Finite Group Databasebeta

← Group #109921

Character table — Group #109921

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92
size11111111111111112222222244444444444444448888888888888888888888888888888888888888888888888888
order12222222444444442222444422224444444444444444444444444444444444444444444444448888888888888888
χ111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ311111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1
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
χ51111111111111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1
χ61111111111111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-111111111
χ71111111111111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-11111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111
χ81111111111111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-11111111111111111-1-1-1-1-1-1-1-1
χ911111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-11111-1-1-1-1111111-1-11111-1-1-1-11111-1-1-1-1iiii−i−i−i−iiiii−i−i−i−iiiii−i−i−i−iiiii−i−i−i−i
χ1011111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-11111-1-1-1-1111111-1-11111-1-1-1-11111-1-1-1-1−i−i−i−iiiii−i−i−i−iiiii−i−i−i−iiiii−i−i−i−iiiii
χ1111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-11111-1-1-1-1111111-1-1-1-1-1-11111-1-1-1-11111iiii−i−i−i−iiiii−i−i−i−i−i−i−i−iiiii−i−i−i−iiiii
χ1211111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-11111-1-1-1-1111111-1-1-1-1-1-11111-1-1-1-11111−i−i−i−iiiii−i−i−i−iiiiiiiii−i−i−i−iiiii−i−i−i−i
χ1311111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1111111-1-1-1-1-1-1-1-11111iiii−i−i−i−i−i−i−i−iiiiiiiii−i−i−i−i−i−i−i−iiiii
χ1411111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1111111-1-1-1-1-1-1-1-11111−i−i−i−iiiiiiiii−i−i−i−i−i−i−i−iiiiiiiii−i−i−i−i
χ1511111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-111-1-1-1-111111111-1-1-1-1iiii−i−i−i−i−i−i−i−iiiii−i−i−i−iiiiiiiii−i−i−i−i
χ1611111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-111-1-1-1-111111111-1-1-1-1−i−i−i−iiiiiiiii−i−i−i−iiiii−i−i−i−i−i−i−i−iiiii
χ17111-1-11-1-11111-1-1-1-1-1-11111-1-11-11-1ii−i−iii−i−i11-1-1i−ii−iii−i−iii−i−i11-1-111-1-111-1-111-1-1ii−i−iii−i−iii−i−iii−i−i11-1-111-1-1
χ18111-1-11-1-11111-1-1-1-1-1-11111-1-11-11-1ii−i−iii−i−i11-1-1i−ii−iii−i−iii−i−i11-1-111-1-1-1-111-1-111−i−iii−i−iii−i−iii−i−iii-1-111-1-111
χ19111-1-11-1-11111-1-1-1-1-1-11111-1-11-11-1ii−i−iii−i−i11-1-1i−ii−i−i−iii−i−iii-1-111-1-11111-1-111-1-1ii−i−iii−i−i−i−iii−i−iii-1-111-1-111
χ20111-1-11-1-11111-1-1-1-1-1-11111-1-11-11-1ii−i−iii−i−i11-1-1i−ii−i−i−iii−i−iii-1-111-1-111-1-111-1-111−i−iii−i−iiiii−i−iii−i−i11-1-111-1-1
χ21111-1-11-1-11111-1-1-1-1-1-11111-1-11-11-1−i−iii−i−iii11-1-1−ii−iiii−i−iii−i−i-1-111-1-11111-1-111-1-1−i−iii−i−iiiii−i−iii−i−i-1-111-1-111
χ22111-1-11-1-11111-1-1-1-1-1-11111-1-11-11-1−i−iii−i−iii11-1-1−ii−iiii−i−iii−i−i-1-111-1-111-1-111-1-111ii−i−iii−i−i−i−iii−i−iii11-1-111-1-1
χ23111-1-11-1-11111-1-1-1-1-1-11111-1-11-11-1−i−iii−i−iii11-1-1−ii−ii−i−iii−i−iii11-1-111-1-111-1-111-1-1−i−iii−i−iii−i−iii−i−iii11-1-111-1-1
χ24111-1-11-1-11111-1-1-1-1-1-11111-1-11-11-1−i−iii−i−iii11-1-1−ii−ii−i−iii−i−iii11-1-111-1-1-1-111-1-111ii−i−iii−i−iii−i−iii−i−i-1-111-1-111
χ25111-1-11-1-1-1-1-1-11111-1-111-1-111-11-11ii−i−i−i−iii11-1-1i−i−iiii−i−i−i−iii11-1-1-1-111ii−i−i−i−iii-1-11111-1-1-1-11111-1-1ii−i−i−i−iii
χ26111-1-11-1-1-1-1-1-11111-1-111-1-111-11-11ii−i−i−i−iii11-1-1i−i−iiii−i−i−i−iii11-1-1-1-111−i−iiiii−i−i11-1-1-1-11111-1-1-1-111−i−iiiii−i−i
χ27111-1-11-1-1-1-1-1-11111-1-111-1-111-11-11ii−i−i−i−iii11-1-1i−i−ii−i−iiiii−i−i-1-11111-1-1ii−i−i−i−iii-1-11111-1-111-1-1-1-111−i−iiiii−i−i
χ28111-1-11-1-1-1-1-1-11111-1-111-1-111-11-11ii−i−i−i−iii11-1-1i−i−ii−i−iiiii−i−i-1-11111-1-1−i−iiiii−i−i11-1-1-1-111-1-11111-1-1ii−i−i−i−iii
χ29111-1-11-1-1-1-1-1-11111-1-111-1-111-11-11−i−iiiii−i−i11-1-1−iii−iii−i−i−i−iii-1-11111-1-1ii−i−i−i−iii11-1-1-1-111-1-11111-1-1−i−iiiii−i−i
χ30111-1-11-1-1-1-1-1-11111-1-111-1-111-11-11−i−iiiii−i−i11-1-1−iii−iii−i−i−i−iii-1-11111-1-1−i−iiiii−i−i-1-11111-1-111-1-1-1-111ii−i−i−i−iii
χ31111-1-11-1-1-1-1-1-11111-1-111-1-111-11-11−i−iiiii−i−i11-1-1−iii−i−i−iiiii−i−i11-1-1-1-111ii−i−i−i−iii11-1-1-1-11111-1-1-1-111ii−i−i−i−iii
χ32111-1-11-1-1-1-1-1-11111-1-111-1-111-11-11−i−iiiii−i−i11-1-1−iii−i−i−iiiii−i−i11-1-1-1-111−i−iiiii−i−i-1-11111-1-1-1-11111-1-1−i−iiiii−i−i
χ33222222222222222222222222-2-2-2-222222222-2-2-2-2-2-2-2-2000000000000000000000000000000000000000000000000
χ34222222222222222222222222-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-22222000000000000000000000000000000000000000000000000
χ352222222222222222-2-2-2-2-2-2-2-22-2-22000000002-22-2000000000000000000000000000000000000000000002-22-22-22-2
χ362222222222222222-2-2-2-2-2-2-2-22-2-22000000002-22-200000000000000000000000000000000000000000000-22-22-22-22
χ372222222222222222-2-2-2-2-2-2-2-2-222-200000000-22-220000000000000000000000000000000000002-22-22-22-200000000
χ382222222222222222-2-2-2-2-2-2-2-2-222-200000000-22-22000000000000000000000000000000000000-22-22-22-2200000000
χ3922222222-2-2-2-2-2-2-2-22222-2-2-2-222222222-2-2-2-2-2-2-2-2-2-222000000000000000000000000000000000000000000000000
χ4022222222-2-2-2-2-2-2-2-22222-2-2-2-22222-2-2-2-22222-2-2-2-222-2-2000000000000000000000000000000000000000000000000
χ4122222222-2-2-2-2-2-2-2-2-2-2-2-222222-2-2200000000-22-220000000000000000000000000000000000002i−2i2i−2i−2i2i−2i2i00000000
χ4222222222-2-2-2-2-2-2-2-2-2-2-2-222222-2-2200000000-22-22000000000000000000000000000000000000−2i2i−2i2i2i−2i2i−2i00000000
χ4322222222-2-2-2-2-2-2-2-2-2-2-2-22222-222-2000000002-22-2000000000000000000000000000000000000000000002i−2i2i−2i−2i2i−2i2i
χ4422222222-2-2-2-2-2-2-2-2-2-2-2-22222-222-2000000002-22-200000000000000000000000000000000000000000000−2i2i−2i2i2i−2i2i−2i
χ45222-2-22-2-22222-2-2-2-222-2-2-2-22222-2-2000000002-2-22000000000000000000000000000000000000000000002-2-222-2-22
χ46222-2-22-2-22222-2-2-2-222-2-2-2-22222-2-2000000002-2-2200000000000000000000000000000000000000000000-222-2-222-2
χ47222-2-22-2-22222-2-2-2-222-2-2-2-222-2-22200000000-222-20000000000000000000000000000000000002i−2i−2i2i2i−2i−2i2i00000000
χ48222-2-22-2-22222-2-2-2-222-2-2-2-222-2-22200000000-222-2000000000000000000000000000000000000−2i2i2i−2i−2i2i2i−2i00000000
χ49222-2-22-2-22222-2-2-2-2-2-22222-2-2-22-222i2i−2i−2i2i2i−2i−2i-2-222−2i2i−2i2i000000000000000000000000000000000000000000000000
χ50222-2-22-2-22222-2-2-2-2-2-22222-2-2-22-22−2i−2i2i2i−2i−2i2i2i-2-2222i−2i2i−2i000000000000000000000000000000000000000000000000
χ51222-2-22-2-2-2-2-2-2222222-2-222-2-222-2-200000000-222-20000000000000000000000000000000000002-2-22-222-200000000
χ52222-2-22-2-2-2-2-2-2222222-2-222-2-222-2-200000000-222-2000000000000000000000000000000000000-222-22-2-2200000000
χ53222-2-22-2-2-2-2-2-2222222-2-222-2-2-2-222000000002-2-22000000000000000000000000000000000000000000002i−2i−2i2i−2i2i2i−2i
χ54222-2-22-2-2-2-2-2-2222222-2-222-2-2-2-222000000002-2-2200000000000000000000000000000000000000000000−2i2i2i−2i2i−2i−2i2i
χ55222-2-22-2-2-2-2-2-22222-2-222-2-2222-22-22i2i−2i−2i−2i−2i2i2i-2-222−2i2i2i−2i000000000000000000000000000000000000000000000000
χ56222-2-22-2-2-2-2-2-22222-2-222-2-2222-22-2−2i−2i2i2i2i2i−2i−2i-2-2222i−2i−2i2i000000000000000000000000000000000000000000000000
χ5722-22-2-22-22i2i−2i−2i2i2i−2i−2i2-22-22i−2i2i−2i00002-22-22i−2i2i−2i0000000000000000000000001+i−1−i1+i−1−i1−i−1+i1−i−1+i1+i−1−i1+i−1−i1−i−1+i1−i−1+i0000000000000000
χ5822-22-2-22-22i2i−2i−2i2i2i−2i−2i2-22-22i−2i2i−2i00002-22-22i−2i2i−2i000000000000000000000000−1−i1+i−1−i1+i−1+i1−i−1+i1−i−1−i1+i−1−i1+i−1+i1−i−1+i1−i0000000000000000
χ5922-22-2-22-22i2i−2i−2i2i2i−2i−2i2-22-22i−2i2i−2i0000-22-22−2i2i−2i2i0000000000000000000000001+i−1−i1+i−1−i1−i−1+i1−i−1+i−1−i1+i−1−i1+i−1+i1−i−1+i1−i0000000000000000
χ6022-22-2-22-22i2i−2i−2i2i2i−2i−2i2-22-22i−2i2i−2i0000-22-22−2i2i−2i2i000000000000000000000000−1−i1+i−1−i1+i−1+i1−i−1+i1−i1+i−1−i1+i−1−i1−i−1+i1−i−1+i0000000000000000
χ6122-22-2-22-2−2i−2i2i2i−2i−2i2i2i2-22-2−2i2i−2i2i00002-22-2−2i2i−2i2i0000000000000000000000001−i−1+i1−i−1+i1+i−1−i1+i−1−i1−i−1+i1−i−1+i1+i−1−i1+i−1−i0000000000000000
χ6222-22-2-22-2−2i−2i2i2i−2i−2i2i2i2-22-2−2i2i−2i2i00002-22-2−2i2i−2i2i000000000000000000000000−1+i1−i−1+i1−i−1−i1+i−1−i1+i−1+i1−i−1+i1−i−1−i1+i−1−i1+i0000000000000000
χ6322-22-2-22-2−2i−2i2i2i−2i−2i2i2i2-22-2−2i2i−2i2i0000-22-222i−2i2i−2i0000000000000000000000001−i−1+i1−i−1+i1+i−1−i1+i−1−i−1+i1−i−1+i1−i−1−i1+i−1−i1+i0000000000000000
χ6422-22-2-22-2−2i−2i2i2i−2i−2i2i2i2-22-2−2i2i−2i2i0000-22-222i−2i2i−2i000000000000000000000000−1+i1−i−1+i1−i−1−i1+i−1−i1+i1−i−1+i1−i−1+i1+i−1−i1+i−1−i0000000000000000
χ6522-2-22-2-222i2i−2i−2i−2i−2i2i2i-222-22i−2i−2i2i00002i−2i−2i2i-222-20000000000000000000000001+i−1−i−1−i1+i1−i−1+i−1+i1−i−1+i1−i1−i−1+i1+i−1−i−1−i1+i0000000000000000
χ6622-2-22-2-222i2i−2i−2i−2i−2i2i2i-222-22i−2i−2i2i00002i−2i−2i2i-222-2000000000000000000000000−1−i1+i1+i−1−i−1+i1−i1−i−1+i1−i−1+i−1+i1−i−1−i1+i1+i−1−i0000000000000000
χ6722-2-22-2-222i2i−2i−2i−2i−2i2i2i-222-22i−2i−2i2i0000−2i2i2i−2i2-2-220000000000000000000000001+i−1−i−1−i1+i1−i−1+i−1+i1−i1−i−1+i−1+i1−i−1−i1+i1+i−1−i0000000000000000
χ6822-2-22-2-222i2i−2i−2i−2i−2i2i2i-222-22i−2i−2i2i0000−2i2i2i−2i2-2-22000000000000000000000000−1−i1+i1+i−1−i−1+i1−i1−i−1+i−1+i1−i1−i−1+i1+i−1−i−1−i1+i0000000000000000
χ6922-2-22-2-22−2i−2i2i2i2i2i−2i−2i-222-2−2i2i2i−2i00002i−2i−2i2i2-2-220000000000000000000000001−i−1+i−1+i1−i1+i−1−i−1−i1+i1+i−1−i−1−i1+i−1+i1−i1−i−1+i0000000000000000
χ7022-2-22-2-22−2i−2i2i2i2i2i−2i−2i-222-2−2i2i2i−2i00002i−2i−2i2i2-2-22000000000000000000000000−1+i1−i1−i−1+i−1−i1+i1+i−1−i−1−i1+i1+i−1−i1−i−1+i−1+i1−i0000000000000000
χ7122-2-22-2-22−2i−2i2i2i2i2i−2i−2i-222-2−2i2i2i−2i0000−2i2i2i−2i-222-20000000000000000000000001−i−1+i−1+i1−i1+i−1−i−1−i1+i−1−i1+i1+i−1−i1−i−1+i−1+i1−i0000000000000000
χ7222-2-22-2-22−2i−2i2i2i2i2i−2i−2i-222-2−2i2i2i−2i0000−2i2i2i−2i-222-2000000000000000000000000−1+i1−i1−i−1+i−1−i1+i1+i−1−i1+i−1−i−1−i1+i−1+i1−i1−i−1+i0000000000000000
χ7344-44-4-44-44i4i−4i−4i4i4i−4i−4i-44-44−4i4i−4i4i00000000000000000000000000000000000000000000000000000000000000000000
χ7444-44-4-44-4−4i−4i4i4i−4i−4i4i4i-44-444i−4i4i−4i00000000000000000000000000000000000000000000000000000000000000000000
χ7544-4-44-4-444i4i−4i−4i−4i−4i4i4i4-4-44−4i4i4i−4i00000000000000000000000000000000000000000000000000000000000000000000
χ7644-4-44-4-44−4i−4i4i4i4i4i−4i−4i4-4-444i−4i−4i4i00000000000000000000000000000000000000000000000000000000000000000000
χ774-444-4-4-444i−4i4i−4i4i−4i4i−4i0000000000000000000000000000000000002i−2i2i−2i2-22-200000000000000000000000000000000
χ784-444-4-4-444i−4i4i−4i4i−4i4i−4i000000000000000000000000000000000000−2i2i−2i2i-22-2200000000000000000000000000000000
χ794-444-4-4-44−4i4i−4i4i−4i4i−4i4i0000000000000000000000000000000000002i−2i2i−2i-22-2200000000000000000000000000000000
χ804-444-4-4-44−4i4i−4i4i−4i4i−4i4i000000000000000000000000000000000000−2i2i−2i2i2-22-200000000000000000000000000000000
χ814-44-44-44-44i−4i4i−4i−4i4i−4i4i0000000000000000000000000000000000002i−2i−2i2i2-2-2200000000000000000000000000000000
χ824-44-44-44-44i−4i4i−4i−4i4i−4i4i000000000000000000000000000000000000−2i2i2i−2i-222-200000000000000000000000000000000
χ834-44-44-44-4−4i4i−4i4i4i−4i4i−4i0000000000000000000000000000000000002i−2i−2i2i-222-200000000000000000000000000000000
χ844-44-44-44-4−4i4i−4i4i4i−4i4i−4i000000000000000000000000000000000000−2i2i2i−2i2-2-2200000000000000000000000000000000
χ854-4-4444-4-44-4-444-4-4400000000000000000000000000002i−2i2i−2i2i−2i2i−2i0000000000000000000000000000000000000000
χ864-4-4444-4-44-4-444-4-440000000000000000000000000000−2i2i−2i2i−2i2i−2i2i0000000000000000000000000000000000000000
χ874-4-4444-4-4-444-4-444-400000000000000000000000000002i−2i2i−2i−2i2i−2i2i0000000000000000000000000000000000000000
χ884-4-4444-4-4-444-4-444-40000000000000000000000000000−2i2i−2i2i2i−2i2i−2i0000000000000000000000000000000000000000
χ894-4-4-4-44444-4-44-444-400000000000000000000000000002-2-222-2-220000000000000000000000000000000000000000
χ904-4-4-4-44444-4-44-444-40000000000000000000000000000-222-2-222-20000000000000000000000000000000000000000
χ914-4-4-4-4444-444-44-4-4400000000000000000000000000002-2-22-222-20000000000000000000000000000000000000000
χ924-4-4-4-4444-444-44-4-440000000000000000000000000000-222-22-2-220000000000000000000000000000000000000000

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