Finite Group Databasebeta

← Group #313678

Character table — Group #313678

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80
size11111111222222222222222244444444444444444444444444888888888888888888161616161616161616163232
order12222222444444448888888844444488888888888888888888224444444488888888444444888844
χ111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111111111111111111111-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1
χ31111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-11111-1-1-1-11111111111-1-1-1-1-1-1
χ41111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1111111
χ5111111111111111111111111-1-1-1-11111111111111111111111-1-1-1-1-1-11111-1-1-1-1-1-1-1-11-1-11-1-11111-1-1
χ6111111111111111111111111-1-1-1-11111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-111-1-1-1-111
χ7111111111111111111111111-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-11-1-11-1-1-1-1-1-111
χ8111111111111111111111111-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1-1-1-111-1111111-1-1
χ91111111111111111-1-1-1-1-1-1-1-1111111-1-1-1-111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1111-1-1-1-1-1111-1
χ101111111111111111-1-1-1-1-1-1-1-1111111-1-1-1-111111111-1-1-1-1-1-1-1-1111111-1-111-1-1-1-1-1-1-1-1-1-1-111111-1-1-11
χ111111111111111111-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-11111111111-1-1-1-111-1-11111-1-1-1-1111-1-1-111-1-1-11
χ121111111111111111-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-1111111-1-1-1-1-1-1-1111-1-1111-1
χ131111111111111111-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1111111111-1-1-111-1-111-11
χ141111111111111111-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111-1111-1-111-1-11-1
χ151111111111111111-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1111111-1-1-1-1-1-111111-1-1-11111-1-11-1
χ161111111111111111-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-11111-1-111-1-1-1-11111-1111-1-1-1-111-11
χ17222222222-22-22-22-2000000002222-2-200002222-2-2-2-200000000-2-222-2-2000000000000000000000000
χ18222222222-22-22-22-2000000002222-2-20000-2-2-2-2222200000000-2-2-2-222000000000000000000000000
χ19222222222-22-22-22-200000000-2-2-2-2-2-200002222-2-2-2-20000000022-2-222000000000000000000000000
χ20222222222-22-22-22-200000000-2-2-2-2-2-20000-2-2-2-22222000000002222-2-2000000000000000000000000
χ2122222222-22-22-22-22222222220000-2-2-2-2-2-20000000000000000000000222200000000-200-200000000
χ2222222222-22-22-22-22222222220000-2-2-2-2-2-20000000000000000000000-2-2-2-200000000200200000000
χ2322222222-22-22-22-22-2-2-2-2-2-2-2-20000-2-22222000000000000000000000022-2-200000000-200200000000
χ2422222222-22-22-22-22-2-2-2-2-2-2-2-20000-2-222220000000000000000000000-2-22200000000200-200000000
χ25222-22-2-2-20-20-202022222-2-2-2-2000000000022−2−222−2−22222−2−2−2−20000002i−2i2i−2i00000000000000i2−i2i2−i200
χ26222-22-2-2-20-20-202022222-2-2-2-2000000000022−2−222−2−22222−2−2−2−2000000−2i2i−2i2i00000000000000−i2i2−i2i200
χ27222-22-2-2-20-20-202022222-2-2-2-20000000000−2−222−2−222−2−2−2−222220000002i−2i2i−2i00000000000000−i2i2−i2i200
χ28222-22-2-2-20-20-202022222-2-2-2-20000000000−2−222−2−222−2−2−2−22222000000−2i2i−2i2i00000000000000i2−i2i2−i200
χ29222-22-2-2-20-20-20202-2-2-2-22222000000000022−2−222−2−2−2−2−2−222220000002i−2i−2i2i00000000000000−i2i2i2−i200
χ30222-22-2-2-20-20-20202-2-2-2-22222000000000022−2−222−2−2−2−2−2−22222000000−2i2i2i−2i00000000000000i2−i2−i2i200
χ31222-22-2-2-20-20-20202-2-2-2-222220000000000−2−222−2−2222222−2−2−2−20000002i−2i−2i2i00000000000000i2−i2−i2i200
χ32222-22-2-2-20-20-20202-2-2-2-222220000000000−2−222−2−2222222−2−2−2−2000000−2i2i2i−2i00000000000000−i2i2i2−i200
χ3322-22-22-2-2-20-20202022−2−222−2−22i2i−2i−2i0022−2−22i−2i2i−2i0000i2i2−i2−i2i2i2−i2−i2002-200000022−2−2i2i2−i2−i2000000000000
χ3422-22-22-2-2-20-20202022−2−222−2−22i2i−2i−2i0022−2−2−2i2i−2i2i0000−i2−i2i2i2−i2−i2i2i200-22000000−2−222i2i2−i2−i2000000000000
χ3522-22-22-2-2-20-20202022−2−222−2−2−2i−2i2i2i0022−2−22i−2i2i−2i0000i2i2−i2−i2i2i2−i2−i200-22000000−2−222−i2−i2i2i2000000000000
χ3622-22-22-2-2-20-20202022−2−222−2−2−2i−2i2i2i0022−2−2−2i2i−2i2i0000−i2−i2i2i2−i2−i2i2i2002-200000022−2−2−i2−i2i2i2000000000000
χ3722-22-22-2-2-20-202020−2−222−2−2222i2i−2i−2i00−2−2222i−2i2i−2i0000−i2−i2i2i2−i2−i2i2i2002-2000000−2−222−i2−i2i2i2000000000000
χ3822-22-22-2-2-20-202020−2−222−2−2222i2i−2i−2i00−2−222−2i2i−2i2i0000i2i2−i2−i2i2i2−i2−i200-2200000022−2−2−i2−i2i2i2000000000000
χ3922-22-22-2-2-20-202020−2−222−2−222−2i−2i2i2i00−2−2222i−2i2i−2i0000−i2−i2i2i2−i2−i2i2i200-2200000022−2−2i2i2−i2−i2000000000000
χ4022-22-22-2-2-20-202020−2−222−2−222−2i−2i2i2i00−2−222−2i2i−2i2i0000i2i2−i2−i2i2i2−i2−i2002-2000000−2−222i2i2−i2−i2000000000000
χ412-22-2-222-2-202020-20i2−i2i2−i2i2−i2i2−i22i−2i2i−2i00i2−i2i2−i200002i−2i2i−2i2−22−22−22−200002-20000i2−i2i2−i22−22−2000000000000
χ422-22-2-222-2-202020-20i2−i2i2−i2i2−i2i2−i22i−2i2i−2i00i2−i2i2−i20000−2i2i−2i2i−22−22−22−220000-220000−i2i2−i2i22−22−2000000000000
χ432-22-2-222-2-202020-20i2−i2i2−i2i2−i2i2−i2−2i2i−2i2i00i2−i2i2−i200002i−2i2i−2i2−22−22−22−20000-220000−i2i2−i2i2−22−22000000000000
χ442-22-2-222-2-202020-20i2−i2i2−i2i2−i2i2−i2−2i2i−2i2i00i2−i2i2−i20000−2i2i−2i2i−22−22−22−2200002-20000i2−i2i2−i2−22−22000000000000
χ452-22-2-222-2-202020-20−i2i2−i2i2−i2i2−i2i22i−2i2i−2i00−i2i2−i2i200002i−2i2i−2i−22−22−22−2200002-20000−i2i2−i2i2−22−22000000000000
χ462-22-2-222-2-202020-20−i2i2−i2i2−i2i2−i2i22i−2i2i−2i00−i2i2−i2i20000−2i2i−2i2i2−22−22−22−20000-220000i2−i2i2−i2−22−22000000000000
χ472-22-2-222-2-202020-20−i2i2−i2i2−i2i2−i2i2−2i2i−2i2i00−i2i2−i2i200002i−2i2i−2i−22−22−22−220000-220000i2−i2i2−i22−22−2000000000000
χ482-22-2-222-2-202020-20−i2i2−i2i2−i2i2−i2i2−2i2i−2i2i00−i2i2−i2i20000−2i2i−2i2i2−22−22−22−200002-20000−i2i2−i2i22−22−2000000000000
χ492-2-2-222-2222-2-222-2-22i−2i−2i2i2i−2i−2i2i2-2-22-222i−2i−2i2i00000000000000002-2000000000000−2i2i2i−2i000000000000
χ502-2-2-222-2222-2-222-2-22i−2i−2i2i2i−2i−2i2i-222-2-222i−2i−2i2i0000000000000000-220000000000002i−2i−2i2i000000000000
χ512-2-2-222-2222-2-222-2-2−2i2i2i−2i−2i2i2i−2i2-2-22-22−2i2i2i−2i00000000000000002-20000000000002i−2i−2i2i000000000000
χ522-2-2-222-2222-2-222-2-2−2i2i2i−2i−2i2i2i−2i-222-2-22−2i2i2i−2i0000000000000000-22000000000000−2i2i2i−2i000000000000
χ532-2-2-222-222-2-222-2-22000000002-2-222-20000000000002i−2i−2i2i2i−2i−2i2i-2200000000−2i2i2i−2i0000000000000000
χ542-2-2-222-222-2-222-2-22000000002-2-222-2000000000000−2i2i2i−2i−2i2i2i−2i-22000000002i−2i−2i2i0000000000000000
χ552-2-2-222-222-2-222-2-2200000000-222-22-20000000000002i−2i−2i2i2i−2i−2i2i2-2000000002i−2i−2i2i0000000000000000
χ562-2-2-222-222-2-222-2-2200000000-222-22-2000000000000−2i2i2i−2i−2i2i2i−2i2-200000000−2i2i2i−2i0000000000000000
χ572-2-2-222-22-222-2-222-22i−2i−2i2i2i−2i−2i2i00002-2−2i2i2i−2i000000000000000000000000000000000002i−2i02-2000000
χ582-2-2-222-22-222-2-222-22i−2i−2i2i2i−2i−2i2i00002-2−2i2i2i−2i00000000000000000000000000000000000−2i2i0-22000000
χ592-2-2-222-22-222-2-222-2−2i2i2i−2i−2i2i2i−2i00002-22i−2i−2i2i000000000000000000000000000000000002i−2i0-22000000
χ602-2-2-222-22-222-2-222-2−2i2i2i−2i−2i2i2i−2i00002-22i−2i−2i2i00000000000000000000000000000000000−2i2i02-2000000
χ6144444444-4-4-4-4-4-4-4-40000000000004400000000000000000000000000000000000000000000000000
χ62444-44-4-4-404040-40-40000000000000000002222−22−22−22−22222200000000000000000000000000000000000000
χ63444-44-4-4-404040-40-4000000000000000000−22−2222222222−22−2200000000000000000000000000000000000000
χ6444-44-44-4-44040-40-402222−22−222222−22−22000000−22−2222220000000000000000000000000000000000000000000000
χ6544-44-44-4-44040-40-40−22−222222−22−2222220000002222−22−220000000000000000000000000000000000000000000000
χ6644-4-4-4-444000000002222−22−22−22−22222200000000002i2−2i2−2i22i200002i2i−2i−2i−2i−2i2i2i000000000000000000000000000000
χ6744-4-4-4-444000000002222−22−22−22−2222220000000000−2i22i22i2−2i20000−2i−2i2i2i2i2i−2i−2i000000000000000000000000000000
χ6844-4-4-4-44400000000−22−2222222222−22−2200000000002i2−2i2−2i22i20000−2i−2i2i2i2i2i−2i−2i000000000000000000000000000000
χ6944-4-4-4-44400000000−22−2222222222−22−220000000000−2i22i22i2−2i200002i2i−2i−2i−2i−2i2i2i000000000000000000000000000000
χ704-444-4-4-44000000002i2−2i22i2−2i2−2i22i2−2i22i2000000000000002i2−2i2−2i22i22-22-2-22-22000000000000000000000000000000
χ714-444-4-4-44000000002i2−2i22i2−2i2−2i22i2−2i22i200000000000000−2i22i22i2−2i2-22-222-22-2000000000000000000000000000000
χ724-444-4-4-4400000000−2i22i2−2i22i22i2−2i22i2−2i2000000000000002i2−2i2−2i22i2-22-222-22-2000000000000000000000000000000
χ734-444-4-4-4400000000−2i22i2−2i22i22i2−2i22i2−2i200000000000000−2i22i22i2−2i22-22-2-22-22000000000000000000000000000000
χ744-44-4-444-440-40-40402i2−2i22i2−2i22i2−2i22i2−2i2000000−2i22i2−2i22i20000000000000000000000000000000000000000000000
χ754-44-4-444-440-40-4040−2i22i2−2i22i2−2i22i2−2i22i20000002i2−2i22i2−2i20000000000000000000000000000000000000000000000
χ764-4-444-44-4040-40-404000000000000000000000000002i2−2i2−2i22i2−2i22i22i2−2i2000000000000000000000000000000
χ774-4-444-44-4040-40-40400000000000000000000000000−2i22i22i2−2i22i2−2i2−2i22i2000000000000000000000000000000
χ784-4-444-44-40-404040-44i−4i−4i4i−4i4i4i−4i00000000000000000000000000000000000000000000000000000000
χ794-4-444-44-40-404040-4−4i4i4i−4i4i−4i−4i4i00000000000000000000000000000000000000000000000000000000
χ804-4-4-444-44-4-444-4-444000000000000-4400000000000000000000000000000000000000000000000000

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