i−2i2i−2i00000000000000002-22-200000000000000000000
χ622-22222-2-2-2-2-2-222-22-222-22-2-22000000002i−2i2i−2i−2i2i−2i2i00000000−2i2i−2i2i0000000000000000-22-2200000000000000000000
χ632-22222-2-2-2-2-2-222-22-222-22-2-2200000000−2i2i−2i2i2i−2i2i−2i000000002i−2i2i−2i0000000000000000-22-2200000000000000000000
χ642-22222-2-2-2-2-2-222-22-222-22-2-2200000000−2i2i−2i2i2i−2i2i−2i00000000−2i2i−2i2i00000000000000002-22-200000000000000000000
χ652-2-2-222222-2-2-2-222-22-22-2-22-22000000002-2-222-2-2200002i−2i−2i2i0000−2i2i2i−2i000000000000000000000000000000000000
χ662-2-2-222222-2-2-2-222-22-22-2-22-22000000002-2-222-2-220000−2i2i2i−2i00002i−2i−2i2i000000000000000000000000000000000000
χ672-2-2-222222-2-2-2-222-22-22-2-22-2200000000-222-2-222-200002i−2i−2i2i00002i−2i−2i2i000000000000000000000000000000000000
χ682-2-2-222222-2-2-2-222-22-22-2-22-2200000000-222-2-222-20000−2i2i2i−2i0000−2i2i2i−2i000000000000000000000000000000000000
χ692-2-2-222222-2-2-2-222-2-22-222-22-2000000002-2-22-222-2000000002i−2i−2i2i0000000000000000−2i2i2i−2i00000000000000000000
χ702-2-2-222222-2-2-2-222-2-22-222-22-2000000002-2-22-222-200000000−2i2i2i−2i00000000000000002i−2i−2i2i00000000000000000000
χ712-2-2-222222-2-2-2-222-2-22-222-22-200000000-222-22-2-22000000002i−2i−2i2i00000000000000002i−2i−2i2i00000000000000000000
χ722-2-2-222222-2-2-2-222-2-22-222-22-200000000-222-22-2-2200000000−2i2i2i−2i0000000000000000−2i2i2i−2i00000000000000000000
χ7344444-44-4-4-44-4-4-44-400000000000000000000000000000000000000000000000000000000000000000000000022−2222−22
χ7444444-44-4-4-44-4-4-44-4000000000000000000000000000000000000000000000000000000000000000000000000−2222−2222
χ75444-4-444-44-4-444-4-4-40000000000000000000000000000000000000000000000000000000000000000000022−2222−220000
χ76444-4-444-44-4-444-4-4-400000000000000000000000000000000000000000000000000000000000000000000−2222−22220000
χ7744-44-44-44-4-4-44-4-444000000000000000000000000000000000000000000000000000000000000000000002i2−2i2−2i22i20000
χ7844-44-44-44-4-4-44-4-44400000000000000000000000000000000000000000000000000000000000000000000−2i22i22i2−2i20000
χ7944-4-44-4-444-44-44-4-440000000000000000000000000000000000000000000000000000000000000000000000002i2−2i2−2i22i2
χ8044-4-44-4-444-44-44-4-44000000000000000000000000000000000000000000000000000000000000000000000000−2i22i22i2−2i2
χ814-4444-4-4444-44-4-4-4-4000000000000000000000000000000000000000000000000000000000000000022−2222−2200000000
χ824-4444-4-4444-44-4-4-4-40000000000000000000000000000000000000000000000000000000000000000−2222−222200000000
χ834-44-4-44-44-444-44-44-40000000000000000000000000000000000000000000000000000000000002i2−2i22i2−2i2000000000000
χ844-44-4-44-44-444-44-44-4000000000000000000000000000000000000000000000000000000000000−2i22i2−2i22i2000000000000
χ854-44-4-4-4-4-44-444-444444-4-4-4-44400000000000000000000000000000000000000000000000000000000000000000000
χ864-44-4-4-4-4-44-444-4444-4-44444-4-400000000000000000000000000000000000000000000000000000000000000000000
χ874-4-44-444-4444-4-4-4-440000000000000000000000000000000000000000000000000000000000002i2−2i2−2i22i2000000000000
χ884-4-44-444-4444-4-4-4-44000000000000000000000000000000000000000000000000000000000000−2i22i22i2−2i2000000000000
χ894-4-44-4-444-4-44444-4-44444-4-4-4-400000000000000000000000000000000000000000000000000000000000000000000
χ904-4-44-4-444-4-44444-4-4-4-4-4-4444400000000000000000000000000000000000000000000000000000000000000000000
χ914-4-4-44-44-4-44-444-444000000000000000000000000000000000000000000000000000000000000000022−22−222200000000
χ924-4-4-44-44-4-44-444-4440000000000000000000000000000000000000000000000000000000000000000−222222−2200000000

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