Finite Group Databasebeta

← Group #337159

Character table — Group #337159

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59
size11111111222222224444448888888888888888888888161616161616161616161616323232
order12222222444444444488882222444488888888888888444444888888444
χ111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111-1-1-1-1-1-1111111-1-1-1-111-11-1-1-1-1-1-1-1-11-11
χ3111111111111111111111111-1-1111111111111111111-1-11-1-1-111-1-1-1-1-1-1-1
χ4111111111111111111111111-1-111-1-1-1-1-1-1111111-1-1-1-1-1-1-1-111-1-11111-11-1
χ51111111111111111111111-1-111-1-111-1-1-1-111-1-1-1-1-1-1-1-111111111-1-1-1-1-11-1
χ61111111111111111111111-1-111-1-1-1-1111111-1-1-1-1111111-11-1-1-1-11111-1-1-1
χ71111111111111111111111-1-1-1-1-1-111-1-1-1-111-1-1-1-1-1-1-1-1-1-11-1-1-11111111-11
χ81111111111111111111111-1-1-1-1-1-1-1-1111111-1-1-1-11111-1-1-1-111-1-1-1-1-1-1111
χ9111111111111111111-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-11-11-111-1-111-1-11-1-1
χ10111111111111111111-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-111111-1-1-1-1-111-1-11111-1
χ11111111111111111111-1-1-1-111-1-111111111-1-1-1-1-1-1-1-1-1-1-1111-1-1-1-1-1-111-111
χ12111111111111111111-1-1-1-111-1-111-1-1-1-1-1-1-1-1-1-1-1-11111-11-11111111-1-1-1-11
χ13111111111111111111-1-1-1-1-1-111-1-111-1-1-1-1-1-1111111111-11-111-1-1-1-111-1-11
χ14111111111111111111-1-1-1-1-1-111-1-1-1-11111-1-11111-1-1-1-11-1-1-1-1-11111-1-1-111
χ15111111111111111111-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-111111111-1111-1-1-1-111-1-111-1
χ16111111111111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-11111-1-1-1-1-11-111111-1-1111-1-1
χ17222222222-2-222-2-22-2-200002200-2-22222-2-2000000000000-2000000000000
χ18222222222-2-222-2-22-2-200002200-2-2-2-2-2-2220000000000002000000000000
χ19222222222-2-222-2-22-2-20000-2-2002222-2-222000000000000-2000000000000
χ20222222222-2-222-2-22-2-20000-2-20022-2-222-2-20000000000002000000000000
χ2122222222-222-2-222-2-2-22222002200000000-2-200000000-2-20200000000000
χ2222222222-222-2-222-2-2-2222200-2-200000000-2-200000000220-200000000000
χ2322222222-222-2-222-2-2-2-2-2-2-20022000000002200000000-220-200000000000
χ2422222222-222-2-222-2-2-2-2-2-2-200-2-20000000022000000002-20200000000000
χ252-222-2-22-2-2-2-22222-22-200000000000000000022-2-2000000002i−2i00002i−2i000
χ262-222-2-22-2-2-2-22222-22-200000000000000000022-2-200000000−2i2i0000−2i2i000
χ272-222-2-22-2-2-2-22222-22-2000000000000000000-2-222000000002i−2i0000−2i2i000
χ282-222-2-22-2-2-2-22222-22-2000000000000000000-2-22200000000−2i2i00002i−2i000
χ292-2-222-2-222002-200-20022−2−200002i−2i2-2002i−2i2−2i2−i2i2−i2i2i2−i2−i20000002−20000000
χ302-2-222-2-222002-200-20022−2−200002i−2i-2200−2i2i2−2i2−i2i2−i2−i2−i2i2i2000000−220000000
χ312-2-222-2-222002-200-20022−2−20000−2i2i2-200−2i2i2−2−i2i2−i2i2−i2−i2i2i20000002−20000000
χ322-2-222-2-222002-200-20022−2−20000−2i2i-22002i−2i2−2−i2i2−i2i2i2i2−i2−i2000000−220000000
χ332-2-222-2-222002-200-200−2−22200002i−2i2-2002i−2i−22−i2i2−i2i2−i2−i2i2i2000000−220000000
χ342-2-222-2-222002-200-200−2−22200002i−2i-2200−2i2i−22−i2i2−i2i2i2i2−i2−i20000002−20000000
χ352-2-222-2-222002-200-200−2−2220000−2i2i2-200−2i2i−22i2−i2i2−i2i2i2−i2−i2000000−220000000
χ362-2-222-2-222002-200-200−2−2220000−2i2i-22002i−2i−22i2−i2i2−i2−i2−i2i2i20000002−20000000
χ3744444444-4-4-4-4-4-4-4-44400000000000000000000000000000000000000000
χ3844-44-44-4-4400-4400-40000004-400000000000000000000000000000000000
χ3944-44-44-4-4400-4400-4000000-4400000000000000000000000000000000000
χ4044-44-44-4-4-4004-4004000000000000000000002i2−2i2−2i22i20000000000000000000
χ4144-44-44-4-4-4004-400400000000000000000000−2i22i22i2−2i20000000000000000000
χ4244-4-44-44-404-4004-400000000000000000000000002i2−2i22i2−2i2000000000000000
χ4344-4-44-44-404-4004-40000000000000000000000000−2i22i2−2i22i2000000000000000
χ4444-4-44-44-40-4400-440004i−4i4i−4i0000000000000000000000000000000000000
χ4544-4-44-44-40-4400-44000−4i4i−4i4i0000000000000000000000000000000000000
χ464-444-4-44-4444-4-4-4-444-400000000000000000000000000000000000000000
χ474-444-4-44-44-4-4-4-4444-4400000000000000000000000000000000000000000
χ484-444-4-44-4-44444-4-4-4-4400000000000000000000000000000000000000000
χ494-44-444-4-400000000002i2−2i2−2i22i2000000002i2−2i2000000002-2-22000000000000000
χ504-44-444-4-400000000002i2−2i2−2i22i200000000−2i22i200000000-222-2000000000000000
χ514-44-444-4-40000000000−2i22i22i2−2i2000000002i2−2i200000000-222-2000000000000000
χ524-44-444-4-40000000000−2i22i22i2−2i200000000−2i22i2000000002-2-22000000000000000
χ534-4-444-4-44-400-44004002222−22−22000000000000−222200000000000000000000000
χ544-4-444-4-44-400-4400400−22−22222200000000000022−2200000000000000000000000
χ554-4-4-4-444404-400-44000000000000000000000000000000000000022−2200000
χ564-4-4-4-444404-400-440000000000000000000000000000000000000−222200000
χ574-4-4-4-44440-44004-40000000004-4000000000000000000000000000000000
χ584-4-4-4-44440-44004-4000000000-44000000000000000000000000000000000
χ59888-8-8-8-88000000000000000000000000000000000000000000000000000

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