Finite Group Databasebeta

← Group #312311

Character table — Group #312311

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65
size11111111222222224444444444888888888888888888888888161616161616161616161616161632
order12222222444444444444448888444444444488888888888888222244448888884
χ111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111-1-11111-1-11111-1-1-1-1-1-111-1-11-111-1-1-1-1-1-1-1
χ31111111111111111111111111111-1-1-1-111-1-111111111111111-1-1-1-1-11-1-1-1-111-1-1-1
χ41111111111111111111111111111-1-1-1-1-1-1-1-111-1-11111-1-1-1-1-1-1-1-111-1-1-1-111-1-1111
χ51111111111111111111111-1-1-1-11111-1-11111-1-111-1-1-1-111-1-1-1-11111-11-1-111-1-1-1-1-1
χ61111111111111111111111-1-1-1-11111-1-1-1-111-1-1-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-111111
χ71111111111111111111111-1-1-1-111-1-11111-1-1-1-111-1-1-1-111-1-1-1-1-1-1-1-11111-1-1-1-1111
χ81111111111111111111111-1-1-1-111-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1111-1111111-1-1-1
χ911111111111111111-1-1-1-111111-1-11111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-111-1-11
χ1011111111111111111-1-1-1-111111-1-11111-1-1111111-1-1-1-1111111-1-1-1-11-1-1-111-1-111-1
χ1111111111111111111-1-1-1-111111-1-1-1-1-1-111-1-111-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1111111111-1
χ1211111111111111111-1-1-1-111111-1-1-1-1-1-1-1-1-1-11111-1-1-1-11111111111-1-111-1-1-1-1-1-11
χ1311111111111111111-1-1-1-11-1-1-1-1-1-111-1-11111-1-1-1-11111-1-11111-1-111-1111-1-1-1-111-1
χ1411111111111111111-1-1-1-11-1-1-1-1-1-111-1-1-1-111-1-111111111-1-1-1-1-1-1-1-1-1-1111111-1-11
χ1511111111111111111-1-1-1-11-1-1-1-1-1-1-1-11111-1-1-1-1-1-11111-1-1111111-1-111-1-111-1-1-1-11
χ1611111111111111111-1-1-1-11-1-1-1-1-1-1-1-111-1-1-1-1-1-111111111-1-1-1-111111-1-1-1-1-11111-1
χ17222222222-22-22-22-2-20000-222220022-2-200-2-2-2-2000000000000000020000000000
χ18222222222-22-22-22-2-20000-2222200-2-2220022-2-20000000000000000-20000000000
χ19222222222-22-22-22-2-20000-2-2-2-2-200222200-2-2220000000000000000-20000000000
χ20222222222-22-22-22-2-20000-2-2-2-2-200-2-2-2-2002222000000000000000020000000000
χ2122222222-22-22-22-22-22222-20000-2-20000220000-2-2000022000000000-2000000000
χ2222222222-22-22-22-22-22222-20000-2-20000-2-20000220000-2-20000000002000000000
χ2322222222-22-22-22-22-2-2-2-2-2-20000220000220000220000-2-2000000000-2000000000
χ2422222222-22-22-22-22-2-2-2-2-2-20000220000-2-20000-2-20000220000000002000000000
χ25222-2-2-22-22-2-222-2-22-22i2i−2i−2i200002i−2i0000000000000000000000002-200002i−2i00000
χ26222-2-2-22-22-2-222-2-22-22i2i−2i−2i200002i−2i000000000000000000000000-220000−2i2i00000
χ27222-2-2-22-22-2-222-2-22-2−2i−2i2i2i20000−2i2i0000000000000000000000002-20000−2i2i00000
χ28222-2-2-22-22-2-222-2-22-2−2i−2i2i2i20000−2i2i000000000000000000000000-2200002i−2i00000
χ29222-2-2-22-2-222-2-222-2-2000020000002i−2i00002i−2i00002i2i−2i−2i0000000000002-20000000
χ30222-2-2-22-2-222-2-222-2-2000020000002i−2i00002i−2i0000−2i−2i2i2i000000000000-220000000
χ31222-2-2-22-2-222-2-222-2-200002000000−2i2i0000−2i2i00002i2i−2i−2i000000000000-220000000
χ32222-2-2-22-2-222-2-222-2-200002000000−2i2i0000−2i2i0000−2i−2i2i2i0000000000002-20000000
χ33222-2-2-22-2-2-222-2-22222i2i−2i−2i-20000−2i2i2i−2i0000−2i2i000000000000002-20000000000000
χ34222-2-2-22-2-2-222-2-22222i2i−2i−2i-20000−2i2i−2i2i00002i−2i00000000000000-220000000000000
χ35222-2-2-22-2-2-222-2-2222−2i−2i2i2i-200002i−2i2i−2i0000−2i2i00000000000000-220000000000000
χ36222-2-2-22-2-2-222-2-2222−2i−2i2i2i-200002i−2i−2i2i00002i−2i000000000000002-20000000000000
χ3722-222-2-2-2020-20-20202i−2i2i−2i0i2i2−i2−i20000002i−2i00i2−i2002−22−22-2i2i2−i2−i200000000002−2000
χ3822-222-2-2-2020-20-20202i−2i2i−2i0i2i2−i2−i2000000−2i2i00i2−i2002−22−2-22−i2−i2i2i20000000000−22000
χ3922-222-2-2-2020-20-20202i−2i2i−2i0−i2−i2i2i20000002i−2i00−i2i200−22−222-2−i2−i2i2i20000000000−22000
χ4022-222-2-2-2020-20-20202i−2i2i−2i0−i2−i2i2i2000000−2i2i00−i2i200−22−22-22i2i2−i2−i200000000002−2000
χ4122-222-2-2-2020-20-2020−2i2i−2i2i0i2i2−i2−i20000002i−2i00i2−i200−22−22-22−i2−i2i2i200000000002−2000
χ4222-222-2-2-2020-20-2020−2i2i−2i2i0i2i2−i2−i2000000−2i2i00i2−i200−22−222-2i2i2−i2−i20000000000−22000
χ4322-222-2-2-2020-20-2020−2i2i−2i2i0−i2−i2i2i20000002i−2i00−i2i2002−22−2-22i2i2−i2−i20000000000−22000
χ4422-222-2-2-2020-20-2020−2i2i−2i2i0−i2−i2i2i2000000−2i2i00−i2i2002−22−22-2−i2−i2i2i200000000002−2000
χ4544444444-4-4-4-4-4-4-4-44000040000000000000000000000000000000000000000000
χ46444-4-4-44-444-4-444-4-440000-40000000000000000000000000000000000000000000
χ4744-444-4-4-40-404040-40000002i22i2−2i2−2i20000000000−2i22i2000000000000000000000000000
χ4844-444-4-4-40-404040-4000000−2i2−2i22i22i200000000002i2−2i2000000000000000000000000000
χ4944-4-4-44-4404040-40-40000000000000000000000002i2−2i2−2i22i2000000000000000000000
χ5044-4-4-44-4404040-40-4000000000000000000000000−2i22i22i2−2i2000000000000000000000
χ5144-4-4-44-440-40-4040404-4-4400000000000000000000000000000000000000000000
χ5244-4-4-44-440-40-404040-444-400000000000000000000000000000000000000000000
χ534-444-44-4-440-40-40400000000000000000000000000000002i2−2i22i2−2i2000000000000000
χ544-444-44-4-440-40-4040000000000000000000000000000000−2i22i2−2i22i2000000000000000
χ554-444-44-4-4-404040-400000004i−4i4i−4i000000000000000000000000000000000000000
χ564-444-44-4-4-404040-40000000−4i4i−4i4i000000000000000000000000000000000000000
χ574-44-44-4-444040-40-40000000000000004i−4i000000000000000000000000000000000
χ584-44-44-4-444040-40-4000000000000000−4i4i000000000000000000000000000000000
χ594-44-44-4-44-40-404040000000000000000000000000000000000000000000000022−220
χ604-44-44-4-44-40-4040400000000000000000000000000000000000000000000000−22220
χ614-4-44-4-4440000000000000022−22−222200000000000022−220000002-2-22000000000000000
χ624-4-44-4-4440000000000000022−22−2222000000000000−2222000000-222-2000000000000000
χ634-4-44-4-44400000000000000−222222−2200000000000022−22000000-222-2000000000000000
χ644-4-44-4-44400000000000000−222222−22000000000000−22220000002-2-22000000000000000
χ658-8-8-8888-8000000000000000000000000000000000000000000000000000000000

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