Finite Group Databasebeta

← Group #314296

Character table — Group #314296

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68
size11111111222222224444444444444444444444444488888888161616161616161616161616161616163232
order12222222444444444488888888888888888888888844444444222444448888888844
χ111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111111111-1-111-1-1-1-1-11-1-1-1111-1-111-1-1-1-1
χ3111111111111111111111111111111111111111111-1-111-1-1111-1-1-11-1-1-1-1-111-1-111-1-1
χ4111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-111-1-111-1-1-1-1-1-1-1-1-111
χ51111111111111111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-111111111111-1111-1-1-1-1-111-1-1-1-1
χ61111111111111111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-111-1-111-1-1-1-1-1-1-1-1-1-1-1-111111111
χ71111111111111111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1111-1-111-1-1111-1-1-1-1-1-111
χ81111111111111111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111-11111111-1-111-1-1
χ9111111111111111111-1-1-1-11111-1-1-1-11111-1-1-1-1-1-1-1-1111111-1-11111-1-1-11-1-111-1-1-1-11-1
χ10111111111111111111-1-1-1-11111-1-1-1-11111-1-1-1-1-1-1-1-111-1-11111-1-1-111111-1-1-1-1-1-111-11
χ11111111111111111111-1-1-1-11111-1-1-1-11111-1-1-1-1-1-1-1-1-1-111-1-1-1-11-1-1-1-111-1111111-1-1-11
χ12111111111111111111-1-1-1-11111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-111-111-11-1-1-111-1-111111-1
χ13111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111111111-1-1111-1-1-1-1-111-1-1-1-111-11
χ14111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111-1-11111-1-1-1-1111-11111-1-1-1-11-1
χ15111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-111-1-1-1-11-1-11-1111-1-1-1-111111-1
χ16111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-111-11111-1-11-1-11111-1-1-11
χ17222222222-22-22-22-2-2-222220000-2-2-2-200000000000000220022-2000-20000000000000
χ18222222222-22-22-22-2-2-222220000-2-2-2-200000000000000-2-200-2-2200020000000000000
χ19222222222-22-22-22-2-2-2-2-2-2-200002222000000000000002200-2-2-200020000000000000
χ20222222222-22-22-22-2-2-2-2-2-2-20000222200000000000000-2-200222000-20000000000000
χ2122222222-22-22-22-22-2-2000022220000-2-2-2-2000000002200-2-200000-200020000000000
χ2222222222-22-22-22-22-2-2000022220000-2-2-2-200000000-2-20022000002000-20000000000
χ2322222222-22-22-22-22-2-20000-2-2-2-200002222000000002200-2-2000002000-20000000000
χ2422222222-22-22-22-22-2-20000-2-2-2-20000222200000000-2-2002200000-200020000000000
χ25222-2-2-2-2220-20-2020002i2i−2i−2ii2i2−i2−i20000i2i2−i2−i22222−2−2−2−2002i−2i002-200000000002−200i2−i200
χ26222-2-2-2-2220-20-2020002i2i−2i−2ii2i2−i2−i20000i2i2−i2−i22222−2−2−2−200−2i2i00-220000000000−2200−i2i200
χ27222-2-2-2-2220-20-2020002i2i−2i−2i−i2−i2i2i20000−i2−i2i2i2−2−2−2−22222002i−2i002-20000000000−2200−i2i200
χ28222-2-2-2-2220-20-2020002i2i−2i−2i−i2−i2i2i20000−i2−i2i2i2−2−2−2−2222200−2i2i00-2200000000002−200i2−i200
χ29222-2-2-2-2220-20-202000−2i−2i2i2ii2i2−i2−i20000i2i2−i2−i2−2−2−2−22222002i−2i00-2200000000002−200−i2i200
χ30222-2-2-2-2220-20-202000−2i−2i2i2ii2i2−i2−i20000i2i2−i2−i2−2−2−2−2222200−2i2i002-20000000000−2200i2−i200
χ31222-2-2-2-2220-20-202000−2i−2i2i2i−i2−i2i2i20000−i2−i2i2i22222−2−2−2−2002i−2i00-220000000000−2200i2−i200
χ32222-2-2-2-2220-20-202000−2i−2i2i2i−i2−i2i2i20000−i2−i2i2i22222−2−2−2−200−2i2i002-200000000002−200−i2i200
χ3322-2-2-222-222-2-222-2-2-222i−2i2i−2i00002i2i−2i−2i0000000000002-2002-2000000000000002i−2i0000
χ3422-2-2-222-222-2-222-2-2-222i−2i2i−2i00002i2i−2i−2i000000000000-2200-2200000000000000−2i2i0000
χ3522-2-2-222-222-2-222-2-2-22−2i2i−2i2i0000−2i−2i2i2i0000000000002-2002-200000000000000−2i2i0000
χ3622-2-2-222-222-2-222-2-2-22−2i2i−2i2i0000−2i−2i2i2i000000000000-2200-22000000000000002i−2i0000
χ3722-2-2-222-22-2-222-2-222-22i−2i2i−2i0000−2i−2i2i2i0000000000000000000002-2002i−2i00000000000
χ3822-2-2-222-22-2-222-2-222-22i−2i2i−2i0000−2i−2i2i2i000000000000000000000-2200−2i2i00000000000
χ3922-2-2-222-22-2-222-2-222-2−2i2i−2i2i00002i2i−2i−2i0000000000000000000002-200−2i2i00000000000
χ4022-2-2-222-22-2-222-2-222-2−2i2i−2i2i00002i2i−2i−2i000000000000000000000-22002i−2i00000000000
χ4122-2-2-222-2-222-2-222-22-200000000000000002i2i−2i−2i2i2i−2i−2i2-200-2200000000002i−2i00000000
χ4222-2-2-222-2-222-2-222-22-200000000000000002i2i−2i−2i2i2i−2i−2i-22002-20000000000−2i2i00000000
χ4322-2-2-222-2-222-2-222-22-20000000000000000−2i−2i2i2i−2i−2i2i2i2-200-220000000000−2i2i00000000
χ4422-2-2-222-2-222-2-222-22-20000000000000000−2i−2i2i2i−2i−2i2i2i-22002-200000000002i−2i00000000
χ4544444444-4-4-4-4-4-4-4-44400000000000000000000000000000000000000000000000000
χ46444-4-4-4-44-404040-400000002i22i2−2i2−2i20000−2i2−2i22i22i20000000000000000000000000000000000
χ47444-4-4-4-44-404040-40000000−2i2−2i22i22i200002i22i2−2i2−2i20000000000000000000000000000000000
χ4844-444-4-4-44040-40-40004-4-440000000000000000000000000000000000000000000000
χ4944-444-4-4-44040-40-4000-444-40000000000000000000000000000000000000000000000
χ5044-444-4-4-4-40-4040400000000000000000002i22i2−2i2−2i2−2i2−2i22i22i200000000000000000000000000
χ5144-444-4-4-4-40-404040000000000000000000−2i2−2i22i22i22i22i2−2i2−2i200000000000000000000000000
χ5244-4-4-444-4-4-444-4-444-4400000000000000000000000000000000000000000000000000
χ534-444-4-44-40000000000000022−2222−222i2−2i22i2−2i200002i−2i2i−2i2i−2i2i−2i00000000000000000000000000
χ544-444-4-44-40000000000000022−2222−22−2i22i2−2i22i20000−2i2i−2i2i−2i2i−2i2i00000000000000000000000000
χ554-444-4-44-400000000000000−2222−22222i2−2i22i2−2i20000−2i2i−2i2i−2i2i−2i2i00000000000000000000000000
χ564-444-4-44-400000000000000−2222−2222−2i22i2−2i22i200002i−2i2i−2i2i−2i2i−2i00000000000000000000000000
χ574-44-444-4-4040-40-4040000004i−4i−4i4i000000000000000000000000000000000000000000
χ584-44-444-4-4040-40-404000000−4i4i4i−4i000000000000000000000000000000000000000000
χ594-44-444-4-40-404040-40000000000000000002i2−2i22i2−2i2−2i22i2−2i22i200000000000000000000000000
χ604-44-444-4-40-404040-4000000000000000000−2i22i2−2i22i22i2−2i22i2−2i200000000000000000000000000
χ614-4-44-44-4404040-40-4000000000000004i−4i4i−4i0000000000000000000000000000000000
χ624-4-44-44-4404040-40-400000000000000−4i4i−4i4i0000000000000000000000000000000000
χ634-4-44-44-440-40-4040400000000000000000022−22−2222−222222−2200000000000000000000000000
χ644-4-44-44-440-40-40404000000000000000000−222222−2222−22−222200000000000000000000000000
χ654-4-4-44-44400000000000000000022−22−222222−22−22222-2-222-2-2200000000000000000000000000
χ664-4-4-44-44400000000000000000022−22−2222−222222−22-222-2-222-200000000000000000000000000
χ674-4-4-44-444000000000000000000−222222−2222−22−2222-222-2-222-200000000000000000000000000
χ684-4-4-44-444000000000000000000−222222−22−222222−222-2-222-2-2200000000000000000000000000

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