Finite Group Databasebeta

← Group #405273

Character table — Group #405273

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74
size11111111222222222222444444444444888888888888888888888888888888161616161616161616161616
order12224444222222444444222244444444222222444444444444444488888888444444448888
χ111111111111111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111111-1-11111-1-1-1-1-1-111111111111111-1-1-1-1-1-1-1-1-1-1-1-1
χ311111111111111111111111111111111-1-1-1-111-1-1-1-1111111111111-1-1-1-1-1-1-1-111-1-1-1-111-1-1-1-1
χ411111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1-1-11111-1-11111
χ51111111111111111111111111111-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-1-1
χ61111111111111111111111111111-1-1-1-11111-1-11111-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-11111
χ71111111111111111111111111111-1-1-1-1-1-1-1-111-1-1-1-111-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1111111
χ81111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-111111111111111-1-1-1-1-1-1
χ911111111111111111111-1-1-1-1-1-1-1-1111111-1-11111-1-111111111-1-1-1-11111-1-1-1-1-1-111-1-1-1-111-1-1
χ1011111111111111111111-1-1-1-1-1-1-1-1111111-1-1-1-111-1-1-1-1-1-1-1-111-1-1-1-11111-1-1-1-111-1-11111-1-111
χ1111111111111111111111-1-1-1-1-1-1-1-11111-1-11111-1-11111111111-1-1-1-1-1-1-1-11111-1-1-1-111-1-1-1-111
χ1211111111111111111111-1-1-1-1-1-1-1-11111-1-111-1-1-1-111-1-1-1-1-1-111-1-1-1-1-1-1-1-111111111-1-11111-1-1
χ1311111111111111111111-1-1-1-1-1-1-1-1-1-1-1-111-1-11111-1-111-1-1-1-1-1-11111-1-1-1-111111111-1-1-1-1-1-111
χ1411111111111111111111-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-111-1-1-1-11111-1-11111-1-1-1-11111-1-1-1-1111111-1-1
χ1511111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-11111-1-1-1-1-1-111111111-1-1-1-111-1-111-1-111-1-1
χ1611111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-111-1-11111-1-111111111-1-1-1-1-1-111-1-111-1-111
χ1722222222-2-22-2-2222-2-2-2-222-2-222-2-222220000000000000000-2-222-2-200000000000000000000
χ1822222222-2-22-2-2222-2-2-2-222-2-222-2-2-2-2-2-2000000000000000022-2-22200000000000000000000
χ1922222222-2-22-2-2222-2-2-2-2-2-222-2-22222220000000000000000-2-2-2-22200000000000000000000
χ2022222222-2-22-2-2222-2-2-2-2-2-222-2-222-2-2-2-200000000000000002222-2-200000000000000000000
χ212222-2-2-2-2222222-2-2-2-2-2-222-2-2-2-22200000000220000-2-20000000000000000000000002-20000
χ222222-2-2-2-2222222-2-2-2-2-2-222-2-2-2-22200000000-2-2000022000000000000000000000000-220000
χ232222-2-2-2-2222222-2-2-2-2-2-2-2-22222-2-200000000220000-2-2000000000000000000000000-220000
χ242222-2-2-2-2222222-2-2-2-2-2-2-2-22222-2-200000000-2-20000220000000000000000000000002-20000
χ252222-2-2-2-22-2-22-2-2222-22-2000000002i2i−2i−2i00220000-2-20000002i−2i000000002i2i−2i−2i000000000000
χ262222-2-2-2-22-2-22-2-2222-22-2000000002i2i−2i−2i00-2-20000220000002i−2i00000000−2i−2i2i2i000000000000
χ272222-2-2-2-22-2-22-2-2222-22-200000000−2i−2i2i2i00220000-2-2000000−2i2i00000000−2i−2i2i2i000000000000
χ282222-2-2-2-22-2-22-2-2222-22-200000000−2i−2i2i2i00-2-2000022000000−2i2i000000002i2i−2i−2i000000000000
χ292222-2-2-2-2-22-2-22-222-22-22000000002i2i−2i−2i220000-2-200000000−2i2i00002i2i−2i−2i0000000000000000
χ302222-2-2-2-2-22-2-22-222-22-22000000002i2i−2i−2i-2-200002200000000−2i2i0000−2i−2i2i2i0000000000000000
χ312222-2-2-2-2-22-2-22-222-22-2200000000−2i−2i2i2i220000-2-2000000002i−2i0000−2i−2i2i2i0000000000000000
χ322222-2-2-2-2-22-2-22-222-22-2200000000−2i−2i2i2i-2-2000022000000002i−2i00002i2i−2i−2i0000000000000000
χ332222-2-2-2-2-2-22-2-22-2-222222222-2-2-2-2000000000000000022-2-2000000000000002-20000000000
χ342222-2-2-2-2-2-22-2-22-2-222222222-2-2-2-20000000000000000-2-22200000000000000-220000000000
χ352222-2-2-2-2-2-22-2-22-2-22222-2-2-2-22222000000000000000022-2-200000000000000-220000000000
χ362222-2-2-2-2-2-22-2-22-2-22222-2-2-2-222220000000000000000-2-222000000000000002-20000000000
χ372-2-2222-2-222-2-2-222-222-2-22-22-22-22-20000000000000000000000000000000000000000002i−2i2i−2i
χ382-2-2222-2-222-2-2-222-222-2-22-22-22-22-2000000000000000000000000000000000000000000−2i2i−2i2i
χ392-2-2222-2-222-2-2-222-222-2-2-22-22-22-220000000000000000000000000000000000000000002i−2i−2i2i
χ402-2-2222-2-222-2-2-222-222-2-2-22-22-22-22000000000000000000000000000000000000000000−2i2i2i−2i
χ412-2-2222-2-22-22-22-2-22-222-20000000000002-200002-200000000002i−2i2i−2i00002i−2i2i−2i000000000000
χ422-2-2222-2-22-22-22-2-22-222-20000000000002-200002-20000000000−2i2i−2i2i0000−2i2i−2i2i000000000000
χ432-2-2222-2-22-22-22-2-22-222-2000000000000-220000-2200000000002i−2i2i−2i0000−2i2i−2i2i000000000000
χ442-2-2222-2-22-22-22-2-22-222-2000000000000-220000-220000000000−2i2i−2i2i00002i−2i2i−2i000000000000
χ452-2-2222-2-2-2222-2-2-222-2-22000000000000002-200002-2000000002i−2i−2i2i2i−2i2i−2i0000000000000000
χ462-2-2222-2-2-2222-2-2-222-2-22000000000000002-200002-200000000−2i2i2i−2i−2i2i−2i2i0000000000000000
χ472-2-2222-2-2-2222-2-2-222-2-2200000000000000-220000-22000000002i−2i−2i2i−2i2i−2i2i0000000000000000
χ482-2-2222-2-2-2222-2-2-222-2-2200000000000000-220000-2200000000−2i2i2i−2i2i−2i2i−2i0000000000000000
χ492-2-2222-2-2-2-2-22222-2-2-2222-2-222-2-220000000000000000000000000000000000002-22-2000000
χ502-2-2222-2-2-2-2-22222-2-2-2222-2-222-2-22000000000000000000000000000000000000-22-22000000
χ512-2-2222-2-2-2-2-22222-2-2-222-222-2-222-20000000000000000000000000000000000002-2-22000000
χ522-2-2222-2-2-2-2-22222-2-2-222-222-2-222-2000000000000000000000000000000000000-222-2000000
χ532-2-22-2-22222-2-2-22-22-2-2222-2-22-222-2000000000000000000000000002-2-222-2-22000000000000
χ542-2-22-2-22222-2-2-22-22-2-2222-2-22-222-200000000000000000000000000-222-2-222-2000000000000
χ552-2-22-2-22222-2-2-22-22-2-222-222-22-2-22000000000000000000000000002-2-22-222-2000000000000
χ562-2-22-2-22222-2-2-22-22-2-222-222-22-2-2200000000000000000000000000-222-22-2-22000000000000
χ572-2-22-2-222-2-2-2222-2222-2-22-22-2-22-2200002-22-200-22-2200000000000000000000000000000000
χ582-2-22-2-222-2-2-2222-2222-2-22-22-2-22-220000-22-22002-22-200000000000000000000000000000000
χ592-2-22-2-222-2-2-2222-2222-2-2-22-222-22-200002-2-2200-222-200000000000000000000000000000000
χ602-2-22-2-222-2-2-2222-2222-2-2-22-222-22-20000-222-2002-2-2200000000000000000000000000000000
χ61444444444-4-44-4-4-4-4-44-44000000000000000000000000000000000000000000000000000000
χ6244444444-44-4-44-4-4-44-44-4000000000000000000000000000000000000000000000000000000
χ6344-4-44i−4i4i−4i000000000000000000002+2i−2−2i2−2i−2+2i00002-200002i−2i2-22i−2i00000000000000000000000000
χ6444-4-44i−4i4i−4i000000000000000000002+2i−2−2i2−2i−2+2i0000-220000−2i2i-22−2i2i00000000000000000000000000
χ6544-4-44i−4i4i−4i00000000000000000000−2−2i2+2i−2+2i2−2i00002-200002i−2i-22−2i2i00000000000000000000000000
χ6644-4-44i−4i4i−4i00000000000000000000−2−2i2+2i−2+2i2−2i0000-220000−2i2i2-22i−2i00000000000000000000000000
χ6744-4-4−4i4i−4i4i000000000000000000002−2i−2+2i2+2i−2−2i00002-20000−2i2i2-2−2i2i00000000000000000000000000
χ6844-4-4−4i4i−4i4i000000000000000000002−2i−2+2i2+2i−2−2i0000-2200002i−2i-222i−2i00000000000000000000000000
χ6944-4-4−4i4i−4i4i00000000000000000000−2+2i2−2i−2−2i2+2i00002-20000−2i2i-222i−2i00000000000000000000000000
χ7044-4-4−4i4i−4i4i00000000000000000000−2+2i2−2i−2−2i2+2i0000-2200002i−2i2-2−2i2i00000000000000000000000000
χ714-4-44-4-4444-44-44-44-44-4-44000000000000000000000000000000000000000000000000000000
χ724-4-44-4-444-4444-4-44-4-444-4000000000000000000000000000000000000000000000000000000
χ738-88-88i−8i−8i8i000000000000000000000000000000000000000000000000000000000000000000
χ748-88-8−8i8i8i−8i000000000000000000000000000000000000000000000000000000000000000000

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