Finite Group Databasebeta

← Group #72322234

Character table — Group #72322234

Order 1024.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76
size11112222222222222244444444888816161616161616161616161616161616161616161616161616161616161616161616323232323232323232323232
order12222222224444444488888888444444444444444488888816161616161616161616161616161616244488888888
χ11111111111111111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-111-1-1
χ31111111111111111111111111111111111-1-11111-1-111-1-1-1-11111-1-1-1-11111-1-1-1-111-1-1-1-1-1-1-1-111
χ41111111111111111111111111111111111-1-11111-1-111-1-1-1-1-1-1-1-11111-1-1-1-11111-1-111-1-111-1-1-1-1
χ5111111111111111111111111111111-1-1-1-111-1-1-1-1111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1
χ6111111111111111111111111111111-1-1-1-111-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-111-1-111
χ7111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-11111-1-1-1-11111-1-1-1-1-1-111111111-1-1
χ8111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-11111-1-1-1-1111111-1-111-1-11111
χ911111111111111111111111111-1-1-1-1111111-1-1-1-1-1-1-1-111-1-11111-1-1-1-1-1-1-1-1111111-1-1-1-11111-1-1
χ1011111111111111111111111111-1-1-1-1111111-1-1-1-1-1-1-1-111-1-1-1-1-1-111111111-1-1-1-1-1-111-1-1-1-11111
χ1111111111111111111111111111-1-1-1-11111-1-1-1-1-1-111-1-1-1-11111111111-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1
χ1211111111111111111111111111-1-1-1-11111-1-1-1-1-1-111-1-1-1-111-1-1-1-1-1-1-1-111111111-1-1-1-11111-1-111
χ1311111111111111111111111111-1-1-1-1-1-1-1-1111111-1-1-1-111-1-11111-1-1-1-1-1-1-1-11111-1-11111-1-1-1-111
χ1411111111111111111111111111-1-1-1-1-1-1-1-1111111-1-1-1-111-1-1-1-1-1-111111111-1-1-1-111-1-11111-1-1-1-1
χ1511111111111111111111111111-1-1-1-1-1-1-1-1-1-1111111-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111
χ1611111111111111111111111111-1-1-1-1-1-1-1-1-1-1111111-1-1-1-111-1-1-1-1-1-1-1-1111111111111-1-1-1-111-1-1
χ17222222222222222222-2-2-2-2-2-2-2-22222000022000022-2-2-2-2-2-20000000000000000000000000000
χ18222222222222222222-2-2-2-2-2-2-2-222220000-2-20000-2-2-2-222220000000000000000000000000000
χ19222222222222222222-2-2-2-2-2-2-2-2-2-2-2-20000220000-2-222-2-2220000000000000000000000000000
χ20222222222222222222-2-2-2-2-2-2-2-2-2-2-2-20000-2-20000222222-2-20000000000000000000000000000
χ21222222-2-2-2-22222-2-2-2-2222-2-22-2-2000022-2-20000000000000022-2-20000000000002-20000000000
χ22222222-2-2-2-22222-2-2-2-2222-2-22-2-2000022-2-200000000000000-2-222000000000000-220000000000
χ23222222-2-2-2-22222-2-2-2-2222-2-22-2-20000-2-2220000000000000022-2-2000000000000-220000000000
χ24222222-2-2-2-22222-2-2-2-2222-2-22-2-20000-2-22200000000000000-2-2220000000000002-20000000000
χ252222-2-222-2-22-2-222-2-2222-22-2-22-200000000002i2i−2i−2i00000000000022-2-2000000000000002i−2i0000
χ262222-2-222-2-22-2-222-2-2222-22-2-22-200000000002i2i−2i−2i000000000000-2-22200000000000000−2i2i0000
χ272222-2-222-2-22-2-222-2-2222-22-2-22-20000000000−2i−2i2i2i00000000000022-2-200000000000000−2i2i0000
χ282222-2-222-2-22-2-222-2-2222-22-2-22-20000000000−2i−2i2i2i000000000000-2-222000000000000002i−2i0000
χ292-22-22-22-22-2-22-2222-2-22-22-2-2-22200002i−2i2i−2i0000000000000000002-22-200000000002i−2i00000000
χ302-22-22-22-22-2-22-2222-2-22-22-2-2-22200002i−2i2i−2i000000000000000000-22-220000000000−2i2i00000000
χ312-22-22-22-22-2-22-2222-2-22-22-2-2-2220000−2i2i−2i2i0000000000000000002-22-20000000000−2i2i00000000
χ322-22-22-22-22-2-22-2222-2-22-22-2-2-2220000−2i2i−2i2i000000000000000000-22-2200000000002i−2i00000000
χ332-22-22-2-22-22-22-22-2-2222-2222-2-2-200002i−2i−2i2i0000002-200002-2000000000000000000002i−2i000000
χ342-22-22-2-22-22-22-22-2-2222-2222-2-2-200002i−2i−2i2i000000-220000-2200000000000000000000−2i2i000000
χ352-22-22-2-22-22-22-22-2-2222-2222-2-2-20000−2i2i2i−2i0000002-200002-200000000000000000000−2i2i000000
χ362-22-22-2-22-22-22-22-2-2222-2222-2-2-20000−2i2i2i−2i000000-220000-22000000000000000000002i−2i000000
χ372-22-22-2-22-22-22-22-2-222-22-2-2-222200000000002-22-22-20000-220000000000000000000000002-200
χ382-22-22-2-22-22-22-22-2-222-22-2-2-222200000000002-22-2-2200002-2000000000000000000000000-2200
χ392-22-22-2-22-22-22-22-2-222-22-2-2-22220000000000-22-222-20000-22000000000000000000000000-2200
χ402-22-22-2-22-22-22-22-2-222-22-2-2-22220000000000-22-22-2200002-20000000000000000000000002-200
χ412-22-2-222-2-22-2-2222-22-22-2-2-2222-22i2i−2i−2i0000000000002i−2i000000002-2-2200002i2i−2i−2i000000000000
χ422-22-2-222-2-22-2-2222-22-22-2-2-2222-22i2i−2i−2i0000000000002i−2i00000000-222-20000−2i−2i2i2i000000000000
χ432-22-2-222-2-22-2-2222-22-22-2-2-2222-2−2i−2i2i2i000000000000−2i2i000000002-2-220000−2i−2i2i2i000000000000
χ442-22-2-222-2-22-2-2222-22-22-2-2-2222-2−2i−2i2i2i000000000000−2i2i00000000-222-200002i2i−2i−2i000000000000
χ452-22-2-222-2-22-2-2222-22-2-2222-2-2-222i2i−2i−2i000000000000−2i2i00002i−2i2i−2i000022-2-20000000000000000
χ462-22-2-222-2-22-2-2222-22-2-2222-2-2-222i2i−2i−2i000000000000−2i2i0000−2i2i−2i2i0000-2-2220000000000000000
χ472-22-2-222-2-22-2-2222-22-2-2222-2-2-22−2i−2i2i2i0000000000002i−2i00002i−2i2i−2i0000-2-2220000000000000000
χ482-22-2-222-2-22-2-2222-22-2-2222-2-2-22−2i−2i2i2i0000000000002i−2i0000−2i2i−2i2i000022-2-20000000000000000
χ492-22-2-22-222-2-2-222-22-22-222-22-22-200000000002i−2i−2i2i000000002i−2i−2i2i00000000000000000000002-2
χ502-22-2-22-222-2-2-222-22-22-222-22-22-200000000002i−2i−2i2i00000000−2i2i2i−2i0000000000000000000000-22
χ512-22-2-22-222-2-2-222-22-22-222-22-22-20000000000−2i2i2i−2i000000002i−2i−2i2i0000000000000000000000-22
χ522-22-2-22-222-2-2-222-22-22-222-22-22-20000000000−2i2i2i−2i00000000−2i2i2i−2i00000000000000000000002-2
χ534444444444-4-4-4-4-4-4-4-4000000000000000000000000004i−4i000000000000000000000000000000
χ544444444444-4-4-4-4-4-4-4-400000000000000000000000000−4i4i000000000000000000000000000000
χ55444444-4-4-4-44444-4-4-4-4-4-4-444-44400000000000000000000000000000000000000000000000000
χ56444444-4-4-4-4-4-4-4-4444400000000000000000000000000000000000000000022−2222−22000000000000
χ57444444-4-4-4-4-4-4-4-44444000000000000000000000000000000000000000000−2222−2222000000000000
χ584444-4-444-4-44-4-444-4-44-4-44-444-4400000000000000000000000000000000000000000000000000
χ594444-4-444-4-4-444-4-444-4000000000000000000000000000000000000002i2−2i22i2−2i20000000000000000
χ604444-4-444-4-4-444-4-444-400000000000000000000000000000000000000−2i22i2−2i22i20000000000000000
χ614444-4-4-4-4444-4-44-444-444-4-44-4-4400000000000000000000000000000000000000000000000000
χ624444-4-4-4-4444-4-44-444-4-4-444-444-400000000000000000000000000000000000000000000000000
χ634444-4-4-4-444-444-44-4-44000000004-44-40000000000000000000000000000000000000000000000
χ644444-4-4-4-444-444-44-4-4400000000-44-440000000000000000000000000000000000000000000000
χ654-44-44-44-44-44-44-4-4-444000000000000000000000000000000000000002i2−2i2−2i22i20000000000000000
χ664-44-44-44-44-44-44-4-4-44400000000000000000000000000000000000000−2i22i22i2−2i20000000000000000
χ674-44-44-44-44-4-44-4444-4-4-44-4444-4-400000000000000000000000000000000000000000000000000
χ684-44-44-4-44-444-44-444-4-4000000004i−4i−4i4i0000000000000000000000000000000000000000000000
χ694-44-44-4-44-444-44-444-4-400000000−4i4i4i−4i0000000000000000000000000000000000000000000000
χ704-44-4-444-4-4444-4-4-44-4400000000000000004i−4i0000000000000000000000000000000000000000
χ714-44-4-444-4-4444-4-4-44-440000000000000000−4i4i0000000000000000000000000000000000000000
χ724-44-4-44-444-444-4-44-44-40000000000000000000000000000000000000000002i2−2i2−2i22i2000000000000
χ734-44-4-44-444-444-4-44-44-4000000000000000000000000000000000000000000−2i22i22i2−2i2000000000000
χ744-44-4-44-444-4-4-444-44-444-4-44-44-4400000000000000000000000000000000000000000000000000
χ751616-16-16000000000000000000000000000000000000000000000000000000000000000000000000
χ7616-16-1616000000000000000000000000000000000000000000000000000000000000000000000000

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