Finite Group Databasebeta

← Group #342129

Character table — Group #342129

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68
size11111111222222224444444444444444444444444488888888161616161616161616161616161616163232
order12222222444444444488888888888888888888888844444444224444448888888844
χ111111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111111111-1-1-1-11-11-1-1-1-1-111-1-1-1-111-1-1
χ3111111111111111111111111111111111111111111-1-1-1-11111-11-1-1-11-1-1-1-11111-1-1-1-1
χ4111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-111-111-1-1-1-1-1-1-1-111
χ511111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111-1-111111-1-1-1-1-111-1-1-1-11-1
χ611111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1111-11-1-1111-1-1-1-111-1-1-11
χ711111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-11-1-1-1-1111111-1-111-11
χ811111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1111-1-111-1-111111-1
χ9111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-111-1-11111-111111-1-1-1-1-1-1-1-111-11
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
χ12111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-111-1-1-1-11-1-111-1-1-1111111-1-1-11
χ13111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111-1-111-1-1-11111-11111-1-111-1-1-1-1
χ14111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111-1-1-1-111-1-11-1-11-1-11111-1-1-1-111
χ15111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-11111-1-111-1-1-1-1-1-1-1-1-1-1111111
χ16111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-111-1-1111-1-111111-1-111-1-111-1-1
χ172222222222-2-22-2-22-2-2000000002222-2-2-2-200000000000022-2-20-20002000000000000
χ182222222222-2-22-2-22-2-2000000002222-2-2-2-2000000000000-2-22202000-2000000000000
χ192222222222-2-22-2-22-2-200000000-2-2-2-2222200000000000022220-2000-2000000000000
χ202222222222-2-22-2-22-2-200000000-2-2-2-22222000000000000-2-2-2-2020002000000000000
χ2122222222-2-222-222-2-2-22222-2-2-2-2000000000000000022220000-20-2000000000000000
χ2222222222-2-222-222-2-2-22222-2-2-2-20000000000000000-2-2-2-20000202000000000000000
χ2322222222-2-222-222-2-2-2-2-2-2-22222000000000000000022-2-2000020-2000000000000000
χ2422222222-2-222-222-2-2-2-2-2-2-222220000000000000000-2-2220000-202000000000000000
χ25222-2-22-2-2-2-20020020022−2−222−2−2000022-2-22222−2−2−2−200002i−2i2i−2i0000000000i2−i2i2−i20000
χ26222-2-22-2-2-2-20020020022−2−222−2−2000022-2-22222−2−2−2−20000−2i2i−2i2i0000000000−i2i2−i2i20000
χ27222-2-22-2-2-2-20020020022−2−222−2−20000-2-222−2−2−2−2222200002i−2i−2i2i0000000000i2−i2−i2i20000
χ28222-2-22-2-2-2-20020020022−2−222−2−20000-2-222−2−2−2−222220000−2i2i2i−2i0000000000−i2i2i2−i20000
χ29222-2-22-2-2-2-200200200−2−222−2−222000022-2-2−2−2−2−2222200002i−2i2i−2i0000000000−i2i2−i2i20000
χ30222-2-22-2-2-2-200200200−2−222−2−222000022-2-2−2−2−2−222220000−2i2i−2i2i0000000000i2−i2i2−i20000
χ31222-2-22-2-2-2-200200200−2−222−2−2220000-2-2222222−2−2−2−200002i−2i−2i2i0000000000−i2i2i2−i20000
χ32222-2-22-2-2-2-200200200−2−222−2−2220000-2-2222222−2−2−2−20000−2i2i2i−2i0000000000i2−i2−i2i20000
χ3322-22-2-22-2002-202-20002i−2i2i−2i0000i2i2−i2−i2i2−i2i2−i222−2−222−2−22-22i−2i0000000000002−20000i2−i200
χ3422-22-2-22-2002-202-20002i−2i2i−2i0000i2i2−i2−i2i2−i2i2−i222−2−222−2−2-22−2i2i000000000000−220000−i2i200
χ3522-22-2-22-2002-202-20002i−2i2i−2i0000−i2−i2i2i2−i2i2−i2i2−2−222−2−2222-22i−2i000000000000−220000−i2i200
χ3622-22-2-22-2002-202-20002i−2i2i−2i0000−i2−i2i2i2−i2i2−i2i2−2−222−2−222-22−2i2i0000000000002−20000i2−i200
χ3722-22-2-22-2002-202-2000−2i2i−2i2i0000i2i2−i2−i2i2−i2i2−i2−2−222−2−2222-2−2i2i000000000000−220000i2−i200
χ3822-22-2-22-2002-202-2000−2i2i−2i2i0000i2i2−i2−i2i2−i2i2−i2−2−222−2−222-222i−2i0000000000002−20000−i2i200
χ3922-22-2-22-2002-202-2000−2i2i−2i2i0000−i2−i2i2i2−i2i2−i2i222−2−222−2−22-2−2i2i0000000000002−20000−i2i200
χ4022-22-2-22-2002-202-2000−2i2i−2i2i0000−i2−i2i2i2−i2i2−i2i222−2−222−2−2-222i−2i000000000000−220000i2−i200
χ412-2-2-2-22222-2222-2-2-22-200000000000000002i−2i2i−2i2i−2i2i−2i000000000002i−2i02-20000000000
χ422-2-2-2-22222-2222-2-2-22-200000000000000002i−2i2i−2i2i−2i2i−2i00000000000−2i2i0-220000000000
χ432-2-2-2-22222-2222-2-2-22-20000000000000000−2i2i−2i2i−2i2i−2i2i000000000002i−2i0-220000000000
χ442-2-2-2-22222-2222-2-2-22-20000000000000000−2i2i−2i2i−2i2i−2i2i00000000000−2i2i02-20000000000
χ4544444444-4-4-4-4-4-4-4-44400000000000000000000000000000000000000000000000000
χ46444-4-44-4-44400-400-4002222−22−22−22−222222000000000000000000000000000000000000000000
χ47444-4-44-4-44400-400-400−22−2222222222−22−22000000000000000000000000000000000000000000
χ4844-44-4-44-400-440-44000000000002i22i2−2i2−2i2−2i22i2−2i22i20000000000000000000000000000000000
χ4944-44-4-44-400-440-4400000000000−2i2−2i22i22i22i2−2i22i2−2i20000000000000000000000000000000000
χ5044-4-44-4-4400000000002i2−2i2−2i22i2000000002i2−2i2−2i22i222-2-2-2-22200000000000000000000000000
χ5144-4-44-4-4400000000002i2−2i2−2i22i200000000−2i22i22i2−2i2-2-22222-2-200000000000000000000000000
χ5244-4-44-4-440000000000−2i22i22i2−2i2000000002i2−2i2−2i22i2-2-22222-2-200000000000000000000000000
χ5344-4-44-4-440000000000−2i22i22i2−2i200000000−2i22i22i2−2i222-2-2-2-22200000000000000000000000000
χ544-444-4-4-44000000000000002i2−2i22i2−2i222−2222−2200002i−2i−2i2i−2i2i2i−2i00000000000000000000000000
χ554-444-4-4-44000000000000002i2−2i22i2−2i2−2222−22220000−2i2i2i−2i2i−2i−2i2i00000000000000000000000000
χ564-444-4-4-4400000000000000−2i22i2−2i22i222−2222−220000−2i2i2i−2i2i−2i−2i2i00000000000000000000000000
χ574-444-4-4-4400000000000000−2i22i2−2i22i2−2222−222200002i−2i−2i2i−2i2i2i−2i00000000000000000000000000
χ584-44-44-44-4004-40-4400000000000000000002i2−2i2−2i22i22i2−2i2−2i22i200000000000000000000000000
χ594-44-44-44-4004-40-440000000000000000000−2i22i22i2−2i2−2i22i22i2−2i200000000000000000000000000
χ604-44-44-44-400-4404-400000004i−4i−4i4i000000000000000000000000000000000000000000
χ614-44-44-44-400-4404-40000000−4i4i4i−4i000000000000000000000000000000000000000000
χ624-4-4444-4-44-400-400400000000004i−4i−4i4i00000000000000000000000000000000000000
χ634-4-4444-4-44-400-40040000000000−4i4i4i−4i00000000000000000000000000000000000000
χ644-4-4444-4-4-4400400-40000000000000000002i2−2i22i2−2i2−2i22i2−2i22i200000000000000000000000000
χ654-4-4444-4-4-4400400-4000000000000000000−2i22i2−2i22i22i2−2i22i2−2i200000000000000000000000000
χ664-4-4-4-44444-4-4-4444-4-4400000000000000000000000000000000000000000000000000
χ674-4-4-4-4444-4444-4-4-44-4400000000000000000000000000000000000000000000000000
χ684-4-4-4-4444-44-4-4-44444-400000000000000000000000000000000000000000000000000

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