Finite Group Databasebeta

← Group #186570

Character table — Group #186570

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92
size1111111122222222222222222222444444444444444444444444444488888888888888888888888888881616161616161616
order12224444222244444444444444442224444444444444444444444444222222244444444444448888888888888888
χ111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-111-1-1-1-11-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1
χ31111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ41111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11-1-1-1-1-1-111-1-1-1-11-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111
χ51111111111111111111111111111-1-1111-1-1-1-11-1-11111111111111111-11111-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-11111-1-1-1-1
χ61111111111111111111111111111-1-1111-1-1-1-11-1-11111111111111111-1-1-1-1-111-1-11111-1-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-11111
χ71111111111111111111111111111-1-1111-1-1-1-11-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-11111-1-111111111-1-1-1-11111
χ81111111111111111111111111111-1-1111-1-1-1-11-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-11111-1-1-1-1-111111111111111-1-1-1-1
χ911111111-1-1-1-11111-1-1-1-1-1-1-1-11111111-1-1-1-1-1-111111111111-1-1-1-1-1-1-1-1-111-1-11-11111-1-1-111-1-11-11111-1-1-1-111-1-111-1-1
χ1011111111-1-1-1-11111-1-1-1-1-1-1-1-11111111-1-1-1-1-1-111111111111-1-1-1-1-1-1-1-1-1-1-111-1111-1-111-1-1-111-111111-1-1-1-1-1-111-1-111
χ1111111111-1-1-1-11111-1-1-1-1-1-1-1-11111111-1-1-1-1-1-1111-1-1-1-1-1-1-1-111111111-111-1-11-11111-1-1-111-1-11-1-1-1-1-11111-1-111-1-111
χ1211111111-1-1-1-11111-1-1-1-1-1-1-1-11111111-1-1-1-1-1-1111-1-1-1-1-1-1-1-111111111-1-1-111-1111-1-111-1-1-111-11-1-1-1-1111111-1-111-1-1
χ1311111111-1-1-1-11111-1-1-1-1-1-1-1-11111-1-11-1-111111-1-111111111-1-1-1-1-1-1-1-1111-1-1-11-1-1-1-111111-1-1-11-1-1-1-1111111-1-1-1-111
χ1411111111-1-1-1-11111-1-1-1-1-1-1-1-11111-1-11-1-111111-1-111111111-1-1-1-1-1-1-1-11-1-1111-1-1-111-1-11-1-1111-1-1-1-1-11111-1-11111-1-1
χ1511111111-1-1-1-11111-1-1-1-1-1-1-1-11111-1-11-1-111111-1-1-1-1-1-1-1-1-1-111111111111-1-1-11-1-1-1-111111-1-1-111111-1-1-1-1-1-11111-1-1
χ1611111111-1-1-1-11111-1-1-1-1-1-1-1-11111-1-11-1-111111-1-1-1-1-1-1-1-1-1-1111111111-1-1111-1-1-111-1-11-1-1111-11111-1-1-1-111-1-1-1-111
χ171111-1-1-1-111-1-1111111-1-111-1-1-1-1-1-111-11-111-1-11-1-1iiii−i−i−i−iiiii−i−i−i−i111-1-11-11-11-11-1-1-1-111-11ii−i−iii−i−ii−ii−ii−ii−i
χ181111-1-1-1-111-1-1111111-1-111-1-1-1-1-1-111-11-111-1-11-1-1iiii−i−i−i−iiiii−i−i−i−i1-1-111-111-1-11-11-111-1-11-1ii−i−iii−i−i−ii−ii−ii−ii
χ191111-1-1-1-111-1-1111111-1-111-1-1-1-1-1-111-11-111-1-11-1-1−i−i−i−iiiii−i−i−i−iiiii111-1-11-11-11-11-1-1-1-111-11−i−iii−i−iii−ii−ii−ii−ii
χ201111-1-1-1-111-1-1111111-1-111-1-1-1-1-1-111-11-111-1-11-1-1−i−i−i−iiiii−i−i−i−iiiii1-1-111-111-1-11-11-111-1-11-1−i−iii−i−iiii−ii−ii−ii−i
χ211111-1-1-1-111-1-1111111-1-111-1-1-1-1-1-1-1-1-11-1-1-111111iiii−i−i−i−iiiii−i−i−i−i-111-1-1-11-11-11-111-1-1111-1−i−iii−i−iiii−ii−i−ii−ii
χ221111-1-1-1-111-1-1111111-1-111-1-1-1-1-1-1-1-1-11-1-1-111111iiii−i−i−i−iiiii−i−i−i−i-1-1-1111-1-111-11-1111-1-1-11−i−iii−i−iii−ii−iii−ii−i
χ231111-1-1-1-111-1-1111111-1-111-1-1-1-1-1-1-1-1-11-1-1-111111−i−i−i−iiiii−i−i−i−iiiii-111-1-1-11-11-11-111-1-1111-1ii−i−iii−i−i−ii−iii−ii−i
χ241111-1-1-1-111-1-1111111-1-111-1-1-1-1-1-1-1-1-11-1-1-111111−i−i−i−iiiii−i−i−i−iiiii-1-1-1111-1-111-11-1111-1-1-11ii−i−iii−i−ii−ii−i−ii−ii
χ251111-1-1-1-1-1-1111111-1-111-1-111-1-1-1-111-1-11-1-1111-1-1iiii−i−i−i−i−i−i−i−iiiii-11111111-11-1-111-1-1-1-1-1-1ii−i−i−i−iiii−i−iii−i−ii
χ261111-1-1-1-1-1-1111111-1-111-1-111-1-1-1-111-1-11-1-1111-1-1iiii−i−i−i−i−i−i−i−iiiii-1-1-1-1-1-1-11-1-111-11111111ii−i−i−i−iii−iii−i−iii−i
χ271111-1-1-1-1-1-1111111-1-111-1-111-1-1-1-111-1-11-1-1111-1-1−i−i−i−iiiiiiiii−i−i−i−i-11111111-11-1-111-1-1-1-1-1-1−i−iiiii−i−i−iii−i−iii−i
χ281111-1-1-1-1-1-1111111-1-111-1-111-1-1-1-111-1-11-1-1111-1-1−i−i−i−iiiiiiiii−i−i−i−i-1-1-1-1-1-1-11-1-111-11111111−i−iiiii−i−ii−i−iii−i−ii
χ291111-1-1-1-1-1-1111111-1-111-1-111-1-1-1-1-1-1-1-1111-1-1111iiii−i−i−i−i−i−i−i−iiiii11111-1-1-11-111-1-1-1-1-1-111−i−iiiii−i−ii−i−ii−iii−i
χ301111-1-1-1-1-1-1111111-1-111-1-111-1-1-1-1-1-1-1-1111-1-1111iiii−i−i−i−i−i−i−i−iiiii1-1-1-1-111-111-1-11-11111-1-1−i−iiiii−i−i−iii−ii−i−ii
χ311111-1-1-1-1-1-1111111-1-111-1-111-1-1-1-1-1-1-1-1111-1-1111−i−i−i−iiiiiiiii−i−i−i−i11111-1-1-11-111-1-1-1-1-1-111ii−i−i−i−iii−iii−ii−i−ii
χ321111-1-1-1-1-1-1111111-1-111-1-111-1-1-1-1-1-1-1-1111-1-1111−i−i−i−iiiiiiiii−i−i−i−i1-1-1-1-111-111-1-11-11111-1-1ii−i−i−i−iiii−i−ii−iii−i
χ33222222222222-2-2-2-2-2-2-2-22222-2-2-2-2002-2-20000200000000000000000002-22-20000000002-22-2000000000000000000
χ34222222222222-2-2-2-2-2-2-2-22222-2-2-2-2002-2-2000020000000000000000000-22-22000000000-22-22000000000000000000
χ352222222222-2-222-2-22222-2-22222-2-200-2-2-20000-2000000000000000000000002200-2-2-2-200000220000000000000000
χ362222222222-2-222-2-22222-2-22222-2-200-2-2-20000-200000000000000000000000-2-200222200000-2-20000000000000000
χ372222222222-2-2-2-222-2-2-2-2-2-222-2-22222-222-2-2-2-2-22200000000000000002000000-2-2000020000000000000000000000
χ382222222222-2-2-2-222-2-2-2-2-2-222-2-222-2-2-2222222-2-2-20000000000000000-2000000220000-20000000000000000000000
χ3922222222-2-22222-2-2-2-2-2-222-2-222-2-200-2220000-2000000000000000000000002-200-2-222000002-20000000000000000
χ4022222222-2-22222-2-2-2-2-2-222-2-222-2-200-2220000-200000000000000000000000-220022-2-200000-220000000000000000
χ4122222222-2-222-2-222222222-2-2-2-22222-2-2-22222-2220000000000000000-2000000-2-20000-20000000000000000000000
χ4222222222-2-222-2-222222222-2-2-2-222-2-2-2-2-2-2-2-2-2-2-2-20000000000000000200000022000020000000000000000000000
χ4322222222-2-2-2-2-2-2-2-22222-2-2-2-2-2-2-2-2002220000200000000000000000002-2-220000000002-2-22000000000000000000
χ4422222222-2-2-2-2-2-2-2-22222-2-2-2-2-2-2-2-200222000020000000000000000000-222-2000000000-222-2000000000000000000
χ452222-2-2-2-2222222-2-222-2-2-2-2-2-2-2-222002-220000-2000000000000000000000002-200-22-2200000-220000000000000000
χ462222-2-2-2-2222222-2-222-2-2-2-2-2-2-2-222002-220000-200000000000000000000000-22002-22-2000002-20000000000000000
χ472222-2-2-2-22222-2-222-2-222-2-2-2-222-2-22222-2-2-222-2-2-200000000000000002000000-220000-20000000000000000000000
χ482222-2-2-2-22222-2-222-2-222-2-2-2-222-2-2-2-222-222-2-2-2220000000000000000-20000002-2000020000000000000000000000
χ492222-2-2-2-222-2-2-2-2-2-2-2-22222-2-2222200-2-220000200000000000000000002-2-22000000000-222-2000000000000000000
χ502222-2-2-2-222-2-2-2-2-2-2-2-22222-2-2222200-2-22000020000000000000000000-222-20000000002-2-22000000000000000000
χ512222-2-2-2-2-2-222-2-2-2-222-2-2-2-222222200-22-20000200000000000000000002-22-2000000000-22-22000000000000000000
χ522222-2-2-2-2-2-222-2-2-2-222-2-2-2-222222200-22-2000020000000000000000000-22-220000000002-22-2000000000000000000
χ532222-2-2-2-2-2-2-2-222-2-2-2-2222222-2-2220022-20000-2000000000000000000000002200-222-200000-2-20000000000000000
χ542222-2-2-2-2-2-2-2-222-2-2-2-2222222-2-2220022-20000-200000000000000000000000-2-2002-2-2200000220000000000000000
χ552222-2-2-2-2-2-2-2-2-2-22222-2-2222222-2-2222-2222-2-2-2-2-20000000000000000-2000000-22000020000000000000000000000
χ562222-2-2-2-2-2-2-2-2-2-22222-2-2222222-2-2-2-22-22-2-222-222000000000000000020000002-20000-20000000000000000000000
χ5722-2-22i−2i2i−2i002-2002-22i−2i2-22i−2i00002i−2i2-20002i−2i2-202i−2i1+i1+i−1−i−1−i1−i1−i−1+i−1+i1−i1−i−1+i−1+i1+i1+i−1−i−1−i000000000000000000001+i−1−i1−i−1+i1−i−1+i1+i−1−i00000000
χ5822-2-22i−2i2i−2i002-2002-22i−2i2-22i−2i00002i−2i2-20002i−2i2-202i−2i−1−i−1−i1+i1+i−1+i−1+i1−i1−i−1+i−1+i1−i1−i−1−i−1−i1+i1+i00000000000000000000−1−i1+i−1+i1−i−1+i1−i−1−i1+i00000000
χ5922-2-22i−2i2i−2i002-2002-22i−2i2-22i−2i00002i−2i-22000−2i2i-220−2i2i1+i1+i−1−i−1−i1−i1−i−1+i−1+i1−i1−i−1+i−1+i1+i1+i−1−i−1−i00000000000000000000−1−i1+i−1+i1−i−1+i1−i−1−i1+i00000000
χ6022-2-22i−2i2i−2i002-2002-22i−2i2-22i−2i00002i−2i-22000−2i2i-220−2i2i−1−i−1−i1+i1+i−1+i−1+i1−i1−i−1+i−1+i1−i1−i−1−i−1−i1+i1+i000000000000000000001+i−1−i1−i−1+i1−i−1+i1+i−1−i00000000
χ6122-2-22i−2i2i−2i00-22002-2−2i2i-22−2i2i00002i−2i2-2000−2i2i-2202i−2i1+i1+i−1−i−1−i1−i1−i−1+i−1+i−1+i−1+i1−i1−i−1−i−1−i1+i1+i000000000000000000001+i−1−i1−i−1+i−1+i1−i−1−i1+i00000000
χ6222-2-22i−2i2i−2i00-22002-2−2i2i-22−2i2i00002i−2i2-2000−2i2i-2202i−2i−1−i−1−i1+i1+i−1+i−1+i1−i1−i1−i1−i−1+i−1+i1+i1+i−1−i−1−i00000000000000000000−1−i1+i−1+i1−i1−i−1+i1+i−1−i00000000
χ6322-2-22i−2i2i−2i00-22002-2−2i2i-22−2i2i00002i−2i-220002i−2i2-20−2i2i1+i1+i−1−i−1−i1−i1−i−1+i−1+i−1+i−1+i1−i1−i−1−i−1−i1+i1+i00000000000000000000−1−i1+i−1+i1−i1−i−1+i1+i−1−i00000000
χ6422-2-22i−2i2i−2i00-22002-2−2i2i-22−2i2i00002i−2i-220002i−2i2-20−2i2i−1−i−1−i1+i1+i−1+i−1+i1−i1−i1−i1−i−1+i−1+i1+i1+i−1−i−1−i000000000000000000001+i−1−i1−i−1+i−1+i1−i−1−i1+i00000000
χ6522-2-2−2i2i−2i2i002-2002-2−2i2i2-2−2i2i0000−2i2i2-2000−2i2i2-20−2i2i1−i1−i−1+i−1+i1+i1+i−1−i−1−i1+i1+i−1−i−1−i1−i1−i−1+i−1+i000000000000000000001−i−1+i1+i−1−i1+i−1−i1−i−1+i00000000
χ6622-2-2−2i2i−2i2i002-2002-2−2i2i2-2−2i2i0000−2i2i2-2000−2i2i2-20−2i2i−1+i−1+i1−i1−i−1−i−1−i1+i1+i−1−i−1−i1+i1+i−1+i−1+i1−i1−i00000000000000000000−1+i1−i−1−i1+i−1−i1+i−1+i1−i00000000
χ6722-2-2−2i2i−2i2i002-2002-2−2i2i2-2−2i2i0000−2i2i-220002i−2i-2202i−2i1−i1−i−1+i−1+i1+i1+i−1−i−1−i1+i1+i−1−i−1−i1−i1−i−1+i−1+i00000000000000000000−1+i1−i−1−i1+i−1−i1+i−1+i1−i00000000
χ6822-2-2−2i2i−2i2i002-2002-2−2i2i2-2−2i2i0000−2i2i-220002i−2i-2202i−2i−1+i−1+i1−i1−i−1−i−1−i1+i1+i−1−i−1−i1+i1+i−1+i−1+i1−i1−i000000000000000000001−i−1+i1+i−1−i1+i−1−i1−i−1+i00000000
χ6922-2-2−2i2i−2i2i00-22002-22i−2i-222i−2i0000−2i2i2-20002i−2i-220−2i2i1−i1−i−1+i−1+i1+i1+i−1−i−1−i−1−i−1−i1+i1+i−1+i−1+i1−i1−i000000000000000000001−i−1+i1+i−1−i−1−i1+i−1+i1−i00000000
χ7022-2-2−2i2i−2i2i00-22002-22i−2i-222i−2i0000−2i2i2-20002i−2i-220−2i2i−1+i−1+i1−i1−i−1−i−1−i1+i1+i1+i1+i−1−i−1−i1−i1−i−1+i−1+i00000000000000000000−1+i1−i−1−i1+i1+i−1−i1−i−1+i00000000
χ7122-2-2−2i2i−2i2i00-22002-22i−2i-222i−2i0000−2i2i-22000−2i2i2-202i−2i1−i1−i−1+i−1+i1+i1+i−1−i−1−i−1−i−1−i1+i1+i−1+i−1+i1−i1−i00000000000000000000−1+i1−i−1−i1+i1+i−1−i1−i−1+i00000000
χ7222-2-2−2i2i−2i2i00-22002-22i−2i-222i−2i0000−2i2i-22000−2i2i2-202i−2i−1+i−1+i1−i1−i−1−i−1−i1+i1+i1+i1+i−1−i−1−i1−i1−i−1+i−1+i000000000000000000001−i−1+i1+i−1−i−1−i1+i−1+i1−i00000000
χ7344-4-44i−4i4i−4i004-400-44−4i4i-444i−4i0000−4i4i0000000000000000000000000000000000000000000000000000000000000000
χ7444-4-44i−4i4i−4i00-4400-444i−4i4-4−4i4i0000−4i4i0000000000000000000000000000000000000000000000000000000000000000
χ7544-4-4−4i4i−4i4i004-400-444i−4i-44−4i4i00004i−4i0000000000000000000000000000000000000000000000000000000000000000
χ7644-4-4−4i4i−4i4i00-4400-44−4i4i4-44i−4i00004i−4i0000000000000000000000000000000000000000000000000000000000000000
χ774-44-44i−4i−4i4i00004-400000000004i−4i00000000000000000000002+2i−2−2i2+2i−2−2i2−2i−2+2i2−2i−2+2i000000000000000000000000000000000000
χ784-44-44i−4i−4i4i00004-400000000004i−4i0000000000000000000000−2−2i2+2i−2−2i2+2i−2+2i2−2i−2+2i2−2i000000000000000000000000000000000000
χ794-44-44i−4i−4i4i0000-440000000000−4i4i000000000000002−2i−2+2i2−2i−2+2i2+2i−2−2i2+2i−2−2i00000000000000000000000000000000000000000000
χ804-44-44i−4i−4i4i0000-440000000000−4i4i00000000000000−2+2i2−2i−2+2i2−2i−2−2i2+2i−2−2i2+2i00000000000000000000000000000000000000000000
χ814-44-4−4i4i4i−4i00004-40000000000−4i4i00000000000000000000002−2i−2+2i2−2i−2+2i2+2i−2−2i2+2i−2−2i000000000000000000000000000000000000
χ824-44-4−4i4i4i−4i00004-40000000000−4i4i0000000000000000000000−2+2i2−2i−2+2i2−2i−2−2i2+2i−2−2i2+2i000000000000000000000000000000000000
χ834-44-4−4i4i4i−4i0000-4400000000004i−4i000000000000002+2i−2−2i2+2i−2−2i2−2i−2+2i2−2i−2+2i00000000000000000000000000000000000000000000
χ844-44-4−4i4i4i−4i0000-4400000000004i−4i00000000000000−2−2i2+2i−2−2i2+2i−2+2i2−2i−2+2i2−2i00000000000000000000000000000000000000000000
χ854-4-4444-4-44-40000000000004-400000000000000002i−2i−2i2i−2i2i2i−2i2i−2i−2i2i−2i2i2i−2i000000000000000000000000000000000000
χ864-4-4444-4-44-40000000000004-40000000000000000−2i2i2i−2i2i−2i−2i2i−2i2i2i−2i2i−2i−2i2i000000000000000000000000000000000000
χ874-4-4444-4-4-44000000000000-4400000000000000002i−2i−2i2i−2i2i2i−2i−2i2i2i−2i2i−2i−2i2i000000000000000000000000000000000000
χ884-4-4444-4-4-44000000000000-440000000000000000−2i2i2i−2i2i−2i−2i2i2i−2i−2i2i−2i2i2i−2i000000000000000000000000000000000000
χ894-4-44-4-4444-4000000000000-4400000000000000002-2-222-2-222-2-222-2-22000000000000000000000000000000000000
χ904-4-44-4-4444-4000000000000-440000000000000000-222-2-222-2-222-2-222-2000000000000000000000000000000000000
χ914-4-44-4-444-440000000000004-400000000000000002-2-222-2-22-222-2-222-2000000000000000000000000000000000000
χ924-4-44-4-444-440000000000004-40000000000000000-222-2-222-22-2-222-2-22000000000000000000000000000000000000

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