Finite Group Databasebeta

← Group #148129

Character table — Group #148129

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80
size111111112222222222222222222244444444444444444444888888888888888816161616161616161616161616161616
order12224444222222444444888888888888161616161616161616161616161616164444888816161616161616162244444488888888
χ111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ3111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-11111
χ4111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1
χ511111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1
χ611111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111
χ711111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-11111-1-1-1-1
χ811111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-11111-1-1-1-11111
χ91-1-1111-1-1111-1-1-11-1-1-11111-1-111-1-111-1-111111111-1-1-1-1-1-1-1-1ii−i−iii−i−iiiii−i−i−i−i1-11-1ii−i−iii−i−i11-1-1
χ101-1-1111-1-1111-1-1-11-1-1-11111-1-111-1-111-1-111111111-1-1-1-1-1-1-1-1ii−i−iii−i−iiiii−i−i−i−i-11-11−i−iii−i−iii-1-111
χ111-1-1111-1-1111-1-1-11-1-1-11111-1-111-1-111-1-111111111-1-1-1-1-1-1-1-1−i−iii−i−iii−i−i−i−iiiii1-11-1−i−iii−i−iii11-1-1
χ121-1-1111-1-1111-1-1-11-1-1-11111-1-111-1-111-1-111111111-1-1-1-1-1-1-1-1−i−iii−i−iii−i−i−i−iiiii-11-11ii−i−iii−i−i-1-111
χ131-1-1111-1-1111-1-1-11-1-1-11111-1-111-1-111-1-1-1-1-1-1-1-1-1-111111111ii−i−iii−i−i−i−i−i−iiiii1-11-1ii−i−i−i−iii-1-111
χ141-1-1111-1-1111-1-1-11-1-1-11111-1-111-1-111-1-1-1-1-1-1-1-1-1-111111111ii−i−iii−i−i−i−i−i−iiiii-11-11−i−iiiii−i−i11-1-1
χ151-1-1111-1-1111-1-1-11-1-1-11111-1-111-1-111-1-1-1-1-1-1-1-1-1-111111111−i−iii−i−iiiiiii−i−i−i−i1-11-1−i−iiiii−i−i-1-111
χ161-1-1111-1-1111-1-1-11-1-1-11111-1-111-1-111-1-1-1-1-1-1-1-1-1-111111111−i−iii−i−iiiiiii−i−i−i−i-11-11ii−i−i−i−iii11-1-1
χ1722222222222222222222-2-2-2-2-2-2-2-2-2-2-2-200000000000000002222-2-2-2-2000000000000000000000000
χ1822222222222222222222-2-2-2-2-2-2-2-2-2-2-2-20000000000000000-2-2-2-22222000000000000000000000000
χ19222222222-2-2-22-2-22-2-22-222222222-2-2-2-200000000000000000000000022-2-222-2-20000000000000000
χ20222222222-2-2-22-2-22-2-22-222222222-2-2-2-2000000000000000000000000-2-222-2-2220000000000000000
χ21222222222-2-2-22-2-22-2-22-2-2-2-2-2-2-2-2-222222i2i2i2i−2i−2i−2i−2i2i2i2i2i−2i−2i−2i−2i00000000000000000000000000000000
χ22222222222-2-2-22-2-22-2-22-2-2-2-2-2-2-2-2-22222−2i−2i−2i−2i2i2i2i2i−2i−2i−2i−2i2i2i2i2i00000000000000000000000000000000
χ232222-2-2-2-2222222-2-2-2-2-2-2000000000000i2i2−i2−i2i2i2−i2−i2i2i2−i2−i2i2i2−i2−i22-22-20000i2−i2i2−i2i2−i2i2−i20000000000000000
χ242222-2-2-2-2222222-2-2-2-2-2-2000000000000i2i2−i2−i2i2i2−i2−i2i2i2−i2−i2i2i2−i2−i2-22-220000−i2i2−i2i2−i2i2−i2i20000000000000000
χ252222-2-2-2-2222222-2-2-2-2-2-2000000000000−i2−i2i2i2−i2−i2i2i2−i2−i2i2i2−i2−i2i2i22-22-20000−i2i2−i2i2−i2i2−i2i20000000000000000
χ262222-2-2-2-2222222-2-2-2-2-2-2000000000000−i2−i2i2i2−i2−i2i2i2−i2−i2i2i2−i2−i2i2i2-22-220000i2−i2i2−i2i2−i2i2−i20000000000000000
χ272222-2-2-2-22-2-2-22-22-222-2200000000000022−2−2−2−22222−2−2−2−22200002i−2i2i−2ii2−i2−i2i2i2−i2−i2i20000000000000000
χ282222-2-2-2-22-2-2-22-22-222-2200000000000022−2−2−2−22222−2−2−2−2220000−2i2i−2i2i−i2i2i2−i2−i2i2i2−i20000000000000000
χ292222-2-2-2-22-2-2-22-22-222-22000000000000−2−22222−2−2−2−22222−2−200002i−2i2i−2i−i2i2i2−i2−i2i2i2−i20000000000000000
χ302222-2-2-2-22-2-2-22-22-222-22000000000000−2−22222−2−2−2−22222−2−20000−2i2i−2i2ii2−i2−i2i2i2−i2−i2i20000000000000000
χ312222-2-2-2-2-22-22-2-2222-22-22222-2-2-2-22-22-20000000000000000000000000000000022-2-2000000000000
χ322222-2-2-2-2-22-22-2-2222-22-22222-2-2-2-22-22-200000000000000000000000000000000-2-222000000000000
χ332222-2-2-2-2-22-22-2-2222-22-2-2-2-2-22222-22-220000000000000000000000000000000000002i−2i2i−2i00000000
χ342222-2-2-2-2-22-22-2-2222-22-2-2-2-2-22222-22-22000000000000000000000000000000000000−2i2i−2i2i00000000
χ352222-2-2-2-2-2-22-2-22-22-22222222-2-2-2-2-22-2200000000000000000000000000000000000000002i−2i2i−2i0000
χ362222-2-2-2-2-2-22-2-22-22-22222222-2-2-2-2-22-220000000000000000000000000000000000000000−2i2i−2i2i0000
χ372222-2-2-2-2-2-22-2-22-22-2222-2-2-2-222222-22-2000000000000000000000000000000000000000000002-22-2
χ382222-2-2-2-2-2-22-2-22-22-2222-2-2-2-222222-22-200000000000000000000000000000000000000000000-22-22
χ392-2-2222-2-2222-2-2-22-2-2-222-2-222-2-222-2-22200000000000000002i2i−2i−2i−2i−2i2i2i000000000000000000000000
χ402-2-2222-2-2222-2-2-22-2-2-222-2-222-2-222-2-2220000000000000000−2i−2i2i2i2i2i−2i−2i000000000000000000000000
χ412-2-2222-2-22-2-22-22-2-2222-222-2-222-2-2-2-2220000000000000000000000002i2i−2i−2i−2i−2i2i2i0000000000000000
χ422-2-2222-2-22-2-22-22-2-2222-222-2-222-2-2-2-222000000000000000000000000−2i−2i2i2i2i2i−2i−2i0000000000000000
χ432-2-2222-2-22-2-22-22-2-2222-2-2-222-2-22222-2-22i2i2i2i−2i−2i−2i−2i−2i−2i−2i−2i2i2i2i2i00000000000000000000000000000000
χ442-2-2222-2-22-2-22-22-2-2222-2-2-222-2-22222-2-2−2i−2i−2i−2i2i2i2i2i2i2i2i2i−2i−2i−2i−2i00000000000000000000000000000000
χ452-2-22-2-222222-2-2-2-2222-2-2000000000000i2i2−i2−i2i2i2−i2−i2−i2−i2i2i2−i2−i2i2i22i−2i−2i2i0000−22−222−22−20000000000000000
χ462-2-22-2-222222-2-2-2-2222-2-2000000000000i2i2−i2−i2i2i2−i2−i2−i2−i2i2i2−i2−i2i2i2−2i2i2i−2i00002−22−2−22−220000000000000000
χ472-2-22-2-222222-2-2-2-2222-2-2000000000000−i2−i2i2i2−i2−i2i2i2i2i2−i2−i2i2i2−i2−i22i−2i−2i2i00002−22−2−22−220000000000000000
χ482-2-22-2-222222-2-2-2-2222-2-2000000000000−i2−i2i2i2−i2−i2i2i2i2i2−i2−i2i2i2−i2−i2−2i2i2i−2i0000−22−222−22−20000000000000000
χ492-2-22-2-2222-2-22-2222-2-2-2200000000000022−2−2−2−222−2−22222−2−200002-2-222−2−22−222−20000000000000000
χ502-2-22-2-2222-2-22-2222-2-2-2200000000000022−2−2−2−222−2−22222−2−20000-222-2−222−22−2−220000000000000000
χ512-2-22-2-2222-2-22-2222-2-2-22000000000000−2−22222−2−222−2−2−2−22200002-2-22−222−22−2−220000000000000000
χ522-2-22-2-2222-2-22-2222-2-2-22000000000000−2−22222−2−222−2−2−2−2220000-222-22−2−22−222−20000000000000000
χ532-2-22-2-222-22-2-2222-2-222-222-2-2-2-2222-2-22000000000000000000000000000000002-2-22000000000000
χ542-2-22-2-222-22-2-2222-2-222-222-2-2-2-2222-2-2200000000000000000000000000000000-222-2000000000000
χ552-2-22-2-222-22-2-2222-2-222-2-2-22222-2-2-222-20000000000000000000000000000000000002-2-2200000000
χ562-2-22-2-222-22-2-2222-2-222-2-2-22222-2-2-222-2000000000000000000000000000000000000-222-200000000
χ572-2-22-2-222-2-2222-2-2-22-22222-2-2-2-222-222-200000000000000000000000000000000000000002-2-220000
χ582-2-22-2-222-2-2222-2-2-22-22222-2-2-2-222-222-20000000000000000000000000000000000000000-222-20000
χ592-2-22-2-222-2-2222-2-2-22-222-2-22222-2-22-2-22000000000000000000000000000000000000000000002-2-22
χ602-2-22-2-222-2-2222-2-2-22-222-2-22222-2-22-2-2200000000000000000000000000000000000000000000-222-2
χ6144444444-44-44-4-4-4-4-44-44000000000000000000000000000000000000000000000000000000000000
χ6244444444-4-44-4-444-44-4-4-4000000000000000000000000000000000000000000000000000000000000
χ6344-4-44i−4i4i−4i00000000000022−2222−222i2−2i22i2−2i200002ζ−2ζ2ζ5−2ζ52ζ3−2ζ32ζ7−2ζ72ζ−2ζ2ζ5−2ζ52ζ3−2ζ32ζ7−2ζ700000000000000000000000000000000
χ6444-4-44i−4i4i−4i00000000000022−2222−222i2−2i22i2−2i20000−2ζ2ζ−2ζ52ζ5−2ζ32ζ3−2ζ72ζ7−2ζ2ζ−2ζ52ζ5−2ζ32ζ3−2ζ72ζ700000000000000000000000000000000
χ6544-4-44i−4i4i−4i000000000000−2222−2222−2i22i2−2i22i200002ζ5−2ζ5−2ζ2ζ−2ζ72ζ72ζ3−2ζ32ζ5−2ζ5−2ζ2ζ−2ζ72ζ72ζ3−2ζ300000000000000000000000000000000
χ6644-4-44i−4i4i−4i000000000000−2222−2222−2i22i2−2i22i20000−2ζ52ζ52ζ−2ζ2ζ7−2ζ7−2ζ32ζ3−2ζ52ζ52ζ−2ζ2ζ7−2ζ7−2ζ32ζ300000000000000000000000000000000
χ6744-4-4−4i4i−4i4i00000000000022−2222−22−2i22i2−2i22i200002ζ7−2ζ72ζ3−2ζ32ζ5−2ζ52ζ−2ζ2ζ7−2ζ72ζ3−2ζ32ζ5−2ζ52ζ−2ζ00000000000000000000000000000000
χ6844-4-4−4i4i−4i4i00000000000022−2222−22−2i22i2−2i22i20000−2ζ72ζ7−2ζ32ζ3−2ζ52ζ5−2ζ2ζ−2ζ72ζ7−2ζ32ζ3−2ζ52ζ5−2ζ2ζ00000000000000000000000000000000
χ6944-4-4−4i4i−4i4i000000000000−2222−22222i2−2i22i2−2i200002ζ3−2ζ3−2ζ72ζ7−2ζ2ζ2ζ5−2ζ52ζ3−2ζ3−2ζ72ζ7−2ζ2ζ2ζ5−2ζ500000000000000000000000000000000
χ7044-4-4−4i4i−4i4i000000000000−2222−22222i2−2i22i2−2i20000−2ζ32ζ32ζ7−2ζ72ζ−2ζ−2ζ52ζ5−2ζ32ζ32ζ7−2ζ72ζ−2ζ−2ζ52ζ500000000000000000000000000000000
χ714-44-44i−4i−4i4i00000000000022−22−22222i2−2i2−2i22i200002ζ−2ζ2ζ5−2ζ52ζ3−2ζ32ζ7−2ζ7−2ζ2ζ−2ζ52ζ5−2ζ32ζ3−2ζ72ζ700000000000000000000000000000000
χ724-44-44i−4i−4i4i00000000000022−22−22222i2−2i2−2i22i20000−2ζ2ζ−2ζ52ζ5−2ζ32ζ3−2ζ72ζ72ζ−2ζ2ζ5−2ζ52ζ3−2ζ32ζ7−2ζ700000000000000000000000000000000
χ734-44-44i−4i−4i4i000000000000−222222−22−2i22i22i2−2i200002ζ5−2ζ5−2ζ2ζ−2ζ72ζ72ζ3−2ζ3−2ζ52ζ52ζ−2ζ2ζ7−2ζ7−2ζ32ζ300000000000000000000000000000000
χ744-44-44i−4i−4i4i000000000000−222222−22−2i22i22i2−2i20000−2ζ52ζ52ζ−2ζ2ζ7−2ζ7−2ζ32ζ32ζ5−2ζ5−2ζ2ζ−2ζ72ζ72ζ3−2ζ300000000000000000000000000000000
χ754-44-4−4i4i4i−4i00000000000022−22−2222−2i22i22i2−2i200002ζ7−2ζ72ζ3−2ζ32ζ5−2ζ52ζ−2ζ−2ζ72ζ7−2ζ32ζ3−2ζ52ζ5−2ζ2ζ00000000000000000000000000000000
χ764-44-4−4i4i4i−4i00000000000022−22−2222−2i22i22i2−2i20000−2ζ72ζ7−2ζ32ζ3−2ζ52ζ5−2ζ2ζ2ζ7−2ζ72ζ3−2ζ32ζ5−2ζ52ζ−2ζ00000000000000000000000000000000
χ774-44-4−4i4i4i−4i000000000000−222222−222i2−2i2−2i22i200002ζ3−2ζ3−2ζ72ζ7−2ζ2ζ2ζ5−2ζ5−2ζ32ζ32ζ7−2ζ72ζ−2ζ−2ζ52ζ500000000000000000000000000000000
χ784-44-4−4i4i4i−4i000000000000−222222−222i2−2i2−2i22i20000−2ζ32ζ32ζ7−2ζ72ζ−2ζ−2ζ52ζ52ζ3−2ζ3−2ζ72ζ7−2ζ2ζ2ζ5−2ζ500000000000000000000000000000000
χ794-4-4444-4-4-44-4-444-444-4-44000000000000000000000000000000000000000000000000000000000000
χ804-4-4444-4-4-4-4444-444-44-4-4000000000000000000000000000000000000000000000000000000000000

Here ζ is a primitive root of unity of order 16 (ζ16 = 1); i = ζ4.