Finite Group Databasebeta

← Group #349050

Character table — Group #349050

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68
size11112222222222224444444444444444444444488888888888888888161616161616161632323232
order12222244444488882222444444488888888888822244444888888888888888884488
χ111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1
χ3111111111111111111-1-1111-1-11111111111-1-1-1-11-1-1-11-1-1-11-1-111-1-1-1-11111-1-1-1-111-1-1
χ4111111111111111111-1-1111-1-11111111111-1-1-1-11-1-1-11-1-1-11-1-111-1-1-1-1-1-1-1-11111-1-111
χ51111111111111111-1-1111-1-111111111-1-1-1-11111-1-1-11-1-1-11111-1-1-1-1-1-111111111-1-1-1-1
χ61111111111111111-1-1111-1-111111111-1-1-1-11111-1-1-11-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-11111
χ71111111111111111-1-1-1-11-1-1-1-1111111-1-1-1-1-1-1-1-1-111-1-111-11-1-1-1-111111111-1-1-1-1-1-111
χ81111111111111111-1-1-1-11-1-1-1-1111111-1-1-1-1-1-1-1-1-111-1-111-11-1-1-1-11111-1-1-1-1111111-1-1
χ9111111111111-1-1-1-111111111111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-111-1-111-1-11-11-1
χ10111111111111-1-1-1-111111111111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-111-1-111-11-11
χ11111111111111-1-1-1-111-1-1111-1-111-1-1-1-1-1-1-1-111111-1-1-11-1-1-1-111-1-1111111-1-1-1-1111-1-11
χ12111111111111-1-1-1-111-1-1111-1-111-1-1-1-1-1-1-1-111111-1-1-11-1-1-1-111-1-11111-1-11111-1-1-111-1
χ13111111111111-1-1-1-1-1-1111-1-11111-1-1-1-11111-1-1-1-1-1-1-11-1-1-11-1-1-111111111-1-111-1-1-11-11
χ14111111111111-1-1-1-1-1-1111-1-11111-1-1-1-11111-1-1-1-1-1-1-11-1-1-11-1-1-1111111-1-111-1-1111-11-1
χ15111111111111-1-1-1-1-1-1-1-11-1-1-1-111-1-1-1-111111111-111-1-111-1-11111-1-1-1-111-1-1-1-111-111-1
χ16111111111111-1-1-1-1-1-1-1-11-1-1-1-111-1-1-1-111111111-111-1-111-1-11111-1-1-1-1-1-11111-1-11-1-11
χ172222222-2-22-2-2000022002-2-200-2-2000000002i2i−2i−2i2000-200002i−2i002i2i−2i−2i000000000000
χ182222222-2-22-2-2000022002-2-200-2-200000000−2i−2i2i2i2000-20000−2i2i00−2i−2i2i2i000000000000
χ192222222-2-22-2-20000-2-20022200-2-2000000002i2i−2i−2i-2000200002i−2i00−2i−2i2i2i000000000000
χ202222222-2-22-2-20000-2-20022200-2-200000000−2i−2i2i2i-200020000−2i2i002i2i−2i−2i000000000000
χ21222222-222-22222220022-20022-2-2-2-22200002222000-2000-2-2-2-2000000000000000000
χ22222222-222-222222200-2-2-200-2-2-2-2-2-2220000-2-2-2-200020002-222000000000000000000
χ23222222-222-222-2-2-2-20022-20022-2-222-2-20000-2-2-2-2000-2000-2222000000000000000000
χ24222222-222-222-2-2-2-200-2-2-200-2-2-2-222-2-200002222000200022-2-2000000000000000000
χ25222222-2-2-2-2-2-200000000-200002200002i2i−2i−2i2i2i−2i−2i02-2002-200−2i2i2i−2i0000000000000000
χ26222222-2-2-2-2-2-200000000-200002200002i2i−2i−2i−2i−2i2i2i0-2200-22002i−2i2i−2i0000000000000000
χ27222222-2-2-2-2-2-200000000-20000220000−2i−2i2i2i2i2i−2i−2i0-2200-2200−2i2i−2i2i0000000000000000
χ28222222-2-2-2-2-2-200000000-20000220000−2i−2i2i2i−2i−2i2i2i02-2002-2002i−2i−2i2i0000000000000000
χ292222-2-222-222-200002222-2-2-2-2-2-22000000000000-22222-2-2-2000000000000000000000
χ302222-2-222-222-2000022-2-2-2-2-222-22000000000000-2-2-2-22222000000000000000000000
χ312222-2-222-222-20000-2-222-222-2-2-220000000000002-2-22-222-2000000000000000000000
χ322222-2-222-222-20000-2-2-2-2-22222-22000000000000222-2-2-2-22000000000000000000000
χ332222-2-22-222-2222222200-222002-222-2-222220000-2000-2000-200-2-20000000000000000
χ342222-2-22-222-222222-2-200-2-2-2002-222-2-2-2-2-2-2000020002000-200220000000000000000
χ352222-2-22-222-22-2-2-2-22200-222002-2-2-222-2-2-2-20000-2000-2000200220000000000000000
χ362222-2-22-222-22-2-2-2-2-2-200-2-2-2002-2-2-2222222000020002000200-2-20000000000000000
χ372222-2-2-22-2-22-200000022200-2-22-200002i2i−2i−2i0000000-20002000−2i2i2i−2i2i−2i000000000000
χ382222-2-2-22-2-22-200000022200-2-22-20000−2i−2i2i2i0000000-200020002i−2i−2i2i−2i2i000000000000
χ392222-2-2-22-2-22-2000000-2-2200222-200002i2i−2i−2i00000002000-2000−2i2i−2i2i−2i2i000000000000
χ402222-2-2-22-2-22-2000000-2-2200222-20000−2i−2i2i2i00000002000-20002i−2i2i−2i2i−2i000000000000
χ412222-2-2-2-22-2-222222000020000-22-2-2-2-20000000002-200-220200002-2-22000000000000
χ422222-2-2-2-22-2-222222000020000-22-2-2-2-2000000000-22002-2020000-222-2000000000000
χ432222-2-2-2-22-2-22-2-2-2-2000020000-2222220000000002-200-220-20000-222-2000000000000
χ442222-2-2-2-22-2-22-2-2-2-2000020000-222222000000000-22002-20-200002-2-22000000000000
χ452-22-22-202-20-2222-2-2002-20002-200002-200002-22-200000000000000000i2−i2i2−i2i2−i2i2−i20000
χ462-22-22-202-20-2222-2-2002-20002-200002-200002-22-200000000000000000−i2i2−i2i2−i2i2−i2i20000
χ472-22-22-202-20-2222-2-200-22000-2200002-20000-22-2200000000000000000i2−i2i2−i2−i2i2−i2i20000
χ482-22-22-202-20-2222-2-200-22000-2200002-20000-22-2200000000000000000−i2i2−i2i2i2−i2i2−i20000
χ492-22-22-202-20-22-2-222002-20002-20000-220000-22-2200000000000000000i2−i2−i2i2i2−i2−i2i20000
χ502-22-22-202-20-22-2-222002-20002-20000-220000-22-2200000000000000000−i2i2i2−i2−i2i2i2−i20000
χ512-22-22-202-20-22-2-22200-22000-220000-2200002-22-200000000000000000i2−i2−i2i2−i2i2i2−i20000
χ522-22-22-202-20-22-2-22200-22000-220000-2200002-22-200000000000000000−i2i2i2−i2i2−i2−i2i20000
χ5344-4-400400-40022−2222−224-400000000022−220022−2222−22000000000000000000000000000000000
χ5444-4-400400-40022−2222−22-4400000000022−2200−2222−2222000000000000000000000000000000000
χ5544-4-400400-400−2222−22224-4000000000−222200−2222−2222000000000000000000000000000000000
χ5644-4-400400-400−2222−2222-44000000000−22220022−2222−22000000000000000000000000000000000
χ5744-4-400-40040022−2222−22000004i−4i0000−2222002i2−2i2−2i22i2000000000000000000000000000000000
χ5844-4-400-40040022−2222−2200000−4i4i0000−222200−2i22i22i2−2i2000000000000000000000000000000000
χ5944-4-400-400400−2222−2222000004i−4i000022−2200−2i22i22i2−2i2000000000000000000000000000000000
χ6044-4-400-400400−2222−222200000−4i4i000022−22002i2−2i2−2i22i2000000000000000000000000000000000
χ614-44-44-40-4404-4000000000000000000000004i−4i−4i4i00000000000000000000000000000
χ624-44-44-40-4404-400000000000000000000000−4i4i4i−4i00000000000000000000000000000
χ634-44-4-440440-4-40000004-4000-440000000000000000000000000000000000000000000
χ644-44-4-440440-4-4000000-440004-40000000000000000000000000000000000000000000
χ654-44-4-440-4-404444-4-40000000000000-440000000000000000000000000000000000000
χ664-44-4-440-4-4044-4-44400000000000004-40000000000000000000000000000000000000
χ678-8-880000000042−42−42420000000000000000000000000000000000000000000000000000
χ688-8-8800000000−424242−420000000000000000000000000000000000000000000000000000

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