Finite Group Databasebeta

← Group #306348

Character table — Group #306348

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71
size111111112222222244444444444444444488888888888888888888888816161616161616161616161632
order12222222444444444444444444888888882244444488888888888888884444444488882
χ111111111111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111-1-1-1-1-1-1111111-1-1-1-1-1-1111111-1-1-1-1-111111-1-1-1-1-1-1-1
χ311111111111111111111111111-1-1-1-11111111111-1-1111111-1-1-1-1-1-1-1-1-1-1111-1-1-111-1-1-1-1-1
χ411111111111111111111111111-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-111-1-1-1-1-111111
χ5111111111111111111111-1-1-1-11111111111111-1-1-1-111-1-1-1-111111111111-1-1-1-1-1-1-111-1-1-1
χ6111111111111111111111-1-1-1-111111-1-1-1-1-1-111-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-111-1-1111
χ7111111111111111111111-1-1-1-11-1-1-1-111111111-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-11-1-1111-1-1-1-1111
χ8111111111111111111111-1-1-1-11-1-1-1-1-1-1-1-1-1-111-1-111-1-11111-1-1-1-1-1-11111-1-1-11111111-1-1-1
χ911111111111111111-1-1-1-11111111111111-1-1-1-1111111111111-1-1-1-11111-1-1-1-1-11-1-1-1-111-1
χ1011111111111111111-1-1-1-1111111111-1-1-1-111-1-11111-1-1-1-1-1-111-1-1-1-1-1-1-1-11-1-1-1-111111-1-11
χ1111111111111111111-1-1-1-111111-1-1-1-11111-1-1-1-111-1-1111111-1-11111-1-1-1-1-1-1-111-1-1-111-1-11
χ1211111111111111111-1-1-1-111111-1-1-1-1-1-1-1-111-1-111-1-1-1-1-1-1-1-1-1-1111111111-1-111-111-1-111-1
χ1311111111111111111-1-1-1-1-1-1-1-1111111111-1-1-1-1-1-1-1-111-1-1-1-111-1-1-1-11111-11111-111-1-1-1-11
χ1411111111111111111-1-1-1-1-1-1-1-111111-1-1-1-111-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-111111-1-1-11111-1
χ1511111111111111111-1-1-1-1-1-1-1-11-1-1-1-11111-1-1-1-1-1-11111-1-1-1-1-1-11111-1-1-1-1-111-1-11111111-1
χ1611111111111111111-1-1-1-1-1-1-1-11-1-1-1-1-1-1-1-111-1-1-1-111-1-11111-1-111111111111-1-11-1-1-1-1-1-11
χ17222222222-22-22-22-2-200002222-2222200000000-2-222000000-2-20000000000000-20000000
χ18222222222-22-22-22-2-200002222-2-2-2-2-200000000-2-2-2-200000022000000000000020000000
χ19222222222-22-22-22-2-20000-2-2-2-2-222220000000022-2-2000000-2-2000000000000020000000
χ20222222222-22-22-22-2-20000-2-2-2-2-2-2-2-2-2000000002222000000220000000000000-20000000
χ2122222222-22-22-22-22-222220000-20000222222-2-20000-2-200000000000000-2000000000000
χ2222222222-22-22-22-22-222220000-20000-2-2-2-2-2-2-2-2000022000000000000002000000000000
χ2322222222-22-22-22-22-2-2-2-2-20000-200002222-2-2220000-2-2000000000000002000000000000
χ2422222222-22-22-22-22-2-2-2-2-20000-20000-2-2-2-2222200002200000000000000-2000000000000
χ252222-2-2-2-22-2-222-2-22-222-2-20000200000000002-20000002i2i−2i−2i00000000000000002i−2i00000
χ262222-2-2-2-22-2-222-2-22-222-2-20000200000000002-2000000−2i−2i2i2i0000000000000000−2i2i00000
χ272222-2-2-2-22-2-222-2-22-2-2-222000020000000000-220000002i2i−2i−2i0000000000000000−2i2i00000
χ282222-2-2-2-22-2-222-2-22-2-2-222000020000000000-22000000−2i−2i2i2i00000000000000002i−2i00000
χ292222-2-2-2-2-222-2-222-2-200002i2i−2i−2i20000000000002i−2i000000000022-2-200000002i−2i00000000
χ302222-2-2-2-2-222-2-222-2-200002i2i−2i−2i20000000000002i−2i0000000000-2-2220000000−2i2i00000000
χ312222-2-2-2-2-222-2-222-2-20000−2i−2i2i2i2000000000000−2i2i000000000022-2-20000000−2i2i00000000
χ322222-2-2-2-2-222-2-222-2-20000−2i−2i2i2i2000000000000−2i2i0000000000-2-22200000002i−2i00000000
χ332222-2-2-2-2-2-222-2-222222-2-22i2i−2i−2i-20000000000-22−2i2i00000000000000000002i−2i0000000000
χ342222-2-2-2-2-2-222-2-222222-2-2−2i−2i2i2i-20000000000-222i−2i0000000000000000000−2i2i0000000000
χ352222-2-2-2-2-2-222-2-2222-2-2222i2i−2i−2i-200000000002-2−2i2i0000000000000000000−2i2i0000000000
χ362222-2-2-2-2-2-222-2-2222-2-222−2i−2i2i2i-200000000002-22i−2i00000000000000000002i−2i0000000000
χ3722-2-222-2-220-20-2020000002i−2i2i−2i02i2i−2i−2ii2i2−i2−i20000002-2i2−i22−22−200000022−2−20000000000i2−i20
χ3822-2-222-2-220-20-2020000002i−2i2i−2i02i2i−2i−2i−i2−i2i2i20000002-2−i2i2−22−22000000−2−2220000000000−i2i20
χ3922-2-222-2-220-20-2020000002i−2i2i−2i0−2i−2i2i2ii2i2−i2−i2000000-22i2−i22−22−2000000−2−2220000000000−i2i20
χ4022-2-222-2-220-20-2020000002i−2i2i−2i0−2i−2i2i2i−i2−i2i2i2000000-22−i2i2−22−2200000022−2−20000000000i2−i20
χ4122-2-222-2-220-20-202000000−2i2i−2i2i02i2i−2i−2ii2i2−i2−i2000000-22i2−i2−22−2200000022−2−20000000000−i2i20
χ4222-2-222-2-220-20-202000000−2i2i−2i2i02i2i−2i−2i−i2−i2i2i2000000-22−i2i22−22−2000000−2−2220000000000i2−i20
χ4322-2-222-2-220-20-202000000−2i2i−2i2i0−2i−2i2i2ii2i2−i2−i20000002-2i2−i2−22−22000000−2−2220000000000i2−i20
χ4422-2-222-2-220-20-202000000−2i2i−2i2i0−2i−2i2i2i−i2−i2i2i20000002-2−i2i22−22−200000022−2−20000000000−i2i20
χ452-22-22-2-2202020-20-202i−2i2i−2i000002−22−22i−2i2i−2i2-20000000000002−2i2−i2i2−i2i2−i2i2−i2000000002−2000
χ462-22-22-2-2202020-20-202i−2i2i−2i000002−22−2−2i2i−2i2i-220000000000002−2i2−i2i2−i2−i2i2−i2i200000000−22000
χ472-22-22-2-2202020-20-202i−2i2i−2i00000−22−222i−2i2i−2i2-2000000000000−22−i2i2−i2i2−i2i2−i2i200000000−22000
χ482-22-22-2-2202020-20-202i−2i2i−2i00000−22−22−2i2i−2i2i-22000000000000−22−i2i2−i2i2i2−i2i2−i2000000002−2000
χ492-22-22-2-2202020-20-20−2i2i−2i2i000002−22−22i−2i2i−2i-220000000000002−2−i2i2−i2i2i2−i2i2−i200000000−22000
χ502-22-22-2-2202020-20-20−2i2i−2i2i000002−22−2−2i2i−2i2i2-20000000000002−2−i2i2−i2i2−i2i2−i2i2000000002−2000
χ512-22-22-2-2202020-20-20−2i2i−2i2i00000−22−222i−2i2i−2i-22000000000000−22i2−i2i2−i2−i2i2−i2i2000000002−2000
χ522-22-22-2-2202020-20-20−2i2i−2i2i00000−22−22−2i2i−2i2i2-2000000000000−22i2−i2i2−i2i2−i2i2−i200000000−22000
χ5344444444-4-4-4-4-4-4-4-44000000004000000000000000000000000000000000000000000000
χ544444-4-4-4-444-4-444-4-4400000000-4000000000000000000000000000000000000000000000
χ5544-4-444-4-4-404040-40000000000000002i22i2−2i2−2i200000000−2i22i2000000000000000000000000000
χ5644-4-444-4-4-404040-4000000000000000−2i2−2i22i22i2000000002i2−2i2000000000000000000000000000
χ5744-4-4-4-4444040-40-4000000000000000000000000000002i2−2i2−2i22i200000000000000000000000
χ5844-4-4-4-4444040-40-400000000000000000000000000000−2i22i22i2−2i200000000000000000000000
χ5944-4-4-4-444-40-404040000004-4-440000000000000000000000000000000000000000000000
χ6044-4-4-4-444-40-40404000000-444-40000000000000000000000000000000000000000000000
χ614-44-44-4-440-40-40404000000000022−2222−22000000000000000000−2222000000000000000000000
χ624-44-44-4-440-40-404040000000000−2222−222200000000000000000022−22000000000000000000000
χ634-44-4-444-4040-40-40400000000000000000000000000000000002i2−2i2−2i22i200000000000000000
χ644-44-4-444-4040-40-4040000000000000000000000000000000000−2i22i22i2−2i200000000000000000
χ654-44-4-444-40-404040-404i−4i−4i4i00000000000000000000000000000000000000000000000000
χ664-44-4-444-40-404040-40−4i4i4i−4i00000000000000000000000000000000000000000000000000
χ674-4-444-44-40000000000000000002i2−2i2−2i22i222−22−222200000000000000000000−2i2i2i−2i0000000000000
χ684-4-444-44-40000000000000000002i2−2i2−2i22i2−222222−22000000000000000000002i−2i−2i2i0000000000000
χ694-4-444-44-4000000000000000000−2i22i22i2−2i222−22−2222000000000000000000002i−2i−2i2i0000000000000
χ704-4-444-44-4000000000000000000−2i22i22i2−2i2−222222−2200000000000000000000−2i2i2i−2i0000000000000
χ718-8-88-88-88000000000000000000000000000000000000000000000000000000000000000

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