Finite Group Databasebeta

← Group #72320716

Character table — Group #72320716

Order 1024.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76
size11112222222222222244444444888816161616161616161616161616161616161616161616161616161616161616161616323232323232323232323232
order12222222224444444488888888444422444444444488888816161616161616161616161616161616224444448888
χ11111111111111111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1
χ31111111111111111111111111111111111-1-11111-1-1-1-111-1-111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1
χ41111111111111111111111111111111111-1-11111-1-1-1-111-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-11111
χ5111111111111111111111111111111-1-1-1-111-1-1-1-1111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1
χ6111111111111111111111111111111-1-1-1-111-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111
χ7111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-111111111-1-1-1-1-1-1-1-11111-1-1-1-11111
χ8111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-11111111111111111-1-1-1-1
χ911111111111111111111111111-1-1-1-1111111-1-1-1-1-1-111-1-1-1-11111-1-1-1-11111-1-1-1-1-1-11111-1-111-1-1
χ1011111111111111111111111111-1-1-1-1111111-1-1-1-1-1-111-1-1-1-1-1-1-1-11111-1-1-1-11111-1-111-1-111-1-111
χ1111111111111111111111111111-1-1-1-11111-1-1-1-1-1-111-1-1-1-1111111-1-1-1-1-1-1-1-1111111-1-111-1-1-1-111
χ1211111111111111111111111111-1-1-1-11111-1-1-1-1-1-111-1-1-1-111-1-1-1-111111111-1-1-1-111-1-1-1-11111-1-1
χ1311111111111111111111111111-1-1-1-1-1-1-1-1111111-1-111-1-1-1-11111-1-1-1-11111-1-1-1-111-1-1-1-111-1-111
χ1411111111111111111111111111-1-1-1-1-1-1-1-1111111-1-111-1-1-1-1-1-1-1-11111-1-1-1-1111111-1-111-1-111-1-1
χ1511111111111111111111111111-1-1-1-1-1-1-1-1-1-1111111-1-1-1-1111111-1-1-1-1-1-1-1-11111-1-111-1-11111-1-1
χ1611111111111111111111111111-1-1-1-1-1-1-1-1-1-1111111-1-1-1-111-1-1-1-111111111-1-1-1-1-1-11111-1-1-1-111
χ17222222222222222222-2-2-2-2-2-2-2-22222000022000022-2-2-2-2-2-20000000000000000000000000000
χ18222222222222222222-2-2-2-2-2-2-2-222220000-2-20000-2-222-2-2220000000000000000000000000000
χ19222222222222222222-2-2-2-2-2-2-2-2-2-2-2-20000220000-2-2-2-222220000000000000000000000000000
χ20222222222222222222-2-2-2-2-2-2-2-2-2-2-2-20000-2-20000222222-2-20000000000000000000000000000
χ21222222-2-2-2-2222-22-2-2-22-2-2-2222-200000000002i2i−2i−2i0000000000002i2i−2i−2i0000000000002-2000000
χ22222222-2-2-2-2222-22-2-2-22-2-2-2222-200000000002i2i−2i−2i000000000000−2i−2i2i2i000000000000-22000000
χ23222222-2-2-2-2222-22-2-2-22-2-2-2222-20000000000−2i−2i2i2i0000000000002i2i−2i−2i000000000000-22000000
χ24222222-2-2-2-2222-22-2-2-22-2-2-2222-20000000000−2i−2i2i2i000000000000−2i−2i2i2i0000000000002-2000000
χ252222-2-22-22-22-2-222-22-2222-22-2-2-200000000002i−2i2i−2i000000000000000022-2-2000000000000002i−2i
χ262222-2-22-22-22-2-222-22-2222-22-2-2-200000000002i−2i2i−2i0000000000000000-2-22200000000000000−2i2i
χ272222-2-22-22-22-2-222-22-2222-22-2-2-20000000000−2i2i−2i2i000000000000000022-2-200000000000000−2i2i
χ282222-2-22-22-22-2-222-22-2222-22-2-2-20000000000−2i2i−2i2i0000000000000000-2-222000000000000002i−2i
χ292222-2-2-22-222-2-2-222-222-2-222-2-2200000000002-2-222-200002-20000000000000000002-200000000
χ302222-2-2-22-222-2-2-222-222-2-222-2-2200000000002-2-22-220000-22000000000000000000-2200000000
χ312222-2-2-22-222-2-2-222-222-2-222-2-220000000000-222-22-200002-2000000000000000000-2200000000
χ322222-2-2-22-222-2-2-222-222-2-222-2-220000000000-222-2-220000-220000000000000000002-200000000
χ332222-2-2-22-222-2-2-222-22-222-2-222-2000022-2-20000002-20000-2200000000000000002-20000000000
χ342222-2-2-22-222-2-2-222-22-222-2-222-2000022-2-2000000-2200002-20000000000000000-220000000000
χ352222-2-2-22-222-2-2-222-22-222-2-222-20000-2-2220000002-20000-220000000000000000-220000000000
χ362222-2-2-22-222-2-2-222-22-222-2-222-20000-2-222000000-2200002-200000000000000002-20000000000
χ3722-2-22-22-2-22-22-222-2-2222-22-22-2-200002-22-20000000000000000002i−2i2i−2i000000000000002i−2i0000
χ3822-2-22-22-2-22-22-222-2-2222-22-22-2-200002-22-2000000000000000000−2i2i−2i2i00000000000000−2i2i0000
χ3922-2-22-22-2-22-22-222-2-2222-22-22-2-20000-22-220000000000000000002i−2i2i−2i00000000000000−2i2i0000
χ4022-2-22-22-2-22-22-222-2-2222-22-22-2-20000-22-22000000000000000000−2i2i−2i2i000000000000002i−2i0000
χ4122-2-22-2-222-2-22-2-2222-22-22-2-22-222i2i−2i−2i000000000000002i−2i002i2i−2i−2i2-2-2200000000000000000000
χ4222-2-22-2-222-2-22-2-2222-22-22-2-22-222i2i−2i−2i000000000000002i−2i00−2i−2i2i2i-222-200000000000000000000
χ4322-2-22-2-222-2-22-2-2222-22-22-2-22-22−2i−2i2i2i00000000000000−2i2i002i2i−2i−2i-222-200000000000000000000
χ4422-2-22-2-222-2-22-2-2222-22-22-2-22-22−2i−2i2i2i00000000000000−2i2i00−2i−2i2i2i2-2-2200000000000000000000
χ4522-2-22-2-222-2-22-2-2222-2-22-222-22-22i2i−2i−2i00000000000000−2i2i00000000002-22-22i2i−2i−2i000000000000
χ4622-2-22-2-222-2-22-2-2222-2-22-222-22-22i2i−2i−2i00000000000000−2i2i0000000000-22-22−2i−2i2i2i000000000000
χ4722-2-22-2-222-2-22-2-2222-2-22-222-22-2−2i−2i2i2i000000000000002i−2i00000000002-22-2−2i−2i2i2i000000000000
χ4822-2-22-2-222-2-22-2-2222-2-22-222-22-2−2i−2i2i2i000000000000002i−2i0000000000-22-222i2i−2i−2i000000000000
χ4922-2-2-22-2-222-2-22-22-222-22-2-222-2200002-2-2200000000000000000000002-2-220000000000002-200
χ5022-2-2-22-2-222-2-22-22-222-22-2-222-2200002-2-220000000000000000000000-222-2000000000000-2200
χ5122-2-2-22-2-222-2-22-22-222-22-2-222-220000-222-200000000000000000000002-2-22000000000000-2200
χ5222-2-2-22-2-222-2-22-22-222-22-2-222-220000-222-20000000000000000000000-222-20000000000002-200
χ534444444444-4-4-4-4-4-4-4-4000000004-44-40000000000000000000000000000000000000000000000
χ544444444444-4-4-4-4-4-4-4-400000000-44-440000000000000000000000000000000000000000000000
χ55444444-4-4-4-4444-44-4-4-4-4444-4-4-4400000000000000000000000000000000000000000000000000
χ56444444-4-4-4-4-4-4-44-444400000000000000000000000000000022−2222−22000000000000000000000000
χ57444444-4-4-4-4-4-4-44-4444000000000000000000000000000000−2222−2222000000000000000000000000
χ584444-4-44-44-44-4-444-44-4-4-4-44-444400000000000000000000000000000000000000000000000000
χ594444-4-44-44-4-444-4-44-4400000000000000000000000000000000000000000022−2222−22000000000000
χ604444-4-44-44-4-444-4-44-44000000000000000000000000000000000000000000−2222−2222000000000000
χ614444-4-4-44-44-4444-4-44-400000000000000004-40000000000000000000000000000000000000000
χ624444-4-4-44-44-4444-4-44-40000000000000000-440000000000000000000000000000000000000000
χ6344-4-44-44-4-444-44-4-444-40000000000000000000000000000002i2−2i2−2i22i2000000000000000000000000
χ6444-4-44-44-4-444-44-4-444-4000000000000000000000000000000−2i22i22i2−2i2000000000000000000000000
χ6544-4-44-44-4-44-44-444-4-44-4-44-44-44400000000000000000000000000000000000000000000000000
χ6644-4-44-4-444-44-444-4-4-44000000004i−4i−4i4i0000000000000000000000000000000000000000000000
χ6744-4-44-4-444-44-444-4-4-4400000000−4i4i4i−4i0000000000000000000000000000000000000000000000
χ6844-4-4-4444-4-444-4-4-4-4440000000000000000000000004i−4i00000000000000000000000000000000
χ6944-4-4-4444-4-444-4-4-4-444000000000000000000000000−4i4i00000000000000000000000000000000
χ7044-4-4-4444-4-4-4-44444-4-444-4-4-4-44400000000000000000000000000000000000000000000000000
χ7144-4-4-4444-4-4-4-44444-4-4-4-44444-4-400000000000000000000000000000000000000000000000000
χ7244-4-4-44-4-44444-44-44-4-40000000000000000000000000000000000000000002i2−2i2−2i22i2000000000000
χ7344-4-4-44-4-44444-44-44-4-4000000000000000000000000000000000000000000−2i22i22i2−2i2000000000000
χ7444-4-4-44-4-444-4-44-44-4444-444-4-44-400000000000000000000000000000000000000000000000000
χ7516-1616-16000000000000000000000000000000000000000000000000000000000000000000000000
χ7616-16-1616000000000000000000000000000000000000000000000000000000000000000000000000

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