Finite Group Databasebeta

← Group #306426

Character table — Group #306426

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71
size111111112222222244444444444444444488888888888888888888888816161616161616161616161632
order12222222444444444444444444888888884444444488888888888888884444444488884
χ111111111111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111-1-1-1-11111-1-111-1-1-1-1-1-1111111-1-1-1-1-111111-1-1-1-1-1-1-1
χ311111111111111111111111111-1-1-1-11111-1-1111111111111-1-1-1-1-1-1-1-1-1-11-1-1-11111-1-1-1-1-1
χ411111111111111111111111111-1-1-1-1-1-1-1-1-1-111-1-111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-111-1-111111
χ5111111111111111111111-1-1-1-111111111111-1-1-1-11111111111-1-1-1-11111-11-1-1-1-1-1-1-1-111-1
χ6111111111111111111111-1-1-1-111111-1-1-1-111-1-11111-1-1-1-1-1-111-1-1-1-1-1-1-1-111-1-1-1-11111-1-11
χ7111111111111111111111-1-1-1-11-1-1-1-11111-1-1-1-1-1-111111111-1-11111-1-1-1-1-1-111-1-1-1-111-1-11
χ8111111111111111111111-1-1-1-11-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1111111111-111-1-111-1-111-1
χ91111111111111111-1-1-1-111111111111111-1-11111-1-111-1-1-1-111111111111-1-1-1-1-1-1-111-1-1-1
χ101111111111111111-1-1-1-11111111111-1-1-1-1-1-111-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-111-1-1111
χ111111111111111111-1-1-1-1111111-1-1-1-11111111111-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1111
χ121111111111111111-1-1-1-1111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-11111-1-1-1-1-1-11111-1111-1-11111-1-1-1
χ131111111111111111-1-1-1-11-1-1-1-1111111111-1-1-1-1-1-1-1-111-1-1-1-111-1-1-1-11111-1-1111111-1-1-1-11
χ141111111111111111-1-1-1-11-1-1-1-111111-1-1-1-1-1-1-1-111-1-1-1-1111111-1-1-1-1-1-1-1-11-11111-1-11111-1
χ151111111111111111-1-1-1-11-1-1-1-11-1-1-1-1111111-1-1-1-1-1-111-1-1-1-1-1-11111-1-1-1-1-11-1-111111111-1
χ161111111111111111-1-1-1-11-1-1-1-11-1-1-1-1-1-1-1-111-1-111-1-1-1-11111-1-11111111111-1-111-1-1-1-1-1-11
χ17222222222-22-22-22-22222-20000-222220000220000-2-2000000-2-2000000000-200000000000
χ18222222222-22-22-22-22222-20000-2-2-2-2-20000-2-20000-2-200000022000000000200000000000
χ19222222222-22-22-22-2-2-2-2-2-20000-222220000-2-2000022000000-2-2000000000200000000000
χ20222222222-22-22-22-2-2-2-2-2-20000-2-2-2-2-200002200002200000022000000000-200000000000
χ2122222222-22-22-22-220000-22222-20000222200-2-22200-2-200000000000000-2000000000000
χ2222222222-22-22-22-220000-22222-20000-2-2-2-200-2-2-2-20022000000000000002000000000000
χ2322222222-22-22-22-220000-2-2-2-2-2-2000022220022-2-200-2-2000000000000002000000000000
χ2422222222-22-22-22-220000-2-2-2-2-2-20000-2-2-2-2002222002200000000000000-2000000000000
χ252222-2-2-2-22020-20-2022-2-200000022-2-222−2−22-20000002−222−2−200000022−2−200000000002−20
χ262222-2-2-2-22020-20-2022-2-200000022-2-2−2−2222-2000000−22−2−222000000−2−2220000000000−220
χ272222-2-2-2-22020-20-2022-2-2000000-2-22222−2−2-220000002−222−2−2000000−2−2220000000000−220
χ282222-2-2-2-22020-20-2022-2-2000000-2-222−2−222-22000000−22−2−22200000022−2−200000000002−20
χ292222-2-2-2-22020-20-20-2-22200000022-2-222−2−2-220000002−2−2−22200000022−2−20000000000−220
χ302222-2-2-2-22020-20-20-2-22200000022-2-2−2−222-22000000−2222−2−2000000−2−22200000000002−20
χ312222-2-2-2-22020-20-20-2-222000000-2-22222−2−22-20000002−2−2−222000000−2−22200000000002−20
χ322222-2-2-2-22020-20-20-2-222000000-2-222−2−2222-2000000−2222−2−200000022−2−20000000000−220
χ3322-2-22-22-22-2-222-2-220000-222-2-2200000000002-20000002i−2i2i−2i00000000000000002i−2i00000
χ3422-2-22-22-22-2-222-2-220000-222-2-2200000000002-2000000−2i2i−2i2i0000000000000000−2i2i00000
χ3522-2-22-22-22-2-222-2-220000-2-2-22220000000000-220000002i−2i2i−2i0000000000000000−2i2i00000
χ3622-2-22-22-22-2-222-2-220000-2-2-22220000000000-22000000−2i2i−2i2i00000000000000002i−2i00000
χ3722-2-22-22-2-222-2-222-22i−2i2i−2i-200002000000000000002i−2i0000000022-2-20000002i−2i000000000
χ3822-2-22-22-2-222-2-222-22i−2i2i−2i-200002000000000000002i−2i00000000-2-222000000−2i2i000000000
χ3922-2-22-22-2-222-2-222-2−2i2i−2i2i-20000200000000000000−2i2i0000000022-2-2000000−2i2i000000000
χ4022-2-22-22-2-222-2-222-2−2i2i−2i2i-20000200000000000000−2i2i00000000-2-2220000002i−2i000000000
χ4122-2-22-22-2-2-222-2-2222i−2i2i−2i222-2-2-20000000000-2200−2i2i000000000000000000002i−2i0000000
χ4222-2-22-22-2-2-222-2-2222i−2i2i−2i2-2-222-200000000002-200−2i2i00000000000000000000−2i2i0000000
χ4322-2-22-22-2-2-222-2-222−2i2i−2i2i222-2-2-20000000000-22002i−2i00000000000000000000−2i2i0000000
χ4422-2-22-22-2-2-222-2-222−2i2i−2i2i2-2-222-200000000002-2002i−2i000000000000000000002i−2i0000000
χ452-22-2-222-2020-20-202000002-22-20i2−i2i2−i22-22-200002-200000000i2−i2i2−i2i2−i2i2−i2i2−i200000000i2−i2000
χ462-22-2-222-2020-20-202000002-22-20i2−i2i2−i2-22-220000-2200000000i2−i2i2−i2i2−i2−i2i2−i2i200000000−i2i2000
χ472-22-2-222-2020-20-202000002-22-20−i2i2−i2i22-22-200002-200000000−i2i2−i2i2−i2i2−i2i2−i2i200000000−i2i2000
χ482-22-2-222-2020-20-202000002-22-20−i2i2−i2i2-22-220000-2200000000−i2i2−i2i2−i2i2i2−i2i2−i200000000i2−i2000
χ492-22-2-222-2020-20-20200000-22-220i2−i2i2−i22-22-20000-2200000000i2−i2−i2i2−i2i2i2−i2i2−i200000000−i2i2000
χ502-22-2-222-2020-20-20200000-22-220i2−i2i2−i2-22-2200002-200000000i2−i2−i2i2−i2i2−i2i2−i2i200000000i2−i2000
χ512-22-2-222-2020-20-20200000-22-220−i2i2−i2i22-22-20000-2200000000−i2i2i2−i2i2−i2−i2i2−i2i200000000i2−i2000
χ522-22-2-222-2020-20-20200000-22-220−i2i2−i2i2-22-2200002-200000000−i2i2i2−i2i2−i2i2−i2i2−i200000000−i2i2000
χ5344444444-4-4-4-4-4-4-4-40000400004000000000000000000000000000000000000000000000
χ544444-4-4-4-4-40-404040000000000000002222−22−2200000000−2222000000000000000000000000000
χ554444-4-4-4-4-40-40404000000000000000−22−2222220000000022−22000000000000000000000000000
χ5644-4-44-44-444-4-444-4-4000040000-4000000000000000000000000000000000000000000000
χ5744-4-4-44-4440-40-404000000000000000000000000000002i2−2i2−2i22i200000000000000000000000
χ5844-4-4-44-4440-40-40400000000000000000000000000000−2i22i22i2−2i200000000000000000000000
χ5944-4-4-44-44-404040-404i−4i−4i4i000000000000000000000000000000000000000000000000000
χ6044-4-4-44-44-404040-40−4i4i4i−4i000000000000000000000000000000000000000000000000000
χ614-44-44-4-440000000000000000002i2−2i2−2i22i222−22−2222000000000000000000002i−2i−2i2i0000000000000
χ624-44-44-4-440000000000000000002i2−2i2−2i22i2−222222−2200000000000000000000−2i2i2i−2i0000000000000
χ634-44-44-4-44000000000000000000−2i22i22i2−2i222−22−222200000000000000000000−2i2i2i−2i0000000000000
χ644-44-44-4-44000000000000000000−2i22i22i2−2i2−222222−22000000000000000000002i−2i−2i2i0000000000000
χ654-44-4-444-40-404040-400000000002i2−2i22i2−2i2000000000000000000−2i22i2000000000000000000000
χ664-44-4-444-40-404040-40000000000−2i22i2−2i22i20000000000000000002i2−2i2000000000000000000000
χ674-4-44-4-44404040-40-400000000000000000000000000000000002i2−2i2−2i22i200000000000000000
χ684-4-44-4-44404040-40-40000000000000000000000000000000000−2i22i22i2−2i200000000000000000
χ694-4-44-4-4440-40-40404000004-4-440000000000000000000000000000000000000000000000
χ704-4-44-4-4440-40-4040400000-444-40000000000000000000000000000000000000000000000
χ718-8-8888-8-8000000000000000000000000000000000000000000000000000000000000000

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