Finite Group Databasebeta

← Group #116331

Character table — Group #116331

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80
size1111111111111111222222224444444488888888888888888888888888888888888888881616161616161616
order12222222444444442222444444444444444444444444444444444444888888888888888844448888
χ111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ3111111111111111111111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-11111111111111111-1-1-1-1-1-1-1-1
χ4111111111111111111111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111
χ511111111111111111111111111111111-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-11111-1-1-1-1
χ611111111111111111111111111111111-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-11111
χ711111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111111111-1-1-1-1-1-1-1-1-1-1-1-11111
χ811111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1111111111111-1-1-1-1
χ91-1-1-1-11111111-1-1-1-11-11-111-1-1111-1-1-11-1ii−i−i1111-1-1-1-1ii−i−iiiii−i−i−i−i1111-1-1-1-1iiii−i−i−i−i11-1-1ii−i−i
χ101-1-1-1-11111111-1-1-1-11-11-111-1-1111-1-1-11-1ii−i−i1111-1-1-1-1ii−i−iiiii−i−i−i−i-1-1-1-11111−i−i−i−iiiii-1-111−i−iii
χ111-1-1-1-11111111-1-1-1-11-11-111-1-1111-1-1-11-1ii−i−i-1-1-1-11111ii−i−i−i−i−i−iiiii1111-1-1-1-1iiii−i−i−i−i-1-111−i−iii
χ121-1-1-1-11111111-1-1-1-11-11-111-1-1111-1-1-11-1ii−i−i-1-1-1-11111ii−i−i−i−i−i−iiiii-1-1-1-11111−i−i−i−iiiii11-1-1ii−i−i
χ131-1-1-1-11111111-1-1-1-11-11-111-1-1111-1-1-11-1−i−iii1111-1-1-1-1−i−iii−i−i−i−iiiii1111-1-1-1-1−i−i−i−iiiii11-1-1−i−iii
χ141-1-1-1-11111111-1-1-1-11-11-111-1-1111-1-1-11-1−i−iii1111-1-1-1-1−i−iii−i−i−i−iiiii-1-1-1-11111iiii−i−i−i−i-1-111ii−i−i
χ151-1-1-1-11111111-1-1-1-11-11-111-1-1111-1-1-11-1−i−iii-1-1-1-11111−i−iiiiiii−i−i−i−i1111-1-1-1-1−i−i−i−iiiii-1-111ii−i−i
χ161-1-1-1-11111111-1-1-1-11-11-111-1-1111-1-1-11-1−i−iii-1-1-1-11111−i−iiiiiii−i−i−i−i-1-1-1-11111iiii−i−i−i−i11-1-1−i−iii
χ17222222222222222222222222-2-2-2-2-2-2-2-2222200000000-2-2-2-200000000000000000000000000000000
χ18222222222222222222222222-2-2-2-2-2-2-2-2-2-2-2-200000000222200000000000000000000000000000000
χ192222222222222222-2-2-2-2-2-2-2-222-22-2-2-220000000000000000000000002i2i−2i−2i2i2i−2i−2i0000000000000000
χ202222222222222222-2-2-2-2-2-2-2-222-22-2-2-22000000000000000000000000−2i−2i2i2i−2i−2i2i2i0000000000000000
χ212222222222222222-2-2-2-2-2-2-2-2-2-22-2222-2000000000000000000000000000000002i2i−2i−2i2i2i−2i−2i00000000
χ222222222222222222-2-2-2-2-2-2-2-2-2-22-2222-200000000000000000000000000000000−2i−2i2i2i−2i−2i2i2i00000000
χ2322222222-2-2-2-2-2-2-2-22222-2-2-2-22-22-22-2-22000000000000000022-2-222-2-2000000000000000000000000
χ2422222222-2-2-2-2-2-2-2-22222-2-2-2-22-22-22-2-220000000000000000-2-222-2-222000000000000000000000000
χ2522222222-2-2-2-2-2-2-2-22222-2-2-2-2-22-22-222-2000022-2-222-2-2000000000000000000000000000000000000
χ2622222222-2-2-2-2-2-2-2-22222-2-2-2-2-22-22-222-20000-2-222-2-222000000000000000000000000000000000000
χ2722222222-2-2-2-2-2-2-2-2-2-2-2-222222-2-2-2-2222000000000000000000000000000000000000000000002i−2i2i−2i
χ2822222222-2-2-2-2-2-2-2-2-2-2-2-222222-2-2-2-222200000000000000000000000000000000000000000000−2i2i−2i2i
χ2922222222-2-2-2-2-2-2-2-2-2-2-2-22222-22222-2-2-200000000000000000000000000000000000000002-22-20000
χ3022222222-2-2-2-2-2-2-2-2-2-2-2-22222-22222-2-2-20000000000000000000000000000000000000000-22-220000
χ31222-2-22-2-222-2-222-2-222-2-22-22-2000000002-22-2000000000000000000002−22−22−22−22−22−22−22−200000000
χ32222-2-22-2-222-2-222-2-222-2-22-22-2000000002-22-200000000000000000000−22−22−22−22−22−22−22−2200000000
χ33222-2-22-2-222-2-222-2-222-2-22-22-200000000-22-22000000000000000000002−22−22−22−2−22−22−22−2200000000
χ34222-2-22-2-222-2-222-2-222-2-22-22-200000000-22-2200000000000000000000−22−22−22−222−22−22−22−200000000
χ35222-2-22-2-222-2-222-2-2-2-222-22-22000000000000000000002-22-200000000i2−i2−i2i2i2−i2−i2i2i2−i2−i2i2i2−i2−i2i200000000
χ36222-2-22-2-222-2-222-2-2-2-222-22-22000000000000000000002-22-200000000−i2i2i2−i2−i2i2i2−i2−i2i2i2−i2−i2i2i2−i200000000
χ37222-2-22-2-222-2-222-2-2-2-222-22-2200000000000000000000-22-2200000000i2−i2−i2i2i2−i2−i2i2−i2i2i2−i2−i2i2i2−i200000000
χ38222-2-22-2-222-2-222-2-2-2-222-22-2200000000000000000000-22-2200000000−i2i2i2−i2−i2i2i2−i2i2−i2−i2i2i2−i2−i2i200000000
χ392-2-2222-2-222-2-2-2-2222-2-222-2-22000000002i−2i−2i2i000000000000000000002−22−2−22−22i2−i2i2−i2−i2i2−i2i200000000
χ402-2-2222-2-222-2-2-2-2222-2-222-2-22000000002i−2i−2i2i00000000000000000000−22−222−22−2−i2i2−i2i2i2−i2i2−i200000000
χ412-2-2222-2-222-2-2-2-2222-2-222-2-2200000000−2i2i2i−2i000000000000000000002−22−2−22−22−i2i2−i2i2i2−i2i2−i200000000
χ422-2-2222-2-222-2-2-2-2222-2-222-2-2200000000−2i2i2i−2i00000000000000000000−22−222−22−2i2−i2i2−i2−i2i2−i2i200000000
χ432-2-2222-2-222-2-2-2-222-222-2-222-2000000000000000000002i−2i−2i2i00000000i2−i2−i2i2−i2i2i2−i2−222−22−2−2200000000
χ442-2-2222-2-222-2-2-2-222-222-2-222-2000000000000000000002i−2i−2i2i00000000−i2i2i2−i2i2−i2−i2i22−2−22−222−200000000
χ452-2-2222-2-222-2-2-2-222-222-2-222-200000000000000000000−2i2i2i−2i00000000i2−i2−i2i2−i2i2i2−i22−2−22−222−200000000
χ462-2-2222-2-222-2-2-2-222-222-2-222-200000000000000000000−2i2i2i−2i00000000−i2i2i2−i2i2−i2−i2i2−222−22−2−2200000000
χ472-2-2-2-22222222-2-2-2-22-22-222-2-2-2-2-2222-222i2i−2i−2i00000000−2i−2i2i2i00000000000000000000000000000000
χ482-2-2-2-22222222-2-2-2-22-22-222-2-2-2-2-2222-22−2i−2i2i2i000000002i2i−2i−2i00000000000000000000000000000000
χ492-2-2-2-22222222-2-2-2-2-22-22-2-22222-2-222-2-20000000000000000000000002i2i−2i−2i−2i−2i2i2i0000000000000000
χ502-2-2-2-22222222-2-2-2-2-22-22-2-22222-2-222-2-2000000000000000000000000−2i−2i2i2i2i2i−2i−2i0000000000000000
χ512-2-2-2-22222222-2-2-2-2-22-22-2-222-2-222-2-2220000000000000000000000000000000022-2-2-2-22200000000
χ522-2-2-2-22222222-2-2-2-2-22-22-2-222-2-222-2-22200000000000000000000000000000000-2-22222-2-200000000
χ532-2-2-2-2222-2-2-2-222222-22-2-2-2222-222-22-2-200000000000000002i2i−2i−2i−2i−2i2i2i000000000000000000000000
χ542-2-2-2-2222-2-2-2-222222-22-2-2-2222-222-22-2-20000000000000000−2i−2i2i2i2i2i−2i−2i000000000000000000000000
χ552-2-2-2-2222-2-2-2-222222-22-2-2-222-22-2-22-222000022-2-2-2-222000000000000000000000000000000000000
χ562-2-2-2-2222-2-2-2-222222-22-2-2-222-22-2-22-2220000-2-22222-2-2000000000000000000000000000000000000
χ572-2-2-2-2222-2-2-2-22222-22-2222-2-22-2-222-22-2000000000000000000000000000000000000000000002-2-22
χ582-2-2-2-2222-2-2-2-22222-22-2222-2-22-2-222-22-200000000000000000000000000000000000000000000-222-2
χ592-2-2-2-2222-2-2-2-22222-22-2222-2-2-222-2-22-2200000000000000000000000000000000000000002-2-220000
χ602-2-2-2-2222-2-2-2-22222-22-2222-2-2-222-2-22-220000000000000000000000000000000000000000-222-20000
χ61444-4-44-4-4-4-444-4-44444-4-4-44-4400000000000000000000000000000000000000000000000000000000
χ62444-4-44-4-4-4-444-4-444-4-4444-44-400000000000000000000000000000000000000000000000000000000
χ6344-44-4-44-44i−4i4i−4i4i−4i4i−4i000000000000000000002-22i−2i2-22i−2i000000000000000000000000000000000000
χ6444-44-4-44-44i−4i4i−4i4i−4i4i−4i00000000000000000000-22−2i2i-22−2i2i000000000000000000000000000000000000
χ6544-44-4-44-4−4i4i−4i4i−4i4i−4i4i000000000000000000002-2−2i2i2-2−2i2i000000000000000000000000000000000000
χ6644-44-4-44-4−4i4i−4i4i−4i4i−4i4i00000000000000000000-222i−2i-222i−2i000000000000000000000000000000000000
χ6744-4-44-4-444i−4i−4i4i4i−4i−4i4i000000000000000000000000000000002-22i−2i2-22i−2i000000000000000000000000
χ6844-4-44-4-444i−4i−4i4i4i−4i−4i4i00000000000000000000000000000000-22−2i2i-22−2i2i000000000000000000000000
χ6944-4-44-4-44−4i4i4i−4i−4i4i4i−4i000000000000000000000000000000002-2−2i2i2-2−2i2i000000000000000000000000
χ7044-4-44-4-44−4i4i4i−4i−4i4i4i−4i00000000000000000000000000000000-222i−2i-222i−2i000000000000000000000000
χ714-444-4-4-444i−4i−4i4i−4i4i4i−4i000000000000000000000000000000002i−2i-22−2i2i2-2000000000000000000000000
χ724-444-4-4-444i−4i−4i4i−4i4i4i−4i00000000000000000000000000000000−2i2i2-22i−2i-22000000000000000000000000
χ734-444-4-4-44−4i4i4i−4i4i−4i−4i4i000000000000000000000000000000002i−2i2-2−2i2i-22000000000000000000000000
χ744-444-4-4-44−4i4i4i−4i4i−4i−4i4i00000000000000000000000000000000−2i2i-222i−2i2-2000000000000000000000000
χ754-44-44-44-44i−4i4i−4i−4i4i−4i4i000000000000000000002-22i−2i-22−2i2i000000000000000000000000000000000000
χ764-44-44-44-44i−4i4i−4i−4i4i−4i4i00000000000000000000-22−2i2i2-22i−2i000000000000000000000000000000000000
χ774-44-44-44-4−4i4i−4i4i4i−4i4i−4i000000000000000000002-2−2i2i-222i−2i000000000000000000000000000000000000
χ784-44-44-44-4−4i4i−4i4i4i−4i4i−4i00000000000000000000-222i−2i2-2−2i2i000000000000000000000000000000000000
χ794-4-4444-4-4-4-44444-4-44-4-44-444-400000000000000000000000000000000000000000000000000000000
χ804-4-4444-4-4-4-44444-4-4-444-44-4-4400000000000000000000000000000000000000000000000000000000

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