Finite Group Databasebeta

← Group #103992

Character table — Group #103992

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59
size11111111222222224444444488888888888888888161616161616161616161616161616163232
order12222222444444444444444448888888888888888222244448888888844
χ111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111111-1-1-1-111-1-1-1-1-1-1-1-1-1-1
χ3111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-11111-1-11111-1-1-1-1-1-1
χ4111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111
χ51111111111111111111111111-1-1-1-1-1-1-1-111111111-1-11111-1-1-1-1-1-1-1-1-1-111
χ61111111111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-111111111-1-1
χ71111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-11111-1-1
χ81111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-1111111-1-1-1-111
χ92222222222222222-2-2-2-222-2-2-200000000000000000000000022-2-2000000
χ102222222222222222-2-2-2-222-2-2-2000000000000000000000000-2-222000000
χ112222222222-2-222-2-2222-2-2-22-2-20000000000000000220000-2-20000000000
χ122222222222-2-222-2-2222-2-2-22-2-20000000000000000-2-20000220000000000
χ132222222222-2-222-2-2-2-2-22-2-2-222000000000000000000000000000000002-2
χ142222222222-2-222-2-2-2-2-22-2-2-22200000000000000000000000000000000-22
χ1522222222-2-222-2-22222-22-2-2-22-2000000002222-2-2-2-2000000000000000000
χ1622222222-2-222-2-22222-22-2-2-22-200000000-2-2-2-22222000000000000000000
χ1722222222-2-222-2-222-2-22-2-2-22-22000000000000000000000000000022-2-200
χ1822222222-2-222-2-222-2-22-2-2-22-220000000000000000000000000000-2-22200
χ1922222222-2-2-2-2-2-2-2-222-2-222-2-222i2i2i2i−2i−2i−2i−2i00000000000000000000000000
χ2022222222-2-2-2-2-2-2-2-222-2-222-2-22−2i−2i−2i−2i2i2i2i2i00000000000000000000000000
χ2122222222-2-2-2-2-2-2-2-2-2-2222222-200000000000000000022-2-2000000000000
χ2222222222-2-2-2-2-2-2-2-2-2-2222222-2000000000000000000-2-222000000000000
χ23222-2-22-2-22200-2-2002-2-2000200i2i2−i2−i2i2i2−i2−i2i2i2−i2−i2i2i2−i2−i22-20000000000000000
χ24222-2-22-2-22200-2-2002-2-2000200i2i2−i2−i2i2i2−i2−i2−i2−i2i2i2−i2−i2i2i2-220000000000000000
χ25222-2-22-2-22200-2-2002-2-2000200−i2−i2i2i2−i2−i2i2i2i2i2−i2−i2i2i2−i2−i2-220000000000000000
χ26222-2-22-2-22200-2-2002-2-2000200−i2−i2i2i2−i2−i2i2i2−i2−i2i2i2−i2−i2i2i22-20000000000000000
χ27222-2-22-2-2-2-20022002-22000-20022−2−2−2−222i2i2−i2−i2−i2−i2i2i20000002i−2i0000000000
χ28222-2-22-2-2-2-20022002-22000-20022−2−2−2−222−i2−i2i2i2i2i2−i2−i2000000−2i2i0000000000
χ29222-2-22-2-2-2-20022002-22000-200−2−22222−2−2i2i2−i2−i2−i2−i2i2i2000000−2i2i0000000000
χ30222-2-22-2-2-2-20022002-22000-200−2−22222−2−2−i2−i2i2i2i2i2−i2−i20000002i−2i0000000000
χ312-2-2-2-22222-2-2-22-22200002-2000000000002−22−22−22−200000000002-22−22−200
χ322-2-2-2-22222-2-2-22-22200002-2000000000002−22−22−22−20000000000-22−22−2200
χ332-2-2-2-22222-2-2-22-22200002-200000000000−22−22−22−2200000000002-2−22−2200
χ342-2-2-2-22222-2-2-22-22200002-200000000000−22−22−22−220000000000-222−22−200
χ352-2-2-2-2222-22-2-2-22220000-22000000000002−22−2−22−22000000002-2002−2−2200
χ362-2-2-2-2222-22-2-2-22220000-22000000000002−22−2−22−2200000000-2200−222−200
χ372-2-2-2-2222-22-2-2-22220000-2200000000000−22−222−22−2000000002-200−222−200
χ382-2-2-2-2222-22-2-2-22220000-2200000000000−22−222−22−200000000-22002−2−2200
χ39444-4-44-4-44400-4-400-444000-4000000000000000000000000000000000000
χ40444-4-44-4-4-4-4004400-44-40004000000000000000000000000000000000000
χ4144-44-4-44-4004i−4i004i−4i0000000002ζ−2ζ2ζ−2ζ2ζ3−2ζ32ζ3−2ζ300000000000000000000000000
χ4244-44-4-44-4004i−4i004i−4i000000000−2ζ2ζ−2ζ2ζ−2ζ32ζ3−2ζ32ζ300000000000000000000000000
χ4344-44-4-44-400−4i4i00−4i4i0000000002ζ3−2ζ32ζ3−2ζ32ζ−2ζ2ζ−2ζ00000000000000000000000000
χ4444-44-4-44-400−4i4i00−4i4i000000000−2ζ32ζ3−2ζ32ζ3−2ζ2ζ−2ζ2ζ00000000000000000000000000
χ4544-4-44-4-44000000000004000-402i−2i−2i2i−2i2i2i−2i00000000000000000000000000
χ4644-4-44-4-44000000000004000-40−2i2i2i−2i2i−2i−2i2i00000000000000000000000000
χ4744-4-44-4-4400000000000-4000402-2-222-2-2200000000000000000000000000
χ4844-4-44-4-4400000000000-400040-222-2-222-200000000000000000000000000
χ494-44-44-44-4004i−4i00−4i4i0000000000000000000000000002-22i−2i000000000000
χ504-44-44-44-4004i−4i00−4i4i000000000000000000000000000-22−2i2i000000000000
χ514-44-44-44-400−4i4i004i−4i0000000000000000000000000002-2−2i2i000000000000
χ524-44-44-44-400−4i4i004i−4i000000000000000000000000000-222i−2i000000000000
χ534-4-4444-4-44-400-4400000000000000000002i−2i−2i2i2i−2i−2i2i000000000000000000
χ544-4-4444-4-44-400-440000000000000000000−2i2i2i−2i−2i2i2i−2i000000000000000000
χ554-4-4444-4-4-44004-400000000000000000002i−2i−2i2i−2i2i2i−2i000000000000000000
χ564-4-4444-4-4-44004-40000000000000000000−2i2i2i−2i2i−2i−2i2i000000000000000000
χ574-4-4-4-44444-4444-4-4-40000-440000000000000000000000000000000000000
χ584-4-4-4-4444-4444-44-4-400004-40000000000000000000000000000000000000
χ598-888-8-8-88000000000000000000000000000000000000000000000000000

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