Finite Group Databasebeta

← Group #312300

Character table — Group #312300

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65
size11111111222222224444444444888888888888888888888888161616161616161616161616161632
order12222222444444444444448888444444444488888888888888222222448888884
χ111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111-1-1-1-1111111-1-1-1-1-1-11111-1-1-11-1-1-1-1-1-1-1
χ31111111111111111111111111111-1-1-1-1-1-11111111111111111-1-1-1-1-1-11-1-1-111-1-1-1
χ41111111111111111111111111111-1-1-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1-1-111-1-111-1-1111
χ51111111111111111111111-1-1-1-1111111-1-11111-1-1-1-1-1-111-1-1-1-111-1-1111-111-1-1-1-1-1
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
χ71111111111111111111111-1-1-1-111-1-1-1-1111111-1-1-1-1-1-111-1-1-1-1-1-111-1-111-1-1-1-1111
χ81111111111111111111111-1-1-1-111-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-11111-1-11111-111111-1-1-1
χ911111111111111111-1-1-1-111111-1-111111111-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-11111-1-111-1-11
χ1011111111111111111-1-1-1-111111-1-1111111-1-111-1-1-1-111111111-1-1-1-1-1-1-1111-1-111-1
χ1111111111111111111-1-1-1-111111-1-1-1-1-1-1-1-111-1-1-1-1-1-111-1-1-1-1-1-11111-1-11-1111111-1
χ1211111111111111111-1-1-1-111111-1-1-1-1-1-1-1-1-1-111-1-1-1-111111111111111-1-1-1-1-1-1-1-11
χ1311111111111111111-1-1-1-11-1-1-1-1-1-11111-1-111-1-11111-1-1-1-11111-1-111111-1-1-1-1-111-1
χ1411111111111111111-1-1-1-11-1-1-1-1-1-11111-1-1-1-1111111-1-111-1-1-1-1-1-111-1-1-1-11111-1-11
χ1511111111111111111-1-1-1-11-1-1-1-1-1-1-1-1-1-11111-1-11111-1-1-1-1111111-1-1-1-11111-1-1-1-11
χ1611111111111111111-1-1-1-11-1-1-1-1-1-1-1-1-1-111-1-1111111-1-111-1-1-1-111-1-111-11-1-11111-1
χ17222222222-22-22-22-2-20000-222220022-2-22200000000-2-20000000000000-20000000
χ18222222222-22-22-22-2-20000-2222200-2-222-2-200000000-2-2000000000000020000000
χ19222222222-22-22-22-2-20000-2-2-2-2-20022-2-2-2-20000000022000000000000020000000
χ20222222222-22-22-22-2-20000-2-2-2-2-200-2-2222200000000220000000000000-20000000
χ2122222222-22-22-22-22-22222-20000-2-20000002222000000-2-20000000000-200000000
χ2222222222-22-22-22-22-22222-20000-2-2000000-2-2-2-2000000220000000000200000000
χ2322222222-22-22-22-22-2-2-2-2-2-200002200000022-2-2000000220000000000-200000000
χ2422222222-22-22-22-22-2-2-2-2-2-2000022000000-2-222000000-2-20000000000200000000
χ252222-2-2-2-22-2-222-2-22-22i2i−2i−2i200002i−2i000000000000000000000000002-2002i−2i00000
χ262222-2-2-2-22-2-222-2-22-22i2i−2i−2i200002i−2i00000000000000000000000000-2200−2i2i00000
χ272222-2-2-2-22-2-222-2-22-2−2i−2i2i2i20000−2i2i000000000000000000000000002-200−2i2i00000
χ282222-2-2-2-22-2-222-2-22-2−2i−2i2i2i20000−2i2i00000000000000000000000000-22002i−2i00000
χ292222-2-2-2-2-222-2-222-2-2000020000002i−2i2i−2i0000002i2i−2i−2i00000000002-200000000000
χ302222-2-2-2-2-222-2-222-2-2000020000002i−2i2i−2i000000−2i−2i2i2i0000000000-2200000000000
χ312222-2-2-2-2-222-2-222-2-200002000000−2i2i−2i2i0000002i2i−2i−2i0000000000-2200000000000
χ322222-2-2-2-2-222-2-222-2-200002000000−2i2i−2i2i000000−2i−2i2i2i00000000002-200000000000
χ332222-2-2-2-2-2-222-2-22222i2i−2i−2i-20000−2i2i2i−2i−2i2i0000000000000000002-20000000000000
χ342222-2-2-2-2-2-222-2-22222i2i−2i−2i-20000−2i2i−2i2i2i−2i000000000000000000-220000000000000
χ352222-2-2-2-2-2-222-2-2222−2i−2i2i2i-200002i−2i2i−2i−2i2i000000000000000000-220000000000000
χ362222-2-2-2-2-2-222-2-2222−2i−2i2i2i-200002i−2i−2i2i2i−2i0000000000000000002-20000000000000
χ3722-2-222-2-202020-20-202i−2i2i−2i022−2−2000000002i−2i2-2i2−i2i2−i22−20022−2−20000000000i2−i2000
χ3822-2-222-2-202020-20-202i−2i2i−2i022−2−200000000−2i2i-22i2−i2i2−i22−200−2−2220000000000−i2i2000
χ3922-2-222-2-202020-20-202i−2i2i−2i0−2−222000000002i−2i2-2−i2i2−i2i2−2200−2−2220000000000−i2i2000
χ4022-2-222-2-202020-20-202i−2i2i−2i0−2−22200000000−2i2i-22−i2i2−i2i2−220022−2−20000000000i2−i2000
χ4122-2-222-2-202020-20-20−2i2i−2i2i022−2−2000000002i−2i-22−i2i2−i2i22−200−2−2220000000000i2−i2000
χ4222-2-222-2-202020-20-20−2i2i−2i2i022−2−200000000−2i2i2-2−i2i2−i2i22−20022−2−20000000000−i2i2000
χ4322-2-222-2-202020-20-20−2i2i−2i2i0−2−222000000002i−2i-22i2−i2i2−i2−220022−2−20000000000−i2i2000
χ4422-2-222-2-202020-20-20−2i2i−2i2i0−2−22200000000−2i2i2-2i2−i2i2−i2−2200−2−2220000000000i2−i2000
χ4544444444-4-4-4-4-4-4-4-44000040000000000000000000000000000000000000000000
χ464444-4-4-4-444-4-444-4-440000-40000000000000000000000000000000000000000000
χ4744-4-444-4-40-40-404040000002222−22−220000000000000000−2222000000000000000000000
χ4844-4-444-4-40-40-40404000000−22−222222000000000000000022−22000000000000000000000
χ4944-4-4-4-444040-40-404000000000000000000000022−22−222200000000000000000000000
χ5044-4-4-4-444040-40-4040000000000000000000000−222222−2200000000000000000000000
χ5144-4-4-4-4440-404040-404-4-4400000000000000000000000000000000000000000000
χ5244-4-4-4-4440-404040-40-444-400000000000000000000000000000000000000000000
χ534-44-44-44-44040-40-4000000000000000004i−4i0000000000000000000000000000000
χ544-44-44-44-44040-40-400000000000000000−4i4i0000000000000000000000000000000
χ554-44-44-44-4-40-404040000000000000000000000000000000000000000000000022−220
χ564-44-44-44-4-40-4040400000000000000000000000000000000000000000000000−22220
χ574-44-4-44-4440-40-404000000000000000000000000000000022−2222−22000000000000000
χ584-44-4-44-4440-40-4040000000000000000000000000000000−2222−2222000000000000000
χ594-44-4-44-44-404040-400000004-44-4000000000000000000000000000000000000000
χ604-44-4-44-44-404040-40000000-44-44000000000000000000000000000000000000000
χ614-4-44-444-40000000000000022−22−222200000000000000000022−222-2-22000000000000000
χ624-4-44-444-40000000000000022−22−2222000000000000000000−2222-222-2000000000000000
χ634-4-44-444-400000000000000−222222−2200000000000000000022−22-222-2000000000000000
χ644-4-44-444-400000000000000−222222−22000000000000000000−22222-2-22000000000000000
χ658-8-888-8-88000000000000000000000000000000000000000000000000000000000

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