Finite Group Databasebeta

← Group #224656

Character table — Group #224656

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95
size11111111222222222222222222224444444444444444444444444444448888888888888888888888888888888161616161616
order12222222444444444444444444444444444444444488888888888888884444444888888888888888888888888444444
χ111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1111-1-1-1-11111-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ3111111111111111111111111111111111111111111-1-1-1-1-1-1-1-111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1
χ4111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111
χ511111111111111111111-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1iiii−i−i−i−iiiii−i−i−i−i11111-1-1ii−i−iii−i−iiiii−i−i−i−iiiii−i−i−i−i1-111-1-1
χ611111111111111111111-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1iiii−i−i−i−i−i−i−i−iiiii111-1-111ii−i−i−i−iiiiiii−i−i−i−i−i−i−i−iiiii-11-1-111
χ711111111111111111111-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1−i−i−i−iiiiiiiii−i−i−i−i111-1-111−i−iiiii−i−i−i−i−i−iiiiiiiii−i−i−i−i-11-1-111
χ811111111111111111111-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1−i−i−i−iiiii−i−i−i−iiiii11111-1-1−i−iii−i−iii−i−i−i−iiiii−i−i−i−iiiii1-111-1-1
χ9111111111111-1-1-1-1-1-1-1-1111111111111-1-1-1-111-1-1-1-111111111111111111-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-1
χ10111111111111-1-1-1-1-1-1-1-1111111111111-1-1-1-111-1-1-1-111111111-1-1-1-1-1-1-1-11-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-11111
χ11111111111111-1-1-1-1-1-1-1-1111111111111-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1111111111-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-11111
χ12111111111111-1-1-1-1-1-1-1-1111111111111-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11-1-11111-1-1-1-1-1-1-1-1111111111111111111-1-1-1-1
χ13111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-11111-1-11111iiii−i−i−i−iiiii−i−i−i−i1-1-111-1-1ii−i−iii−i−i−i−i−i−iiiii−i−i−i−iiiii1-1-1-111
χ14111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-11111-1-11111iiii−i−i−i−i−i−i−i−iiiii1-1-1-1-111ii−i−i−i−iii−i−i−i−iiiiiiiii−i−i−i−i-1111-1-1
χ15111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-11111-1-11111−i−i−i−iiiiiiiii−i−i−i−i1-1-1-1-111−i−iiiii−i−iiiii−i−i−i−i−i−i−i−iiiii-1111-1-1
χ16111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-11111-1-11111−i−i−i−iiiii−i−i−i−iiiii1-1-111-1-1−i−iii−i−iiiiiii−i−i−i−iiiii−i−i−i−i1-1-1-111
χ1711111111-1-1-1-11111-1-1-1-11111111111-1-111-1-1-1-111-1-11111111111111111-11-11111-1-1-1-1-1-1-1-111-1-111-1-111-1-111-1-1-1-11-11-1
χ1811111111-1-1-1-11111-1-1-1-11111111111-1-111-1-1-1-111-1-111111111-1-1-1-1-1-1-1-1-11-1-1-1-1-1-1-1-1-1111111-1-111-1-1-1-111-1-11111-11-11
χ1911111111-1-1-1-11111-1-1-1-11111111111-1-111-1-1-1-111-1-1-1-1-1-1-1-1-1-111111111-11-1-1-1-1-11111-1-1-1-1-1-111-1-11111-1-111-1-111-11-11
χ2011111111-1-1-1-11111-1-1-1-11111111111-1-111-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11-1111111111111-1-111-1-111-1-111-1-111-1-11-11-1
χ2111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-11111-1-11111-1-111iiii−i−i−i−iiiii−i−i−i−i-11-111-1-1−i−iii−i−iiiii−i−i−i−iiiii−i−i−i−iii-111-1-11
χ2211111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-11111-1-11111-1-111iiii−i−i−i−i−i−i−i−iiiii-11-1-1-111−i−iiiii−i−iii−i−i−i−iii−i−iiiii−i−i1-1-111-1
χ2311111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-11111-1-11111-1-111−i−i−i−iiiiiiiii−i−i−i−i-11-1-1-111ii−i−i−i−iii−i−iiiii−i−iii−i−i−i−iii1-1-111-1
χ2411111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-11111-1-11111-1-111−i−i−i−iiiii−i−i−i−iiiii-11-111-1-1ii−i−iii−i−i−i−iiiii−i−i−i−iiiii−i−i-111-1-11
χ2511111111-1-1-1-1-1-1-1-111111111111111-1-1-1-111-1-1-1-1111111111111111111-1-111111-1-1-1-1-1-1-1-1-1-111-1-111-1-111-1-111-1-1-11-11
χ2611111111-1-1-1-1-1-1-1-111111111111111-1-1-1-111-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-11-1-1-1-1-1-1-1-11111-1-111-1-11111-1-111-1-1111-11-1
χ2711111111-1-1-1-1-1-1-1-111111111111111-1-1-1-111-1-1-1-111-1-1-1-1-1-1-1-111111111-1-11-1-1-1-11111-1-1-1-111-1-111-1-1-1-111-1-111111-11-1
χ2811111111-1-1-1-1-1-1-1-111111111111111-1-1-1-111-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111111-1-111-1-111-1-111-1-1-1-1-11-11
χ2911111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1111111-1-11111-1-1iiii−i−i−i−iiiii−i−i−i−i-1-1111-1-1−i−iii−i−iii−i−iiiii−i−i−i−iiiii−i−i-11-111-1
χ3011111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1111111-1-11111-1-1iiii−i−i−i−i−i−i−i−iiiii-1-11-1-111−i−iiiii−i−i−i−iiiii−i−iii−i−i−i−iii1-11-1-11
χ3111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1111111-1-11111-1-1−i−i−i−iiiiiiiii−i−i−i−i-1-11-1-111ii−i−i−i−iiiii−i−i−i−iii−i−iiiii−i−i1-11-1-11
χ3211111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1111111-1-11111-1-1−i−i−i−iiiii−i−i−i−iiiii-1-1111-1-1ii−i−iii−i−iii−i−i−i−iiiii−i−i−i−iii-11-111-1
χ33222222222222222222222-222-2-22-2-2-2-2-2222222-2-2-2-20000000000000000-2-2-20000000000000000000000000000000000
χ3422222222222222222222-22-2-222-22-2-222-2-2-2-2-2-222220000000000000000-2-2-20000000000000000000000000000000000
χ35222222222222-2-2-2-2-2-2-2-22-222-2-22-2-2-2-2-2-2-2-2-22222220000000000000000-2220000000000000000000000000000000000
χ36222222222222-2-2-2-2-2-2-2-2-22-2-222-22-2-2222222-2-2-2-2-2-20000000000000000-2220000000000000000000000000000000000
χ3722222222-2-2-2-22222-2-2-2-22-222-2-22-2-2-22222-2-2-2-2-2-22200000000000000002-220000000000000000000000000000000000
χ3822222222-2-2-2-22222-2-2-2-2-22-2-222-22-2-2-2-2-2-2222222-2-200000000000000002-220000000000000000000000000000000000
χ3922222222-2-2-2-2-2-2-2-222222-222-2-22-2-2-222-2-222-2-222-2-2000000000000000022-20000000000000000000000000000000000
χ4022222222-2-2-2-2-2-2-2-22222-22-2-222-22-2-2-2-222-2-222-2-222000000000000000022-20000000000000000000000000000000000
χ4122-2-2-22-220000000000002-22-22-2-222-200000000000022-2-222-2-22i2i−2i−2i2i2i−2i−2i0002i−2i2i−2i000000000000000000000000000000
χ4222-2-2-22-220000000000002-22-22-2-222-200000000000022-2-222-2-2−2i−2i2i2i−2i−2i2i2i000−2i2i−2i2i000000000000000000000000000000
χ4322-2-2-22-220000000000002-22-22-2-222-2000000000000-2-222-2-2222i2i−2i−2i2i2i−2i−2i000−2i2i−2i2i000000000000000000000000000000
χ4422-2-2-22-220000000000002-22-22-2-222-2000000000000-2-222-2-222−2i−2i2i2i−2i−2i2i2i0002i−2i2i−2i000000000000000000000000000000
χ4522-2-2-22-22000000000000-22-22-222-22-20000000000002i2i−2i−2i−2i−2i2i2i22-2-2-2-222000−2i2i2i−2i000000000000000000000000000000
χ4622-2-2-22-22000000000000-22-22-222-22-20000000000002i2i−2i−2i−2i−2i2i2i-2-22222-2-20002i−2i−2i2i000000000000000000000000000000
χ4722-2-2-22-22000000000000-22-22-222-22-2000000000000−2i−2i2i2i2i2i−2i−2i22-2-2-2-2220002i−2i−2i2i000000000000000000000000000000
χ4822-2-2-22-22000000000000-22-22-222-22-2000000000000−2i−2i2i2i2i2i−2i−2i-2-22222-2-2000−2i2i2i−2i000000000000000000000000000000
χ492-222-2-2-2222-2-22i2i−2i−2i2i2i−2i−2i0200-2-202002-20000002i−2i2i−2i2−22−22−22−20000000000000002−22−20000i2−i2i2−i2i2−i2i2−i200000000000000
χ502-222-2-2-2222-2-22i2i−2i−2i2i2i−2i−2i0200-2-202002-20000002i−2i2i−2i−22−22−22−22000000000000000−22−220000−i2i2−i2i2−i2i2−i2i200000000000000
χ512-222-2-2-2222-2-22i2i−2i−2i2i2i−2i−2i0-200220-200-22000000−2i2i−2i2ii2−i2i2−i2−i2i2−i2i2000000000000000i2−i2−i2i20000−22−222−22−200000000000000
χ522-222-2-2-2222-2-22i2i−2i−2i2i2i−2i−2i0-200220-200-22000000−2i2i−2i2i−i2i2−i2i2i2−i2i2−i2000000000000000−i2i2i2−i200002−22−2−22−2200000000000000
χ532-222-2-2-2222-2-2−2i−2i2i2i−2i−2i2i2i0200-2-202002-2000000−2i2i−2i2i2−22−22−22−20000000000000002−22−20000−i2i2−i2i2−i2i2−i2i200000000000000
χ542-222-2-2-2222-2-2−2i−2i2i2i−2i−2i2i2i0200-2-202002-2000000−2i2i−2i2i−22−22−22−22000000000000000−22−220000i2−i2i2−i2i2−i2i2−i200000000000000
χ552-222-2-2-2222-2-2−2i−2i2i2i−2i−2i2i2i0-200220-200-220000002i−2i2i−2ii2−i2i2−i2−i2i2−i2i2000000000000000i2−i2−i2i200002−22−2−22−2200000000000000
χ562-222-2-2-2222-2-2−2i−2i2i2i−2i−2i2i2i0-200220-200-220000002i−2i2i−2i−i2i2−i2i2i2−i2i2−i2000000000000000−i2i2i2−i20000−22−222−22−200000000000000
χ572-222-2-2-22-2-2222i2i−2i−2i−2i−2i2i2i0200-2-20200-220000002i−2i−2i2i2−22−22−22−2000000000000000−22−220000i2−i2−i2i2i2−i2−i2i200000000000000
χ582-222-2-2-22-2-2222i2i−2i−2i−2i−2i2i2i0200-2-20200-220000002i−2i−2i2i−22−22−22−220000000000000002−22−20000−i2i2i2−i2−i2i2i2−i200000000000000
χ592-222-2-2-22-2-2222i2i−2i−2i−2i−2i2i2i0-200220-2002-2000000−2i2i2i−2ii2−i2i2−i2−i2i2−i2i2000000000000000−i2i2i2−i20000−222−22−2−2200000000000000
χ602-222-2-2-22-2-2222i2i−2i−2i−2i−2i2i2i0-200220-2002-2000000−2i2i2i−2i−i2i2−i2i2i2−i2i2−i2000000000000000i2−i2−i2i200002−2−22−222−200000000000000
χ612-222-2-2-22-2-222−2i−2i2i2i2i2i−2i−2i0200-2-20200-22000000−2i2i2i−2i2−22−22−22−2000000000000000−22−220000−i2i2i2−i2−i2i2i2−i200000000000000
χ622-222-2-2-22-2-222−2i−2i2i2i2i2i−2i−2i0200-2-20200-22000000−2i2i2i−2i−22−22−22−220000000000000002−22−20000i2−i2−i2i2i2−i2−i2i200000000000000
χ632-222-2-2-22-2-222−2i−2i2i2i2i2i−2i−2i0-200220-2002-20000002i−2i−2i2ii2−i2i2−i2−i2i2−i2i2000000000000000−i2i2i2−i200002−2−22−222−200000000000000
χ642-222-2-2-22-2-222−2i−2i2i2i2i2i−2i−2i0-200220-2002-20000002i−2i−2i2i−i2i2−i2i2i2−i2i2−i2000000000000000i2−i2−i2i20000−222−22−2−2200000000000000
χ652-22-2-222-22-22-22i−2i2i−2i2i−2i2i−2i20-2-2002000002i−2i2i−2i2-2000000000000i2−i2i2−i2i2−i2i2−i200000000000i2−i2i2−i2000000002−22−22−22−2000000
χ662-22-2-222-22-22-22i−2i2i−2i2i−2i2i−2i20-2-2002000002i−2i2i−2i2-2000000000000−i2i2−i2i2−i2i2−i2i200000000000−i2i2−i2i200000000−22−22−22−22000000
χ672-22-2-222-22-22-22i−2i2i−2i2i−2i2i−2i-202200-200000−2i2i−2i2i-220000000000002−22−2−22−22000000000002−2−2200000000−i2i2−i2i2i2−i2i2−i2000000
χ682-22-2-222-22-22-22i−2i2i−2i2i−2i2i−2i-202200-200000−2i2i−2i2i-22000000000000−22−222−22−200000000000−222−200000000i2−i2i2−i2−i2i2−i2i2000000
χ692-22-2-222-22-22-2−2i2i−2i2i−2i2i−2i2i20-2-200200000−2i2i−2i2i2-2000000000000i2−i2i2−i2i2−i2i2−i200000000000i2−i2i2−i200000000−22−22−22−22000000
χ702-22-2-222-22-22-2−2i2i−2i2i−2i2i−2i2i20-2-200200000−2i2i−2i2i2-2000000000000−i2i2−i2i2−i2i2−i2i200000000000−i2i2−i2i2000000002−22−22−22−2000000
χ712-22-2-222-22-22-2−2i2i−2i2i−2i2i−2i2i-202200-2000002i−2i2i−2i-220000000000002−22−2−22−22000000000002−2−2200000000i2−i2i2−i2−i2i2−i2i2000000
χ722-22-2-222-22-22-2−2i2i−2i2i−2i2i−2i2i-202200-2000002i−2i2i−2i-22000000000000−22−222−22−200000000000−222−200000000−i2i2−i2i2i2−i2i2−i2000000
χ732-22-2-222-2-22-222i−2i2i−2i−2i2i−2i2i20-2-2002000002i−2i−2i2i-22000000000000i2−i2i2−i2i2−i2i2−i200000000000−i2i2−i2i2000000002−2−222−2−22000000
χ742-22-2-222-2-22-222i−2i2i−2i−2i2i−2i2i20-2-2002000002i−2i−2i2i-22000000000000−i2i2−i2i2−i2i2−i2i200000000000i2−i2i2−i200000000−222−2−222−2000000
χ752-22-2-222-2-22-222i−2i2i−2i−2i2i−2i2i-202200-200000−2i2i2i−2i2-20000000000002−22−2−22−2200000000000−222−200000000−i2i2i2−i2i2−i2−i2i2000000
χ762-22-2-222-2-22-222i−2i2i−2i−2i2i−2i2i-202200-200000−2i2i2i−2i2-2000000000000−22−222−22−2000000000002−2−2200000000i2−i2−i2i2−i2i2i2−i2000000
χ772-22-2-222-2-22-22−2i2i−2i2i2i−2i2i−2i20-2-200200000−2i2i2i−2i-22000000000000i2−i2i2−i2i2−i2i2−i200000000000−i2i2−i2i200000000−222−2−222−2000000
χ782-22-2-222-2-22-22−2i2i−2i2i2i−2i2i−2i20-2-200200000−2i2i2i−2i-22000000000000−i2i2−i2i2−i2i2−i2i200000000000i2−i2i2−i2000000002−2−222−2−22000000
χ792-22-2-222-2-22-22−2i2i−2i2i2i−2i2i−2i-202200-2000002i−2i−2i2i2-20000000000002−22−2−22−2200000000000−222−200000000i2−i2−i2i2−i2i2i2−i2000000
χ802-22-2-222-2-22-22−2i2i−2i2i2i−2i2i−2i-202200-2000002i−2i−2i2i2-2000000000000−22−222−22−2000000000002−2−2200000000−i2i2i2−i2i2−i2−i2i2000000
χ81444-44-4-4-44-4-444-4-444-4-44000000000000000000000000000000000000000000000000000000000000000000000000000
χ82444-44-4-4-44-4-44-444-4-444-4000000000000000000000000000000000000000000000000000000000000000000000000000
χ83444-44-4-4-4-444-44-4-44-444-4000000000000000000000000000000000000000000000000000000000000000000000000000
χ84444-44-4-4-4-444-4-444-44-4-44000000000000000000000000000000000000000000000000000000000000000000000000000
χ8544-4-4-44-44000000000000444-4-44-4-4-4400000000000000000000000000000000000000000000000000000000000000000
χ8644-4-4-44-44000000000000-4-4-444-444-4400000000000000000000000000000000000000000000000000000000000000000
χ874-4-4444-4-400000000000040-4400-40000000000000000000000022−22−222222−22−22220000000000000000000000000000000000000
χ884-4-4444-4-400000000000040-4400-400000000000000000000000−222222−22−222222−220000000000000000000000000000000000000
χ894-4-4444-4-4000000000000-404-4004000000000000000000000002i2−2i2−2i22i2−2i22i22i2−2i20000000000000000000000000000000000000
χ904-4-4444-4-4000000000000-404-400400000000000000000000000−2i22i22i2−2i22i2−2i2−2i22i20000000000000000000000000000000000000
χ914-4-4-44-44400000000000004004-40-4000000000000002i2−2i2−2i22i2−2i22i22i2−2i2000000000000000000000000000000000000000000000
χ924-4-4-44-44400000000000004004-40-400000000000000−2i22i22i2−2i22i2−2i2−2i22i2000000000000000000000000000000000000000000000
χ934-4-4-44-4440000000000000-400-44040000000000000022−22−222222−22−2222000000000000000000000000000000000000000000000
χ944-4-4-44-4440000000000000-400-440400000000000000−222222−22−222222−22000000000000000000000000000000000000000000000
χ9588-88-8-88-8000000000000000000000000000000000000000000000000000000000000000000000000000000000000000

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