Finite Group Databasebeta

← Group #401102

Character table — Group #401102

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80
size111111112222222222222222222244444444444444444444888888888888888816161616161616161616161616161616
order12222222222244444444444444444444888888888888888822222222444444444444888888888888
χ111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ3111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1
χ4111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111
χ511111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1-1-11111-1-1-1-11111-1-1-1-1
χ611111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1-1-1-1-1-1-11111-1-1-1-11111
χ711111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-111111111-1-1-1-1-1-1-1-11111
χ811111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1-1-111111111-1-1-1-1
χ9111111111111111-1-1-1-1-1-1-1-111111-1-1-1-111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-111-1-1-1-11111-1-111-1-1
χ10111111111111111-1-1-1-1-1-1-1-111111-1-1-1-111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-11111-1-1-1-111-1-111
χ11111111111111111-1-1-1-1-1-1-1-111111-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111-1-1-1-111-1-111-1-111
χ12111111111111111-1-1-1-1-1-1-1-111111-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-11111-1-111-1-111-1-1
χ13111111111111111-1-1-1-1-1-1-1-111111-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-1111111-1-111-1-111-1-1-1-111
χ14111111111111111-1-1-1-1-1-1-1-111111-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-11111-1-111-1-111-1-11111-1-1
χ15111111111111111-1-1-1-1-1-1-1-111111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-111111111-1-1-1-111-1-111-1-1-1-11111-1-1
χ16111111111111111-1-1-1-1-1-1-1-111111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-111111111-1-1-1-1-1-111-1-11111-1-1-1-111
χ17222222222222-2-2-222222222-2-2-2-2-2-2-2-2-20000000000000000000000000000000000002i−2i2i−2i00000000
χ18222222222222-2-2-222222222-2-2-2-2-2-2-2-2-2000000000000000000000000000000000000−2i2i−2i2i00000000
χ19222222222222-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-222220000000000000000000000000000000000002i−2i−2i2i00000000
χ20222222222222-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-22222000000000000000000000000000000000000−2i2i2i−2i00000000
χ2122222222-2-2-2-222-22222-2-2-2-2-2-222-222-2-2000000000000000000000000000000002-22-2000000000000
χ2222222222-2-2-2-222-22222-2-2-2-2-2-222-222-2-200000000000000000000000000000000-22-22000000000000
χ2322222222-2-2-2-222-2-2-2-2-22222-2-222-2-2-222000000000000000000000000000000002-2-22000000000000
χ2422222222-2-2-2-222-2-2-2-2-22222-2-222-2-2-22200000000000000000000000000000000-222-2000000000000
χ2522222222-2-2-2-2-2-222222-2-2-2-222-2-22-2-2222222-2-2-2-22222-2-2-2-200000000000000000000000000000000
χ2622222222-2-2-2-2-2-222222-2-2-2-222-2-22-2-222-2-2-2-22222-2-2-2-2222200000000000000000000000000000000
χ2722222222-2-2-2-2-2-22-2-2-2-2222222-2-2222-2-22222-2-2-2-2-2-2-2-2222200000000000000000000000000000000
χ2822222222-2-2-2-2-2-22-2-2-2-2222222-2-2222-2-2-2-2-2-222222222-2-2-2-200000000000000000000000000000000
χ292222-2-2-2-222-2-2222000000002-2-2-2-2000022-2-222-2-20000000022-2-222-2-2000000000000000000000000
χ302222-2-2-2-222-2-2222000000002-2-2-2-2000022-2-222-2-200000000-2-222-2-222000000000000000000000000
χ312222-2-2-2-222-2-2222000000002-2-2-2-20000-2-222-2-2220000000022-2-2-2-222000000000000000000000000
χ322222-2-2-2-222-2-2222000000002-2-2-2-20000-2-222-2-22200000000-2-22222-2-2000000000000000000000000
χ332222-2-2-2-2-2-222-2-22000000002-222-2000022-2-2-2-22200000000000000002i2i−2i−2i2i2i−2i−2i0000000000000000
χ342222-2-2-2-2-2-222-2-22000000002-222-2000022-2-2-2-2220000000000000000−2i−2i2i2i−2i−2i2i2i0000000000000000
χ352222-2-2-2-2-2-222-2-22000000002-222-20000-2-22222-2-200000000000000002i2i−2i−2i−2i−2i2i2i0000000000000000
χ362222-2-2-2-2-2-222-2-22000000002-222-20000-2-22222-2-20000000000000000−2i−2i2i2i2i2i−2i−2i0000000000000000
χ372-2-2222-2-22-22-22-222i2i−2i−2i2i2i−2i−2i-2-22-222i−2i2i−2i000000000000000000000000000000000000000000002-22i−2i
χ382-2-2222-2-22-22-22-222i2i−2i−2i2i2i−2i−2i-2-22-222i−2i2i−2i00000000000000000000000000000000000000000000-22−2i2i
χ392-2-2222-2-22-22-22-22−2i−2i2i2i−2i−2i2i2i-2-22-22−2i2i−2i2i000000000000000000000000000000000000000000002-2−2i2i
χ402-2-2222-2-22-22-22-22−2i−2i2i2i−2i−2i2i2i-2-22-22−2i2i−2i2i00000000000000000000000000000000000000000000-222i−2i
χ412-2-2222-2-22-22-2-22-22i2i−2i−2i2i2i−2i−2i22-22-2−2i2i−2i2i00000000000000002-22-200002i−2i2i−2i00000000000000000000
χ422-2-2222-2-22-22-2-22-22i2i−2i−2i2i2i−2i−2i22-22-2−2i2i−2i2i0000000000000000-22-220000−2i2i−2i2i00000000000000000000
χ432-2-2222-2-22-22-2-22-2−2i−2i2i2i−2i−2i2i2i22-22-22i−2i2i−2i00000000000000002-22-20000−2i2i−2i2i00000000000000000000
χ442-2-2222-2-22-22-2-22-2−2i−2i2i2i−2i−2i2i2i22-22-22i−2i2i−2i0000000000000000-22-2200002i−2i2i−2i00000000000000000000
χ452-2-2222-2-2-22-222-2-22i2i−2i−2i−2i−2i2i2i222-2-22i−2i−2i2i000000000000000000002-22-200002i−2i2i−2i0000000000000000
χ462-2-2222-2-2-22-222-2-22i2i−2i−2i−2i−2i2i2i222-2-22i−2i−2i2i00000000000000000000-22-220000−2i2i−2i2i0000000000000000
χ472-2-2222-2-2-22-222-2-2−2i−2i2i2i2i2i−2i−2i222-2-2−2i2i2i−2i000000000000000000002-22-20000−2i2i−2i2i0000000000000000
χ482-2-2222-2-2-22-222-2-2−2i−2i2i2i2i2i−2i−2i222-2-2−2i2i2i−2i00000000000000000000-22-2200002i−2i2i−2i0000000000000000
χ492-2-2222-2-2-22-22-2222i2i−2i−2i−2i−2i2i2i-2-2-222−2i2i2i−2i00000000000000000000000000000000000000002-22i−2i0000
χ502-2-2222-2-2-22-22-2222i2i−2i−2i−2i−2i2i2i-2-2-222−2i2i2i−2i0000000000000000000000000000000000000000-22−2i2i0000
χ512-2-2222-2-2-22-22-222−2i−2i2i2i2i2i−2i−2i-2-2-2222i−2i−2i2i00000000000000000000000000000000000000002-2−2i2i0000
χ522-2-2222-2-2-22-22-222−2i−2i2i2i2i2i−2i−2i-2-2-2222i−2i−2i2i0000000000000000000000000000000000000000-222i−2i0000
χ532-2-22-2-2222-2-22-22-2000000002-22-2200000000000022-2-222-2-22-2-22000000002-2-220000000000000000
χ542-2-22-2-2222-2-22-22-2000000002-22-2200000000000022-2-222-2-2-222-200000000-222-20000000000000000
χ552-2-22-2-2222-2-22-22-2000000002-22-22000000000000-2-222-2-2222-2-2200000000-222-20000000000000000
χ562-2-22-2-2222-2-22-22-2000000002-22-22000000000000-2-222-2-222-222-2000000002-2-220000000000000000
χ572-2-22-2-222-222-22-2-2000000002-2-22200000000000022-2-2-2-22200002-2-222-2-2200000000000000000000
χ582-2-22-2-222-222-22-2-2000000002-2-22200000000000022-2-2-2-2220000-222-2-222-200000000000000000000
χ592-2-22-2-222-222-22-2-2000000002-2-222000000000000-2-22222-2-200002-2-22-222-200000000000000000000
χ602-2-22-2-222-222-22-2-2000000002-2-222000000000000-2-22222-2-20000-222-22-2-2200000000000000000000
χ614444-4-4-4-444-4-4-4-4-400000000-444440000000000000000000000000000000000000000000000000000
χ624444-4-4-4-4-4-44444-400000000-44-4-440000000000000000000000000000000000000000000000000000
χ6344-4-44-44-4000000000004i−4i4i−4i000000000000022−2222−222i2−2i22i2−2i2000000000000000000000000000000000000
χ6444-4-44-44-4000000000004i−4i4i−4i0000000000000−2222−2222−2i22i2−2i22i2000000000000000000000000000000000000
χ6544-4-44-44-400000000000−4i4i−4i4i000000000000022−2222−22−2i22i2−2i22i2000000000000000000000000000000000000
χ6644-4-44-44-400000000000−4i4i−4i4i0000000000000−2222−22222i2−2i22i2−2i2000000000000000000000000000000000000
χ6744-4-4-44-4400000004-44-40000000000000000022−22−2222000022−2222−2200000000000000000000000000000000
χ6844-4-4-44-4400000004-44-400000000000000000−222222−220000−2222−222200000000000000000000000000000000
χ6944-4-4-44-440000000-44-440000000000000000022−22−22220000−2222−222200000000000000000000000000000000
χ7044-4-4-44-440000000-44-4400000000000000000−222222−22000022−2222−2200000000000000000000000000000000
χ714-44-44-4-44000000000004-4-4400000000022−2222−220000000022−22−222200000000000000000000000000000000
χ724-44-44-4-44000000000004-4-44000000000−2222−222200000000−222222−2200000000000000000000000000000000
χ734-44-44-4-4400000000000-444-400000000022−2222−2200000000−222222−2200000000000000000000000000000000
χ744-44-44-4-4400000000000-444-4000000000−2222−22220000000022−22−222200000000000000000000000000000000
χ754-44-4-444-400000004i−4i−4i4i000000000000022−22−222200002i2−2i2−2i22i2000000000000000000000000000000000000
χ764-44-4-444-400000004i−4i−4i4i0000000000000−222222−220000−2i22i22i2−2i2000000000000000000000000000000000000
χ774-44-4-444-40000000−4i4i4i−4i000000000000022−22−22220000−2i22i22i2−2i2000000000000000000000000000000000000
χ784-44-4-444-40000000−4i4i4i−4i0000000000000−222222−2200002i2−2i2−2i22i2000000000000000000000000000000000000
χ794-4-44-4-4444-4-444-4400000000-44-44-40000000000000000000000000000000000000000000000000000
χ804-4-44-4-444-444-4-44400000000-444-4-40000000000000000000000000000000000000000000000000000

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