Finite Group Databasebeta

← Group #342010

Character table — Group #342010

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68
size11111111222222224444444444444444444444444488888888161616161616161616161616161616163232
order12222222444444444488888888888888888888888822444444244444448888888844
χ111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111111111-1-111-1-11-11-1-1-1-1-1-1-1-1-11111-1-1
χ3111111111111111111111111111111111111111111-1-111-1-111-11-11-1-1-1-11111-1-1-1-1-1-1
χ4111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-111
χ511111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-111-1111-1-111-1-1-1-111-1-1-11
χ611111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-11-111-1-1111111-1-11-1
χ711111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1111-1-1-1-1-1-1-1-1111-1
χ811111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-11-1-1-1-1-1111111-1-111-11
χ9111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1111111-1-1111-111-1-1-1-111-1-1-1-1-11
χ10111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-111-1-111111-111-1-11111-1-1-1-1-1-11-1
χ11111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-111-1-1-1-1-11-1-1-1-111-1-11111111-1
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
χ13111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-1-111-1-1-1-1-111-1-1-1-11111
χ14111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111-1-1-1-111-1-1111111-1-111-1-111-1-1
χ15111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-11111-1-111-1-1111111-1-111-1-1-1-1
χ16111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-111111-1-11-1-1-1-1-1-11111-1-111
χ17222222222-22-2-222-2-2-2000000002222-2-2-2-20000000022002200-20-2000000000000000
χ18222222222-22-2-222-2-2-2000000002222-2-2-2-200000000-2-200-2-200202000000000000000
χ19222222222-22-2-222-2-2-200000000-2-2-2-22222000000002200-2-20020-2000000000000000
χ20222222222-22-2-222-2-2-200000000-2-2-2-2222200000000-2-2002200-202000000000000000
χ2122222222-22-222-2-22-2-22222-2-2-2-20000000000000000002200220-20-200000000000000
χ2222222222-22-222-2-22-2-22222-2-2-2-2000000000000000000-2-200-2-2020200000000000000
χ2322222222-22-222-2-22-2-2-2-2-2-222220000000000000000002200-2-20-20200000000000000
χ2422222222-22-222-2-22-2-2-2-2-2-22222000000000000000000-2-20022020-200000000000000
χ25222-2-2-22-2-20-2002200022−2−222−2−22i2i−2i−2i0000i2i2i2i2−i2−i2−i2−i22-2002i−2i000000000000002−2i2−i200
χ26222-2-2-22-2-20-2002200022−2−222−2−22i2i−2i−2i0000i2i2i2i2−i2−i2−i2−i2-2200−2i2i00000000000000−22−i2i200
χ27222-2-2-22-2-20-2002200022−2−222−2−2−2i−2i2i2i0000−i2−i2−i2−i2i2i2i2i22-200−2i2i000000000000002−2−i2i200
χ28222-2-2-22-2-20-2002200022−2−222−2−2−2i−2i2i2i0000−i2−i2−i2−i2i2i2i2i2-22002i−2i00000000000000−22i2−i200
χ29222-2-2-22-2-20-20022000−2−222−2−2222i2i−2i−2i0000−i2−i2−i2−i2i2i2i2i22-2002i−2i00000000000000−22−i2i200
χ30222-2-2-22-2-20-20022000−2−222−2−2222i2i−2i−2i0000−i2−i2−i2−i2i2i2i2i2-2200−2i2i000000000000002−2i2−i200
χ31222-2-2-22-2-20-20022000−2−222−2−222−2i−2i2i2i0000i2i2i2i2−i2−i2−i2−i22-200−2i2i00000000000000−22i2−i200
χ32222-2-2-22-2-20-20022000−2−222−2−222−2i−2i2i2i0000i2i2i2i2−i2−i2−i2−i2-22002i−2i000000000000002−2−i2i200
χ3322-22-22-2-20-202-2002002-22-200002−22−222−2−222−2−222−2−2002i−2i002i−2i00000000i2−i2i2−i2000000
χ3422-22-22-2-20-202-2002002-22-200002−22−222−2−222−2−222−2−200−2i2i00−2i2i00000000−i2i2−i2i2000000
χ3522-22-22-2-20-202-2002002-22-20000−22−22−2−222−2−222−2−222002i−2i002i−2i00000000−i2i2−i2i2000000
χ3622-22-22-2-20-202-2002002-22-20000−22−22−2−222−2−222−2−22200−2i2i00−2i2i00000000i2−i2i2−i2000000
χ3722-22-22-2-20-202-200200-22-2200002−22−222−2−2−2−222−2−222002i−2i00−2i2i00000000−i2i2i2−i2000000
χ3822-22-22-2-20-202-200200-22-2200002−22−222−2−2−2−222−2−22200−2i2i002i−2i00000000i2−i2−i2i2000000
χ3922-22-22-2-20-202-200200-22-220000−22−22−2−22222−2−222−2−2002i−2i00−2i2i00000000i2−i2−i2i2000000
χ4022-22-22-2-20-202-200200-22-220000−22−22−2−22222−2−222−2−200−2i2i002i−2i00000000−i2i2i2−i2000000
χ412-22-2-22-222-2-2222-2-22-200000000000000002i−2i2i−2i2i−2i2i−2i0000000000002i−2i2-20000000000
χ422-22-2-22-222-2-2222-2-22-200000000000000002i−2i2i−2i2i−2i2i−2i000000000000−2i2i-220000000000
χ432-22-2-22-222-2-2222-2-22-20000000000000000−2i2i−2i2i−2i2i−2i2i0000000000002i−2i-220000000000
χ442-22-2-22-222-2-2222-2-22-20000000000000000−2i2i−2i2i−2i2i−2i2i000000000000−2i2i2-20000000000
χ4544444444-4-4-4-4-4-4-4-44400000000000000000000000000000000000000000000000000
χ46444-4-4-44-440400-4-40002222−22−22−22−222222000000000000000000000000000000000000000000
χ47444-4-4-44-440400-4-4000−22−2222222222−22−22000000000000000000000000000000000000000000
χ4844-44-44-4-4040-4400-4000000000022−2222−22−22−2222220000000000000000000000000000000000
χ4944-44-44-4-4040-4400-40000000000−2222−22222222−22−220000000000000000000000000000000000
χ5044-4-44-4-44000000000022−22−222200002i2−2i2−2i22i200002i2i−2i−2i−2i−2i2i2i00000000000000000000000000
χ5144-4-44-4-44000000000022−22−22220000−2i22i22i2−2i20000−2i−2i2i2i2i2i−2i−2i00000000000000000000000000
χ5244-4-44-4-440000000000−222222−2200002i2−2i2−2i22i20000−2i−2i2i2i2i2i−2i−2i00000000000000000000000000
χ5344-4-44-4-440000000000−222222−220000−2i22i22i2−2i200002i2i−2i−2i−2i−2i2i2i00000000000000000000000000
χ544-4444-4-4-440-400-440000000000000004-44-40000000000000000000000000000000000
χ554-4444-4-4-440-400-44000000000000000-44-440000000000000000000000000000000000
χ564-4444-4-4-4-404004-4000000000000000000022−2222−22−2222−222200000000000000000000000000
χ574-4444-4-4-4-404004-40000000000000000000−2222−222222−2222−2200000000000000000000000000
χ584-44-4-44-4444-4-4-44-44-4400000000000000000000000000000000000000000000000000
χ594-44-4-44-44-444-4-4-4444-400000000000000000000000000000000000000000000000000
χ604-44-4-44-44-4-4444-44-4-4400000000000000000000000000000000000000000000000000
χ614-4-44-4-4440000000000000022−2222−22000022−22−22222-2-22-222-200000000000000000000000000
χ624-4-44-4-4440000000000000022−2222−220000−222222−22-222-22-2-2200000000000000000000000000
χ634-4-44-4-44400000000000000−2222−2222000022−22−2222-222-22-2-2200000000000000000000000000
χ644-4-44-4-44400000000000000−2222−22220000−222222−222-2-22-222-200000000000000000000000000
χ654-4-4-4444-40404-400-40000000000000000002i2−2i2−2i22i22i2−2i2−2i22i200000000000000000000000000
χ664-4-4-4444-40404-400-4000000000000000000−2i22i22i2−2i2−2i22i22i2−2i200000000000000000000000000
χ674-4-4-4444-40-40-440040000004-4-44000000000000000000000000000000000000000000
χ684-4-4-4444-40-40-44004000000-444-4000000000000000000000000000000000000000000

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