Finite Group Databasebeta

← Group #116299

Character table — Group #116299

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74
size11111111222222222222222244444488888888888888888888888888888888161616161616161616161616
order12224444222222444444444444444444444444888888888888888888888888224488888888
χ111111111111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1
χ311111111111111111111111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111
χ411111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-1
χ5111111111111111111111111111111-1-1-1-1-1-1-1-1111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1
χ6111111111111111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-11111
χ7111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-111111111-1-1-1-1
χ8111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-111111111
χ91111-1-1-1-111111111-1-1-1-1-1-1-1-111-1-1-111111-1-1-1-1iiii−i−i−i−iii−i−iii−i−i1111-1-1-1-11-11-1ii−i−iii−i−i
χ101111-1-1-1-111111111-1-1-1-1-1-1-1-111-1-1-111111-1-1-1-1iiii−i−i−i−i−i−iii−i−iii-1-1-1-11111-11-11ii−i−i−i−iii
χ111111-1-1-1-111111111-1-1-1-1-1-1-1-111-1-1-111111-1-1-1-1−i−i−i−iiiiiii−i−iii−i−i-1-1-1-11111-11-11−i−iiiii−i−i
χ121111-1-1-1-111111111-1-1-1-1-1-1-1-111-1-1-111111-1-1-1-1−i−i−i−iiiii−i−iii−i−iii1111-1-1-1-11-11-1−i−iii−i−iii
χ131111-1-1-1-111111111-1-1-1-1-1-1-1-111-1-1-11-1-1-1-11111iiii−i−i−i−iii−i−iii−i−i1111-1-1-1-1-11-11−i−iii−i−iii
χ141111-1-1-1-111111111-1-1-1-1-1-1-1-111-1-1-11-1-1-1-11111iiii−i−i−i−i−i−iii−i−iii-1-1-1-111111-11-1−i−iiiii−i−i
χ151111-1-1-1-111111111-1-1-1-1-1-1-1-111-1-1-11-1-1-1-11111−i−i−i−iiiiiii−i−iii−i−i-1-1-1-111111-11-1ii−i−i−i−iii
χ161111-1-1-1-111111111-1-1-1-1-1-1-1-111-1-1-11-1-1-1-11111−i−i−i−iiiii−i−iii−i−iii1111-1-1-1-1-11-11ii−i−iii−i−i
χ1722222222222222-2-2222-2-2222-2-2-2-2-2-200000000000000002222-2-2-2-200000000000000000000
χ1822222222222222-2-2222-2-2222-2-2-2-2-2-20000000000000000-2-2-2-2222200000000000000000000
χ192222222222-2-2-2-22222-222-2-2-2-2-22-2-220000000000000000000000000000000000002i−2i2i−2i0000
χ202222222222-2-2-2-22222-222-2-2-2-2-22-2-22000000000000000000000000000000000000−2i2i−2i2i0000
χ212222222222-2-2-2-2-2-222-2-2-2-2-2-222-222-2000000000000000000000000000000002-2-2200000000
χ222222222222-2-2-2-2-2-222-2-2-2-2-2-222-222-200000000000000000000000000000000-222-200000000
χ2322222222-2-222-2-222-2-2222-22-22-2-22-2-20000000000000000000000002i2i−2i−2i2i2i−2i−2i000000000000
χ2422222222-2-222-2-222-2-2222-22-22-2-22-2-2000000000000000000000000−2i−2i2i2i−2i−2i2i2i000000000000
χ2522222222-2-222-2-2-2-2-2-22-2-2-22-2-222-222000000002i2i−2i−2i2i2i−2i−2i0000000000000000000000000000
χ2622222222-2-222-2-2-2-2-2-22-2-2-22-2-222-22200000000−2i−2i2i2i−2i−2i2i2i0000000000000000000000000000
χ2722222222-2-2-2-22222-2-2-2222-22-22-2-22-200000000000000000000000000000000000000002-22-2
χ2822222222-2-2-2-22222-2-2-2222-22-22-2-22-20000000000000000000000000000000000000000-22-22
χ2922222222-2-2-2-222-2-2-2-2-2-2-22-222-222-2222-2-222-2-2000000000000000000000000000000000000
χ3022222222-2-2-2-222-2-2-2-2-2-2-22-222-222-22-2-222-2-222000000000000000000000000000000000000
χ312222-2-2-2-2222222-2-2-2-2-222-2-2-2-2-2222-200000000000000002i2i−2i−2i−2i−2i2i2i00000000000000000000
χ322222-2-2-2-2222222-2-2-2-2-222-2-2-2-2-2222-20000000000000000−2i−2i2i2i2i2i−2i−2i00000000000000000000
χ332222-2-2-2-222-2-2-2-222-2-22-2-2222-2-2-22220000000000000000000000000000000000002-2-220000
χ342222-2-2-2-222-2-2-2-222-2-22-2-2222-2-2-2222000000000000000000000000000000000000-222-20000
χ352222-2-2-2-222-2-2-2-2-2-2-2-2222222222-2-2-20000000000000000000000000000000022-2-200000000
χ362222-2-2-2-222-2-2-2-2-2-2-2-2222222222-2-2-200000000000000000000000000000000-2-22200000000
χ372222-2-2-2-2-2-222-2-22222-2-2-22-222-22-22-20000000000000000000000002i2i−2i−2i−2i−2i2i2i000000000000
χ382222-2-2-2-2-2-222-2-22222-2-2-22-222-22-22-2000000000000000000000000−2i−2i2i2i2i2i−2i−2i000000000000
χ392222-2-2-2-2-2-222-2-2-2-222-2222-22-22-22-220000000022-2-2-2-2220000000000000000000000000000
χ402222-2-2-2-2-2-222-2-2-2-222-2222-22-22-22-2200000000-2-22222-2-20000000000000000000000000000
χ412222-2-2-2-2-2-2-2-22222222-2-2-22-2-2222-2-200000000000000000000000000000000000000002i−2i−2i2i
χ422222-2-2-2-2-2-2-2-22222222-2-2-22-2-2222-2-20000000000000000000000000000000000000000−2i2i2i−2i
χ432222-2-2-2-2-2-2-2-222-2-222222-22-22-2-2-22222-2-2-2-222000000000000000000000000000000000000
χ442222-2-2-2-2-2-2-2-222-2-222222-22-22-2-2-222-2-22222-2-2000000000000000000000000000000000000
χ452-2-2222-2-22-22-22-2002-2200-2-22000000000000002−22−22−22−22i−2i2i−2i0000i2−i2i2−i2i2−i2i2−i2000000000000
χ462-2-2222-2-22-22-22-2002-2200-2-22000000000000002−22−22−22−2−2i2i−2i2i0000−i2i2−i2i2−i2i2−i2i2000000000000
χ472-2-2222-2-22-22-22-2002-2200-2-2200000000000000−22−22−22−222i−2i2i−2i0000−i2i2−i2i2−i2i2−i2i2000000000000
χ482-2-2222-2-22-22-22-2002-2200-2-2200000000000000−22−22−22−22−2i2i−2i2i0000i2−i2i2−i2i2−i2i2−i2000000000000
χ492-2-2222-2-2-222-2-2200-222002-2-200000000000000i2−i2−i2i2i2−i2−i2i200002i−2i2i−2i2−2−222−2−22000000000000
χ502-2-2222-2-2-222-2-2200-222002-2-200000000000000i2−i2−i2i2i2−i2−i2i20000−2i2i−2i2i−222−2−222−2000000000000
χ512-2-2222-2-2-222-2-2200-222002-2-200000000000000−i2i2i2−i2−i2i2i2−i200002i−2i2i−2i−222−2−222−2000000000000
χ522-2-2222-2-2-222-2-2200-222002-2-200000000000000−i2i2i2−i2−i2i2i2−i20000−2i2i−2i2i2−2−222−2−22000000000000
χ532-2-22-2-2222-22-22-200-22-20022-200000000000000i2−i2i2−i2−i2i2−i2i22-2-220000−i2i2−i2i2i2−i2i2−i2000000000000
χ542-2-22-2-2222-22-22-200-22-20022-200000000000000i2−i2i2−i2−i2i2−i2i2-222-20000i2−i2i2−i2−i2i2−i2i2000000000000
χ552-2-22-2-2222-22-22-200-22-20022-200000000000000−i2i2−i2i2i2−i2i2−i22-2-220000i2−i2i2−i2−i2i2−i2i2000000000000
χ562-2-22-2-2222-22-22-200-22-20022-200000000000000−i2i2−i2i2i2−i2i2−i2-222-20000−i2i2−i2i2i2−i2i2−i2000000000000
χ572-2-22-2-222-222-2-22002-2-200-222000000000000002−2−22−222−200002-2-222−2−22−222−2000000000000
χ582-2-22-2-222-222-2-22002-2-200-222000000000000002−2−22−222−20000-222-2−222−22−2−22000000000000
χ592-2-22-2-222-222-2-22002-2-200-22200000000000000−222−22−2−2200002-2-22−222−22−2−22000000000000
χ602-2-22-2-222-222-2-22002-2-200-22200000000000000−222−22−2−220000-222-22−2−22−222−2000000000000
χ6144-4-44i−4i4i−4i0000004i−4i0004-40000000002-22i−2i2i−2i2-2000000000000000000000000000000000000
χ6244-4-44i−4i4i−4i0000004i−4i0004-4000000000-22−2i2i−2i2i-22000000000000000000000000000000000000
χ6344-4-44i−4i4i−4i000000−4i4i000-440000000002-2−2i2i2i−2i-22000000000000000000000000000000000000
χ6444-4-44i−4i4i−4i000000−4i4i000-44000000000-222i−2i−2i2i2-2000000000000000000000000000000000000
χ6544-4-4−4i4i−4i4i0000004i−4i000-440000000002-22i−2i−2i2i-22000000000000000000000000000000000000
χ6644-4-4−4i4i−4i4i0000004i−4i000-44000000000-22−2i2i2i−2i2-2000000000000000000000000000000000000
χ6744-4-4−4i4i−4i4i000000−4i4i0004-40000000002-2−2i2i−2i2i2-2000000000000000000000000000000000000
χ6844-4-4−4i4i−4i4i000000−4i4i0004-4000000000-222i−2i2i−2i-22000000000000000000000000000000000000
χ694-4-4444-4-44-4-44-44004-4-40044-400000000000000000000000000000000000000000000000000
χ704-4-4444-4-4-44-444-400-44-400-44400000000000000000000000000000000000000000000000000
χ714-4-44-4-4444-4-44-4400-44400-4-4400000000000000000000000000000000000000000000000000
χ724-4-44-4-444-44-444-4004-44004-4-400000000000000000000000000000000000000000000000000
χ738-88-88i−8i−8i8i000000000000000000000000000000000000000000000000000000000000000000
χ748-88-8−8i8i8i−8i000000000000000000000000000000000000000000000000000000000000000000

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