Finite Group Databasebeta

← Group #312425

Character table — Group #312425

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65
size11111111222222224444444444888888888888888888888888161616161616161616161616161632
order12222222444444444444448888444444444488888888888888222244448888884
χ111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111-1-111-1-11111-1-1-1-1-1-11111-1-11-1-1-1-1-1-1-1-1
χ31111111111111111111111111111-1-1-1-1-1-11111111111111111-1-1-1-1-1-1-11-1-111-1-1-1
χ41111111111111111111111111111-1-1-1-1-1-1-1-111-1-11111-1-1-1-1-1-1-1-1-1-111-1-111-1-1111
χ51111111111111111111111-1-1-1-1111111-1-111-1-111-1-1-1-111-1-1-1-111-1-111-1111-1-1-1-1-1
χ61111111111111111111111-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-111111
χ71111111111111111111111-1-1-1-111-1-1-1-11111-1-111-1-1-1-111-1-1-1-1-1-111-1-111-1-1-1-1111
χ81111111111111111111111-1-1-1-111-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-11111-1-111111-11111-1-1-1
χ911111111111111111-1-1-1-111111-1-11111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-111-1-11
χ1011111111111111111-1-1-1-111111-1-1111111-1-11111-1-1-1-1111111-1-1-1-1-1-11-111-1-111-1
χ1111111111111111111-1-1-1-111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-11111111-1
χ1211111111111111111-1-1-1-111111-1-1-1-1-1-1-1-1-1-11111-1-1-1-1111111111111-1-1-1-1-1-1-1-11
χ1311111111111111111-1-1-1-11-1-1-1-1-1-11111-1-111-1-1-1-11111-1-11111-1-11111-11-1-1-1-111-1
χ1411111111111111111-1-1-1-11-1-1-1-1-1-11111-1-1-1-1-1-111111111-1-1-1-1-1-111-1-1-1-11111-1-11
χ1511111111111111111-1-1-1-11-1-1-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1111111-1-1-1-11111-1-1-1-11
χ1611111111111111111-1-1-1-11-1-1-1-1-1-1-1-1-1-111-1-1-1-111111111-1-1-1-111-1-1111-1-1-11111-1
χ17222222222-22-22-22-2-22222-20000-2-20000002200-2-200002200000000000-20000000
χ18222222222-22-22-22-2-22222-20000-2-2000000-2-200220000-2-20000000000020000000
χ19222222222-22-22-22-2-2-2-2-2-2-20000220000002200220000-2-200000000000-20000000
χ20222222222-22-22-22-2-2-2-2-2-2-2000022000000-2-200-2-20000220000000000020000000
χ2122222222-22-22-22-22-20000-222220022-2-22200-2-2000000000000000000-200000000
χ2222222222-22-22-22-22-20000-2222200-2-222-2-200-2-2000000000000000000200000000
χ2322222222-22-22-22-22-20000-2-2-2-2-20022-2-2-2-20022000000000000000000200000000
χ2422222222-22-22-22-22-20000-2-2-2-2-200-2-222220022000000000000000000-200000000
χ25222-22-2-2-22-2-222-2-22-2000020000002i−2i2i−2i000000002i2i−2i−2i000000002-200000000000
χ26222-22-2-2-22-2-222-2-22-2000020000002i−2i2i−2i00000000−2i−2i2i2i00000000-2200000000000
χ27222-22-2-2-22-2-222-2-22-200002000000−2i2i−2i2i000000002i2i−2i−2i00000000-2200000000000
χ28222-22-2-2-22-2-222-2-22-200002000000−2i2i−2i2i00000000−2i−2i2i2i000000002-200000000000
χ29222-22-2-2-2-222-2-222-2-22i2i−2i−2i200002i−2i000000000000000000000000002-2002i−2i00000
χ30222-22-2-2-2-222-2-222-2-22i2i−2i−2i200002i−2i00000000000000000000000000-2200−2i2i00000
χ31222-22-2-2-2-222-2-222-2-2−2i−2i2i2i20000−2i2i000000000000000000000000002-200−2i2i00000
χ32222-22-2-2-2-222-2-222-2-2−2i−2i2i2i20000−2i2i00000000000000000000000000-22002i−2i00000
χ33222-22-2-2-2-2-222-2-22222i2i−2i−2i-20000−2i2i2i−2i−2i2i0000000000000000002-20000000000000
χ34222-22-2-2-2-2-222-2-22222i2i−2i−2i-20000−2i2i−2i2i2i−2i000000000000000000-220000000000000
χ35222-22-2-2-2-2-222-2-2222−2i−2i2i2i-200002i−2i2i−2i−2i2i000000000000000000-220000000000000
χ36222-22-2-2-2-2-222-2-2222−2i−2i2i2i-200002i−2i−2i2i2i−2i0000000000000000002-20000000000000
χ3722-2-2-222-22020-20-2002-22-2022−2−2000000002i−2i2−2002−22−22i−2ii2i2−i2−i20000000000i2−i2000
χ3822-2-2-222-22020-20-2002-22-2022−2−200000000−2i2i2−2002−22−2−2i2i−i2−i2i2i20000000000−i2i2000
χ3922-2-2-222-22020-20-2002-22-20−2−222000000002i−2i−2200−22−222i−2i−i2−i2i2i20000000000−i2i2000
χ4022-2-2-222-22020-20-2002-22-20−2−22200000000−2i2i−2200−22−22−2i2ii2i2−i2−i20000000000i2−i2000
χ4122-2-2-222-22020-20-200-22-22022−2−2000000002i−2i2−200−22−22−2i2i−i2−i2i2i20000000000i2−i2000
χ4222-2-2-222-22020-20-200-22-22022−2−200000000−2i2i2−200−22−222i−2ii2i2−i2−i20000000000−i2i2000
χ4322-2-2-222-22020-20-200-22-220−2−222000000002i−2i−22002−22−2−2i2ii2i2−i2−i20000000000−i2i2000
χ4422-2-2-222-22020-20-200-22-220−2−22200000000−2i2i−22002−22−22i−2i−i2−i2i2i20000000000i2−i2000
χ4544444444-4-4-4-4-4-4-4-44000040000000000000000000000000000000000000000000
χ46444-44-4-4-444-4-444-4-440000-40000000000000000000000000000000000000000000
χ4744-44-4-4-4440-40-40400000000000000000000000002i2−2i2−2i22i2000000000000000000000
χ4844-44-4-4-4440-40-4040000000000000000000000000−2i22i22i2−2i2000000000000000000000
χ4944-44-4-4-44-404040-4004i−4i−4i4i00000000000000000000000000000000000000000000
χ5044-44-4-4-44-404040-400−4i4i4i−4i00000000000000000000000000000000000000000000
χ5144-4-4-444-4-40-4040400000002222−22−220000000000−2222000000000000000000000000000
χ5244-4-4-444-4-40-404040000000−22−222222000000000022−22000000000000000000000000000
χ534-444-44-4-40000000000000022−2222−220000000000002i2−2i20000002i−2i2i−2i000000000000000
χ544-444-44-4-40000000000000022−2222−22000000000000−2i22i2000000−2i2i−2i2i000000000000000
χ554-444-44-4-400000000000000−2222−22220000000000002i2−2i2000000−2i2i−2i2i000000000000000
χ564-444-44-4-400000000000000−2222−2222000000000000−2i22i20000002i−2i2i−2i000000000000000
χ574-4-444-44-404040-40-400000000000000000000000000000000000000000000002i2−2i20
χ584-4-444-44-404040-40-40000000000000000000000000000000000000000000000−2i22i20
χ594-4-444-44-40-40-4040400000000000000004-40000000000000000000000000000000
χ604-4-444-44-40-40-404040000000000000000-440000000000000000000000000000000
χ614-4-4-444-44040-40-4040000004-4-44000000000000000000000000000000000000000
χ624-4-4-444-44040-40-404000000-444-4000000000000000000000000000000000000000
χ634-4-4-444-440-404040-400000000000000000000000000000022−22−2222000000000000000
χ644-4-4-444-440-404040-4000000000000000000000000000000−222222−22000000000000000
χ658-88-8-8-888000000000000000000000000000000000000000000000000000000000

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