Finite Group Databasebeta

← Group #316256

Character table — Group #316256

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
χ511111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1-1-1
χ611111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-11111
χ711111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-11111
χ811111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-111111111-1-1-1-1
χ911111111-1-1-1-11111111111111111-1-111-1-1-1-1-1-1-1-11111-1-1-1-111-1-111-1-11111-1-1-1-111-1-111-1-111-1-111-1-1
χ1011111111-1-1-1-11111111111111111-1-111-1-1-1-1-1-1-1-11111-1-1-1-111-1-111-1-11111-1-1-1-1-1-111-1-111-1-111-1-111
χ1111111111-1-1-1-11111111111111111-1-111-1-1-1-1-1-1-1-11111-1-1-1-1-1-111-1-111-1-1-1-1111111-1-111-1-1-1-111-1-111
χ1211111111-1-1-1-11111111111111111-1-111-1-1-1-1-1-1-1-11111-1-1-1-1-1-111-1-111-1-1-1-11111-1-111-1-11111-1-111-1-1
χ1311111111-1-1-1-111111111-1-1-1-1-1-1-1-1-1-111-1-1-1-11111-1-1-1-1111111-1-111-1-1-1-1-1-1111111-1-1-1-11111-1-1-1-111
χ1411111111-1-1-1-111111111-1-1-1-1-1-1-1-1-1-111-1-1-1-11111-1-1-1-1111111-1-111-1-1-1-1-1-11111-1-11111-1-1-1-11111-1-1
χ1511111111-1-1-1-111111111-1-1-1-1-1-1-1-1-1-111-1-1-1-11111-1-1-1-11111-1-111-1-1111111-1-1-1-111-1-1-1-111-1-11111-1-1
χ1611111111-1-1-1-111111111-1-1-1-1-1-1-1-1-1-111-1-1-1-11111-1-1-1-11111-1-111-1-1111111-1-1-1-1-1-11111-1-111-1-1-1-111
χ172222222222222-2-2222-2-222222222-2-2-2-2-2-222-2-2-2-2-2-2-2-2222200000000000000000000000000000000
χ182222222222222-2-2222-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-22222222222-2-2-2-200000000000000000000000000000000
χ19222222222222-222-2-2-22200000000-2-2-2-222-2-20000000000002222-2-2-2-2000000000000000000000000
χ20222222222222-222-2-2-22200000000-2-2-2-222-2-2000000000000-2-2-2-22222000000000000000000000000
χ21222222222222-2-2-2-2-2-2-2-2000000002222-2-2-2-2000000000000000000002i2i−2i−2i2i2i−2i−2i0000000000000000
χ22222222222222-2-2-2-2-2-2-2-2000000002222-2-2-2-200000000000000000000−2i−2i2i2i−2i−2i2i2i0000000000000000
χ2322222222-2-2-2-22-2-2222-2-22222222222-2-222-2-22222-2-2-2-2-2-2-2-200000000000000000000000000000000
χ2422222222-2-2-2-22-2-2222-2-2-2-2-2-2-2-2-2-222-2-222-2-2-2-2-2-22222222200000000000000000000000000000000
χ2522222222-2-2-2-2-222-2-2-2220000000022-2-2-2-22200000000000022-2-2-2-222000000000000000000000000
χ2622222222-2-2-2-2-222-2-2-2220000000022-2-2-2-222000000000000-2-22222-2-2000000000000000000000000
χ2722222222-2-2-2-2-2-2-2-2-2-2-2-200000000-2-2222222000000000000000000002i2i−2i−2i−2i−2i2i2i0000000000000000
χ2822222222-2-2-2-2-2-2-2-2-2-2-2-200000000-2-222222200000000000000000000−2i−2i2i2i2i2i−2i−2i0000000000000000
χ292-222-2-2-222i2i−2i−2i02-20002-2i2i2i2i2−i2−i2−i2−i200002i−2i0022−2−2i2i2−i2−i222−2−200002i−2i2-22−22−2i2−i2i2−i20000000000000000
χ302-222-2-2-222i2i−2i−2i02-20002-2i2i2i2i2−i2−i2−i2−i200002i−2i0022−2−2i2i2−i2−i222−2−20000−2i2i-22−22−22−i2i2−i2i20000000000000000
χ312-222-2-2-222i2i−2i−2i02-20002-2−i2−i2−i2−i2i2i2i2i200002i−2i00−2−222−i2−i2i2i2−2−22200002i−2i2-2−22−22−i2i2−i2i20000000000000000
χ322-222-2-2-222i2i−2i−2i02-20002-2−i2−i2−i2−i2i2i2i2i200002i−2i00−2−222−i2−i2i2i2−2−2220000−2i2i-222−22−2i2−i2i2−i20000000000000000
χ332-222-2-2-222i2i−2i−2i0-22000-22i2i2i2i2−i2−i2−i2−i20000−2i2i00−2−222−i2−i2i2i222−2−22-22i−2i0000i2−i2−i2i2−222−20000000000000000
χ342-222-2-2-222i2i−2i−2i0-22000-22i2i2i2i2−i2−i2−i2−i20000−2i2i00−2−222−i2−i2i2i222−2−2-22−2i2i0000−i2i2i2−i22−2−220000000000000000
χ352-222-2-2-222i2i−2i−2i0-22000-22−i2−i2−i2−i2i2i2i2i20000−2i2i0022−2−2i2i2−i2−i2−2−2222-22i−2i0000−i2i2i2−i22−2−220000000000000000
χ362-222-2-2-222i2i−2i−2i0-22000-22−i2−i2−i2−i2i2i2i2i20000−2i2i0022−2−2i2i2−i2−i2−2−222-22−2i2i0000i2−i2−i2i2−222−20000000000000000
χ372-222-2-2-22−2i−2i2i2i02-20002-2i2i2i2i2−i2−i2−i2−i20000−2i2i00−2−222i2i2−i2−i2−2−22200002i−2i-222−22−2−i2i2−i2i20000000000000000
χ382-222-2-2-22−2i−2i2i2i02-20002-2i2i2i2i2−i2−i2−i2−i20000−2i2i00−2−222i2i2−i2−i2−2−2220000−2i2i2-2−22−22i2−i2i2−i20000000000000000
χ392-222-2-2-22−2i−2i2i2i02-20002-2−i2−i2−i2−i2i2i2i2i20000−2i2i0022−2−2−i2−i2i2i222−2−200002i−2i-22−22−22i2−i2i2−i20000000000000000
χ402-222-2-2-22−2i−2i2i2i02-20002-2−i2−i2−i2−i2i2i2i2i20000−2i2i0022−2−2−i2−i2i2i222−2−20000−2i2i2-22−22−2−i2i2−i2i20000000000000000
χ412-222-2-2-22−2i−2i2i2i0-22000-22i2i2i2i2−i2−i2−i2−i200002i−2i0022−2−2−i2−i2i2i2−2−2222-2−2i2i0000i2−i2−i2i22−2−220000000000000000
χ422-222-2-2-22−2i−2i2i2i0-22000-22i2i2i2i2−i2−i2−i2−i200002i−2i0022−2−2−i2−i2i2i2−2−222-222i−2i0000−i2i2i2−i2−222−20000000000000000
χ432-222-2-2-22−2i−2i2i2i0-22000-22−i2−i2−i2−i2i2i2i2i200002i−2i00−2−222i2i2−i2−i222−2−22-2−2i2i0000−i2i2i2−i2−222−20000000000000000
χ442-222-2-2-22−2i−2i2i2i0-22000-22−i2−i2−i2−i2i2i2i2i200002i−2i00−2−222i2i2−i2−i222−2−2-222i−2i0000i2−i2−i2i22−2−220000000000000000
χ452-22-2-222-22i−2i2i−2i200-2-22002i2i−2i−2i2i2i−2i−2i0000002i−2i000000002-22-2000000000000000000000000i2−i22−22−2i2−i2
χ462-22-2-222-22i−2i2i−2i200-2-22002i2i−2i−2i2i2i−2i−2i0000002i−2i000000002-22-2000000000000000000000000−i2i2−22−22−i2i2
χ472-22-2-222-22i−2i2i−2i200-2-2200−2i−2i2i2i−2i−2i2i2i0000002i−2i00000000-22-22000000000000000000000000i2−i22−2−22−i2i2
χ482-22-2-222-22i−2i2i−2i200-2-2200−2i−2i2i2i−2i−2i2i2i0000002i−2i00000000-22-22000000000000000000000000−i2i2−222−2i2−i2
χ492-22-2-222-2−2i2i−2i2i200-2-22002i2i−2i−2i2i2i−2i−2i000000−2i2i00000000-22-22000000000000000000000000i2−i2−222−2−i2i2
χ502-22-2-222-2−2i2i−2i2i200-2-22002i2i−2i−2i2i2i−2i−2i000000−2i2i00000000-22-22000000000000000000000000−i2i22−2−22i2−i2
χ512-22-2-222-2−2i2i−2i2i200-2-2200−2i−2i2i2i−2i−2i2i2i000000−2i2i000000002-22-2000000000000000000000000i2−i2−22−22i2−i2
χ522-22-2-222-2−2i2i−2i2i200-2-2200−2i−2i2i2i−2i−2i2i2i000000−2i2i000000002-22-2000000000000000000000000−i2i22−22−2−i2i2
χ532-2-2-222-22000022-22-2-2-222i−2i2i−2i2i−2i2i−2i002-2000000002i−2i2i−2i000000000000000000002i−2i002-20000000000
χ542-2-2-222-22000022-22-2-2-222i−2i2i−2i2i−2i2i−2i002-2000000002i−2i2i−2i00000000000000000000−2i2i00-220000000000
χ552-2-2-222-22000022-22-2-2-22−2i2i−2i2i−2i2i−2i2i002-200000000−2i2i−2i2i000000000000000000002i−2i00-220000000000
χ562-2-2-222-22000022-22-2-2-22−2i2i−2i2i−2i2i−2i2i002-200000000−2i2i−2i2i00000000000000000000−2i2i002-20000000000
χ572-2-2-222-2200002-222-2-22-22i−2i2i−2i2i−2i2i−2i00-2200000000−2i2i−2i2i00000000000000000000002i−2i002-200000000
χ582-2-2-222-2200002-222-2-22-22i−2i2i−2i2i−2i2i−2i00-2200000000−2i2i−2i2i0000000000000000000000−2i2i00-2200000000
χ592-2-2-222-2200002-222-2-22-2−2i2i−2i2i−2i2i−2i2i00-22000000002i−2i2i−2i00000000000000000000002i−2i00-2200000000
χ602-2-2-222-2200002-222-2-22-2−2i2i−2i2i−2i2i−2i2i00-22000000002i−2i2i−2i0000000000000000000000−2i2i002-200000000
χ61444-44-4-4-44-4-44000000002222−22−22−22−222222000000000000000022−22−222200000000000000000000000000000000
χ62444-44-4-4-44-4-4400000000−22−2222222222−22−220000000000000000−222222−2200000000000000000000000000000000
χ63444-44-4-4-4-444-4000000002222−22−22−22−2222220000000000000000−222222−2200000000000000000000000000000000
χ64444-44-4-4-4-444-400000000−22−2222222222−22−22000000000000000022−22−222200000000000000000000000000000000
χ6544-44-44-4-40000400-44-4004-4-444-4-440000000000000000000000000000000000000000000000000000
χ6644-44-44-4-40000400-44-400-444-4-444-40000000000000000000000000000000000000000000000000000
χ6744-44-44-4-40000-4004-440000000000000000004i−4i4i−4i0000000000000000000000000000000000000000
χ6844-44-44-4-40000-4004-44000000000000000000−4i4i−4i4i0000000000000000000000000000000000000000
χ6944-4-4-4-4440000044000-4-422−2222−22−2222−222200000000000022−22−2222000000000000000000000000000000000000
χ7044-4-4-4-4440000044000-4-4−2222−222222−2222−22000000000000−222222−22000000000000000000000000000000000000
χ7144-4-4-4-44400000-4-40004422−2222−22−2222−2222000000000000−222222−22000000000000000000000000000000000000
χ7244-4-4-4-44400000-4-400044−2222−222222−2222−2200000000000022−22−2222000000000000000000000000000000000000
χ734-44-4-444-44i−4i4i−4i-40044-40000000000000000−4i4i00000000000000000000000000000000000000000000
χ744-44-4-444-4−4i4i−4i4i-40044-400000000000000004i−4i00000000000000000000000000000000000000000000
χ754-4-444-44-40000000000002i2−2i2−2i22i2−2i22i22i2−2i24-40000002i2−2i2−2i22i20000000000000000000000000000000000000000
χ764-4-444-44-40000000000002i2−2i2−2i22i2−2i22i22i2−2i2-44000000−2i22i22i2−2i20000000000000000000000000000000000000000
χ774-4-444-44-4000000000000−2i22i22i2−2i22i2−2i2−2i22i24-4000000−2i22i22i2−2i20000000000000000000000000000000000000000
χ784-4-444-44-4000000000000−2i22i22i2−2i22i2−2i2−2i22i2-440000002i2−2i2−2i22i20000000000000000000000000000000000000000
χ794-4-4-444-440000-44-4-444-440000000000-44000000000000000000000000000000000000000000000000
χ804-4-4-444-440000-4-44-4444-400000000004-4000000000000000000000000000000000000000000000000

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