Finite Group Databasebeta

← Group #405491

Character table — Group #405491

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80
size111111112222222222222222222244444444444444444444888888888888888816161616161616161616161616161616
order12222222222222224444444444442244888888888888888888888888888888882224444444448888
χ111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ3111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1111111-1-1-1-1-1-1
χ4111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-1111111
χ511111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1-1-1
χ611111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-11111
χ711111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-111-1-11111
χ811111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1111111-1-111-1-1-1-1
χ9111111111111-1-1-1-1111-1-1-1-111111-1-1-1-111111111-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1-1-1111-111-1-1-1-11-111-1-1
χ10111111111111-1-1-1-1111-1-1-1-111111-1-1-1-111111111-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1-1-1-1-1-11-1-11111-11-1-111
χ11111111111111-1-1-1-1111-1-1-1-111111-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1111111-1111-1-1-1-1-11-1-111
χ12111111111111-1-1-1-1111-1-1-1-111111-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-11111-1-11-1-1-111111-111-1-1
χ13111111111111-1-1-1-1111-1-1-1-111111-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-11111111-1-1-111-1-11-1-1-111
χ14111111111111-1-1-1-1111-1-1-1-111111-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-11111-1-1-1111-1-111-1111-1-1
χ15111111111111-1-1-1-1111-1-1-1-111111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-111111111-1-1-1-111-11-1-111-1-1-1111-1-1
χ16111111111111-1-1-1-1111-1-1-1-111111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-111111111-1-1-1-1-1-11-111-1-1111-1-1-111
χ172222222222222222-2-2-2-2-2-2-2-2-2-2-2-222-2-2000000000000000000000000000000000000000000002i−2i2i−2i
χ182222222222222222-2-2-2-2-2-2-2-2-2-2-2-222-2-200000000000000000000000000000000000000000000−2i2i−2i2i
χ19222222222222-2-2-2-2-2-2-22222-2-2-2-2-2-2-222000000000000000000000000000000000000000000002i−2i−2i2i
χ20222222222222-2-2-2-2-2-2-22222-2-2-2-2-2-2-22200000000000000000000000000000000000000000000−2i2i2i−2i
χ2122222222-2-2-2-2222222-22222-2-222-2-2-2-2-200000000000000000000000000000000002-2000000-220000
χ2222222222-2-2-2-2222222-22222-2-222-2-2-2-2-20000000000000000000000000000000000-220000002-20000
χ2322222222-2-2-2-22222-2-22-2-2-2-222-2-22-2-2222222-2-2-2-22222-2-2-2-200000000000000000000000000000000
χ2422222222-2-2-2-22222-2-22-2-2-2-222-2-22-2-222-2-2-2-22222-2-2-2-2222200000000000000000000000000000000
χ2522222222-2-2-2-2-2-2-2-222-2-2-2-2-2-2-222-22222000000000000000000000000000000000022000000-2-20000
χ2622222222-2-2-2-2-2-2-2-222-2-2-2-2-2-2-222-222220000000000000000000000000000000000-2-2000000220000
χ2722222222-2-2-2-2-2-2-2-2-2-22222222-2-2222-2-22222-2-2-2-2-2-2-2-2222200000000000000000000000000000000
χ2822222222-2-2-2-2-2-2-2-2-2-22222222-2-2222-2-2-2-2-2-222222222-2-2-2-200000000000000000000000000000000
χ2922-2-22-22-222-2-200002-2200002-22-2-20000000000002i2i−2i−2i2i2i−2i−2i00002i2i−2i−2i22-2-200000000000000000000
χ3022-2-22-22-222-2-200002-2200002-22-2-20000000000002i2i−2i−2i2i2i−2i−2i0000−2i−2i2i2i-2-22200000000000000000000
χ3122-2-22-22-222-2-200002-2200002-22-2-2000000000000−2i−2i2i2i−2i−2i2i2i00002i2i−2i−2i-2-22200000000000000000000
χ3222-2-22-22-222-2-200002-2200002-22-2-2000000000000−2i−2i2i2i−2i−2i2i2i0000−2i−2i2i2i22-2-200000000000000000000
χ3322-2-22-22-2-2-2220000-22200002-2-22-20000000000002i2i−2i−2i−2i−2i2i2i22-2-2000000002i2i−2i−2i0000000000000000
χ3422-2-22-22-2-2-2220000-22200002-2-22-20000000000002i2i−2i−2i−2i−2i2i2i-2-22200000000−2i−2i2i2i0000000000000000
χ3522-2-22-22-2-2-2220000-22200002-2-22-2000000000000−2i−2i2i2i2i2i−2i−2i22-2-200000000−2i−2i2i2i0000000000000000
χ3622-2-22-22-2-2-2220000-22200002-2-22-2000000000000−2i−2i2i2i2i2i−2i−2i-2-222000000002i2i−2i−2i0000000000000000
χ372-22-2-222-22-22-200002-220000-22-22-200002i2i−2i−2i2i2i−2i−2i000000002-22-200002i−2i2i−2i00000000000000000000
χ382-22-2-222-22-22-200002-220000-22-22-200002i2i−2i−2i2i2i−2i−2i00000000-22-220000−2i2i−2i2i00000000000000000000
χ392-22-2-222-22-22-200002-220000-22-22-20000−2i−2i2i2i−2i−2i2i2i000000002-22-20000−2i2i−2i2i00000000000000000000
χ402-22-2-222-22-22-200002-220000-22-22-20000−2i−2i2i2i−2i−2i2i2i00000000-22-2200002i−2i2i−2i00000000000000000000
χ412-22-2-222-2-22-220000-2220000-222-2-200002i2i−2i−2i−2i−2i2i2i0000000000002i−2i2i−2i00002-22-20000000000000000
χ422-22-2-222-2-22-220000-2220000-222-2-200002i2i−2i−2i−2i−2i2i2i000000000000−2i2i−2i2i0000-22-220000000000000000
χ432-22-2-222-2-22-220000-2220000-222-2-20000−2i−2i2i2i2i2i−2i−2i0000000000002i−2i2i−2i0000-22-220000000000000000
χ442-22-2-222-2-22-220000-2220000-222-2-20000−2i−2i2i2i2i2i−2i−2i000000000000−2i2i−2i2i00002-22-20000000000000000
χ452-2-22-2-2222-2-2222-2-222222-2-2-2-2-2-222-22-20000000000000000000000002i−2i−2i2i2i−2i−2i2i0000000000000000
χ462-2-22-2-2222-2-2222-2-222222-2-2-2-2-2-222-22-2000000000000000000000000−2i2i2i−2i−2i2i2i−2i0000000000000000
χ472-2-22-2-2222-2-2222-2-2-2-2-2-2-2222222-22-2-22000000000000000000000000000000002-20000002-2000000
χ482-2-22-2-2222-2-2222-2-2-2-2-2-2-2222222-22-2-2200000000000000000000000000000000-22000000-22000000
χ492-2-22-2-2222-2-22-2-222222-2-222-2-2-2-22-22-220000000000000000000000002i−2i−2i2i−2i2i2i−2i0000000000000000
χ502-2-22-2-2222-2-22-2-222222-2-222-2-2-2-22-22-22000000000000000000000000−2i2i2i−2i2i−2i−2i2i0000000000000000
χ512-2-22-2-2222-2-22-2-222-2-2-222-2-22222-2-222-2000000000000000000000000000000002-2000000-22000000
χ522-2-22-2-2222-2-22-2-222-2-2-222-2-22222-2-222-200000000000000000000000000000000-220000002-2000000
χ532-2-22-2-222-222-222-2-222-222-2-222-2-2-2-22-220000000000000000000000000000000000002i−2i2i−2i00000000
χ542-2-22-2-222-222-222-2-222-222-2-222-2-2-2-22-22000000000000000000000000000000000000−2i2i−2i2i00000000
χ552-2-22-2-222-222-222-2-2-2-22-2-222-2-2222-222-200000000000000002-2-222-2-22000000000000000000000000
χ562-2-22-2-222-222-222-2-2-2-22-2-222-2-2222-222-20000000000000000-222-2-222-2000000000000000000000000
χ572-2-22-2-222-222-2-2-22222-2-2-22222-2-2-22-22-20000000000000000000000000000000000002i−2i−2i2i00000000
χ582-2-22-2-222-222-2-2-22222-2-2-22222-2-2-22-22-2000000000000000000000000000000000000−2i2i2i−2i00000000
χ592-2-22-2-222-222-2-2-222-2-2222-2-2-2-22222-2-2200000000000000002-2-22-222-2000000000000000000000000
χ602-2-22-2-222-222-2-2-222-2-2222-2-2-2-22222-2-220000000000000000-222-22-2-22000000000000000000000000
χ61444-4-4-4-4400004-44-4000000000000000000002i2−2i22i2−2i200002i2−2i22i2−2i200000000000000000000000000000000
χ62444-4-4-4-4400004-44-400000000000000000000−2i22i2−2i22i20000−2i22i2−2i22i200000000000000000000000000000000
χ63444-4-4-4-440000-44-44000000000000000000002i2−2i22i2−2i20000−2i22i2−2i22i200000000000000000000000000000000
χ64444-4-4-4-440000-44-4400000000000000000000−2i22i2−2i22i200002i2−2i22i2−2i200000000000000000000000000000000
χ6544-44-44-4-4000000000004i−4i4i−4i0000000002i2−2i22i2−2i20000000022−22−222200000000000000000000000000000000
χ6644-44-44-4-4000000000004i−4i4i−4i000000000−2i22i2−2i22i200000000−222222−2200000000000000000000000000000000
χ6744-44-44-4-400000000000−4i4i−4i4i0000000002i2−2i22i2−2i200000000−222222−2200000000000000000000000000000000
χ6844-44-44-4-400000000000−4i4i−4i4i000000000−2i22i2−2i22i20000000022−22−222200000000000000000000000000000000
χ6944-4-44-44-444-4-40000-44-40000-44-4440000000000000000000000000000000000000000000000000000
χ7044-4-44-44-4-4-44400004-4-40000-444-440000000000000000000000000000000000000000000000000000
χ714-4444-4-4-4000000000004i−4i−4i4i000000000000022−22−22222i2−2i22i2−2i2000000000000000000000000000000000000
χ724-4444-4-4-4000000000004i−4i−4i4i0000000000000−222222−22−2i22i2−2i22i2000000000000000000000000000000000000
χ734-4444-4-4-400000000000−4i4i4i−4i000000000000022−22−2222−2i22i2−2i22i2000000000000000000000000000000000000
χ744-4444-4-4-400000000000−4i4i4i−4i0000000000000−222222−222i2−2i22i2−2i2000000000000000000000000000000000000
χ754-44-4-444-44-44-40000-44-400004-44-440000000000000000000000000000000000000000000000000000
χ764-44-4-444-4-44-4400004-4-400004-4-4440000000000000000000000000000000000000000000000000000
χ774-4-4-444-4400004-4-44000000000000000022−22−2222000022−22−2222000000000000000000000000000000000000
χ784-4-4-444-4400004-4-440000000000000000−222222−220000−222222−22000000000000000000000000000000000000
χ794-4-4-444-440000-444-4000000000000000022−22−22220000−222222−22000000000000000000000000000000000000
χ804-4-4-444-440000-444-40000000000000000−222222−22000022−22−2222000000000000000000000000000000000000

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