Finite Group Databasebeta

← Group #263197

Character table — Group #263197

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74
size11112222222222222222224444444444444444444444444488888888888888161616161616161632323232
order12222244444444888888884444444444444488888888888844444488888888222244448888
χ111111111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1
χ31111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-1-11111-1-1-1-111111111-1-1-1-1
χ41111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-11111
χ5111111111111111111111111-1-1-1-111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-111-1-111-1-1
χ6111111111111111111111111-1-1-1-111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-111-1-111
χ7111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-11111-1-1-1-1111111-1-111-1-1-1-111
χ8111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-11111-1-1-1-11111-1-111-1-11111-1-1
χ911111111111111-1-1-1-1-1-1-1-111111111111111-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-11-11-11-11-11-11-1
χ1011111111111111-1-1-1-1-1-1-1-111111111111111-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1-11-11-11-11-11-11
χ1111111111111111-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-111111111-1-1-1-111-1-1-1-1-1-1-1-111111-11-11-11-1-11-11
χ1211111111111111-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-111111111-1-1-1-111-1-1-1-1-1-1-1-11111-11-11-11-111-11-1
χ1311111111111111-1-1-1-1-1-1-1-111-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111-1-111-1-111-1-11
χ1411111111111111-1-1-1-1-1-1-1-111-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-111-1-111-1-111-1
χ1511111111111111-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-111111111-1-1-1-11-1-111-1-11-111-1
χ1611111111111111-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-111111111-1-1-1-1-111-1-111-11-1-11
χ1722222222-2-2-222-200000000-2-222222222-2-2-2-2000000000000-2-222-2-200000000000000000000
χ1822222222-2-2-222-200000000-2-22222-2-2-2-22222000000000000-2-2-2-22200000000000000000000
χ1922222222-2-2-222-200000000-2-2-2-2-2-22222-2-2-2-200000000000022-2-22200000000000000000000
χ2022222222-2-2-222-200000000-2-2-2-2-2-2-2-2-2-222220000000000002222-2-200000000000000000000
χ21222222-2-2222-2-2222222222-2-222-2-20000000000000000-2-2-2-22-2000022-2-20000000000000000
χ22222222-2-2222-2-2222222222-2-2-2-2220000000000000000-2-2-2-2-220000-2-2220000000000000000
χ23222222-2-2222-2-22-2-2-2-2-2-2-2-2-2-222-2-2000000000000000022222-20000-2-2220000000000000000
χ24222222-2-2222-2-22-2-2-2-2-2-2-2-2-2-2-2-22200000000000000002222-22000022-2-20000000000000000
χ25222222-2-2-2-2-2-2-2-2000000002222-2-2000000002i2i2i2i−2i−2i−2i−2i0000-22000000002i2i−2i−2i000000000000
χ26222222-2-2-2-2-2-2-2-2000000002222-2-200000000−2i−2i−2i−2i2i2i2i2i0000-2200000000−2i−2i2i2i000000000000
χ27222222-2-2-2-2-2-2-2-20000000022-2-222000000002i2i2i2i−2i−2i−2i−2i00002-200000000−2i−2i2i2i000000000000
χ28222222-2-2-2-2-2-2-2-20000000022-2-22200000000−2i−2i−2i−2i2i2i2i2i00002-2000000002i2i−2i−2i000000000000
χ292222-2-22-22-2-22-222222-2-2-2-22-20000000000000000000022-2-200000000000000002200-2-20000
χ302222-2-22-22-2-22-222222-2-2-2-22-20000000000000000000022-2-20000000000000000-2-200220000
χ312222-2-22-22-2-22-22-2-2-2-222222-200000000000000000000-2-22200000000000000002-200-220000
χ322222-2-22-22-2-22-22-2-2-2-222222-200000000000000000000-2-2220000000000000000-22002-20000
χ332222-2-2-222-2-2-2222222-2-2-2-2-2200000000000000000000-2-222000000000000002200-2-2000000
χ342222-2-2-222-2-2-2222222-2-2-2-2-2200000000000000000000-2-22200000000000000-2-20022000000
χ352222-2-2-222-2-2-222-2-2-2-22222-220000000000000000000022-2-2000000000000002-200-22000000
χ362222-2-2-222-2-2-222-2-2-2-22222-220000000000000000000022-2-200000000000000-22002-2000000
χ372-2-222-222000-2-2022−2−222−2−2002-22-22i2i−2i−2i0000i2i2−i2−i2i2i2−i2−i22−22−2002i−2i002−22−2i2−i2i2−i2000000000000
χ382-2-222-222000-2-2022−2−222−2−2002-22-2−2i−2i2i2i0000−i2−i2i2i2−i2−i2i2i22−22−200−2i2i002−22−2−i2i2−i2i2000000000000
χ392-2-222-222000-2-2022−2−222−2−200-22-222i2i−2i−2i0000i2i2−i2−i2i2i2−i2−i22−22−200−2i2i00−22−22−i2i2−i2i2000000000000
χ402-2-222-222000-2-2022−2−222−2−200-22-22−2i−2i2i2i0000−i2−i2i2i2−i2−i2i2i22−22−2002i−2i00−22−22i2−i2i2−i2000000000000
χ412-2-222-222000-2-20−2−222−2−222002-22-22i2i−2i−2i0000−i2−i2i2i2−i2−i2i2i2−22−22002i−2i00−22−22−i2i2−i2i2000000000000
χ422-2-222-222000-2-20−2−222−2−222002-22-2−2i−2i2i2i0000i2i2−i2−i2i2i2−i2−i2−22−2200−2i2i00−22−22i2−i2i2−i2000000000000
χ432-2-222-222000-2-20−2−222−2−22200-22-222i2i−2i−2i0000−i2−i2i2i2−i2−i2i2i2−22−2200−2i2i002−22−2i2−i2i2−i2000000000000
χ442-2-222-222000-2-20−2−222−2−22200-22-22−2i−2i2i2i0000i2i2−i2−i2i2i2−i2−i2−22−22002i−2i002−22−2−i2i2−i2i2000000000000
χ452-2-222-2-2-200022022−2−222−2−2002-2-22000022-2-222−2−2−2−222−22−2200002-22−2−222−2−22000000000000
χ462-2-222-2-2-200022022−2−222−2−2002-2-220000-2-222−2−22222−2−2−22−220000-222−2−22−222−2000000000000
χ472-2-222-2-2-200022022−2−222−2−200-222-2000022-2-222−2−2−2−222−22−220000-22−222−2−222−2000000000000
χ482-2-222-2-2-200022022−2−222−2−200-222-20000-2-222−2−22222−2−2−22−2200002-2−222−22−2−22000000000000
χ492-2-222-2-2-2000220−2−222−2−222002-2-22000022-2-2−2−22222−2−22−22−200002-2−222−2−222−2000000000000
χ502-2-222-2-2-2000220−2−222−2−222002-2-220000-2-22222−2−2−2−2222−22−20000-22−222−22−2−22000000000000
χ512-2-222-2-2-2000220−2−222−2−22200-222-2000022-2-2−2−22222−2−22−22−20000-222−2−222−2−22000000000000
χ522-2-222-2-2-2000220−2−222−2−22200-222-20000-2-22222−2−2−2−2222−22−200002-22−2−22−222−2000000000000
χ534444-4-44-4-4444-4-400000000-4400000000000000000000000000000000000000000000000000
χ544444-4-4-44-444-44-4000000004-400000000000000000000000000000000000000000000000000
χ5544-4-4000040000-44-44-400000000002-22-22-22-22-22-22-22-2000000000000000000000000000000
χ5644-4-4000040000-44-44-40000000000-22-22-22-22-22-22-22-22000000000000000000000000000000
χ5744-4-4000040000-4-44-4400000000002-22-22-22-2-22-22-22-22000000000000000000000000000000
χ5844-4-4000040000-4-44-440000000000-22-22-22-222-22-22-22-2000000000000000000000000000000
χ5944-4-40000-40000400004i−4i4i−4i0000002-22-2-22-222i−2i2i−2i−2i2i−2i2i000000000000000000000000000000
χ6044-4-40000-40000400004i−4i4i−4i000000-22-222-22-2−2i2i−2i2i2i−2i2i−2i000000000000000000000000000000
χ6144-4-40000-4000040000−4i4i−4i4i0000002-22-2-22-22−2i2i−2i2i2i−2i2i−2i000000000000000000000000000000
χ6244-4-40000-4000040000−4i4i−4i4i000000-22-222-22-22i−2i2i−2i−2i2i−2i2i000000000000000000000000000000
χ634-44-4000004i−4i00022−22−22222i2−2i2−2i22i20000002i−2i−2i2i-222-22ζ3−2ζ3−2ζ32ζ32ζ−2ζ−2ζ2ζ000000000000000000000000000000
χ644-44-4000004i−4i00022−22−22222i2−2i2−2i22i2000000−2i2i2i−2i2-2-22−2ζ32ζ32ζ3−2ζ3−2ζ2ζ2ζ−2ζ000000000000000000000000000000
χ654-44-4000004i−4i000−222222−22−2i22i22i2−2i20000002i−2i−2i2i-222-2−2ζ32ζ32ζ3−2ζ3−2ζ2ζ2ζ−2ζ000000000000000000000000000000
χ664-44-4000004i−4i000−222222−22−2i22i22i2−2i2000000−2i2i2i−2i2-2-222ζ3−2ζ3−2ζ32ζ32ζ−2ζ−2ζ2ζ000000000000000000000000000000
χ674-44-400000−4i4i00022−22−2222−2i22i22i2−2i20000002i−2i−2i2i2-2-222ζ−2ζ−2ζ2ζ2ζ3−2ζ3−2ζ32ζ3000000000000000000000000000000
χ684-44-400000−4i4i00022−22−2222−2i22i22i2−2i2000000−2i2i2i−2i-222-2−2ζ2ζ2ζ−2ζ−2ζ32ζ32ζ3−2ζ3000000000000000000000000000000
χ694-44-400000−4i4i000−222222−222i2−2i2−2i22i20000002i−2i−2i2i2-2-22−2ζ2ζ2ζ−2ζ−2ζ32ζ32ζ3−2ζ3000000000000000000000000000000
χ704-44-400000−4i4i000−222222−222i2−2i2−2i22i2000000−2i2i2i−2i-222-22ζ−2ζ−2ζ2ζ2ζ3−2ζ3−2ζ32ζ3000000000000000000000000000000
χ714-4-44-444-4000-4402222−22−22−22−222222000000000000000000000022−22−222200000000000000000000000000
χ724-4-44-444-4000-440−22−2222222222−22−220000000000000000000000−222222−2200000000000000000000000000
χ734-4-44-44-440004-402222−22−22−22−2222220000000000000000000000−222222−2200000000000000000000000000
χ744-4-44-44-440004-40−22−2222222222−22−22000000000000000000000022−22−222200000000000000000000000000

Here ζ is a primitive root of unity of order 8 (ζ8 = 1); i = ζ2.