Finite Group Databasebeta

← Group #312490

Character table — Group #312490

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65
size11111111222222224444444444888888888888888888888888161616161616161616161616161632
order12222222444444444444448888444444444488888888888888222244448888884
χ111111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111-1-1111111-1-11111-1-1-1-1-1-111111-1-1-1-1-1-1-1-1-1-1
χ31111111111111111111111111111-1-111-1-1-1-111111111111111-1-1-1-1-1-1-11-1-111-1-1-1
χ41111111111111111111111111111-1-1-1-1-1-1-1-111-1-11111-1-1-1-1-1-1-1-1-1-1-111-111-1-1111
χ51111111111111111111111-1-1-1-111111111-1-1-1-111-1-1-1-111-1-1-1-111-1-1-111111-1-1-1-1-1
χ61111111111111111111111-1-1-1-11111-1-111-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-111111
χ71111111111111111111111-1-1-1-111-1-111-1-111-1-111-1-1-1-111-1-1-1-1-1-1111-1-11-1-1-1-1111
χ81111111111111111111111-1-1-1-111-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-11111-1-111111-11111-1-1-1
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
χ1011111111111111111-1-1-1-111111-1-111-1-111111111-1-1-1-1111111-1-1-1-11-1-1-111-1-111-1
χ1111111111111111111-1-1-1-111111-1-1-1-111-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-11111111-1
χ1211111111111111111-1-1-1-111111-1-1-1-1-1-1-1-1-1-11111-1-1-1-11111111111-111-1-1-1-1-1-1-11
χ1311111111111111111-1-1-1-11-1-1-1-1-1-1111111-1-1-1-1-1-11111-1-11111-1-111-1111-1-1-1-111-1
χ1411111111111111111-1-1-1-11-1-1-1-1-1-111-1-111-1-1-1-111111111-1-1-1-1-1-111-1-1-1-11111-1-11
χ1511111111111111111-1-1-1-11-1-1-1-1-1-1-1-111-1-111-1-1-1-11111-1-1111111-1-11-1-1111-1-1-1-11
χ1611111111111111111-1-1-1-11-1-1-1-1-1-1-1-1-1-1-1-111-1-111111111-1-1-1-111-1-1111-1-1-11111-1
χ17222222222-22-22-22-2-20000-22222002200-2-2-2-2-2-2000000000000000020000000000
χ18222222222-22-22-22-2-20000-2222200-2-2002222-2-20000000000000000-20000000000
χ19222222222-22-22-22-2-20000-2-2-2-2-2002200-2-222220000000000000000-20000000000
χ20222222222-22-22-22-2-20000-2-2-2-2-200-2-20022-2-222000000000000000020000000000
χ2122222222-22-22-22-22-22222-20000-2-20022000000-2-200002200000000000-20000000
χ2222222222-22-22-22-22-22222-20000-2-200-2-2000000220000-2-20000000000020000000
χ2322222222-22-22-22-22-2-2-2-2-2-20000220022000000220000-2-200000000000-20000000
χ2422222222-22-22-22-22-2-2-2-2-2-200002200-2-2000000-2-20000220000000000020000000
χ25222-2-2-22-22-2-222-2-22-22i2i−2i−2i200002i−2i0000000000000000000000000002-202i−2i00000
χ26222-2-2-22-22-2-222-2-22-22i2i−2i−2i200002i−2i000000000000000000000000000-220−2i2i00000
χ27222-2-2-22-22-2-222-2-22-2−2i−2i2i2i20000−2i2i0000000000000000000000000002-20−2i2i00000
χ28222-2-2-22-22-2-222-2-22-2−2i−2i2i2i20000−2i2i000000000000000000000000000-2202i−2i00000
χ29222-2-2-22-2-222-2-222-2-2000020000002i−2i002i−2i0000002i2i−2i−2i000000002-200000000000
χ30222-2-2-22-2-222-2-222-2-2000020000002i−2i002i−2i000000−2i−2i2i2i00000000-2200000000000
χ31222-2-2-22-2-222-2-222-2-200002000000−2i2i00−2i2i0000002i2i−2i−2i00000000-2200000000000
χ32222-2-2-22-2-222-2-222-2-200002000000−2i2i00−2i2i000000−2i−2i2i2i000000002-200000000000
χ33222-2-2-22-2-2-222-2-22222i2i−2i−2i-20000−2i2i2i−2i00−2i2i00000000000000002-20000000000000
χ34222-2-2-22-2-2-222-2-22222i2i−2i−2i-20000−2i2i−2i2i002i−2i0000000000000000-220000000000000
χ35222-2-2-22-2-2-222-2-2222−2i−2i2i2i-200002i−2i2i−2i00−2i2i0000000000000000-220000000000000
χ36222-2-2-22-2-2-222-2-2222−2i−2i2i2i-200002i−2i−2i2i002i−2i00000000000000002-20000000000000
χ3722-22-2-2-2202020-20-202-22-2022−2−200002i−2i00002−2002−22−22i−2ii2i2−i2−i20000000000i2−i2000
χ3822-22-2-2-2202020-20-202-22-2022−2−20000−2i2i00002−2002−22−2−2i2i−i2−i2i2i20000000000−i2i2000
χ3922-22-2-2-2202020-20-202-22-20−2−22200002i−2i0000−2200−22−222i−2i−i2−i2i2i20000000000−i2i2000
χ4022-22-2-2-2202020-20-202-22-20−2−2220000−2i2i0000−2200−22−22−2i2ii2i2−i2−i20000000000i2−i2000
χ4122-22-2-2-2202020-20-20-22-22022−2−200002i−2i00002−200−22−22−2i2i−i2−i2i2i20000000000i2−i2000
χ4222-22-2-2-2202020-20-20-22-22022−2−20000−2i2i00002−200−22−222i−2ii2i2−i2−i20000000000−i2i2000
χ4322-22-2-2-2202020-20-20-22-220−2−22200002i−2i0000−22002−22−2−2i2ii2i2−i2−i20000000000−i2i2000
χ4422-22-2-2-2202020-20-20-22-220−2−2220000−2i2i0000−22002−22−22i−2i−i2−i2i2i20000000000i2−i2000
χ4544444444-4-4-4-4-4-4-4-44000040000000000000000000000000000000000000000000
χ46444-4-4-44-444-4-444-4-440000-40000000000000000000000000000000000000000000
χ4744-44-4-4-440-40-404040000002222−22−220000000000−2222000000000000000000000000000
χ4844-44-4-4-440-40-40404000000−22−222222000000000022−22000000000000000000000000000
χ4944-4-444-4-4040-40-4040000000000000000000000002i2−2i2−2i22i2000000000000000000000
χ5044-4-444-4-4040-40-404000000000000000000000000−2i22i22i2−2i2000000000000000000000
χ5144-4-444-4-40-404040-404i−4i−4i4i00000000000000000000000000000000000000000000
χ5244-4-444-4-40-404040-40−4i4i4i−4i00000000000000000000000000000000000000000000
χ534-4444-4-4-440-40-40400000000000000000004i−4i00000000000000000000000000000
χ544-4444-4-4-440-40-4040000000000000000000−4i4i00000000000000000000000000000
χ554-4444-4-4-4-404040-4000000000000000000000000000000000000000000000002i2−2i20
χ564-4444-4-4-4-404040-400000000000000000000000000000000000000000000000−2i22i20
χ574-44-4-44-444040-40-400000000000000000000000000000002i2−2i22i2−2i2000000000000000
χ584-44-4-44-444040-40-40000000000000000000000000000000−2i22i2−2i22i2000000000000000
χ594-44-4-44-44-40-4040400000004-44-4000000000000000000000000000000000000000
χ604-44-4-44-44-40-404040000000-44-44000000000000000000000000000000000000000
χ614-4-4-44-4440000000000000022−22−222200000000000022−220000002-2-22000000000000000
χ624-4-4-44-4440000000000000022−22−2222000000000000−2222000000-222-2000000000000000
χ634-4-4-44-44400000000000000−222222−2200000000000022−22000000-222-2000000000000000
χ644-4-4-44-44400000000000000−222222−22000000000000−22220000002-2-22000000000000000
χ658-8-88-888-8000000000000000000000000000000000000000000000000000000000

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