Finite Group Databasebeta

← Group #96079

Character table — Group #96079

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92
size1111111122222222222222222222222222224444444444444444888888888888888888888888888888881616161616161616
order12222222222244444444444444444444444444444444444444448888888888888888888888888888888888888888
χ111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ31111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111111111-1-1-1-1-1-1-1-1
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
χ51111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1iiiiiiii−i−i−i−i−i−i−i−i11111111-1-1-1-1-1-1-1-1iiii−i−i−i−i
χ61111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1iiiiiiii−i−i−i−i−i−i−i−i-1-1-1-1-1-1-1-111111111−i−i−i−iiiii
χ71111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1−i−i−i−i−i−i−i−iiiiiiiii11111111-1-1-1-1-1-1-1-1−i−i−i−iiiii
χ81111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1−i−i−i−i−i−i−i−iiiiiiiii-1-1-1-1-1-1-1-111111111iiii−i−i−i−i
χ9111111111111-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-11111-1-11111-1-1-1-1-1-1iiii−i−i−i−iiiii−i−i−i−iiiii−i−i−i−iiiii−i−i−i−i11-1-111-1-1
χ10111111111111-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-11111-1-11111-1-1-1-1-1-1iiii−i−i−i−iiiii−i−i−i−i−i−i−i−iiiii−i−i−i−iiiii-1-111-1-111
χ11111111111111-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-11111-1-11111-1-1-1-1-1-1−i−i−i−iiiii−i−i−i−iiiiiiiii−i−i−i−iiiii−i−i−i−i-1-111-1-111
χ12111111111111-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-11111-1-11111-1-1-1-1-1-1−i−i−i−iiiii−i−i−i−iiiii−i−i−i−iiiii−i−i−i−iiiii11-1-111-1-1
χ13111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-11111-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-11111iiii−i−i−i−i−i−i−i−iiiii−i−iiiii−i−i
χ14111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-11111-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-11111−i−i−i−iiiiiiiii−i−i−i−iii−i−i−i−iii
χ15111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-11111-1-1-1-1-1-1111111-1-1-1-111111111-1-1-1-1iiii−i−i−i−i−i−i−i−iiiiiii−i−i−i−iii
χ16111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-11111-1-1-1-1-1-1111111-1-1-1-111111111-1-1-1-1−i−i−i−iiiiiiiii−i−i−i−i−i−iiiii−i−i
χ1711111111-1-1-1-111111111-1-11111-1-1-1-11111-1-111-1-1-1-111-1-111-1-1-1-111-1-111-1-111-1-111-1-1ii−i−iii−i−iii−i−iii−i−ii−ii−ii−ii−i
χ1811111111-1-1-1-111111111-1-11111-1-1-1-11111-1-111-1-1-1-111-1-111-1-1-1-111-1-111-1-111-1-111-1-1−i−iii−i−iii−i−iii−i−iii−ii−ii−ii−ii
χ1911111111-1-1-1-111111111-1-11111-1-1-1-11111-1-111-1-1-1-111-1-111-1-1-1-1-1-111-1-111-1-111-1-111ii−i−iii−i−iii−i−iii−i−i−ii−ii−ii−ii
χ2011111111-1-1-1-111111111-1-11111-1-1-1-11111-1-111-1-1-1-111-1-111-1-1-1-1-1-111-1-111-1-111-1-111−i−iii−i−iii−i−iii−i−iiii−ii−ii−ii−i
χ2111111111-1-1-1-111111111-1-1-1-1-1-11111-1-1-1-1-1-111-1-1-1-1-1-111-1-11111ii−i−iii−i−i−i−iii−i−iiiii−i−iii−i−i−i−iii−i−iii-11-111-11-1
χ2211111111-1-1-1-111111111-1-1-1-1-1-11111-1-1-1-1-1-111-1-1-1-1-1-111-1-11111ii−i−iii−i−i−i−iii−i−iii−i−iii−i−iiiii−i−iii−i−i1-11-1-11-11
χ2311111111-1-1-1-111111111-1-1-1-1-1-11111-1-1-1-1-1-111-1-1-1-1-1-111-1-11111−i−iii−i−iiiii−i−iii−i−iii−i−iii−i−i−i−iii−i−iii1-11-1-11-11
χ2411111111-1-1-1-111111111-1-1-1-1-1-11111-1-1-1-1-1-111-1-1-1-1-1-111-1-11111−i−iii−i−iiiii−i−iii−i−i−i−iii−i−iiiii−i−iii−i−i-11-111-11-1
χ2511111111-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-11111-1-11111-1-1-1-11111ii−i−i−i−iiiii−i−i−i−iii11-1-1-1-11111-1-1-1-111−iii−i−iii−i
χ2611111111-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-11111-1-11111-1-1-1-11111ii−i−i−i−iiiii−i−i−i−iii-1-11111-1-1-1-11111-1-1i−i−iii−i−ii
χ2711111111-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-11111-1-11111-1-1-1-11111−i−iiiii−i−i−i−iiiii−i−i11-1-1-1-11111-1-1-1-111i−i−iii−i−ii
χ2811111111-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-11111-1-11111-1-1-1-11111−i−iiiii−i−i−i−iiiii−i−i-1-11111-1-1-1-11111-1-1−iii−i−iii−i
χ2911111111-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-1111111111111-1-111-1-11111-1-1-1-111-1-1-1-111-1-11111-1-111-1-1-1-111-1-11111-1-1-111-11-1-11
χ3011111111-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-1111111111111-1-111-1-11111-1-1-1-111-1-1-1-111-1-11111-1-1-1-11111-1-111-1-1-1-1111-1-11-111-1
χ3111111111-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-1111111111111-1-111-1-11111-1-1-1-1-1-11111-1-111-1-1-1-11111-1-1-1-111-1-11111-1-11-1-11-111-1
χ3211111111-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-1111111111111-1-111-1-11111-1-1-1-1-1-11111-1-111-1-1-1-111-1-11111-1-111-1-1-1-111-111-11-1-11
χ332222222222222222-2-2-2-22222222222-2-2-2-222-2-2-2-2-2-2-2-2-2-22222-2-20000000000000000000000000000000000000000
χ342222222222222222-2-2-2-222-2-2-2-2-2-2-2-2222222-2-2-2-2-2-22222-2-2-2-2220000000000000000000000000000000000000000
χ35222222222222-2-2-2-22222-2-2222222222222-2-2-2-2-2-222-2-2-2-2-2-2-2-2220000000000000000000000000000000000000000
χ36222222222222-2-2-2-22222-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-22222222222-2-20000000000000000000000000000000000000000
χ3722222222-2-2-2-22222-2-2-2-2-2-22222-2-2-2-2-2-2-2-2-2-2-2-22222-2-22222-2-2220000000000000000000000000000000000000000
χ3822222222-2-2-2-22222-2-2-2-2-2-2-2-2-2-222222222-2-2-2-2222222-2-2-2-222-2-20000000000000000000000000000000000000000
χ3922222222-2-2-2-2-2-2-2-22222222222-2-2-2-2222222-2-222-2-2-2-222-2-222-2-20000000000000000000000000000000000000000
χ4022222222-2-2-2-2-2-2-2-2222222-2-2-2-22222-2-2-2-222-2-222-2-222-2-222-2-2220000000000000000000000000000000000000000
χ412222-2-2-2-222-2-200002i2i−2i−2i0022-2-222-2-22i2i−2i−2i0000002i−2i000000002i−2i00000000000000001+i−1−i1+i−1−i1−i−1+i1−i−1+i1+i−1−i1+i−1−i1−i−1+i1−i−1+i00000000
χ422222-2-2-2-222-2-200002i2i−2i−2i0022-2-222-2-22i2i−2i−2i0000002i−2i000000002i−2i0000000000000000−1−i1+i−1−i1+i−1+i1−i−1+i1−i−1−i1+i−1−i1+i−1+i1−i−1+i1−i00000000
χ432222-2-2-2-222-2-200002i2i−2i−2i00-2-222-2-222−2i−2i2i2i0000002i−2i00000000−2i2i00000000000000001+i−1−i1+i−1−i1−i−1+i1−i−1+i−1−i1+i−1−i1+i−1+i1−i−1+i1−i00000000
χ442222-2-2-2-222-2-200002i2i−2i−2i00-2-222-2-222−2i−2i2i2i0000002i−2i00000000−2i2i0000000000000000−1−i1+i−1−i1+i−1+i1−i−1+i1−i1+i−1−i1+i−1−i1−i−1+i1−i−1+i00000000
χ452222-2-2-2-222-2-20000−2i−2i2i2i0022-2-222-2-2−2i−2i2i2i000000−2i2i00000000−2i2i00000000000000001−i−1+i1−i−1+i1+i−1−i1+i−1−i1−i−1+i1−i−1+i1+i−1−i1+i−1−i00000000
χ462222-2-2-2-222-2-20000−2i−2i2i2i0022-2-222-2-2−2i−2i2i2i000000−2i2i00000000−2i2i0000000000000000−1+i1−i−1+i1−i−1−i1+i−1−i1+i−1+i1−i−1+i1−i−1−i1+i−1−i1+i00000000
χ472222-2-2-2-222-2-20000−2i−2i2i2i00-2-222-2-2222i2i−2i−2i000000−2i2i000000002i−2i00000000000000001−i−1+i1−i−1+i1+i−1−i1+i−1−i−1+i1−i−1+i1−i−1−i1+i−1−i1+i00000000
χ482222-2-2-2-222-2-20000−2i−2i2i2i00-2-222-2-2222i2i−2i−2i000000−2i2i000000002i−2i0000000000000000−1+i1−i−1+i1−i−1−i1+i−1−i1+i1−i−1+i1−i−1+i1+i−1−i1+i−1−i00000000
χ492222-2-2-2-2-2-22200002i2i−2i−2i0022-2-2-2-2222i2i−2i−2i000000−2i2i00000000−2i2i00000000000000001−i−1+i−1+i1−i−1−i1+i1+i−1−i1−i−1+i−1+i1−i−1−i1+i1+i−1−i00000000
χ502222-2-2-2-2-2-22200002i2i−2i−2i0022-2-2-2-2222i2i−2i−2i000000−2i2i00000000−2i2i0000000000000000−1+i1−i1−i−1+i1+i−1−i−1−i1+i−1+i1−i1−i−1+i1+i−1−i−1−i1+i00000000
χ512222-2-2-2-2-2-22200002i2i−2i−2i00-2-22222-2-2−2i−2i2i2i000000−2i2i000000002i−2i00000000000000001−i−1+i−1+i1−i−1−i1+i1+i−1−i−1+i1−i1−i−1+i1+i−1−i−1−i1+i00000000
χ522222-2-2-2-2-2-22200002i2i−2i−2i00-2-22222-2-2−2i−2i2i2i000000−2i2i000000002i−2i0000000000000000−1+i1−i1−i−1+i1+i−1−i−1−i1+i1−i−1+i−1+i1−i−1−i1+i1+i−1−i00000000
χ532222-2-2-2-2-2-2220000−2i−2i2i2i0022-2-2-2-222−2i−2i2i2i0000002i−2i000000002i−2i00000000000000001+i−1−i−1−i1+i−1+i1−i1−i−1+i1+i−1−i−1−i1+i−1+i1−i1−i−1+i00000000
χ542222-2-2-2-2-2-2220000−2i−2i2i2i0022-2-2-2-222−2i−2i2i2i0000002i−2i000000002i−2i0000000000000000−1−i1+i1+i−1−i1−i−1+i−1+i1−i−1−i1+i1+i−1−i1−i−1+i−1+i1−i00000000
χ552222-2-2-2-2-2-2220000−2i−2i2i2i00-2-22222-2-22i2i−2i−2i0000002i−2i00000000−2i2i00000000000000001+i−1−i−1−i1+i−1+i1−i1−i−1+i−1−i1+i1+i−1−i1−i−1+i−1+i1−i00000000
χ562222-2-2-2-2-2-2220000−2i−2i2i2i00-2-22222-2-22i2i−2i−2i0000002i−2i00000000−2i2i0000000000000000−1−i1+i1+i−1−i1−i−1+i−1+i1−i1+i−1−i−1−i1+i−1+i1−i1−i−1+i00000000
χ5722-2-222-2-22-22-22i2i−2i−2i00002i−2i2i−2i2i−2i2i−2i2i−2i00002i−2i00000000002-22-200i2−i2i2−i22−22−22−22−2i2−i2i2−i2000000000000000000000000
χ5822-2-222-2-22-22-22i2i−2i−2i00002i−2i2i−2i2i−2i2i−2i2i−2i00002i−2i00000000002-22-200−i2i2−i2i2−22−22−22−22−i2i2−i2i2000000000000000000000000
χ5922-2-222-2-22-22-22i2i−2i−2i00002i−2i−2i2i−2i2i−2i2i−2i2i00002i−2i0000000000-22-22002−22−2−i2i2−i2i2i2−i2i2−i2−22−22000000000000000000000000
χ6022-2-222-2-22-22-22i2i−2i−2i00002i−2i−2i2i−2i2i−2i2i−2i2i00002i−2i0000000000-22-2200−22−22i2−i2i2−i2−i2i2−i2i22−22−2000000000000000000000000
χ6122-2-222-2-22-22-2−2i−2i2i2i0000−2i2i2i−2i2i−2i2i−2i2i−2i0000−2i2i0000000000-22-22002−22−2i2−i2i2−i2−i2i2−i2i2−22−22000000000000000000000000
χ6222-2-222-2-22-22-2−2i−2i2i2i0000−2i2i2i−2i2i−2i2i−2i2i−2i0000−2i2i0000000000-22-2200−22−22−i2i2−i2i2i2−i2i2−i22−22−2000000000000000000000000
χ6322-2-222-2-22-22-2−2i−2i2i2i0000−2i2i−2i2i−2i2i−2i2i−2i2i0000−2i2i00000000002-22-200i2−i2i2−i2−22−22−22−22i2−i2i2−i2000000000000000000000000
χ6422-2-222-2-22-22-2−2i−2i2i2i0000−2i2i−2i2i−2i2i−2i2i−2i2i0000−2i2i00000000002-22-200−i2i2−i2i22−22−22−22−2−i2i2−i2i2000000000000000000000000
χ6522-2-222-2-2-22-222i2i−2i−2i0000−2i2i2i−2i2i−2i−2i2i−2i2i0000−2i2i00000000002-2-2200i2−i2−i2i22−2−222−2−22i2−i2−i2i2000000000000000000000000
χ6622-2-222-2-2-22-222i2i−2i−2i0000−2i2i2i−2i2i−2i−2i2i−2i2i0000−2i2i00000000002-2-2200−i2i2i2−i2−222−2−222−2−i2i2i2−i2000000000000000000000000
χ6722-2-222-2-2-22-222i2i−2i−2i0000−2i2i−2i2i−2i2i2i−2i2i−2i0000−2i2i0000000000-222-2002−2−22−i2i2i2−i2i2−i2−i2i2−222−2000000000000000000000000
χ6822-2-222-2-2-22-222i2i−2i−2i0000−2i2i−2i2i−2i2i2i−2i2i−2i0000−2i2i0000000000-222-200−222−2i2−i2−i2i2−i2i2i2−i22−2−22000000000000000000000000
χ6922-2-222-2-2-22-22−2i−2i2i2i00002i−2i2i−2i2i−2i−2i2i−2i2i00002i−2i0000000000-222-2002−2−22i2−i2−i2i2−i2i2i2−i2−222−2000000000000000000000000
χ7022-2-222-2-2-22-22−2i−2i2i2i00002i−2i2i−2i2i−2i−2i2i−2i2i00002i−2i0000000000-222-200−222−2−i2i2i2−i2i2−i2−i2i22−2−22000000000000000000000000
χ7122-2-222-2-2-22-22−2i−2i2i2i00002i−2i−2i2i−2i2i2i−2i2i−2i00002i−2i00000000002-2-2200i2−i2−i2i2−222−2−222−2i2−i2−i2i2000000000000000000000000
χ7222-2-222-2-2-22-22−2i−2i2i2i00002i−2i−2i2i−2i2i2i−2i2i−2i00002i−2i00000000002-2-2200−i2i2i2−i22−2−222−2−22−i2i2i2−i2000000000000000000000000
χ7344-4-4-4-4444-4-4400000000004i−4i−4i4i4i−4i−4i4i00000000000000000000000000000000000000000000000000000000000000
χ7444-4-4-4-4444-4-440000000000−4i4i4i−4i−4i4i4i−4i00000000000000000000000000000000000000000000000000000000000000
χ7544-4-4-4-444-444-400000000004i−4i−4i4i−4i4i4i−4i00000000000000000000000000000000000000000000000000000000000000
χ7644-4-4-4-444-444-40000000000−4i4i4i−4i4i−4i−4i4i00000000000000000000000000000000000000000000000000000000000000
χ774-44-44-44-4000000004-44-444000000000000-4-4004-40000000000000000000000000000000000000000000000000000
χ784-44-44-44-4000000004-44-4-4-40000000000004400-440000000000000000000000000000000000000000000000000000
χ794-44-44-44-400000000-44-4444000000000000-4-400-440000000000000000000000000000000000000000000000000000
χ804-44-44-44-400000000-44-44-4-400000000000044004-40000000000000000000000000000000000000000000000000000
χ814-44-4-44-4400004-44-44i−4i−4i4i00000000000000004i−4i000000000000000000000000000000000000000000000000000000
χ824-44-4-44-4400004-44-4−4i4i4i−4i0000000000000000−4i4i000000000000000000000000000000000000000000000000000000
χ834-44-4-44-440000-44-444i−4i−4i4i0000000000000000−4i4i000000000000000000000000000000000000000000000000000000
χ844-44-4-44-440000-44-44−4i4i4i−4i00000000000000004i−4i000000000000000000000000000000000000000000000000000000
χ854-4-444-4-440000000000004i−4i000000004-44-4−4i4i000000004i−4i0000000000000000000000000000000000000000000000
χ864-4-444-4-440000000000004i−4i00000000-44-44−4i4i00000000−4i4i0000000000000000000000000000000000000000000000
χ874-4-444-4-44000000000000−4i4i000000004-44-44i−4i00000000−4i4i0000000000000000000000000000000000000000000000
χ884-4-444-4-44000000000000−4i4i00000000-44-444i−4i000000004i−4i0000000000000000000000000000000000000000000000
χ894-4-44-444-400004i−4i−4i4i000000000000004i−4i−4i4i000000004-4000000000000000000000000000000000000000000000000
χ904-4-44-444-400004i−4i−4i4i00000000000000−4i4i4i−4i00000000-44000000000000000000000000000000000000000000000000
χ914-4-44-444-40000−4i4i4i−4i000000000000004i−4i−4i4i00000000-44000000000000000000000000000000000000000000000000
χ924-4-44-444-40000−4i4i4i−4i00000000000000−4i4i4i−4i000000004-4000000000000000000000000000000000000000000000000

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