Finite Group Databasebeta

← Group #333392

Character table — Group #333392

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68
size11111111222222224444444444444444444444444488888888161616161616161616161616161616163232
order12222222444444444488888888888888888888888844444444224444448888888822
χ111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111111111-1-111-1-11-11-1-1-1-1-111-1-111-1-1-1-1
χ3111111111111111111111111111111111111111111-1-111-1-111-11-11-1-1-1-1-1-111-1-111-1-1
χ4111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-111
χ51111111111111111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1111111-1-11-11111-1-1-1-1-1-1-1-1111-1
χ61111111111111111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-111-1-11111111-1-1-111-1-111-1-1-1-1-11
χ71111111111111111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-1-11-1-11111-1-11111-11
χ81111111111111111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-11-1-111-1-1111111-1-11-1
χ9111111111111111111-1-1-1-11111-1-1-1-11111-1-1-1-1-1-1-1-11111-1-111-111111-1-1-1-1-1-111-1-1-11
χ10111111111111111111-1-1-1-11111-1-1-1-11111-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-11-1-1-111-1-11111111-1
χ11111111111111111111-1-1-1-11111-1-1-1-11111-1-1-1-1-1-1-1-1-1-111111111-11-1-11111-1-1-1-1-1-11-1
χ12111111111111111111-1-1-1-11111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-111-1-11-1-1-111-1-11111-1-111-11
χ13111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-11111111111-1-1-1-1-1-1
χ14111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111-1-1-1-111-111-1-1-1-1-111-1-1-1-11111
χ15111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-11111-1-11-1-11-1-1-1-1-1-11111-1-111
χ16111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1111111-1-11111-1-1-1-11111-1-1
χ17222222222-22-22-22-2-2-2000022220000-2-2-2-200000000002200220-20-200000000000000
χ18222222222-22-22-22-2-2-2000022220000-2-2-2-20000000000-2-200-2-2020200000000000000
χ19222222222-22-22-22-2-2-20000-2-2-2-20000222200000000002200-2-2020-200000000000000
χ20222222222-22-22-22-2-2-20000-2-2-2-2000022220000000000-2-200220-20200000000000000
χ2122222222-22-22-22-22-2-222220000-2-2-2-200000000000022002200-20-2000000000000000
χ2222222222-22-22-22-22-2-222220000-2-2-2-2000000000000-2-200-2-200202000000000000000
χ2322222222-22-22-22-22-2-2-2-2-2-2000022220000000000002200-2-20020-2000000000000000
χ2422222222-22-22-22-22-2-2-2-2-2-200002222000000000000-2-2002200-202000000000000000
χ25222-22-2-2-2020-20-202002i2i−2i−2ii2i2−i2−i20000i2i2−i2−i22222−2−2−2−22-2002i−2i00000000002−200i2−i20000
χ26222-22-2-2-2020-20-202002i2i−2i−2ii2i2−i2−i20000i2i2−i2−i22222−2−2−2−2-2200−2i2i0000000000−2200−i2i20000
χ27222-22-2-2-2020-20-202002i2i−2i−2i−i2−i2i2i20000−i2−i2i2i2−2−2−2−222222-2002i−2i0000000000−2200−i2i20000
χ28222-22-2-2-2020-20-202002i2i−2i−2i−i2−i2i2i20000−i2−i2i2i2−2−2−2−22222-2200−2i2i00000000002−200i2−i20000
χ29222-22-2-2-2020-20-20200−2i−2i2i2ii2i2−i2−i20000i2i2−i2−i2−2−2−2−222222-200−2i2i0000000000−2200i2−i20000
χ30222-22-2-2-2020-20-20200−2i−2i2i2ii2i2−i2−i20000i2i2−i2−i2−2−2−2−22222-22002i−2i00000000002−200−i2i20000
χ31222-22-2-2-2020-20-20200−2i−2i2i2i−i2−i2i2i20000−i2−i2i2i22222−2−2−2−22-200−2i2i00000000002−200−i2i20000
χ32222-22-2-2-2020-20-20200−2i−2i2i2i−i2−i2i2i20000−i2−i2i2i22222−2−2−2−2-22002i−2i0000000000−2200i2−i20000
χ3322-22-22-2-220-20-202000i2−i2i2−i22i−2i2i−2ii2i2−i2−i2000022−2−222−2−2002-2002i−2i00000000002−200i2−i200
χ3422-22-22-2-220-20-202000i2−i2i2−i22i−2i2i−2ii2i2−i2−i2000022−2−222−2−200-2200−2i2i0000000000−2200−i2i200
χ3522-22-22-2-220-20-202000i2−i2i2−i2−2i2i−2i2ii2i2−i2−i20000−2−222−2−222002-200−2i2i0000000000−2200i2−i200
χ3622-22-22-2-220-20-202000i2−i2i2−i2−2i2i−2i2ii2i2−i2−i20000−2−222−2−22200-22002i−2i00000000002−200−i2i200
χ3722-22-22-2-220-20-202000−i2i2−i2i22i−2i2i−2i−i2−i2i2i20000−2−222−2−222002-2002i−2i0000000000−2200−i2i200
χ3822-22-22-2-220-20-202000−i2i2−i2i22i−2i2i−2i−i2−i2i2i20000−2−222−2−22200-2200−2i2i00000000002−200i2−i200
χ3922-22-22-2-220-20-202000−i2i2−i2i2−2i2i−2i2i−i2−i2i2i2000022−2−222−2−2002-200−2i2i00000000002−200−i2i200
χ4022-22-22-2-220-20-202000−i2i2−i2i2−2i2i−2i2i−i2−i2i2i2000022−2−222−2−200-22002i−2i0000000000−2200i2−i200
χ412-2-2-222-22-2-222-2-222-2200000000000000002-22-22-22-20000000000002-22-20000000000
χ422-2-2-222-22-2-222-2-222-2200000000000000002-22-22-22-2000000000000-22-220000000000
χ432-2-2-222-22-2-222-2-222-220000000000000000-22-22-22-220000000000002-2-220000000000
χ442-2-2-222-22-2-222-2-222-220000000000000000-22-22-22-22000000000000-222-20000000000
χ4544444444-4-4-4-4-4-4-4-44400000000000000000000000000000000000000000000000000
χ46444-44-4-4-40-404040-40000002i22i2−2i2−2i20000−2i2−2i22i22i20000000000000000000000000000000000
χ47444-44-4-4-40-404040-4000000−2i2−2i22i22i200002i22i2−2i2−2i20000000000000000000000000000000000
χ4844-44-44-4-4-404040-40002i2−2i22i2−2i20000−2i2−2i22i22i200000000000000000000000000000000000000
χ4944-44-44-4-4-404040-4000−2i22i2−2i22i200002i22i2−2i2−2i200000000000000000000000000000000000000
χ5044-4-4-4-444000000000022−22−222222−22−22220000000022-2-2-2-22200000000000000000000000000
χ5144-4-4-4-444000000000022−22−2222−222222−2200000000-2-22222-2-200000000000000000000000000
χ5244-4-4-4-4440000000000−222222−2222−22−222200000000-2-22222-2-200000000000000000000000000
χ5344-4-4-4-4440000000000−222222−22−222222−220000000022-2-2-2-22200000000000000000000000000
χ544-444-4-4-4400000000000000000022−2222−2222−2222−222-2-22-222-200000000000000000000000000
χ554-444-4-4-4400000000000000000022−2222−22−2222−2222-222-22-2-2200000000000000000000000000
χ564-444-4-4-44000000000000000000−2222−222222−2222−22-222-22-2-2200000000000000000000000000
χ574-444-4-4-44000000000000000000−2222−2222−2222−22222-2-22-222-200000000000000000000000000
χ584-44-4-444-44040-40-40000000000000004i−4i−4i4i0000000000000000000000000000000000
χ594-44-4-444-44040-40-4000000000000000−4i4i4i−4i0000000000000000000000000000000000
χ604-44-4-444-4-40-40404000000000000000000022−22−222222−22−222200000000000000000000000000
χ614-44-4-444-4-40-404040000000000000000000−222222−22−222222−2200000000000000000000000000
χ624-4-444-44-404040-40-400000000004i−4i−4i4i00000000000000000000000000000000000000
χ634-4-444-44-404040-40-40000000000−4i4i4i−4i00000000000000000000000000000000000000
χ644-4-444-44-40-40-4040400000000000000000022−2222−22−2222−222200000000000000000000000000
χ654-4-444-44-40-40-40404000000000000000000−2222−222222−2222−2200000000000000000000000000
χ664-4-4-444-4444-4-444-4-4-4400000000000000000000000000000000000000000000000000
χ674-4-4-444-444-4-444-4-444-400000000000000000000000000000000000000000000000000
χ684-4-4-444-44-444-4-444-44-400000000000000000000000000000000000000000000000000

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