Finite Group Databasebeta

← Group #105136

Character table — Group #105136

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65
size1111111122222222222244444488888888888888888888888881616161616161616161616163232
order12222222444444444444444444488888888888888888888888844448888888844
χ111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1
χ311111111111111111111111111111111111-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1
χ411111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111
χ5111111111111111111111111111-1-1-1-1-1-1-1-11111111111111111-1-1-1-1-1-1-1-11111-1-1
χ6111111111111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-111
χ7111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-11111-1-1-1-111
χ8111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-1
χ922222222222-2-2-222222-2-2-2-222-2-2000000002222-2-2-2-20000000000000000000000
χ1022222222222-2-2-222222-2-2-2-222-2-200000000-2-2-2-222220000000000000000000000
χ112222222222-222222-2-2-22-2-22-2-22-22222-2-2-2-2000000000000000000000000000000
χ122222222222-222222-2-2-22-2-22-2-22-2-2-2-2-22222000000000000000000000000000000
χ132222222222-2-2-2-222-2-2-2-222-2-2-2-2200000000000000000000000000002i2i−2i−2i000000
χ142222222222-2-2-2-222-2-2-2-222-2-2-2-220000000000000000000000000000−2i−2i2i2i000000
χ1522222222-2-22222-2-2222222-2-2-2-2-200000000000000000000000022-2-20000000000
χ1622222222-2-22222-2-2222222-2-2-2-2-2000000000000000000000000-2-2220000000000
χ1722222222-2-22-2-2-2-2-2222-2-2-22-2-2220000000000000000000000000000000000002-2
χ1822222222-2-22-2-2-2-2-2222-2-2-22-2-222000000000000000000000000000000000000-22
χ1922222222-2-2-2222-2-2-2-2-22-2-2-222-2200000000000000002i2i2i2i−2i−2i−2i−2i00000000000000
χ2022222222-2-2-2222-2-2-2-2-22-2-2-222-220000000000000000−2i−2i−2i−2i2i2i2i2i00000000000000
χ2122222222-2-2-2-2-2-2-2-2-2-2-2-2222222-2000000000000000000000000000000002i2i−2i−2i00
χ2222222222-2-2-2-2-2-2-2-2-2-2-2-2222222-200000000000000000000000000000000−2i−2i2i2i00
χ23222-2-22-2-20022-2-200-2-2222-200000i2i2−i2−i2i2i2−i2−i200000000i2i2−i2−i2i2i2−i2−i2002-20000000000
χ24222-2-22-2-20022-2-200-2-2222-200000i2i2−i2−i2i2i2−i2−i200000000−i2−i2i2i2−i2−i2i2i200-220000000000
χ25222-2-22-2-20022-2-200-2-2222-200000−i2−i2i2i2−i2−i2i2i200000000i2i2−i2−i2i2i2−i2−i200-220000000000
χ26222-2-22-2-20022-2-200-2-2222-200000−i2−i2i2i2−i2−i2i2i200000000−i2−i2i2i2−i2−i2i2i2002-20000000000
χ27222-2-22-2-200-22-2-20022-22-2200000i2i2−i2−i2−i2−i2i2i20000000022−2−2−2−2222i−2i000000000000
χ28222-2-22-2-200-22-2-20022-22-2200000i2i2−i2−i2−i2−i2i2i200000000−2−22222−2−2−2i2i000000000000
χ29222-2-22-2-200-22-2-20022-22-2200000−i2−i2i2i2i2i2−i2−i20000000022−2−2−2−222−2i2i000000000000
χ30222-2-22-2-200-22-2-20022-22-2200000−i2−i2i2i2i2i2−i2−i200000000−2−22222−2−22i−2i000000000000
χ3122-22-2-2-2222-2000-2-22-2200002-2000000000000002i2i−2i−2i2−22−22−22−200000000i2−i2i2−i200
χ3222-22-2-2-2222-2000-2-22-2200002-2000000000000002i2i−2i−2i−22−22−22−2200000000−i2i2−i2i200
χ3322-22-2-2-2222-2000-2-22-2200002-200000000000000−2i−2i2i2i2−22−22−22−200000000−i2i2−i2i200
χ3422-22-2-2-2222-2000-2-22-2200002-200000000000000−2i−2i2i2i−22−22−22−2200000000i2−i2i2−i200
χ3522-22-2-2-22-2-2200022-22-200002-200000000002i2i−2i−2i0000i2−i2i2−i2−i2i2−i2i2000000002−2−2200
χ3622-22-2-2-22-2-2200022-22-200002-200000000002i2i−2i−2i0000−i2i2−i2i2i2−i2i2−i200000000−222−200
χ3722-22-2-2-22-2-2200022-22-200002-20000000000−2i−2i2i2i0000i2−i2i2−i2−i2i2−i2i200000000−222−200
χ3822-22-2-2-22-2-2200022-22-200002-20000000000−2i−2i2i2i0000−i2i2−i2i2i2−i2i2−i2000000002−2−2200
χ392-2-22-222-22-2022-22-2000-200-2002000002-22-2i2−i2i2−i2i2−i2i2−i2000000000000i2−i2i2−i2000000
χ402-2-22-222-22-2022-22-2000-200-2002000002-22-2−i2i2−i2i2−i2i2−i2i2000000000000−i2i2−i2i2000000
χ412-2-22-222-22-2022-22-2000-200-200200000-22-22i2−i2i2−i2i2−i2i2−i2000000000000−i2i2−i2i2000000
χ422-2-22-222-22-2022-22-2000-200-200200000-22-22−i2i2−i2i2−i2i2−i2i2000000000000i2−i2i2−i2000000
χ432-2-22-222-22-20-2-222-2000200200-202i−2i2i−2i0000i2−i2i2−i2−i2i2−i2i20000000000002−2−22000000
χ442-2-22-222-22-20-2-222-2000200200-202i−2i2i−2i0000−i2i2−i2i2i2−i2i2−i2000000000000−222−2000000
χ452-2-22-222-22-20-2-222-2000200200-20−2i2i−2i2i0000i2−i2i2−i2−i2i2−i2i2000000000000−222−2000000
χ462-2-22-222-22-20-2-222-2000200200-20−2i2i−2i2i0000−i2i2−i2i2i2−i2i2−i20000000000002−2−22000000
χ47444-4-44-4-4004-44400-4-44-4-440000000000000000000000000000000000000000000
χ48444-4-44-4-400-4-4440044-4-44-40000000000000000000000000000000000000000000
χ4944-44-4-4-44444000-4-4-44-40000-440000000000000000000000000000000000000000
χ5044-44-4-4-44-4-4-4000444-440000-440000000000000000000000000000000000000000
χ5144-4-44-44-4004000004-4-40000000000000000000000002-2-22-222-200000000000000
χ5244-4-44-44-4004000004-4-4000000000000000000000000-222-22-2-2200000000000000
χ5344-4-44-44-400-400000-4440000000000000000000000002i−2i−2i2i2i−2i−2i2i00000000000000
χ5444-4-44-44-400-400000-444000000000000000000000000−2i2i2i−2i−2i2i2i−2i00000000000000
χ554-4444-4-4-44-40000-440000000000000000000000022−22−22220000000000000000000000
χ564-4444-4-4-44-40000-4400000000000000000000000−222222−220000000000000000000000
χ574-4444-4-4-4-4400004-4000000000000000000022−22−222200000000000000000000000000
χ584-4444-4-4-4-4400004-40000000000000000000−222222−2200000000000000000000000000
χ594-4-44-444-4-44044-4-44000-400400-4000000000000000000000000000000000000000
χ604-4-44-444-4-440-4-44-44000400-4004000000000000000000000000000000000000000
χ614-4-4-444-440004-4400000-4000000000002i2−2i2−2i22i2000000000000000000000000000000
χ624-4-4-444-440004-4400000-400000000000−2i22i22i2−2i2000000000000000000000000000000
χ634-4-4-444-44000-44-4000004000000022−22−22220000000000000000000000000000000000
χ644-4-4-444-44000-44-40000040000000−222222−220000000000000000000000000000000000
χ658-88-8-8-888000000000000000000000000000000000000000000000000000000000

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