Finite Group Databasebeta

← Group #336834

Character table — Group #336834

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65
size1111111122222222444444444488888888888888888888888888881616161616161616323232
order12222222444444444488888888224444444444888888888888888844448888444
χ111111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111-1-111-1-1-1-11111-1-1-1-1111111111-1-1-1-1-111-1-1-1
χ311111111111111111111111111-1-1-1-111-1-1111111111111-1-1-1-11111-11-1-111-1-1-1-1-1
χ411111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-11111-1-111-1-1-1-1111
χ51111111111111111111111-1-1-1-11111111111-1-111-1-11111-1-1-1-1-1-1-1-11-1-1-1-1-1-1-1-111
χ61111111111111111111111-1-1-1-11111-1-111-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111-1-11-1-1
χ71111111111111111111111-1-1-1-1-1-1-1-111-1-111-1-111-1-111111111-1-1-1-1-1-111-1-1111-1-1
χ81111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-11111-1-1-1-1-11-1-11111-111
χ9111111111111111111-1-1-1-1111111-1-111111111-1-111-1-1-1-11111-1-1-1-1-11-1-1-1-1-1-111-1
χ10111111111111111111-1-1-1-1111111-1-1-1-111-1-1-1-1-1-11111111111-1-1-1-1-1-11111-1-1-1-11
χ11111111111111111111-1-1-1-11111-1-11111-1-11111-1-111-1-1-1-1-1-1-1-1-1-1-1-11111-1-111-1-11
χ12111111111111111111-1-1-1-11111-1-111-1-1-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-11-1-1-1111111-1
χ13111111111111111111-1-1-1-1-1-1-1-111-1-1111111-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1111111-11-1
χ14111111111111111111-1-1-1-1-1-1-1-111-1-1-1-111-1-111-1-1-1-11111-1-1-1-11111-11-1-1-1-1111-11
χ15111111111111111111-1-1-1-1-1-1-1-1-1-11111-1-111-1-1-1-1-1-1-1-1-1-1111111111-1-1-111-1-11-11
χ16111111111111111111-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-111-1-1-1-11111111111111111-1-1-1-1-11-1
χ17222222222-2-222-22-2-2-222220000222200-2-20000-2-200000000000000-20000000000
χ18222222222-2-222-22-2-2-222220000-2-2-2-200220000-2-20000000000000020000000000
χ19222222222-2-222-22-2-2-2-2-2-2-2000022-2-200-2-20000220000000000000020000000000
χ20222222222-2-222-22-2-2-2-2-2-2-20000-2-222002200002200000000000000-20000000000
χ2122222222-222-2-22-22-2-20000222200002200-2-2-2-200-2-200000000000002000000000
χ2222222222-222-2-22-22-2-2000022220000-2-200222200-2-20000000000000-2000000000
χ2322222222-222-2-22-22-2-20000-2-2-2-200002200-2-22200220000000000000-2000000000
χ2422222222-222-2-22-22-2-20000-2-2-2-20000-2-20022-2-2002200000000000002000000000
χ25222-2-2-2-22-2002-2020002i2i−2i−2i22−2−22-22i−2i00000000002−2000022−2−2i2i2−i2−i2000000i2−i2000
χ26222-2-2-2-22-2002-2020002i2i−2i−2i22−2−2-22−2i2i00000000002−20000−2−222i2i2−i2−i2000000−i2i2000
χ27222-2-2-2-22-2002-2020002i2i−2i−2i−2−2222-22i−2i0000000000−220000−2−222−i2−i2i2i2000000−i2i2000
χ28222-2-2-2-22-2002-2020002i2i−2i−2i−2−222-22−2i2i0000000000−22000022−2−2−i2−i2i2i2000000i2−i2000
χ29222-2-2-2-22-2002-202000−2i−2i2i2i22−2−22-2−2i2i00000000002−2000022−2−2−i2−i2i2i2000000−i2i2000
χ30222-2-2-2-22-2002-202000−2i−2i2i2i22−2−2-222i−2i00000000002−20000−2−222−i2−i2i2i2000000i2−i2000
χ31222-2-2-2-22-2002-202000−2i−2i2i2i−2−2222-2−2i2i0000000000−220000−2−222i2i2−i2−i2000000i2−i2000
χ32222-2-2-2-22-2002-202000−2i−2i2i2i−2−222-222i−2i0000000000−22000022−2−2i2i2−i2−i2000000−i2i2000
χ3322-2-22-22-2-2-2-2222-222-20000000000000000000000002i2i−2i−2i2-22-20000002i−2i0000000
χ3422-2-22-22-2-2-2-2222-222-20000000000000000000000002i2i−2i−2i-22-22000000−2i2i0000000
χ3522-2-22-22-2-2-2-2222-222-2000000000000000000000000−2i−2i2i2i2-22-2000000−2i2i0000000
χ3622-2-22-22-2-2-2-2222-222-2000000000000000000000000−2i−2i2i2i-22-220000002i−2i0000000
χ372-2222-2-2-202-200-202002−22−22-22-2000000002i−2i2i−2i2−200i2−i2i2−i200002−22−20000i2−i200000
χ382-2222-2-2-202-200-202002−22−22-22-200000000−2i2i−2i2i2−200−i2i2−i2i200002−22−20000−i2i200000
χ392-2222-2-2-202-200-202002−22−2-22-22000000002i−2i−2i2i2−200i2−i2i2−i20000−22−220000−i2i200000
χ402-2222-2-2-202-200-202002−22−2-22-2200000000−2i2i2i−2i2−200−i2i2−i2i20000−22−220000i2−i200000
χ412-2222-2-2-202-200-20200−22−222-22-2000000002i−2i2i−2i−2200−i2i2−i2i20000−22−220000−i2i200000
χ422-2222-2-2-202-200-20200−22−222-22-200000000−2i2i−2i2i−2200i2−i2i2−i20000−22−220000i2−i200000
χ432-2222-2-2-202-200-20200−22−22-22-22000000002i−2i−2i2i−2200−i2i2−i2i200002−22−20000i2−i200000
χ442-2222-2-2-202-200-20200−22−22-22-2200000000−2i2i2i−2i−2200i2−i2i2−i200002−22−20000−i2i200000
χ4544444444-4-4-4-4-4-4-4-44400000000000000000000000000000000000000000000000
χ46444-4-4-4-44400-440-400000002222−22−2200000000000000−222200000000000000000000000
χ47444-4-4-4-44400-440-40000000−22−2222220000000000000022−2200000000000000000000000
χ4844-44-44-4-44004-40-4000000000000000000000000000000022−22−2222000000000000000
χ4944-44-44-4-44004-40-40000000000000000000000000000000−222222−22000000000000000
χ5044-44-44-4-4-400-4404000000000000000004i−4i0000000000000000000000000000000
χ5144-44-44-4-4-400-440400000000000000000−4i4i0000000000000000000000000000000
χ5244-4-44-44-4444-4-4-44-44-400000000000000000000000000000000000000000000000
χ5344-4-44-44-44-4-4-4-4444-4400000000000000000000000000000000000000000000000
χ5444-4-44-44-4-44444-4-4-4-4400000000000000000000000000000000000000000000000
χ554-4444-4-4-40-440040-40022−2222−220000000000000000−22220000000000000000000000000
χ564-4444-4-4-40-440040-400−2222−2222000000000000000022−220000000000000000000000000
χ574-44-4-444-400000000002i2−2i2−2i22i222−22−22220000000000000000000000002i−2i−2i2i00000000000
χ584-44-4-444-400000000002i2−2i2−2i22i2−222222−22000000000000000000000000−2i2i2i−2i00000000000
χ594-44-4-444-40000000000−2i22i22i2−2i222−22−2222000000000000000000000000−2i2i2i−2i00000000000
χ604-44-4-444-40000000000−2i22i22i2−2i2−222222−220000000000000000000000002i−2i−2i2i00000000000
χ614-4-4-444-4404-40040-4000000000000004i−4i000000000000000000000000000000000
χ624-4-4-444-4404-40040-400000000000000−4i4i000000000000000000000000000000000
χ634-4-4-444-440-4400-4040000000000000000000000000022−22−22220000000000000000000
χ644-4-4-444-440-4400-40400000000000000000000000000−222222−220000000000000000000
χ658-8-88-8-888000000000000000000000000000000000000000000000000000000000

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