Finite Group Databasebeta

← Group #306764

Character table — Group #306764

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65
size11111111222222224444444444888888888888888888888888161616161616161616161616161632
order12222222444444444444448888444444444488888888888888444444448888884
χ111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111-1-1-1-1111111-1-1-1-1-1-11-1-1-11111-1-1-1-1-1-1-1
χ31111111111111111111111111111-1-1-1-1-1-11111111111111111-11-1-1-1-1-1-1-1-111-1-1-1
χ41111111111111111111111111111-1-1-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-111-1-1-1-111-1-1111
χ51111111111111111111111-1-1-1-1111111-1-11111-1-1-1-1-1-111-1-1-1-1-111111-1-1-1-1-1-111-1
χ61111111111111111111111-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-111-1-11111-1-11
χ71111111111111111111111-1-1-1-111-1-1-1-1111111-1-1-1-1-1-111-1-1-1-111-1-1-1-11111-1-1-1-11
χ81111111111111111111111-1-1-1-111-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-111111-111-1-111-1-11111-1
χ91111111111111111-1-1-1-1111111-1-111111111-1-1-1-1-1-111-1-1-1-1-1-11111-1-1-1-1-1-111-1-11
χ101111111111111111-1-1-1-1111111-1-1111111-1-111-1-1-1-1111111111-1-1-1-1-1-1-111-1-111-1
χ111111111111111111-1-1-1-1111111-1-1-1-1-1-1-1-111-1-1-1-1-1-111-1-1-1-1-1-1-11-1-11111111111-1
χ121111111111111111-1-1-1-1111111-1-1-1-1-1-1-1-1-1-111-1-1-1-111111111-1-1111111-1-1-1-1-1-11
χ131111111111111111-1-1-1-111-1-1-1-1-1-11111-1-111-1-11111-1-1-1-11111-1111-1-11111-1-1-1-1-1
χ141111111111111111-1-1-1-111-1-1-1-1-1-11111-1-1-1-1111111-1-111-1-1-1-1-1-1-1-1-1-111-1-111111
χ151111111111111111-1-1-1-111-1-1-1-1-1-1-1-1-1-11111-1-11111-1-1-1-1111111-1-111-1-1-1-1-1-1111
χ161111111111111111-1-1-1-111-1-1-1-1-1-1-1-1-1-111-1-1111111-1-111-1-1-1-11-11111-1-11111-1-1-1
χ17222222222-22-22-22-22222-2-20000-2-20000002222000000-2-200000-20000000000000
χ18222222222-22-22-22-22222-2-20000-2-2000000-2-2-2-2000000220000020000000000000
χ19222222222-22-22-22-2-2-2-2-2-2-200002200000022-2-20000002200000-20000000000000
χ20222222222-22-22-22-2-2-2-2-2-2-2000022000000-2-222000000-2-20000020000000000000
χ2122222222-22-22-22-220000-2-222220022-2-2-2-200000000-2-2000000200000000000000
χ2222222222-22-22-22-220000-2-2222200-2-2222200000000-2-2000000-200000000000000
χ2322222222-22-22-22-220000-2-2-2-2-2-20022-2-2220000000022000000-200000000000000
χ2422222222-22-22-22-220000-2-2-2-2-2-200-2-222-2-20000000022000000200000000000000
χ25222-2-2-2-22-20-2020202i2i−2i−2i0022−2−2000000002-22i−2ii2i2−i2−i22−200i2i2−i2−i200000000002−2000
χ26222-2-2-2-22-20-2020202i2i−2i−2i0022−2−200000000-22−2i2ii2i2−i2−i22−200−i2−i2i2i20000000000−22000
χ27222-2-2-2-22-20-2020202i2i−2i−2i00−2−222000000002-22i−2i−i2−i2i2i2−2200−i2−i2i2i20000000000−22000
χ28222-2-2-2-22-20-2020202i2i−2i−2i00−2−22200000000-22−2i2i−i2−i2i2i2−2200i2i2−i2−i200000000002−2000
χ29222-2-2-2-22-20-202020−2i−2i2i2i0022−2−2000000002-2−2i2i−i2−i2i2i22−200−i2−i2i2i200000000002−2000
χ30222-2-2-2-22-20-202020−2i−2i2i2i0022−2−200000000-222i−2i−i2−i2i2i22−200i2i2−i2−i20000000000−22000
χ31222-2-2-2-22-20-202020−2i−2i2i2i00−2−222000000002-2−2i2ii2i2−i2−i2−2200i2i2−i2−i20000000000−22000
χ32222-2-2-2-22-20-202020−2i−2i2i2i00−2−22200000000-222i−2ii2i2−i2−i2−2200−i2−i2i2i200000000002−2000
χ3322-2-22-22-22-2-222-2-220000-220000002-22-20000002i−2i2i−2i000000000000002i−2i0000000
χ3422-2-22-22-22-2-222-2-220000-220000002-22-2000000−2i2i−2i2i00000000000000−2i2i0000000
χ3522-2-22-22-22-2-222-2-220000-22000000-22-220000002i−2i2i−2i00000000000000−2i2i0000000
χ3622-2-22-22-22-2-222-2-220000-22000000-22-22000000−2i2i−2i2i000000000000002i−2i0000000
χ3722-2-22-22-2-222-2-222-22i−2i2i−2i-2200002i−2i0000000000000000000000002i−2i000000002-20
χ3822-2-22-22-2-222-2-222-22i−2i2i−2i-2200002i−2i000000000000000000000000−2i2i00000000-220
χ3922-2-22-22-2-222-2-222-2−2i2i−2i2i-220000−2i2i0000000000000000000000002i−2i00000000-220
χ4022-2-22-22-2-222-2-222-2−2i2i−2i2i-220000−2i2i000000000000000000000000−2i2i000000002-20
χ4122-2-22-22-2-2-222-2-2222i−2i2i−2i2-20000−2i2i2-2-2200000000000000000000002i−2i000000000
χ4222-2-22-22-2-2-222-2-2222i−2i2i−2i2-20000−2i2i-222-20000000000000000000000−2i2i000000000
χ4322-2-22-22-2-2-222-2-222−2i2i−2i2i2-200002i−2i2-2-220000000000000000000000−2i2i000000000
χ4422-2-22-22-2-2-222-2-222−2i2i−2i2i2-200002i−2i-222-200000000000000000000002i−2i000000000
χ4544444444-4-4-4-4-4-4-4-40000440000000000000000000000000000000000000000000
χ46444-4-4-4-444040-40-400000002222−22−220000000000000000−2222000000000000000000000
χ47444-4-4-4-444040-40-40000000−22−222222000000000000000022−22000000000000000000000
χ4844-44-44-4-440-40-40404-4-44000000000000000000000000000000000000000000000
χ4944-44-44-4-440-40-4040-444-4000000000000000000000000000000000000000000000
χ5044-44-44-4-4-404040-40000000000000000000000022−22−222200000000000000000000000
χ5144-44-44-4-4-404040-400000000000000000000000−222222−2200000000000000000000000
χ5244-4-44-44-444-4-444-4-400004-40000000000000000000000000000000000000000000
χ534-4444-4-4-4040-40-40400000000000000000000000000000022−2222−22000000000000000
χ544-4444-4-4-4040-40-404000000000000000000000000000000−2222−2222000000000000000
χ554-4444-4-4-40-404040-40000004-44-4000000000000000000000000000000000000000
χ564-4444-4-4-40-404040-4000000-44-44000000000000000000000000000000000000000
χ574-44-4-444-40000000000000022−22−22220000000000000000002i2−2i22i−2i−2i2i000000000000000
χ584-44-4-444-40000000000000022−22−2222000000000000000000−2i22i2−2i2i2i−2i000000000000000
χ594-44-4-444-400000000000000−222222−220000000000000000002i2−2i2−2i2i2i−2i000000000000000
χ604-44-4-444-400000000000000−222222−22000000000000000000−2i22i22i−2i−2i2i000000000000000
χ614-4-4-444-4404040-40-400000000000000004i−4i0000000000000000000000000000000
χ624-4-4-444-4404040-40-40000000000000000−4i4i0000000000000000000000000000000
χ634-4-4-444-440-40-4040400000000000000000000000000000000000000000022−2200000
χ644-4-4-444-440-40-40404000000000000000000000000000000000000000000−222200000
χ658-8-88-8-888000000000000000000000000000000000000000000000000000000000

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