Finite Group Databasebeta

← Group #314683

Character table — Group #314683

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80
size111111112222222222222222222244444444444444444444888888888888888816161616161616161616161616161616
order12222222444444444444888888882244444488888888888844444444888888884444444488888888
χ111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ3111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1
χ4111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111
χ511111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-111-1-111-1-11111-1-1-1-1
χ611111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-111-1-111-1-1-1-11111
χ711111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111-1-111-1-1-1-1-1-11111
χ811111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-111-1-1111111-1-1-1-1
χ911111111111-1-1-1-11111111111111-1-1-1-111-1-1-1-1-1-11111-1-1-1-111-1-1-1-1111111-1-1-1-11111-1-1-1-111-1-111-1-1
χ1011111111111-1-1-1-11111111111111-1-1-1-111-1-1-1-1-1-11111-1-1-1-111-1-1-1-1111111-1-1-1-1-1-1-1-11111-1-111-1-111
χ1111111111111-1-1-1-11111111111111-1-1-1-111-1-1-1-1-1-11111-1-1-1-1-1-11111-1-1-1-1-1-111111111-1-1-1-1-1-111-1-111
χ1211111111111-1-1-1-11111111111111-1-1-1-111-1-1-1-1-1-11111-1-1-1-1-1-11111-1-1-1-1-1-11111-1-1-1-1111111-1-111-1-1
χ1311111111111-1-1-1-111111-1-1-1-1-1-1-1-1-1-1-1-111-1-11111-1-1-1-1111111-1-1-1-111-1-1-1-1111111-1-1-1-11111-1-1-1-111
χ1411111111111-1-1-1-111111-1-1-1-1-1-1-1-1-1-1-1-111-1-11111-1-1-1-1111111-1-1-1-111-1-1-1-11111-1-11111-1-1-1-11111-1-1
χ1511111111111-1-1-1-111111-1-1-1-1-1-1-1-1-1-1-1-111-1-11111-1-1-1-11111-1-11111-1-11111-1-1-1-111-1-1-1-111-1-11111-1-1
χ1611111111111-1-1-1-111111-1-1-1-1-1-1-1-1-1-1-1-111-1-11111-1-1-1-11111-1-11111-1-11111-1-1-1-1-1-11111-1-111-1-1-1-111
χ17222222222-2-22222222-2-222222222-2-2-2-2-2-222-2-2-2-2-2-2-2-2222200000000000000000000000000000000
χ18222222222-2-22222222-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-22222222222-2-2-2-200000000000000000000000000000000
χ19222222222-2-2-2-2-2-2222-2-2222222222222-2-2-2-22222-2-2-2-2-2-2-2-200000000000000000000000000000000
χ20222222222-2-2-2-2-2-2222-2-2-2-2-2-2-2-2-2-22222-2-2-2-2-2-2-2-22222222200000000000000000000000000000000
χ2122222222-2222222-2-2-2220000000022-2-2-2-2-2-20000000000002222-2-2-2-2000000000000000000000000
χ2222222222-2222222-2-2-2220000000022-2-2-2-2-2-2000000000000-2-2-2-22222000000000000000000000000
χ2322222222-222-2-2-2-2-2-2-22200000000-2-222-2-22200000000000022-2-222-2-2000000000000000000000000
χ2422222222-222-2-2-2-2-2-2-22200000000-2-222-2-222000000000000-2-222-2-222000000000000000000000000
χ2522222222-2-2-22222-2-2-2-2-200000000-2-22222-2-2000000000000000000002i2i−2i−2i2i2i−2i−2i0000000000000000
χ2622222222-2-2-22222-2-2-2-2-200000000-2-22222-2-200000000000000000000−2i−2i2i2i−2i−2i2i2i0000000000000000
χ2722222222-2-2-2-2-2-2-2-2-2-2-2-20000000022-2-22222000000000000000000002i2i−2i−2i−2i−2i2i2i0000000000000000
χ2822222222-2-2-2-2-2-2-2-2-2-2-2-20000000022-2-2222200000000000000000000−2i−2i2i2i2i2i−2i−2i0000000000000000
χ292-222-2-2-22-2002i2i−2i−2i22-2002222-2-2-2-20000002i−2i000000002i2i−2i−2i000000000000000000000000i2−i22−2i2−i22−2
χ302-222-2-2-22-2002i2i−2i−2i22-2002222-2-2-2-20000002i−2i000000002i2i−2i−2i000000000000000000000000−i2i2−22−i2i2−22
χ312-222-2-2-22-2002i2i−2i−2i22-200-2-2-2-222220000002i−2i00000000−2i−2i2i2i000000000000000000000000i2−i22−2−i2i2−22
χ322-222-2-2-22-2002i2i−2i−2i22-200-2-2-2-222220000002i−2i00000000−2i−2i2i2i000000000000000000000000−i2i2−22i2−i22−2
χ332-222-2-2-22-200−2i−2i2i2i22-2002222-2-2-2-2000000−2i2i00000000−2i−2i2i2i000000000000000000000000i2−i2−22i2−i2−22
χ342-222-2-2-22-200−2i−2i2i2i22-2002222-2-2-2-2000000−2i2i00000000−2i−2i2i2i000000000000000000000000−i2i22−2−i2i22−2
χ352-222-2-2-22-200−2i−2i2i2i22-200-2-2-2-22222000000−2i2i000000002i2i−2i−2i000000000000000000000000i2−i2−22−i2i22−2
χ362-222-2-2-22-200−2i−2i2i2i22-200-2-2-2-22222000000−2i2i000000002i2i−2i−2i000000000000000000000000−i2i22−2i2−i2−22
χ372-22-222-2-2-22-200002-222-222-2-222-2-200002-200000022-2-20000000000000000000000002i−2i2i−2i00000000
χ382-22-222-2-2-22-200002-222-222-2-222-2-200002-200000022-2-2000000000000000000000000−2i2i−2i2i00000000
χ392-22-222-2-2-22-200002-222-2-2-222-2-22200002-2000000-2-2220000000000000000000000002i−2i−2i2i00000000
χ402-22-222-2-2-22-200002-222-2-2-222-2-22200002-2000000-2-222000000000000000000000000−2i2i2i−2i00000000
χ412-22-222-2-2-2-2200002-22-2222-2-222-2-20000-22000000-2-222000000000000000000002i−2i2i−2i000000000000
χ422-22-222-2-2-2-2200002-22-2222-2-222-2-20000-22000000-2-22200000000000000000000−2i2i−2i2i000000000000
χ432-22-222-2-2-2-2200002-22-22-2-222-2-2220000-2200000022-2-2000000000000000000002i−2i−2i2i000000000000
χ442-22-222-2-2-2-2200002-22-22-2-222-2-2220000-2200000022-2-200000000000000000000−2i2i2i−2i000000000000
χ452-2-2-22-2220222-22-2000-2-22−22−22−22−22-200000022−2−22−22−22−22−22i−2i2i−2i0000i2−i2i2−i2i2−i2i2−i20000000000000000
χ462-2-2-22-2220222-22-2000-2-22−22−22−22−22-200000022−2−22−22−22−22−2−2i2i−2i2i0000−i2i2−i2i2−i2i2−i2i20000000000000000
χ472-2-2-22-2220222-22-2000-2-2−22−22−22−222-2000000−2−222−22−22−22−222i−2i2i−2i0000−i2i2−i2i2−i2i2−i2i20000000000000000
χ482-2-2-22-2220222-22-2000-2-2−22−22−22−222-2000000−2−222−22−22−22−22−2i2i−2i2i0000i2−i2i2−i2i2−i2i2−i20000000000000000
χ492-2-2-22-222022-22-22000-2-22−22−22−22−2-22000000−2−2222−22−2−22−222i−2i−2i2i0000i2−i2i2−i2−i2i2−i2i20000000000000000
χ502-2-2-22-222022-22-22000-2-22−22−22−22−2-22000000−2−2222−22−2−22−22−2i2i2i−2i0000−i2i2−i2i2i2−i2i2−i20000000000000000
χ512-2-2-22-222022-22-22000-2-2−22−22−22−22-2200000022−2−2−22−222−22−22i−2i−2i2i0000−i2i2−i2i2i2−i2i2−i20000000000000000
χ522-2-2-22-222022-22-22000-2-2−22−22−22−22-2200000022−2−2−22−222−22−2−2i2i2i−2i0000i2−i2i2−i2−i2i2−i2i20000000000000000
χ532-2-2-22-2220-2-22-22-2000222−22−22−22−2-22000000−2−222−22−222−22−200002-22-22−2−222−2−220000000000000000
χ542-2-2-22-2220-2-22-22-2000222−22−22−22−2-22000000−2−222−22−222−22−20000-22-22−222−2−222−20000000000000000
χ552-2-2-22-2220-2-22-22-200022−22−22−22−22-2200000022−2−22−22−2−22−2200002-22-2−222−2−222−20000000000000000
χ562-2-2-22-2220-2-22-22-200022−22−22−22−22-2200000022−2−22−22−2−22−220000-22-222−2−222−2−220000000000000000
χ572-2-2-22-2220-2-2-22-22000222−22−22−22−22-200000022−2−2−22−22−22−2200002-2-22−222−22−2−220000000000000000
χ582-2-2-22-2220-2-2-22-22000222−22−22−22−22-200000022−2−2−22−22−22−220000-222-22−2−22−222−20000000000000000
χ592-2-2-22-2220-2-2-22-2200022−22−22−22−222-2000000−2−2222−22−22−22−200002-2-222−2−22−222−20000000000000000
χ602-2-2-22-2220-2-2-22-2200022−22−22−22−222-2000000−2−2222−22−22−22−20000-222-2−222−22−2−220000000000000000
χ61444-4-4-44-440000004-4-40044-4-4-4-4440000000000000000000000000000000000000000000000000000
χ62444-4-4-44-440000004-4-400-4-44444-4-40000000000000000000000000000000000000000000000000000
χ63444-4-4-44-4-4000000-4440000000000000000004i−4i4i−4i0000000000000000000000000000000000000000
χ64444-4-4-44-4-4000000-444000000000000000000−4i4i−4i4i0000000000000000000000000000000000000000
χ6544-444-4-4-404-40000000-4422−22−222222−22−222200000000000022−22−2222000000000000000000000000000000000000
χ6644-444-4-4-404-40000000-44−222222−22−222222−22000000000000−222222−22000000000000000000000000000000000000
χ6744-444-4-4-40-4400000004-422−22−222222−22−2222000000000000−222222−22000000000000000000000000000000000000
χ6844-444-4-4-40-4400000004-4−222222−22−222222−2200000000000022−22−2222000000000000000000000000000000000000
χ6944-4-4-44-440004i−4i−4i4i0000022−2222−22−2222−222200000000000000002i2−2i2−2i22i200000000000000000000000000000000
χ7044-4-4-44-440004i−4i−4i4i00000−2222−222222−2222−220000000000000000−2i22i22i2−2i200000000000000000000000000000000
χ7144-4-4-44-44000−4i4i4i−4i0000022−2222−22−2222−22220000000000000000−2i22i22i2−2i200000000000000000000000000000000
χ7244-4-4-44-44000−4i4i4i−4i00000−2222−222222−2222−2200000000000000002i2−2i2−2i22i200000000000000000000000000000000
χ734-444-4-4-444004i4i−4i−4i-4-440000000000000000−4i4i00000000000000000000000000000000000000000000
χ744-444-4-4-44400−4i−4i4i4i-4-4400000000000000004i−4i00000000000000000000000000000000000000000000
χ754-44-444-4-444-40000-44-44-4000000000000-440000000000000000000000000000000000000000000000
χ764-44-444-4-44-440000-44-4-440000000000004-40000000000000000000000000000000000000000000000
χ774-4-44-444-400000000000022−22−2222−222222−22004i−4i00002i2−2i2−2i22i20000000000000000000000000000000000000000
χ784-4-44-444-400000000000022−22−2222−222222−2200−4i4i0000−2i22i22i2−2i20000000000000000000000000000000000000000
χ794-4-44-444-4000000000000−222222−2222−22−2222004i−4i0000−2i22i22i2−2i20000000000000000000000000000000000000000
χ804-4-44-444-4000000000000−222222−2222−22−222200−4i4i00002i2−2i2−2i22i20000000000000000000000000000000000000000

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