Finite Group Databasebeta

← Group #397948

Character table — Group #397948

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74
size11111111222222222222222244444488888888888888888888888888888888161616161616161616161616
order12224444222222224444444422244422444444444444444444444488888888224444448888
χ111111111111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11-111-1-11-1-1-1-1-1
χ311111111111111111111111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-11-1-111-11-1-1-1-1
χ411111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-11111
χ5111111111111111111111111111111-1-1-1-1-1-1-1-1111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1
χ6111111111111111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11-1-111-111111
χ7111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-11-111-1-11-11111
χ8111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111111111-1-1-1-1
χ9111111111111-1-11111111-1-11-1-1-1-1-1-111-1-1-1-1111111-1-1-1-11111-1-1-1-11111-1-1-1-111-1-1-1-11111-1-1
χ10111111111111-1-11111111-1-11-1-1-1-1-1-111-1-1-1-1111111-1-1-1-1-1-1-1-11111-1-1-1-111111-1-1-1111-1-1-111
χ11111111111111-1-11111111-1-11-1-1-1-1-1-111-1-1-1-111-1-1-1-111111111-1-1-1-1-1-1-1-11111-1111-1-1-11-1-111
χ12111111111111-1-11111111-1-11-1-1-1-1-1-111-1-1-1-111-1-1-1-11111-1-1-1-111111111-1-1-1-1-1-11111-1-111-1-1
χ13111111111111-1-11111111-1-11-1-1-1-1-1-1-1-11111-1-11111-1-1-1-11111-1-1-1-11111-1-1-1-1-1-11111-1-1-1-111
χ14111111111111-1-11111111-1-11-1-1-1-1-1-1-1-11111-1-11111-1-1-1-1-1-1-1-11111-1-1-1-11111-1111-1-1-1111-1-1
χ15111111111111-1-11111111-1-11-1-1-1-1-1-1-1-11111-1-1-1-1-1-111111111-1-1-1-1-1-1-1-111111-1-1-1111-111-1-1
χ16111111111111-1-11111111-1-11-1-1-1-1-1-1-1-11111-1-1-1-1-1-11111-1-1-1-111111111-1-1-1-111-1-1-1-111-1-111
χ172222222222-2-222-2-22-2-2-2-22222-2-22-2-200000000000000000000000022-2-222-2-2000000000000
χ182222222222-2-222-2-22-2-2-2-22222-2-22-2-2000000000000000000000000-2-222-2-222000000000000
χ192222222222-2-2-2-2-2-22-2-2-2-2-2-22-222-22200000000000000000000000022-2-2-2-222000000000000
χ202222222222-2-2-2-2-2-22-2-2-2-2-2-22-222-222000000000000000000000000-2-22222-2-2000000000000
χ2122222222-2-22-2222-2-222-2-222-2-22-2-22-2000000000000000022-2-222-2-200000000000000000000
χ2222222222-2-22-2222-2-222-2-222-2-22-2-22-20000000000000000-2-222-2-22200000000000000000000
χ2322222222-2-22-2-2-22-2-222-2-2-2-2-22-222-22000000000000000022-2-2-2-22200000000000000000000
χ2422222222-2-22-2-2-22-2-222-2-2-2-2-22-222-220000000000000000-2-22222-2-200000000000000000000
χ2522222222-2-2-2222-22-2-2-22222-2-2-22-2-220000000022-2-222-2-20000000000000000000000000000
χ2622222222-2-2-2222-22-2-2-22222-2-2-22-2-2200000000-2-222-2-2220000000000000000000000000000
χ2722222222-2-2-22-2-2-22-2-2-222-2-2-222-222-20000000022-2-2-2-2220000000000000000000000000000
χ2822222222-2-2-22-2-2-22-2-2-222-2-2-222-222-200000000-2-22222-2-20000000000000000000000000000
χ292222-2-2-2-222222222-2-2-2-2-2-2-2-2222-2-2-22222-2-2-2-2000000000000000000000000000000000000
χ302222-2-2-2-222222222-2-2-2-2-2-2-2-2222-2-2-2-2-2-2-22222000000000000000000000000000000000000
χ312222-2-2-2-22222-2-222-2-2-2-2-222-2-2-2-222222-2-222-2-2000000000000000000000000000000000000
χ322222-2-2-2-22222-2-222-2-2-2-2-222-2-2-2-2222-2-222-2-222000000000000000000000000000000000000
χ332222-2-2-2-222-2-222-2-2-22222-2-2-22-2-2-22200000000000000000000000000000000000000002i−2i2i−2i
χ342222-2-2-2-222-2-222-2-2-22222-2-2-22-2-2-2220000000000000000000000000000000000000000−2i2i−2i2i
χ352222-2-2-2-222-2-2-2-2-2-2-2222222-2-2222-2-200000000000000000000000000000000000000002i−2i−2i2i
χ362222-2-2-2-222-2-2-2-2-2-2-2222222-2-2222-2-20000000000000000000000000000000000000000−2i2i2i−2i
χ372222-2-2-2-2-2-22-2222-22-2-222-2-22-22-22-220000000000000000000000000000000002002-20-20000
χ382222-2-2-2-2-2-22-2222-22-2-222-2-22-22-22-22000000000000000000000000000000000-200-22020000
χ392222-2-2-2-2-2-22-2-2-22-22-2-2222222-22-22-2000000000000000000000000000000000200-220-20000
χ402222-2-2-2-2-2-22-2-2-22-22-2-2222222-22-22-2000000000000000000000000000000000-2002-2020000
χ412222-2-2-2-2-2-2-2222-22222-2-2-2-22-2-2222-200000000000000000000000000000000202-200-200000
χ422222-2-2-2-2-2-2-2222-22222-2-2-2-22-2-2222-200000000000000000000000000000000-20-2200200000
χ432222-2-2-2-2-2-2-22-2-2-22222-2-222222-2-2-220000000000000000000000000000000020-2200-200000
χ442222-2-2-2-2-2-2-22-2-2-22222-2-222222-2-2-2200000000000000000000000000000000-202-200200000
χ452-2-2222-2-22-22200-2-2-22-22-20020000000000000000002i−2i2i−2i00002i−2i2i−2i2-22-20000000000000000
χ462-2-2222-2-22-22200-2-2-22-22-20020000000000000000002i−2i2i−2i0000−2i2i−2i2i-22-220000000000000000
χ472-2-2222-2-22-22200-2-2-22-22-2002000000000000000000−2i2i−2i2i00002i−2i2i−2i-22-220000000000000000
χ482-2-2222-2-22-22200-2-2-22-22-2002000000000000000000−2i2i−2i2i0000−2i2i−2i2i2-22-20000000000000000
χ492-2-2222-2-22-2-2-20022-2-22-22002000000000000002-22-200002-22-200002-2-220000000000000000
χ502-2-2222-2-22-2-2-20022-2-22-22002000000000000002-22-20000-22-220000-222-20000000000000000
χ512-2-2222-2-22-2-2-20022-2-22-2200200000000000000-22-2200002-22-20000-222-20000000000000000
χ522-2-2222-2-22-2-2-20022-2-22-2200200000000000000-22-220000-22-2200002-2-220000000000000000
χ532-2-2222-2-2-222-200-2222-2-2200-2000000000000002-2-22000000002i−2i−2i2i00002i−2i2i−2i000000000000
χ542-2-2222-2-2-222-200-2222-2-2200-2000000000000002-2-2200000000−2i2i2i−2i0000−2i2i−2i2i000000000000
χ552-2-2222-2-2-222-200-2222-2-2200-200000000000000-222-2000000002i−2i−2i2i0000−2i2i−2i2i000000000000
χ562-2-2222-2-2-222-200-2222-2-2200-200000000000000-222-200000000−2i2i2i−2i00002i−2i2i−2i000000000000
χ572-2-2222-2-2-22-22002-22-222-200-20000000000000000002i−2i−2i2i2-2-2200000000−2i2i2i−2i000000000000
χ582-2-2222-2-2-22-22002-22-222-200-20000000000000000002i−2i−2i2i-222-2000000002i−2i−2i2i000000000000
χ592-2-2222-2-2-22-22002-22-222-200-2000000000000000000−2i2i2i−2i2-2-22000000002i−2i−2i2i000000000000
χ602-2-2222-2-2-22-22002-22-222-200-2000000000000000000−2i2i2i−2i-222-200000000−2i2i2i−2i000000000000
χ6144-4-44i−4i4i−4i00004-400000004i−4i00000002-22-22i−2i2i−2i000000000000000000000000000000000000
χ6244-4-44i−4i4i−4i00004-400000004i−4i0000000-22-22−2i2i−2i2i000000000000000000000000000000000000
χ6344-4-44i−4i4i−4i0000-440000000−4i4i00000002-2-22−2i2i2i−2i000000000000000000000000000000000000
χ6444-4-44i−4i4i−4i0000-440000000−4i4i0000000-222-22i−2i−2i2i000000000000000000000000000000000000
χ6544-4-4−4i4i−4i4i00004-40000000−4i4i00000002-22-2−2i2i−2i2i000000000000000000000000000000000000
χ6644-4-4−4i4i−4i4i00004-40000000−4i4i0000000-22-222i−2i2i−2i000000000000000000000000000000000000
χ6744-4-4−4i4i−4i4i0000-4400000004i−4i00000002-2-222i−2i−2i2i000000000000000000000000000000000000
χ6844-4-4−4i4i−4i4i0000-4400000004i−4i0000000-222-2−2i2i2i−2i000000000000000000000000000000000000
χ694-4-44-4-4444-44400-4-44-44-4400-400000000000000000000000000000000000000000000000000
χ704-4-44-4-4444-4-4-4004444-44-400-400000000000000000000000000000000000000000000000000
χ714-4-44-4-444-444-400-44-4-444-400400000000000000000000000000000000000000000000000000
χ724-4-44-4-444-44-44004-4-44-4-4400400000000000000000000000000000000000000000000000000
χ738-88-88i−8i−8i8i000000000000000000000000000000000000000000000000000000000000000000
χ748-88-8−8i8i8i−8i000000000000000000000000000000000000000000000000000000000000000000

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