Finite Group Databasebeta

← Group #6818773

Character table — Group #6818773

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86
size11111111222222222222222244444444444444444444444444444488888888888888888888161616161616161616161616
order12222222444444448888888822224444444444444488888888888824444444444488888888244444444444
χ111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111111111111111111-1-111-1-11-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1
χ3111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1111-1111111111-1-111-1-1-1-1-1-111-1-111-1-1
χ4111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-11-1-1-11-1-1-1-111-1-111-1-11111-1-111-1-111
χ511111111111111111111111111-1-1-1-11111-1-1-1-11111111111111111-111-1-111-11111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1
χ611111111111111111111111111-1-1-1-11111-1-1-1-11111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111
χ711111111111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-11111111-1111-11111-1-111-1-111-1-1-1-1-1-111-1-111
χ811111111111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-111111-1-1-11-1-1-1-1-1-1-1-1-111-1-111111111-1-111-1-1
χ91111111111111111-1-1-1-1-1-1-1-1111111111111111111-1-1-1-1-1-1-1-1-1-1-1-111111-1-1111-1-1-1-1-1-1-1-1-1-11-1-111-11-11-11-1
χ101111111111111111-1-1-1-1-1-1-1-1111111111111111111-1-1-1-1-1-1-1-1-1-1-1-11-1-111111-1-111-1-1-1-1-1-1-1-1-111-1-11-11-11-11
χ111111111111111111-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1111-1-1-1111-1-1-1-111-1-111-111-11-1-111-1-11
χ121111111111111111-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-11-1111-1-111-1-111-1-1111-1-11-111-1-111-1
χ131111111111111111-1-1-1-1-1-1-1-111-1-1-1-11111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-1-111-1-1111111111-1-11-11-11-11-11
χ141111111111111111-1-1-1-1-1-1-1-111-1-1-1-11111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-11111111111-111-11-11-11-11-1
χ151111111111111111-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-11111-1-1-1-111111111-1-1-1-1111-11-1-1-111-1-111-1-111-1-1-111-1-111-1-111-1
χ161111111111111111-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-11111-1-1-1-111111111-1-1-1-11-1-1-1111-1-1-11111-1-111-1-11-1-111-1-111-1-11
χ17111111111-1-1-1-111111111111-1-111-1-111-1-111-1-111-1-11111-1-1-1-1-1-1-1-1-111-11111-1-1-1-1-1-11111-1-1-11-11-11-111-11-1
χ18111111111-1-1-1-111111111111-1-111-1-111-1-111-1-111-1-11111-1-1-1-1-1-1-1-1-1-1-1-11-1-111111-1-11111-1-11-11-11-11-1-11-11
χ19111111111-1-1-1-111111111111-1-111-1-1-1-111-1-111-1-111-1-1-1-11111-1-1-1-1111-1-1111-1-1-1-1-1-1-1-111111-11-1-111-11-1-11
χ20111111111-1-1-1-111111111111-1-111-1-1-1-111-1-111-1-111-1-1-1-11111-1-1-1-11-1-1-1-1-1-111111-1-1-1-11111-11-111-1-11-111-1
χ21111111111-1-1-1-111111111111-1-1-1-11111-1-1-1-11111-1-11111-1-1-1-1-1-1-1-11111-111-1-1-1-1-111-1-1-1-111-11-111-11-1-11-11
χ22111111111-1-1-1-111111111111-1-1-1-11111-1-1-1-11111-1-11111-1-1-1-1-1-1-1-11-1-11-1-1-1-1111111-1-1-1-1111-11-1-11-111-11-1
χ23111111111-1-1-1-111111111111-1-1-1-111-1-11111-1-1-1-111-1-1-1-11111-1-1-1-1-1111111-1-1-1-1-11111-1-1-1-11-11-11-1-11-111-1
χ24111111111-1-1-1-111111111111-1-1-1-111-1-11111-1-1-1-111-1-1-1-11111-1-1-1-1-1-1-111-1-1-111111111-1-1-1-1-11-11-111-11-1-11
χ25111111111-1-1-1-1111-1-1-1-1-1-1-1-1-1-111-1-111-1-111-1-111-1-1-1-1-1-111111111-111-11-1-11-1-11111-1-1-1-111-1-111-1-1-1-11111
χ26111111111-1-1-1-1111-1-1-1-1-1-1-1-1-1-111-1-111-1-111-1-111-1-1-1-1-1-111111111-1-1-1-1111111-1-111-1-1-1-11111-1-11111-1-1-1-1
χ27111111111-1-1-1-1111-1-1-1-1-1-1-1-1-1-111-1-1-1-111-1-111-1-1111111-1-1-1-11111111-1-1-1-11-1-1111111-1-1-1-111-1-1-1-11111-1-1
χ28111111111-1-1-1-1111-1-1-1-1-1-1-1-1-1-111-1-1-1-111-1-111-1-1111111-1-1-1-111111-1-1-1-111111-1-11111-1-1-1-1-1-11111-1-1-1-111
χ29111111111-1-1-1-1111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1-1-1-1-1111111111111-1-1-1-1-1-111-1-11111-1-1-1-1111111-1-1-1-1
χ30111111111-1-1-1-1111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1-1-1-1-1111111111-1-11-111-111-1-1-1-11111-1-111-1-1-1-1-1-11111
χ31111111111-1-1-1-1111-1-1-1-1-1-1-1-1-1-1-1-111-1-11111-1-1-1-1111111-1-1-1-11111-11111-1-1-1-1-111-1-1-1-1111111-1-111-1-1-1-111
χ32111111111-1-1-1-1111-1-1-1-1-1-1-1-1-1-1-1-111-1-11111-1-1-1-1111111-1-1-1-11111-1-1-11111-111-1-1-1-1-1-11111-1-111-1-11111-1-1
χ3322222222-22222-2-2-200000000-2-2222222-2-22222-2-222000000000000-200-2-200-2000000000000000000000000
χ3422222222-22222-2-2-200000000-2-22222-2-222-2-2-2-222-2-2000000000000200-2200-2000000000000000000000000
χ3522222222-22222-2-2-200000000-2-2-2-2-2-222-2-2-2-2-2-2-2-22200000000000020022002000000000000000000000000
χ3622222222-22222-2-2-200000000-2-2-2-2-2-2-2-222222222-2-2000000000000-2002-2002000000000000000000000000
χ3722222222-2-2-2-2-2-2-2-2000000002222-2-2222222-2-2-2-2-2-20000000000002002-200-2000000000000000000000000
χ3822222222-2-2-2-2-2-2-2-2000000002222-2-2-2-2-2-2-2-2222222000000000000-2002200-2000000000000000000000000
χ3922222222-2-2-2-2-2-2-2-20000000022-2-2222222-2-222-2-2-2-2000000000000-200-22002000000000000000000000000
χ4022222222-2-2-2-2-2-2-2-20000000022-2-222-2-2-2-222-2-22222000000000000200-2-2002000000000000000000000000
χ412-222-22-2-2-222-2-22-222222-2-2-2-22-200000000000000000000000022-2-202i−2i002i−2i02i−2i2i−2i00000000000000000000
χ422-222-22-2-2-222-2-22-222222-2-2-2-22-200000000000000000000000022-2-20−2i2i00−2i2i0−2i2i−2i2i00000000000000000000
χ432-222-22-2-2-222-2-22-22-2-2-2-222222-2000000000000000000000000-2-22202i−2i00−2i2i02i−2i−2i2i00000000000000000000
χ442-222-22-2-2-222-2-22-22-2-2-2-222222-2000000000000000000000000-2-2220−2i2i002i−2i0−2i2i2i−2i00000000000000000000
χ452-222-22-2-2-2-2-2222-222222-2-2-2-2-22000000000000000000000000-2-22202i−2i002i−2i0−2i2i−2i2i00000000000000000000
χ462-222-22-2-2-2-2-2222-222222-2-2-2-2-22000000000000000000000000-2-2220−2i2i00−2i2i02i−2i2i−2i00000000000000000000
χ472-222-22-2-2-2-2-2222-22-2-2-2-22222-2200000000000000000000000022-2-202i−2i00−2i2i0−2i2i2i−2i00000000000000000000
χ482-222-22-2-2-2-2-2222-22-2-2-2-22222-2200000000000000000000000022-2-20−2i2i002i−2i02i−2i−2i2i00000000000000000000
χ492-22-22-22-202i−2i2i−2i000i2i2−i2−i2i2i2−i2−i2002-22i−2i2-2002-22i−2i002i−2ii2i2−i2−i222−2−22−22−20000000000002−2i2−i2i2−i22−2000000000000
χ502-22-22-22-202i−2i2i−2i000i2i2−i2−i2i2i2−i2−i2002-22i−2i-2200-22−2i2i00−2i2i−i2−i2i2i2−2−2222−22−20000000000002−2−i2i2i2−i2−22000000000000
χ512-22-22-22-202i−2i2i−2i000i2i2−i2−i2i2i2−i2−i200-22−2i2i2-200-22−2i2i002i−2ii2i2−i2−i222−2−22−22−2000000000000−22−i2i2−i2i2−22000000000000
χ522-22-22-22-202i−2i2i−2i000i2i2−i2−i2i2i2−i2−i200-22−2i2i-22002-22i−2i00−2i2i−i2−i2i2i2−2−2222−22−2000000000000−22i2−i2−i2i22−2000000000000
χ532-22-22-22-202i−2i2i−2i000−i2−i2i2i2−i2−i2i2i2002-22i−2i2-2002-22i−2i002i−2i−i2−i2i2i2−2−222−22−22000000000000−22−i2i2−i2i2−22000000000000
χ542-22-22-22-202i−2i2i−2i000−i2−i2i2i2−i2−i2i2i2002-22i−2i-2200-22−2i2i00−2i2ii2i2−i2−i222−2−2−22−22000000000000−22i2−i2−i2i22−2000000000000
χ552-22-22-22-202i−2i2i−2i000−i2−i2i2i2−i2−i2i2i200-22−2i2i2-200-22−2i2i002i−2i−i2−i2i2i2−2−222−22−220000000000002−2i2−i2i2−i22−2000000000000
χ562-22-22-22-202i−2i2i−2i000−i2−i2i2i2−i2−i2i2i200-22−2i2i-22002-22i−2i00−2i2ii2i2−i2−i222−2−2−22−220000000000002−2−i2i2i2−i2−22000000000000
χ572-22-22-22-20−2i2i−2i2i000i2i2−i2−i2i2i2−i2−i2002-2−2i2i2-2002-2−2i2i00−2i2ii2i2−i2−i2−2−222−22−22000000000000−22i2−i2i2−i2−22000000000000
χ582-22-22-22-20−2i2i−2i2i000i2i2−i2−i2i2i2−i2−i2002-2−2i2i-2200-222i−2i002i−2i−i2−i2i2i222−2−2−22−22000000000000−22−i2i2i2−i22−2000000000000
χ592-22-22-22-20−2i2i−2i2i000i2i2−i2−i2i2i2−i2−i200-222i−2i2-200-222i−2i00−2i2ii2i2−i2−i2−2−222−22−220000000000002−2−i2i2−i2i22−2000000000000
χ602-22-22-22-20−2i2i−2i2i000i2i2−i2−i2i2i2−i2−i200-222i−2i-22002-2−2i2i002i−2i−i2−i2i2i222−2−2−22−220000000000002−2i2−i2−i2i2−22000000000000
χ612-22-22-22-20−2i2i−2i2i000−i2−i2i2i2−i2−i2i2i2002-2−2i2i2-2002-2−2i2i00−2i2i−i2−i2i2i222−2−22−22−20000000000002−2−i2i2−i2i22−2000000000000
χ622-22-22-22-20−2i2i−2i2i000−i2−i2i2i2−i2−i2i2i2002-2−2i2i-2200-222i−2i002i−2ii2i2−i2−i2−2−2222−22−20000000000002−2i2−i2−i2i2−22000000000000
χ632-22-22-22-20−2i2i−2i2i000−i2−i2i2i2−i2−i2i2i200-222i−2i2-200-222i−2i00−2i2i−i2−i2i2i222−2−22−22−2000000000000−22i2−i2i2−i2−22000000000000
χ642-22-22-22-20−2i2i−2i2i000−i2−i2i2i2−i2−i2i2i200-222i−2i-22002-2−2i2i002i−2ii2i2−i2−i2−2−2222−22−2000000000000−22−i2i2i2−i22−2000000000000
χ65444-4-4-4-4404i−4i−4i4i0002i22i2−2i2−2i2−2i2−2i22i22i20000000000000000000000000022−22−222200000000000000000000000000000000
χ66444-4-4-4-4404i−4i−4i4i000−2i2−2i22i22i22i22i2−2i2−2i200000000000000000000000000−222222−2200000000000000000000000000000000
χ67444-4-4-4-440−4i4i4i−4i0002i22i2−2i2−2i2−2i2−2i22i22i200000000000000000000000000−222222−2200000000000000000000000000000000
χ68444-4-4-4-440−4i4i4i−4i000−2i2−2i22i22i22i22i2−2i2−2i20000000000000000000000000022−22−222200000000000000000000000000000000
χ6944-444-4-4-40000000022−2222−2222−2222−22000000004-400000000000022−2222−22000000000000000000000000000000000000
χ7044-444-4-4-40000000022−2222−2222−2222−2200000000-44000000000000−2222−2222000000000000000000000000000000000000
χ7144-444-4-4-400000000−2222−2222−2222−2222000000004-4000000000000−2222−2222000000000000000000000000000000000000
χ7244-444-4-4-400000000−2222−2222−2222−222200000000-4400000000000022−2222−22000000000000000000000000000000000000
χ7344-4-4-444-440000-4-44000000000000000000000000004i−4i4i−4i0000000000000000000000000000000000000000
χ7444-4-4-444-440000-4-4400000000000000000000000000−4i4i−4i4i0000000000000000000000000000000000000000
χ7544-4-4-444-4-4000044-44i−4i−4i4i−4i4i4i−4i00000000000000000000000000000000000000000000000000000000000000
χ7644-4-4-444-4-4000044-4−4i4i4i−4i4i−4i−4i4i00000000000000000000000000000000000000000000000000000000000000
χ774-444-44-4-4444-4-4-44-400000000-44000000000000000000000000000000000000000000000000000000000000
χ784-444-44-4-44-4-444-44-4000000004-4000000000000000000000000000000000000000000000000000000000000
χ794-4-44-4-4440000000022−2222−22−2222−2222000000000000004-40022−22−22220000000000000000000000000000000000000000
χ804-4-44-4-4440000000022−2222−22−2222−222200000000000000-4400−222222−220000000000000000000000000000000000000000
χ814-4-44-4-44400000000−2222−222222−2222−22000000000000004-400−222222−220000000000000000000000000000000000000000
χ824-4-44-4-44400000000−2222−222222−2222−2200000000000000-440022−22−22220000000000000000000000000000000000000000
χ834-4-4-444-44400004-4-44i−4i−4i4i4i−4i−4i4i00000000000000000000000000000000000000000000000000000000000000
χ844-4-4-444-44400004-4-4−4i4i4i−4i−4i4i4i−4i00000000000000000000000000000000000000000000000000000000000000
χ854-4-4-444-44-40000-4440000000000000000000000000000004-4-44000000000000000000000000000000000000
χ864-4-4-444-44-40000-444000000000000000000000000000000-444-4000000000000000000000000000000000000

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