Finite Group Databasebeta

← Group #105143

Character table — Group #105143

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59
size11111111222222224444444488888888888888888161616161616161616161616161616163232
order12222222444444444444444448888888888888888444488888888888824
χ111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ3111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1
χ4111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111
χ51111111111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-11111-1-1-1-11111-1-1
χ61111111111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-11111-1-1-1-111
χ71111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-111
χ81111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-111111111-1-1
χ922222222222222222-2-2-2-22-2-2-20000000000000000000022-2-20000000000
χ1022222222222222222-2-2-2-22-2-2-200000000000000000000-2-2220000000000
χ11222222222222-2-2-2-2-22-2-2-2-22-22000000002i2i2i2i−2i−2i−2i−2i000000000000000000
χ12222222222222-2-2-2-2-22-2-2-2-22-2200000000−2i−2i−2i−2i2i2i2i2i000000000000000000
χ13222222222222-2-2-2-2-2-2222-2-22-200000000000000000000000000002i2i−2i−2i00
χ14222222222222-2-2-2-2-2-2222-2-22-20000000000000000000000000000−2i−2i2i2i00
χ1522222222-2-2-2-22222-2222-2-22-2-2000000000000000022-2-200000000000000
χ1622222222-2-2-2-22222-2222-2-22-2-20000000000000000-2-22200000000000000
χ1722222222-2-2-2-22222-2-2-2-22-2-222000000000000000000000000000000002-2
χ1822222222-2-2-2-22222-2-2-2-22-2-22200000000000000000000000000000000-22
χ1922222222-2-2-2-2-2-2-2-222-2-22222-22222-2-2-2-200000000000000000000000000
χ2022222222-2-2-2-2-2-2-2-222-2-22222-2-2-2-2-2222200000000000000000000000000
χ2122222222-2-2-2-2-2-2-2-22-222-22-2-220000000000000000000000002i2i−2i−2i000000
χ2222222222-2-2-2-2-2-2-2-22-222-22-2-22000000000000000000000000−2i−2i2i2i000000
χ23222-2-22-2-222-2-222-2-2-20000200000000000i2i2−i2−i2i2i2−i2−i20000002i−2i00002−22−200
χ24222-2-22-2-222-2-222-2-2-20000200000000000i2i2−i2−i2i2i2−i2−i2000000−2i2i0000−22−2200
χ25222-2-22-2-222-2-222-2-2-20000200000000000−i2−i2i2i2−i2−i2i2i20000002i−2i0000−22−2200
χ26222-2-22-2-222-2-222-2-2-20000200000000000−i2−i2i2i2−i2−i2i2i2000000−2i2i00002−22−200
χ27222-2-22-2-222-2-2-2-22220000-20000000000022−2−2−2−22200002i−2i000000i2−i2−i2i200
χ28222-2-22-2-222-2-2-2-22220000-20000000000022−2−2−2−2220000−2i2i000000−i2i2i2−i200
χ29222-2-22-2-222-2-2-2-22220000-200000000000−2−22222−2−200002i−2i000000−i2i2i2−i200
χ30222-2-22-2-222-2-2-2-22220000-200000000000−2−22222−2−20000−2i2i000000i2−i2−i2i200
χ312-2-22-222-200002-2-22022-200-200i2i2−i2−i2i2i2−i2−i22−22−22−22−2002i−2i00000000000000
χ322-2-22-222-200002-2-22022-200-200i2i2−i2−i2i2i2−i2−i2−22−22−22−2200−2i2i00000000000000
χ332-2-22-222-200002-2-22022-200-200−i2−i2i2i2−i2−i2i2i22−22−22−22−200−2i2i00000000000000
χ342-2-22-222-200002-2-22022-200-200−i2−i2i2i2−i2−i2i2i2−22−22−22−22002i−2i00000000000000
χ352-2-22-222-20000-222-202-2200-200i2i2−i2−i2−i2−i2i2i2i2−i2i2−i2−i2i2−i2i22-20000000000000000
χ362-2-22-222-20000-222-202-2200-200i2i2−i2−i2−i2−i2i2i2−i2i2−i2i2i2−i2i2−i2-220000000000000000
χ372-2-22-222-20000-222-202-2200-200−i2−i2i2i2i2i2−i2−i2i2−i2i2−i2−i2i2−i2i2-220000000000000000
χ382-2-22-222-20000-222-202-2200-200−i2−i2i2i2i2i2−i2−i2−i2i2−i2i2i2−i2i2−i22-20000000000000000
χ39444-4-44-4-4-4-44444-4-440000-40000000000000000000000000000000000000
χ40444-4-44-4-4-4-444-4-444-4000040000000000000000000000000000000000000
χ4144-44-4-4-444i−4i4i−4i00000000000000000000000000000000000002ζ−2ζ2ζ3−2ζ3000000
χ4244-44-4-4-444i−4i4i−4i0000000000000000000000000000000000000−2ζ2ζ−2ζ32ζ3000000
χ4344-44-4-4-44−4i4i−4i4i00000000000000000000000000000000000002ζ3−2ζ32ζ−2ζ000000
χ4444-44-4-4-44−4i4i−4i4i0000000000000000000000000000000000000−2ζ32ζ3−2ζ2ζ000000
χ4544-4-44-44-44i−4i−4i4i00000000000002-22-22i−2i2i−2i00000000000000000000000000
χ4644-4-44-44-44i−4i−4i4i0000000000000-22-22−2i2i−2i2i00000000000000000000000000
χ4744-4-44-44-4−4i4i4i−4i00000000000002-22-2−2i2i−2i2i00000000000000000000000000
χ4844-4-44-44-4−4i4i4i−4i0000000000000-22-222i−2i2i−2i00000000000000000000000000
χ494-44-4-4-444000000000000400-402i2−2i2−2i22i2000000000000000000000000000000
χ504-44-4-4-444000000000000400-40−2i22i22i2−2i2000000000000000000000000000000
χ514-44-4-4-444000000000000-40040000022−22−222200000000000000000000000000
χ524-44-4-4-444000000000000-400400000−222222−2200000000000000000000000000
χ534-4-44-444-400004-4-440-4-44004000000000000000000000000000000000000
χ544-4-44-444-40000-444-40-44-4004000000000000000000000000000000000000
χ554-4-4-444-4400004-44-4000000000000000002i−2i−2i2i2i−2i−2i2i000000000000000000
χ564-4-4-444-4400004-44-400000000000000000−2i2i2i−2i−2i2i2i−2i000000000000000000
χ574-4-4-444-440000-44-44000000000000000002-2-22-222-2000000000000000000
χ584-4-4-444-440000-44-4400000000000000000-222-22-2-22000000000000000000
χ598-8888-8-8-8000000000000000000000000000000000000000000000000000

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