Finite Group Databasebeta

← Group #314686

Character table — Group #314686

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80
size111111112222222222222222222244444444444444444444888888888888888816161616161616161616161616161616
order12222222444444444444888888882244444488888888888822444444888888884444444488888888
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
χ911111111-1-1-1-11111111111111111-1-111-1-1-1-11111-1-1-1-1-1-1-1-111-1-111-1-1-1-1-1-1111111-1-1-1-11111-1-111-1-1
χ1011111111-1-1-1-11111111111111111-1-111-1-1-1-11111-1-1-1-1-1-1-1-111-1-111-1-1-1-1-1-11111-1-11111-1-1-1-111-1-111
χ1111111111-1-1-1-11111111111111111-1-111-1-1-1-11111-1-1-1-1-1-1-1-1-1-111-1-1111111-1-1-1-111-1-1-1-111-1-111-1-111
χ1211111111-1-1-1-11111111111111111-1-111-1-1-1-11111-1-1-1-1-1-1-1-1-1-111-1-1111111-1-1-1-1-1-11111-1-111-1-111-1-1
χ1311111111-1-1-1-111111111-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-11111111111-1-111-1-11111-1-1-1-11111-1-1-1-111-1-1-1-111
χ1411111111-1-1-1-111111111-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-11111111111-1-111-1-11111-1-1-1-1-1-1-1-11111-1-11111-1-1
χ1511111111-1-1-1-111111111-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-111111111-1-111-1-111-1-1-1-111111111-1-1-1-1-1-11111-1-1
χ1611111111-1-1-1-111111111-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-111111111-1-111-1-111-1-1-1-11111-1-1-1-1111111-1-1-1-111
χ172222222222222-2-2-2-222222222222-2-2-2-222-2-2-2-2-2-22222-2-2-2-200000000000000000000000000000000
χ182222222222222-2-2-2-2222-2-2-2-2-2-2-2-2-2-2-2-222-2-22222-2-2-2-2222200000000000000000000000000000000
χ19222222222222-22222-2-2-200000000-2-2-2-2-2-22200000000000022-2-2-2-222000000000000000000000000
χ20222222222222-22222-2-2-200000000-2-2-2-2-2-222000000000000-2-22222-2-2000000000000000000000000
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
χ2322222222-2-2-2-22-2-2-2-22222222222222-2-2-2-222-2-2-2-2-2-2-2-2222200000000000000000000000000000000
χ2422222222-2-2-2-22-2-2-2-2222-2-2-2-2-2-2-2-222-2-2-2-22222222222-2-2-2-200000000000000000000000000000000
χ2522222222-2-2-2-2-22222-2-2-20000000022-2-222-2-20000000000002222-2-2-2-2000000000000000000000000
χ2622222222-2-2-2-2-22222-2-2-20000000022-2-222-2-2000000000000-2-2-2-22222000000000000000000000000
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
χ2922-2-2-222-22i2i−2i−2i-2000022-22i2i2i2i−2i−2i−2i−2i00002i−2i00000022-2-200000000000000000000000000002−2i2−i2i2−i22−2
χ3022-2-2-222-22i2i−2i−2i-2000022-22i2i2i2i−2i−2i−2i−2i00002i−2i00000022-2-20000000000000000000000000000−22−i2i2−i2i2−22
χ3122-2-2-222-22i2i−2i−2i-2000022-2−2i−2i−2i−2i2i2i2i2i00002i−2i000000-2-22200000000000000000000000000002−2i2−i2−i2i2−22
χ3222-2-2-222-22i2i−2i−2i-2000022-2−2i−2i−2i−2i2i2i2i2i00002i−2i000000-2-2220000000000000000000000000000−22−i2i2i2−i22−2
χ3322-2-2-222-2−2i−2i2i2i-2000022-22i2i2i2i−2i−2i−2i−2i0000−2i2i000000-2-22200000000000000000000000000002−2−i2i2i2−i2−22
χ3422-2-2-222-2−2i−2i2i2i-2000022-22i2i2i2i−2i−2i−2i−2i0000−2i2i000000-2-2220000000000000000000000000000−22i2−i2−i2i22−2
χ3522-2-2-222-2−2i−2i2i2i-2000022-2−2i−2i−2i−2i2i2i2i2i0000−2i2i00000022-2-200000000000000000000000000002−2−i2i2−i2i22−2
χ3622-2-2-222-2−2i−2i2i2i-2000022-2−2i−2i−2i−2i2i2i2i2i0000−2i2i00000022-2-20000000000000000000000000000−22i2−i2i2−i2−22
χ372-222-22-2-20000-222-2-22-2222-2-222-2-2002-2000022-2-2000000000000000000000000002i−2i2i−2i0000000000
χ382-222-22-2-20000-222-2-22-2222-2-222-2-2002-2000022-2-200000000000000000000000000−2i2i−2i2i0000000000
χ392-222-22-2-20000-222-2-22-22-2-222-2-222002-20000-2-222000000000000000000000000002i−2i−2i2i0000000000
χ402-222-22-2-20000-222-2-22-22-2-222-2-222002-20000-2-22200000000000000000000000000−2i2i2i−2i0000000000
χ412-222-22-2-20000-2-2-2222-2222-2-222-2-200-220000-2-2220000000000000000000000002i−2i00002i−2i00000000
χ422-222-22-2-20000-2-2-2222-2222-2-222-2-200-220000-2-222000000000000000000000000−2i2i0000−2i2i00000000
χ432-222-22-2-20000-2-2-2222-22-2-222-2-22200-22000022-2-20000000000000000000000002i−2i0000−2i2i00000000
χ442-222-22-2-20000-2-2-2222-22-2-222-2-22200-22000022-2-2000000000000000000000000−2i2i00002i−2i00000000
χ452-22-22-22-22i−2i2i−2i02-22-2000i2−i2i2−i2i2−i2i2−i20000002i−2ii2−i2i2−i22−22−222−2−2002-22i−2i00i2−i2i2−i22−22−20000000000000000
χ462-22-22-22-22i−2i2i−2i02-22-2000i2−i2i2−i2i2−i2i2−i20000002i−2ii2−i2i2−i22−22−222−2−200-22−2i2i00−i2i2−i2i2−22−220000000000000000
χ472-22-22-22-22i−2i2i−2i02-22-2000−i2i2−i2i2−i2i2−i2i20000002i−2i−i2i2−i2i2−22−22−2−222002-22i−2i00−i2i2−i2i2−22−220000000000000000
χ482-22-22-22-22i−2i2i−2i02-22-2000−i2i2−i2i2−i2i2−i2i20000002i−2i−i2i2−i2i2−22−22−2−22200-22−2i2i00i2−i2i2−i22−22−20000000000000000
χ492-22-22-22-22i−2i2i−2i0-22-22000i2−i2i2−i2i2−i2i2−i2000000−2i2i−i2i2−i2i22−22−2−2−2222-200002i−2i2−2−22−i2i2i2−i20000000000000000
χ502-22-22-22-22i−2i2i−2i0-22-22000i2−i2i2−i2i2−i2i2−i2000000−2i2i−i2i2−i2i22−22−2−2−222-220000−2i2i−222−2i2−i2−i2i20000000000000000
χ512-22-22-22-22i−2i2i−2i0-22-22000−i2i2−i2i2−i2i2−i2i2000000−2i2ii2−i2i2−i2−22−2222−2−22-200002i−2i−222−2i2−i2−i2i20000000000000000
χ522-22-22-22-22i−2i2i−2i0-22-22000−i2i2−i2i2−i2i2−i2i2000000−2i2ii2−i2i2−i2−22−2222−2−2-220000−2i2i2−2−22−i2i2i2−i20000000000000000
χ532-22-22-22-2−2i2i−2i2i02-22-2000i2−i2i2−i2i2−i2i2−i2000000−2i2ii2−i2i2−i2−22−22−2−222002-2−2i2i00i2−i2i2−i2−22−220000000000000000
χ542-22-22-22-2−2i2i−2i2i02-22-2000i2−i2i2−i2i2−i2i2−i2000000−2i2ii2−i2i2−i2−22−22−2−22200-222i−2i00−i2i2−i2i22−22−20000000000000000
χ552-22-22-22-2−2i2i−2i2i02-22-2000−i2i2−i2i2−i2i2−i2i2000000−2i2i−i2i2−i2i22−22−222−2−2002-2−2i2i00−i2i2−i2i22−22−20000000000000000
χ562-22-22-22-2−2i2i−2i2i02-22-2000−i2i2−i2i2−i2i2−i2i2000000−2i2i−i2i2−i2i22−22−222−2−200-222i−2i00i2−i2i2−i2−22−220000000000000000
χ572-22-22-22-2−2i2i−2i2i0-22-22000i2−i2i2−i2i2−i2i2−i20000002i−2i−i2i2−i2i2−22−2222−2−22-20000−2i2i−222−2−i2i2i2−i20000000000000000
χ582-22-22-22-2−2i2i−2i2i0-22-22000i2−i2i2−i2i2−i2i2−i20000002i−2i−i2i2−i2i2−22−2222−2−2-2200002i−2i2−2−22i2−i2−i2i20000000000000000
χ592-22-22-22-2−2i2i−2i2i0-22-22000−i2i2−i2i2−i2i2−i2i20000002i−2ii2−i2i2−i22−22−2−2−2222-20000−2i2i2−2−22i2−i2−i2i20000000000000000
χ602-22-22-22-2−2i2i−2i2i0-22-22000−i2i2−i2i2−i2i2−i2i20000002i−2ii2−i2i2−i22−22−2−2−222-2200002i−2i−222−2−i2i2i2−i20000000000000000
χ61444-4-4-4-44000004-4-440002i2−2i2−2i22i22i2−2i2−2i22i2000000002i2−2i2−2i22i20000000000000000000000000000000000000000
χ62444-4-4-4-44000004-4-44000−2i22i22i2−2i2−2i22i22i2−2i200000000−2i22i22i2−2i20000000000000000000000000000000000000000
χ63444-4-4-4-4400000-444-40002i2−2i2−2i22i22i2−2i2−2i22i200000000−2i22i22i2−2i20000000000000000000000000000000000000000
χ64444-4-4-4-4400000-444-4000−2i22i22i2−2i2−2i22i22i2−2i2000000002i2−2i2−2i22i20000000000000000000000000000000000000000
χ6544-444-4-4-400000000000022−22−2222−222222−224-40000000000000022−2222−2200000000000000000000000000000000
χ6644-444-4-4-400000000000022−22−2222−222222−22-4400000000000000−2222−222200000000000000000000000000000000
χ6744-444-4-4-4000000000000−222222−2222−22−22224-400000000000000−2222−222200000000000000000000000000000000
χ6844-444-4-4-4000000000000−222222−2222−22−2222-440000000000000022−2222−2200000000000000000000000000000000
χ6944-4-4-444-44i4i−4i−4i40000-4-44000000000000−4i4i0000000000000000000000000000000000000000000000
χ7044-4-4-444-4−4i−4i4i4i40000-4-440000000000004i−4i0000000000000000000000000000000000000000000000
χ714-444-44-4-40000444-4-4-44-40000000000-44000000000000000000000000000000000000000000000000
χ724-444-44-4-400004-4-444-44-400000000004-4000000000000000000000000000000000000000000000000
χ734-4-44-4-4444-4-440000000022−2222−22−2222−222200000000000022−22−2222000000000000000000000000000000000000
χ744-4-44-4-4444-4-4400000000−2222−222222−2222−22000000000000−222222−22000000000000000000000000000000000000
χ754-4-44-4-444-444-40000000022−2222−22−2222−2222000000000000−222222−22000000000000000000000000000000000000
χ764-4-44-4-444-444-400000000−2222−222222−2222−2200000000000022−22−2222000000000000000000000000000000000000
χ774-4-4-444-440000400004-4-44i4i−4i−4i−4i−4i4i4i0000000000000000000000000000000000000000000000000000
χ784-4-4-444-440000400004-4-4−4i−4i4i4i4i4i−4i−4i0000000000000000000000000000000000000000000000000000
χ794-4-4-444-440000-40000-4440000000000000000000000004-4-4400000000000000000000000000000000
χ804-4-4-444-440000-40000-444000000000000000000000000-444-400000000000000000000000000000000

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