Finite Group Databasebeta

← Group #224205

Character table — Group #224205

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95
size11111111222222222222222222224444444444444444444444444444448888888888888888888888888888888161616161616
order12222222444444444444444444444444444444444488888888888888884444444888888888888888888888888444444
χ111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1111-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ3111111111111111111111111111111111111111111-1-1-1-1-1-1-1-111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1
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
χ5111111111111111-1-1-1-1-1-1-1-1111111111-1-1-1-1-1-111-1-111111111111111111-1-11111-1-1-1-11111-1-1-1-11111-1-1-1-1-1-1-1-1-1-111-1-1
χ6111111111111111-1-1-1-1-1-1-1-1111111111-1-1-1-1-1-111-1-111111111-1-1-1-1-1-1-1-11-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-11111111111-1-111
χ7111111111111111-1-1-1-1-1-1-1-1111111111-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-1111111111-1-1-1-1-1-11111-1-1-1-111111111-1-1-1-1-1-1-1-111-1-111
χ8111111111111111-1-1-1-1-1-1-1-1111111111-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11-1-111111111-1-1-1-11111-1-1-1-111111111-1-111-1-1
χ911111111111-1-1-1-11111-1-1-1-11111111-1-111-1-1-1-1-1-1111111111111111111-11-11111-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1-1-1-1-1-1-111
χ1011111111111-1-1-1-11111-1-1-1-11111111-1-111-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-1-11-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-111111111-1-1
χ1111111111111-1-1-1-11111-1-1-1-11111111-1-111-1-1-1-1-1-111-1-1-1-1-1-1-1-111111111-11-1-1-1-1-111111111-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1
χ1211111111111-1-1-1-11111-1-1-1-11111111-1-111-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11-1111111111111-1-1-1-11111-1-1-1-11111-1-1-1-111
χ1311111111111-1-1-1-1-1-1-1-111111111111-1-1-1-11111-1-1-1-11111111111111111-1-1111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-1-1
χ1411111111111-1-1-1-1-1-1-1-111111111111-1-1-1-11111-1-1-1-111111111-1-1-1-1-1-1-1-1-1-11-1-1-1-11111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-11111
χ1511111111111-1-1-1-1-1-1-1-111111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-11-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-11111-1-11111
χ1611111111111-1-1-1-1-1-1-1-111111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111-1-1-1-11111111111111111-1-1-1-111-1-1-1-1
χ1711111111-1-1-1111111111111-1-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1iiii−i−i−i−iiiii−i−i−i−i11111-1-1ii−i−iii−i−iii−i−iii−i−iii−i−iii−i−i1-11-11-1
χ1811111111-1-1-1111111111111-1-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1iiii−i−i−i−i−i−i−i−iiiii111-1-111ii−i−iii−i−iii−i−i−i−iii−i−iii−i−iii-11-11-11
χ1911111111-1-1-1111111111111-1-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1−i−i−i−iiiiiiiii−i−i−i−i111-1-111−i−iii−i−iii−i−iiiii−i−iii−i−iii−i−i-11-11-11
χ2011111111-1-1-1111111111111-1-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1−i−i−i−iiiii−i−i−i−iiiii11111-1-1−i−iii−i−iii−i−iii−i−iii−i−iii−i−iii1-11-11-1
χ2111111111-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1111111-1-111iiii−i−i−i−iiiii−i−i−i−i1-1-111-1-1−i−iiiii−i−i−i−iiiii−i−i−i−iii−i−iii-111-1-11
χ2211111111-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1111111-1-111iiii−i−i−i−i−i−i−i−iiiii1-1-1-1-111−i−iiiii−i−i−i−iii−i−iiiii−i−iii−i−i1-1-111-1
χ2311111111-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1111111-1-111−i−i−i−iiiiiiiii−i−i−i−i1-1-1-1-111ii−i−i−i−iiiii−i−iii−i−i−i−iii−i−iii1-1-111-1
χ2411111111-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1111111-1-111−i−i−i−iiiii−i−i−i−iiiii1-1-111-1-1ii−i−i−i−iiiii−i−i−i−iiiii−i−iii−i−i-111-1-11
χ2511111111-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-11111-1-1111111-1-1iiii−i−i−i−iiiii−i−i−i−i-11-111-1-1−i−iii−i−iiiii−i−i−i−iiiii−i−i−i−iii-11-111-1
χ2611111111-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-11111-1-1111111-1-1iiii−i−i−i−i−i−i−i−iiiii-11-1-1-111−i−iii−i−iiiii−i−iii−i−i−i−iiiii−i−i1-11-1-11
χ2711111111-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-11111-1-1111111-1-1−i−i−i−iiiiiiiii−i−i−i−i-11-1-1-111ii−i−iii−i−i−i−iii−i−iiiii−i−i−i−iii1-11-1-11
χ2811111111-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-11111-1-1111111-1-1−i−i−i−iiiii−i−i−i−iiiii-11-111-1-1ii−i−iii−i−i−i−iiiii−i−i−i−iiiii−i−i-11-111-1
χ2911111111-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1111111-1-1-1-11111iiii−i−i−i−iiiii−i−i−i−i-1-1111-1-1ii−i−i−i−iii−i−iii−i−iii−i−iiiii−i−i1-1-11-11
χ3011111111-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1111111-1-1-1-11111iiii−i−i−i−i−i−i−i−iiiii-1-11-1-111ii−i−i−i−iii−i−iiiii−i−iii−i−i−i−iii-111-11-1
χ3111111111-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1111111-1-1-1-11111−i−i−i−iiiiiiiii−i−i−i−i-1-11-1-111−i−iiiii−i−iii−i−i−i−iii−i−iiiii−i−i-111-11-1
χ3211111111-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1111111-1-1-1-11111−i−i−i−iiiii−i−i−i−iiiii-1-1111-1-1−i−iiiii−i−iii−i−iii−i−iii−i−i−i−iii1-1-11-11
χ33222222222-2-222222222222222-22-2-2-2222222-2-2-2-2-2-20000000000000000-2-2-20000000000000000000000000000000000
χ34222222222-2-22222-2-2-2-2-2-2-2-222-22-2-2-222-2-2-2-222-2-2220000000000000000-2220000000000000000000000000000000000
χ35222222222-2-2-2-2-2-22222-2-2-2-222-22-2-2-2-2-222-2-22222-2-200000000000000002-220000000000000000000000000000000000
χ36222222222-2-2-2-2-2-2-2-2-2-2222222-22-2-2-2-2-2-2-222-2-22222000000000000000022-20000000000000000000000000000000000
χ3722222222-222222222222222-2-22-22-2-2-2-2-2-2-2-22222220000000000000000-2-2-20000000000000000000000000000000000
χ3822222222-2222222-2-2-2-2-2-2-2-2-2-22-22-2-2-2-22222-2-222-2-20000000000000000-2220000000000000000000000000000000000
χ3922222222-222-2-2-2-22222-2-2-2-2-2-22-22-2-222-2-222-2-2-2-22200000000000000002-220000000000000000000000000000000000
χ4022222222-222-2-2-2-2-2-2-2-22222-2-22-22-2-22222-2-222-2-2-2-2000000000000000022-20000000000000000000000000000000000
χ41222-2-22-2-222-20000000000002-22-2-22-200000000000022-2-222-2-222-2-222-2-20002-22-2000000000000000000000000000000
χ42222-2-22-2-222-20000000000002-22-2-22-200000000000022-2-222-2-2-2-222-2-222000-22-22000000000000000000000000000000
χ43222-2-22-2-222-20000000000002-22-2-22-2000000000000-2-222-2-22222-2-222-2-2000-22-22000000000000000000000000000000
χ44222-2-22-2-222-20000000000002-22-2-22-2000000000000-2-222-2-222-2-222-2-2220002-22-2000000000000000000000000000000
χ45222-2-22-2-2-2-22000000000000-22-2222-20000000000002i2i−2i−2i−2i−2i2i2i2i2i−2i−2i−2i−2i2i2i0002-2-22000000000000000000000000000000
χ46222-2-22-2-2-2-22000000000000-22-2222-20000000000002i2i−2i−2i−2i−2i2i2i−2i−2i2i2i2i2i−2i−2i000-222-2000000000000000000000000000000
χ47222-2-22-2-2-2-22000000000000-22-2222-2000000000000−2i−2i2i2i2i2i−2i−2i2i2i−2i−2i−2i−2i2i2i000-222-2000000000000000000000000000000
χ48222-2-22-2-2-2-22000000000000-22-2222-2000000000000−2i−2i2i2i2i2i−2i−2i−2i−2i2i2i2i2i−2i−2i0002-2-22000000000000000000000000000000
χ4922-22-2-2-222002i2i−2i−2i2i2i−2i−2i22-2-2-2-2020002i−2i2i−2i2-2000000000000002−22−22−22−20000000000000000000i2−i2i2−i2i2−i2i2−i22−22−2000000
χ5022-22-2-2-222002i2i−2i−2i2i2i−2i−2i22-2-2-2-2020002i−2i2i−2i2-200000000000000−22−22−22−220000000000000000000−i2i2−i2i2−i2i2−i2i2−22−22000000
χ5122-22-2-2-222002i2i−2i−2i−2i−2i2i2i-2-222-2-2020002i−2i−2i2i-22000000000000002−22−22−22−20000000000000000000i2−i2i2−i2−i2i2−i2i2−22−22000000
χ5222-22-2-2-222002i2i−2i−2i−2i−2i2i2i-2-222-2-2020002i−2i−2i2i-2200000000000000−22−22−22−220000000000000000000−i2i2−i2i2i2−i2i2−i22−22−2000000
χ5322-22-2-2-22200−2i−2i2i2i2i2i−2i−2i-2-222-2-202000−2i2i2i−2i-22000000000000002−22−22−22−20000000000000000000−i2i2−i2i2i2−i2i2−i2−22−22000000
χ5422-22-2-2-22200−2i−2i2i2i2i2i−2i−2i-2-222-2-202000−2i2i2i−2i-2200000000000000−22−22−22−220000000000000000000i2−i2i2−i2−i2i2−i2i22−22−2000000
χ5522-22-2-2-22200−2i−2i2i2i−2i−2i2i2i22-2-2-2-202000−2i2i−2i2i2-2000000000000002−22−22−22−20000000000000000000−i2i2−i2i2−i2i2−i2i22−22−2000000
χ5622-22-2-2-22200−2i−2i2i2i−2i−2i2i2i22-2-2-2-202000−2i2i−2i2i2-200000000000000−22−22−22−220000000000000000000i2−i2i2−i2i2−i2i2−i2−22−22000000
χ5722-22-2-2-22-2002i2i−2i−2i2i2i−2i−2i22-2-2220-2000−2i2i−2i2i-2200000000000000i2−i2i2−i2−i2i2−i2i20000000000000000000−222−2−222−2i2−i2−i2i2000000
χ5822-22-2-2-22-2002i2i−2i−2i2i2i−2i−2i22-2-2220-2000−2i2i−2i2i-2200000000000000−i2i2−i2i2i2−i2i2−i200000000000000000002−2−222−2−22−i2i2i2−i2000000
χ5922-22-2-2-22-2002i2i−2i−2i−2i−2i2i2i-2-222220-2000−2i2i2i−2i2-200000000000000i2−i2i2−i2−i2i2−i2i20000000000000000000−222−22−2−22−i2i2i2−i2000000
χ6022-22-2-2-22-2002i2i−2i−2i−2i−2i2i2i-2-222220-2000−2i2i2i−2i2-200000000000000−i2i2−i2i2i2−i2i2−i200000000000000000002−2−22−222−2i2−i2−i2i2000000
χ6122-22-2-2-22-200−2i−2i2i2i2i2i−2i−2i-2-222220-20002i−2i−2i2i2-200000000000000i2−i2i2−i2−i2i2−i2i200000000000000000002−2−22−222−2−i2i2i2−i2000000
χ6222-22-2-2-22-200−2i−2i2i2i2i2i−2i−2i-2-222220-20002i−2i−2i2i2-200000000000000−i2i2−i2i2i2−i2i2−i20000000000000000000−222−22−2−22i2−i2−i2i2000000
χ6322-22-2-2-22-200−2i−2i2i2i−2i−2i2i2i22-2-2220-20002i−2i2i−2i-2200000000000000i2−i2i2−i2−i2i2−i2i200000000000000000002−2−222−2−22i2−i2−i2i2000000
χ6422-22-2-2-22-200−2i−2i2i2i−2i−2i2i2i22-2-2220-20002i−2i2i−2i-2200000000000000−i2i2−i2i2i2−i2i2−i20000000000000000000−222−2−222−2−i2i2i2−i2000000
χ652-2-2-2-22220222-22-22-22-22-22-200-20-2000000002-22-22-2i2−i2i2−i2i2−i2i2−i2000000000000000i2−i2i2−i2i2−i2i2−i2i2−i2i2−i2000000000000000000
χ662-2-2-2-22220222-22-22-22-22-22-200-20-2000000002-22-22-2−i2i2−i2i2−i2i2−i2i2000000000000000−i2i2−i2i2−i2i2−i2i2−i2i2−i2i2000000000000000000
χ672-2-2-2-22220222-22-2-22-22-22-2200-20-200000000-222-2-22i2−i2i2−i2i2−i2i2−i2000000000000000−i2i2−i2i2i2−i2i2−i2−i2i2−i2i2000000000000000000
χ682-2-2-2-22220222-22-2-22-22-22-2200-20-200000000-222-2-22−i2i2−i2i2−i2i2−i2i2000000000000000i2−i2i2−i2−i2i2−i2i2i2−i2i2−i2000000000000000000
χ692-2-2-2-2222022-22-222-22-2-22-2200-20-200000000-22-222-2i2−i2i2−i2i2−i2i2−i2000000000000000−i2i2−i2i2−i2i2−i2i2i2−i2i2−i2000000000000000000
χ702-2-2-2-2222022-22-222-22-2-22-2200-20-200000000-22-222-2−i2i2−i2i2−i2i2−i2i2000000000000000i2−i2i2−i2i2−i2i2−i2−i2i2−i2i2000000000000000000
χ712-2-2-2-2222022-22-22-22-222-22-200-20-2000000002-2-22-22i2−i2i2−i2i2−i2i2−i2000000000000000i2−i2i2−i2−i2i2−i2i2−i2i2−i2i2000000000000000000
χ722-2-2-2-2222022-22-22-22-222-22-200-20-2000000002-2-22-22−i2i2−i2i2−i2i2−i2i2000000000000000−i2i2−i2i2i2−i2i2−i2i2−i2i2−i2000000000000000000
χ732-2-2-2-22220-2-22-22-22-22-22-22-20020200000000-22-22-222−22−2−22−220000000000000002−2−222−2−222−2−22000000000000000000
χ742-2-2-2-22220-2-22-22-22-22-22-22-20020200000000-22-22-22−22−222−22−2000000000000000−222−2−222−2−222−2000000000000000000
χ752-2-2-2-22220-2-22-22-2-22-22-22-2200202000000002-2-222-22−22−2−22−22000000000000000−222−22−2−22−222−2000000000000000000
χ762-2-2-2-22220-2-22-22-2-22-22-22-2200202000000002-2-222-2−22−222−22−20000000000000002−2−22−222−22−2−22000000000000000000
χ772-2-2-2-22220-2-2-22-222-22-2-22-2200202000000002-22-2-222−22−2−22−22000000000000000−222−2−222−22−2−22000000000000000000
χ782-2-2-2-22220-2-2-22-222-22-2-22-2200202000000002-22-2-22−22−222−22−20000000000000002−2−222−2−22−222−2000000000000000000
χ792-2-2-2-22220-2-2-22-22-22-222-22-20020200000000-222-22-22−22−2−22−220000000000000002−2−22−222−2−222−2000000000000000000
χ802-2-2-2-22220-2-2-22-22-22-222-22-20020200000000-222-22-2−22−222−22−2000000000000000−222−22−2−222−2−22000000000000000000
χ81444-4-44-4-44-440000000000004-4-4-44-4400000000000000000000000000000000000000000000000000000000000000000
χ82444-4-44-4-4-44-4000000000000-4444-4-4400000000000000000000000000000000000000000000000000000000000000000
χ8344-4-44-44-4400000000000000-440-40000000000000000000000022−22−222222−22−22220000000000000000000000000000000000000
χ8444-4-44-44-4400000000000000-440-400000000000000000000000−222222−22−222222−220000000000000000000000000000000000000
χ8544-4-44-44-4-4000000000000004-404000000000000000000000002i2−2i2−2i22i2−2i22i22i2−2i20000000000000000000000000000000000000
χ8644-4-44-44-4-4000000000000004-40400000000000000000000000−2i22i22i2−2i22i2−2i2−2i22i20000000000000000000000000000000000000
χ874-44-44-4-440004i−4i−4i4i4i−4i−4i4i4-4-44000000000000000000000000000000000000000000000000000000000000000000000000
χ884-44-44-4-440004i−4i−4i4i−4i4i4i−4i-444-4000000000000000000000000000000000000000000000000000000000000000000000000
χ894-44-44-4-44000−4i4i4i−4i4i−4i−4i4i-444-4000000000000000000000000000000000000000000000000000000000000000000000000
χ904-44-44-4-44000−4i4i4i−4i−4i4i4i−4i4-4-44000000000000000000000000000000000000000000000000000000000000000000000000
χ914-4-4444-4-404-400000000000000-404000000000000002i2−2i2−2i22i22i2−2i2−2i22i2000000000000000000000000000000000000000000000
χ924-4-4444-4-404-400000000000000-40400000000000000−2i22i22i2−2i2−2i22i22i2−2i2000000000000000000000000000000000000000000000
χ934-4-4444-4-40-440000000000000040-40000000000000022−22−2222−222222−22000000000000000000000000000000000000000000000
χ944-4-4444-4-40-440000000000000040-400000000000000−222222−2222−22−2222000000000000000000000000000000000000000000000
χ958-888-8-88-8000000000000000000000000000000000000000000000000000000000000000000000000000000000000000

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