Finite Group Databasebeta

← Group #263182

Character table — Group #263182

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74
size11112222222222222222224444444444444444444444444488888888888888161616161616161632323232
order12222244444444888888882222444444444488888888888822444488888888222244448888
χ111111111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1
χ31111111111111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-111-1-11111-1-1-1-111111111-1-1-1-1
χ41111111111111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-111-1-11111-1-1-1-1-1-1-1-1-1-1-1-11111
χ51111111111111111111111-1-1-1-11111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-111-1-111-1-1
χ61111111111111111111111-1-1-1-11111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-111-1-111
χ71111111111111111111111-1-1-1-111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-111-1-111-1-1-1-1111111-1-111-1-1-1-111
χ81111111111111111111111-1-1-1-111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-111-1-111-1-1-1-11111-1-111-1-11111-1-1
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
χ1111111111111111-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-111-1-1-1-1-1-111111-11-11-11-1-11-11
χ1211111111111111-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-111-1-1-1-1-1-11111-11-11-11-111-11-1
χ1311111111111111-1-1-1-1-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111-1-111-1-111-1-11
χ1411111111111111-1-1-1-1-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-111-1-111-1-111-1
χ1511111111111111-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-11111111111-1-1111111-1-1-1-11-1-111-1-11-111-1
χ1611111111111111-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-11111111111-1-1111111-1-1-1-1-111-1-111-11-1-11
χ1722222222-2-2-222-2000000002222-2-22222-2-2-2-200000000000022-2-2-2-200000000000000000000
χ1822222222-2-2-222-2000000002222-2-2-2-2-2-22222000000000000-2-2-2-22200000000000000000000
χ1922222222-2-2-222-200000000-2-2-2-2-2-22222-2-2-2-2000000000000-2-2222200000000000000000000
χ2022222222-2-2-222-200000000-2-2-2-2-2-2-2-2-2-222220000000000002222-2-200000000000000000000
χ21222222-2-2222-2-222222222222-2-2-2-200000000-2-2-2-200000000002-20022-2-20000000000000000
χ22222222-2-2222-2-2222222222-2-222-2-200000000-2-2-2-20000000000-2200-2-2220000000000000000
χ23222222-2-2222-2-22-2-2-2-2-2-2-2-222-2-2-2-200000000222200000000002-200-2-2220000000000000000
χ24222222-2-2222-2-22-2-2-2-2-2-2-2-2-2-222-2-20000000022220000000000-220022-2-20000000000000000
χ25222222-2-2-2-2-2-2-2-20000000022-2-2220000000000002i2i2i2i−2i−2i−2i−2i00-220000002i2i−2i−2i000000000000
χ26222222-2-2-2-2-2-2-2-20000000022-2-222000000000000−2i−2i−2i−2i2i2i2i2i00-22000000−2i−2i2i2i000000000000
χ27222222-2-2-2-2-2-2-2-200000000-2-222220000000000002i2i2i2i−2i−2i−2i−2i002-2000000−2i−2i2i2i000000000000
χ28222222-2-2-2-2-2-2-2-200000000-2-22222000000000000−2i−2i−2i−2i2i2i2i2i002-20000002i2i−2i−2i000000000000
χ292222-2-22-22-2-22-222222-2-2-2-200002-20000000022-2-20000000000000000000000002200-2-20000
χ302222-2-22-22-2-22-222222-2-2-2-200002-20000000022-2-2000000000000000000000000-2-200220000
χ312222-2-22-22-2-22-22-2-2-2-2222200002-200000000-2-2220000000000000000000000002-200-220000
χ322222-2-22-22-2-22-22-2-2-2-2222200002-200000000-2-222000000000000000000000000-22002-20000
χ332222-2-2-222-2-2-2222222-2-2-2-20000-2200000000-2-22200000000000000000000002200-2-2000000
χ342222-2-2-222-2-2-2222222-2-2-2-20000-2200000000-2-2220000000000000000000000-2-20022000000
χ352222-2-2-222-2-2-222-2-2-2-222220000-220000000022-2-200000000000000000000002-200-22000000
χ362222-2-2-222-2-2-222-2-2-2-222220000-220000000022-2-20000000000000000000000-22002-2000000
χ372-2-222-222000-2-2022−2−222−2−22-22-20000002i2i−2i−2i2−22−2i2i2−i2−i2i2i2−i2−i200002i−2i2−22−2i2−i2i2−i2000000000000
χ382-2-222-222000-2-2022−2−222−2−22-22-2000000−2i−2i2i2i2−22−2−i2−i2i2i2−i2−i2i2i20000−2i2i2−22−2−i2i2−i2i2000000000000
χ392-2-222-222000-2-2022−2−222−2−2-22-220000002i2i−2i−2i2−22−2i2i2−i2−i2i2i2−i2−i20000−2i2i−22−22−i2i2−i2i2000000000000
χ402-2-222-222000-2-2022−2−222−2−2-22-22000000−2i−2i2i2i2−22−2−i2−i2i2i2−i2−i2i2i200002i−2i−22−22i2−i2i2−i2000000000000
χ412-2-222-222000-2-20−2−222−2−2222-22-20000002i2i−2i−2i−22−22−i2−i2i2i2−i2−i2i2i200002i−2i−22−22−i2i2−i2i2000000000000
χ422-2-222-222000-2-20−2−222−2−2222-22-2000000−2i−2i2i2i−22−22i2i2−i2−i2i2i2−i2−i20000−2i2i−22−22i2−i2i2−i2000000000000
χ432-2-222-222000-2-20−2−222−2−222-22-220000002i2i−2i−2i−22−22−i2−i2i2i2−i2−i2i2i20000−2i2i2−22−2i2−i2i2−i2000000000000
χ442-2-222-222000-2-20−2−222−2−222-22-22000000−2i−2i2i2i−22−22i2i2−i2−i2i2i2−i2−i200002i−2i2−22−2−i2i2−i2i2000000000000
χ452-2-222-2-2-200022022−2−222−2−22-2-220022-2-20000−22−2222−2−2−2−2222-200002−2−222−2−22000000000000
χ462-2-222-2-2-200022022−2−222−2−22-2-2200-2-2220000−22−22−2−22222−2−2-2200002−2−22−222−2000000000000
χ472-2-222-2-2-200022022−2−222−2−2-222-20022-2-20000−22−2222−2−2−2−222-220000−222−2−222−2000000000000
χ482-2-222-2-2-200022022−2−222−2−2-222-200-2-2220000−22−22−2−22222−2−22-20000−222−22−2−22000000000000
χ492-2-222-2-2-2000220−2−222−2−2222-2-220022-2-200002−22−2−2−22222−2−22-20000−222−2−222−2000000000000
χ502-2-222-2-2-2000220−2−222−2−2222-2-2200-2-22200002−22−222−2−2−2−222-220000−222−22−2−22000000000000
χ512-2-222-2-2-2000220−2−222−2−222-222-20022-2-200002−22−2−2−22222−2−2-2200002−2−222−2−22000000000000
χ522-2-222-2-2-2000220−2−222−2−222-222-200-2-22200002−22−222−2−2−2−2222-200002−2−22−222−2000000000000
χ534444-4-44-4-4444-4-4000000000000-440000000000000000000000000000000000000000000000
χ544444-4-4-44-444-44-40000000000004-40000000000000000000000000000000000000000000000
χ5544-4-4000004i−4i00022−2222−222i2−2i22i2−2i20000002-22-22i−2i2i−2i00002ζ−2ζ2ζ−2ζ2ζ3−2ζ32ζ3−2ζ300000000000000000000000000
χ5644-4-4000004i−4i00022−2222−222i2−2i22i2−2i2000000-22-22−2i2i−2i2i0000−2ζ2ζ−2ζ2ζ−2ζ32ζ3−2ζ32ζ300000000000000000000000000
χ5744-4-4000004i−4i000−2222−2222−2i22i2−2i22i20000002-22-22i−2i2i−2i0000−2ζ2ζ−2ζ2ζ−2ζ32ζ3−2ζ32ζ300000000000000000000000000
χ5844-4-4000004i−4i000−2222−2222−2i22i2−2i22i2000000-22-22−2i2i−2i2i00002ζ−2ζ2ζ−2ζ2ζ3−2ζ32ζ3−2ζ300000000000000000000000000
χ5944-4-400000−4i4i00022−2222−22−2i22i2−2i22i20000002-22-2−2i2i−2i2i0000−2ζ32ζ3−2ζ32ζ3−2ζ2ζ−2ζ2ζ00000000000000000000000000
χ6044-4-400000−4i4i00022−2222−22−2i22i2−2i22i2000000-22-222i−2i2i−2i00002ζ3−2ζ32ζ3−2ζ32ζ−2ζ2ζ−2ζ00000000000000000000000000
χ6144-4-400000−4i4i000−2222−22222i2−2i22i2−2i20000002-22-2−2i2i−2i2i00002ζ3−2ζ32ζ3−2ζ32ζ−2ζ2ζ−2ζ00000000000000000000000000
χ6244-4-400000−4i4i000−2222−22222i2−2i22i2−2i2000000-22-222i−2i2i−2i0000−2ζ32ζ3−2ζ32ζ3−2ζ2ζ−2ζ2ζ00000000000000000000000000
χ634-44-4000040000-400004i−4i−4i4i0000002-2-22-222-200002i−2i−2i2i−2i2i2i−2i00000000000000000000000000
χ644-44-4000040000-400004i−4i−4i4i000000-222-22-2-220000−2i2i2i−2i2i−2i−2i2i00000000000000000000000000
χ654-44-4000040000-40000−4i4i4i−4i0000002-2-22-222-20000−2i2i2i−2i2i−2i−2i2i00000000000000000000000000
χ664-44-4000040000-40000−4i4i4i−4i000000-222-22-2-2200002i−2i−2i2i−2i2i2i−2i00000000000000000000000000
χ674-44-40000-4000044-4-4400000000002-2-222-2-2200002-2-222-2-2200000000000000000000000000
χ684-44-40000-4000044-4-440000000000-222-2-222-20000-222-2-222-200000000000000000000000000
χ694-44-40000-400004-444-400000000002-2-222-2-220000-222-2-222-200000000000000000000000000
χ704-44-40000-400004-444-40000000000-222-2-222-200002-2-222-2-2200000000000000000000000000
χ714-4-44-444-4000-4402222−22−22−22−2222220000000000000022−22−22220000000000000000000000000000000000
χ724-4-44-444-4000-440−22−2222222222−22−2200000000000000−222222−220000000000000000000000000000000000
χ734-4-44-44-440004-402222−22−22−22−22222200000000000000−222222−220000000000000000000000000000000000
χ744-4-44-44-440004-40−22−2222222222−22−220000000000000022−22−22220000000000000000000000000000000000

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