Finite Group Databasebeta

← Group #342018

Character table — Group #342018

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68
size11111111222222224444444444444444444444444488888888161616161616161616161616161616163232
order12222222444444444488888888888888888888888844444444444444448888888844
χ111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111111111-1-1-1-111-1-11-1-11-1-11111-1-1-1-1-1-1
χ3111111111111111111111111111111111111111111-1-11111-1-111-1-1-1-1-1-1-1-1-1-11111-1-1
χ4111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-111-111-1-1-1-1-1-1-1-111
χ511111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1111-11111-1-1-1-1-1-111-1-11-1
χ611111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-11111-111-1-1111-1-1-1-1-1-111-11
χ711111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-11-1-1-1-1-111111111-1-1-11
χ811111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-11-111-1-1-11111-1-1111-1
χ9111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1111111-1-111111-1-1-1-1-111-1-1-1-1-11
χ10111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-11-1-1-111-1-11111111-1
χ11111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-111111111-1-1-111111-1-1-1-1-1-11-1
χ12111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1111-1-111-1-11111-11
χ13111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-11-1111-11111-1-1-1-111-1-1
χ14111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111-1-111-1-1-111-1-1-1-1-111-1-111-1-111
χ15111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-111-1-1111-1-1-1-11-1-1-1-111-1-11111
χ16111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-11111-11-111111-1-11111-1-1-1-1
χ17222222222-22-2-222-2-2-2000000002222-2-2-2-20000000000222200-2-20000000000000000
χ18222222222-22-2-222-2-2-2000000002222-2-2-2-20000000000-2-2-2-200220000000000000000
χ19222222222-22-2-222-2-2-200000000-2-2-2-22222000000000022-2-200-220000000000000000
χ20222222222-22-2-222-2-2-200000000-2-2-2-222220000000000-2-222002-20000000000000000
χ2122222222-22-222-2-22-2-22222-2-2-2-200000000000000002200002200-200-2000000000000
χ2222222222-22-222-2-22-2-22222-2-2-2-20000000000000000-2-20000-2-2002002000000000000
χ2322222222-22-222-2-22-2-2-2-2-2-222220000000000000000220000-2-200-2002000000000000
χ2422222222-22-222-2-22-2-2-2-2-2-222220000000000000000-2-200002200200-2000000000000
χ25222-22-2-2-220200-2-200022−2−222−2−222-2-200002222−2−2−2−2002-22-2000000000000002−22−200
χ26222-22-2-2-220200-2-200022−2−222−2−222-2-200002222−2−2−2−200-22-2200000000000000−22−2200
χ27222-22-2-2-220200-2-200022−2−222−2−2-2-2220000−2−2−2−22222002-2-22000000000000002−2−2200
χ28222-22-2-2-220200-2-200022−2−222−2−2-2-2220000−2−2−2−2222200-222-200000000000000−222−200
χ29222-22-2-2-220200-2-2000−2−222−2−22222-2-20000−2−2−2−22222002-22-200000000000000−22−2200
χ30222-22-2-2-220200-2-2000−2−222−2−22222-2-20000−2−2−2−2222200-22-22000000000000002−22−200
χ31222-22-2-2-220200-2-2000−2−222−2−222-2-22200002222−2−2−2−2002-2-2200000000000000−222−200
χ32222-22-2-2-220200-2-2000−2−222−2−222-2-22200002222−2−2−2−200-222-2000000000000002−2−2200
χ3322-2-2-2-2220202-200-2002-22-200002−22−222−2−222−2−222−2−22i−2i00002i−2i00000000i2−i2i2−i2000000
χ3422-2-2-2-2220202-200-2002-22-200002−22−222−2−222−2−222−2−2−2i2i0000−2i2i00000000−i2i2−i2i2000000
χ3522-2-2-2-2220202-200-2002-22-20000−22−22−2−222−2−222−2−2222i−2i00002i−2i00000000−i2i2−i2i2000000
χ3622-2-2-2-2220202-200-2002-22-20000−22−22−2−222−2−222−2−222−2i2i0000−2i2i00000000i2−i2i2−i2000000
χ3722-2-2-2-2220202-200-200-22-2200002−22−222−2−2−2−222−2−2222i−2i0000−2i2i00000000−i2i2i2−i2000000
χ3822-2-2-2-2220202-200-200-22-2200002−22−222−2−2−2−222−2−222−2i2i00002i−2i00000000i2−i2−i2i2000000
χ3922-2-2-2-2220202-200-200-22-220000−22−22−2−22222−2−222−2−22i−2i0000−2i2i00000000i2−i2−i2i2000000
χ4022-2-2-2-2220202-200-200-22-220000−22−22−2−22222−2−222−2−2−2i2i00002i−2i00000000−i2i2i2−i2000000
χ412-2-2-222-222-2-2222-2-22-200000000000000002i−2i2i−2i2i−2i2i−2i000000000002i−2i02-20000000000
χ422-2-2-222-222-2-2222-2-22-200000000000000002i−2i2i−2i2i−2i2i−2i00000000000−2i2i0-220000000000
χ432-2-2-222-222-2-2222-2-22-20000000000000000−2i2i−2i2i−2i2i−2i2i000000000002i−2i0-220000000000
χ442-2-2-222-222-2-2222-2-22-20000000000000000−2i2i−2i2i−2i2i−2i2i00000000000−2i2i02-20000000000
χ4544444444-4-4-4-4-4-4-4-44400000000000000000000000000000000000000000000000000
χ46444-44-4-4-4-40-400440002222−22−22−22−222222000000000000000000000000000000000000000000
χ47444-44-4-4-4-40-40044000−22−2222222222−22−22000000000000000000000000000000000000000000
χ4844-44-44-4-4000000000022−22−2222000022−22−2222000022-2-2-2-22200000000000000000000000000
χ4944-44-44-4-4000000000022−22−22220000−222222−220000-2-22222-2-200000000000000000000000000
χ5044-44-44-4-40000000000−222222−22000022−22−22220000-2-22222-2-200000000000000000000000000
χ5144-44-44-4-40000000000−222222−220000−222222−22000022-2-2-2-22200000000000000000000000000
χ5244-4-4-4-4440-40-44004000000000022−2222−22−22−2222220000000000000000000000000000000000
χ5344-4-4-4-4440-40-440040000000000−2222−22222222−22−220000000000000000000000000000000000
χ544-444-4-4-44040-4400-40000004-44-4000000000000000000000000000000000000000000
χ554-444-4-4-44040-4400-4000000-44-44000000000000000000000000000000000000000000
χ564-444-4-4-440-404-40040000000000000000002i2−2i2−2i22i22i2−2i2−2i22i200000000000000000000000000
χ574-444-4-4-440-404-4004000000000000000000−2i22i22i2−2i2−2i22i22i2−2i200000000000000000000000000
χ584-44-4-444-40000000000000022−22−222200002i2−2i22i2−2i22i−2i−2i2i−2i2i2i−2i00000000000000000000000000
χ594-44-4-444-40000000000000022−22−22220000−2i22i2−2i22i2−2i2i2i−2i2i−2i−2i2i00000000000000000000000000
χ604-44-4-444-400000000000000−222222−2200002i2−2i22i2−2i2−2i2i2i−2i2i−2i−2i2i00000000000000000000000000
χ614-44-4-444-400000000000000−222222−220000−2i22i2−2i22i22i−2i−2i2i−2i2i2i−2i00000000000000000000000000
χ624-4-444-44-440-400-4400000000000000000002i2−2i22i2−2i2−2i22i2−2i22i200000000000000000000000000
χ634-4-444-44-440-400-440000000000000000000−2i22i2−2i22i22i2−2i22i2−2i200000000000000000000000000
χ644-4-444-44-4-404004-40000000000000004i−4i−4i4i0000000000000000000000000000000000
χ654-4-444-44-4-404004-4000000000000000−4i4i4i−4i0000000000000000000000000000000000
χ664-4-4-444-4444-4-4-44-44-4400000000000000000000000000000000000000000000000000
χ674-4-4-444-44-444-4-4-4444-400000000000000000000000000000000000000000000000000
χ684-4-4-444-44-4-4444-44-4-4400000000000000000000000000000000000000000000000000

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