Finite Group Databasebeta

← Group #313646

Character table — Group #313646

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80
size11111111222222222222222244444444444444444444444444888888888888888888161616161616161616163232
order12222222444444448888888844444488888888888888888888224444444488888888244444888844
χ111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111111111111111111111-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1
χ31111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-11111-1-1-1-11111111111-1-1-1-1-1-1
χ41111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1111111
χ5111111111111111111111111-1-1-1-11111111111111111111111-1-1-1-1-1-11111-1-1-1-1-1-1-1-111-1-1-1-11111-1-1
χ6111111111111111111111111-1-1-1-11111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-111
χ7111111111111111111111111-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-111-1-1-1-1-1-1-1-111
χ8111111111111111111111111-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1-1-1-1-111111111-1-1
χ91111111111111111-1-1-1-1-1-1-1-1111111-1-1-1-111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1111-1-1-1-1111-1
χ101111111111111111-1-1-1-1-1-1-1-1111111-1-1-1-111111111-1-1-1-1-1-1-1-1111111-1-111-1-1-1-1-1-1-1-11-1-1-11111-1-1-11
χ111111111111111111-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-11111111111-1-1-1-111-1-11111-1-1-1-1-1111-1-111-1-1-11
χ121111111111111111-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-1111111-1-1-1-11-1-1-111-1-1111-1
χ131111111111111111-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-111111111-11-1-111-1-111-11
χ141111111111111111-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111111-111-1-111-1-11-1
χ151111111111111111-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1111111-1-1-1-1-1-11111-11-1-11111-1-11-1
χ161111111111111111-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-11111-1-111-1-1-1-111111-111-1-1-1-111-11
χ17222222222-22-22-22-2222222220000-2-2-2-2-2-20000000000000000000000222200000000-2-20000000000
χ18222222222-22-22-22-2222222220000-2-2-2-2-2-20000000000000000000000-2-2-2-200000000220000000000
χ19222222222-22-22-22-2-2-2-2-2-2-2-2-20000-2-22222000000000000000000000022-2-2000000002-20000000000
χ20222222222-22-22-22-2-2-2-2-2-2-2-2-20000-2-222220000000000000000000000-2-22200000000-220000000000
χ2122222222-22-22-22-22000000002222-2-200002222-2-2-2-200000000-2-222-2-2000000000000000000000000
χ2222222222-22-22-22-22000000002222-2-20000-2-2-2-2222200000000-2-2-2-222000000000000000000000000
χ2322222222-22-22-22-2200000000-2-2-2-2-2-200002222-2-2-2-20000000022-2-222000000000000000000000000
χ2422222222-22-22-22-2200000000-2-2-2-2-2-20000-2-2-2-22222000000002222-2-2000000000000000000000000
χ252222-2-2-2-2-20-2020202222-2-2-2-2000000000022−2−222−2−22222−2−2−2−20000002i−2i2i−2i00000000000000i2−i2i2−i200
χ262222-2-2-2-2-20-2020202222-2-2-2-2000000000022−2−222−2−22222−2−2−2−2000000−2i2i−2i2i00000000000000−i2i2−i2i200
χ272222-2-2-2-2-20-2020202222-2-2-2-20000000000−2−222−2−222−2−2−2−222220000002i−2i2i−2i00000000000000−i2i2−i2i200
χ282222-2-2-2-2-20-2020202222-2-2-2-20000000000−2−222−2−222−2−2−2−22222000000−2i2i−2i2i00000000000000i2−i2i2−i200
χ292222-2-2-2-2-20-202020-2-2-2-22222000000000022−2−222−2−2−2−2−2−222220000002i−2i−2i2i00000000000000−i2i2i2−i200
χ302222-2-2-2-2-20-202020-2-2-2-22222000000000022−2−222−2−2−2−2−2−22222000000−2i2i2i−2i00000000000000i2−i2−i2i200
χ312222-2-2-2-2-20-202020-2-2-2-222220000000000−2−222−2−2222222−2−2−2−20000002i−2i−2i2i00000000000000i2−i2−i2i200
χ322222-2-2-2-2-20-202020-2-2-2-222220000000000−2−222−2−2222222−2−2−2−2000000−2i2i2i−2i00000000000000−i2i2i2−i200
χ3322-2-22-2-22020-20-202i2i2−i2−i2i2i2−i2−i22i2i−2i−2i00i2i2−i2−i22i−2i2i−2i000022−2−222−2−2002-2000000i2i2−i2−i222−2−2000000000000
χ3422-2-22-2-22020-20-202i2i2−i2−i2i2i2−i2−i22i2i−2i−2i00i2i2−i2−i2−2i2i−2i2i0000−2−222−2−22200-22000000−i2−i2i2i222−2−2000000000000
χ3522-2-22-2-22020-20-202i2i2−i2−i2i2i2−i2−i2−2i−2i2i2i00i2i2−i2−i22i−2i2i−2i000022−2−222−2−200-22000000−i2−i2i2i2−2−222000000000000
χ3622-2-22-2-22020-20-202i2i2−i2−i2i2i2−i2−i2−2i−2i2i2i00i2i2−i2−i2−2i2i−2i2i0000−2−222−2−222002-2000000i2i2−i2−i2−2−222000000000000
χ3722-2-22-2-22020-20-202−i2−i2i2i2−i2−i2i2i22i2i−2i−2i00−i2−i2i2i22i−2i2i−2i0000−2−222−2−222002-2000000−i2−i2i2i2−2−222000000000000
χ3822-2-22-2-22020-20-202−i2−i2i2i2−i2−i2i2i22i2i−2i−2i00−i2−i2i2i2−2i2i−2i2i000022−2−222−2−200-22000000i2i2−i2−i2−2−222000000000000
χ3922-2-22-2-22020-20-202−i2−i2i2i2−i2−i2i2i2−2i−2i2i2i00−i2−i2i2i22i−2i2i−2i0000−2−222−2−22200-22000000i2i2−i2−i222−2−2000000000000
χ4022-2-22-2-22020-20-202−i2−i2i2i2−i2−i2i2i2−2i−2i2i2i00−i2−i2i2i2−2i2i−2i2i000022−2−222−2−2002-2000000−i2−i2i2i222−2−2000000000000
χ412-22-2-22-2222-2-222-2-22i−2i2i−2i2i−2i2i−2i2-22-2-222i−2i2i−2i00000000000000002-20000000000002i−2i2i−2i000000000000
χ422-22-2-22-2222-2-222-2-22i−2i2i−2i2i−2i2i−2i-22-22-222i−2i2i−2i0000000000000000-22000000000000−2i2i−2i2i000000000000
χ432-22-2-22-2222-2-222-2-2−2i2i−2i2i−2i2i−2i2i2-22-2-22−2i2i−2i2i00000000000000002-2000000000000−2i2i−2i2i000000000000
χ442-22-2-22-2222-2-222-2-2−2i2i−2i2i−2i2i−2i2i-22-22-22−2i2i−2i2i0000000000000000-220000000000002i−2i2i−2i000000000000
χ452-22-2-22-222-2-222-2-222i−2i2i−2i2i−2i2i−2i00002-2−2i2i−2i2i0000000000000000000000000000000000002i−2i2-2000000
χ462-22-2-22-222-2-222-2-222i−2i2i−2i2i−2i2i−2i00002-2−2i2i−2i2i000000000000000000000000000000000000−2i2i-22000000
χ472-22-2-22-222-2-222-2-22−2i2i−2i2i−2i2i−2i2i00002-22i−2i2i−2i0000000000000000000000000000000000002i−2i-22000000
χ482-22-2-22-222-2-222-2-22−2i2i−2i2i−2i2i−2i2i00002-22i−2i2i−2i000000000000000000000000000000000000−2i2i2-2000000
χ492-22-2-22-22-222-2-222-2000000002-22-22-20000000000002i−2i2i−2i2i−2i2i−2i-22000000002i−2i2i−2i0000000000000000
χ502-22-2-22-22-222-2-222-2000000002-22-22-2000000000000−2i2i−2i2i−2i2i−2i2i-2200000000−2i2i−2i2i0000000000000000
χ512-22-2-22-22-222-2-222-200000000-22-222-20000000000002i−2i2i−2i2i−2i2i−2i2-200000000−2i2i−2i2i0000000000000000
χ522-22-2-22-22-222-2-222-200000000-22-222-2000000000000−2i2i−2i2i−2i2i−2i2i2-2000000002i−2i2i−2i0000000000000000
χ532-2-22-2-22202020-20-22−2−222−2−222i−2i−2i2i002−2−2200002i−2i2i−2ii2−i2−i2i2i2−i2−i2i200002-20000−222−2−i2i2i2−i2000000000000
χ542-2-22-2-22202020-20-22−2−222−2−222i−2i−2i2i002−2−220000−2i2i−2i2i−i2i2i2−i2−i2i2i2−i20000-2200002−2−22−i2i2i2−i2000000000000
χ552-2-22-2-22202020-20-22−2−222−2−22−2i2i2i−2i002−2−2200002i−2i2i−2ii2−i2−i2i2i2−i2−i2i20000-2200002−2−22i2−i2−i2i2000000000000
χ562-2-22-2-22202020-20-22−2−222−2−22−2i2i2i−2i002−2−220000−2i2i−2i2i−i2i2i2−i2−i2i2i2−i200002-20000−222−2i2−i2−i2i2000000000000
χ572-2-22-2-22202020-20-2−222−2−222−22i−2i−2i2i00−222−200002i−2i2i−2i−i2i2i2−i2−i2i2i2−i200002-200002−2−22i2−i2−i2i2000000000000
χ582-2-22-2-22202020-20-2−222−2−222−22i−2i−2i2i00−222−20000−2i2i−2i2ii2−i2−i2i2i2−i2−i2i20000-220000−222−2i2−i2−i2i2000000000000
χ592-2-22-2-22202020-20-2−222−2−222−2−2i2i2i−2i00−222−200002i−2i2i−2i−i2i2i2−i2−i2i2i2−i20000-220000−222−2−i2i2i2−i2000000000000
χ602-2-22-2-22202020-20-2−222−2−222−2−2i2i2i−2i00−222−20000−2i2i−2i2ii2−i2−i2i2i2−i2−i2i200002-200002−2−22−i2i2i2−i2000000000000
χ6144444444-4-4-4-4-4-4-4-40000000000004400000000000000000000000000000000000000000000000000
χ624444-4-4-4-44040-40-400000000000000000002222−22−22−22−22222200000000000000000000000000000000000000
χ634444-4-4-4-44040-40-40000000000000000000−22−2222222222−22−2200000000000000000000000000000000000000
χ6444-4-44-4-440-404040-42i22i2−2i2−2i22i22i2−2i2−2i2000000−2i2−2i22i22i20000000000000000000000000000000000000000000000
χ6544-4-44-4-440-404040-4−2i2−2i22i22i2−2i2−2i22i22i20000002i22i2−2i2−2i20000000000000000000000000000000000000000000000
χ6644-4-4-444-4000000002i22i2−2i2−2i2−2i2−2i22i22i200000000002i2−2i2−2i22i2000022-2-2-2-222000000000000000000000000000000
χ6744-4-4-444-4000000002i22i2−2i2−2i2−2i2−2i22i22i20000000000−2i22i22i2−2i20000-2-22222-2-2000000000000000000000000000000
χ6844-4-4-444-400000000−2i2−2i22i22i22i22i2−2i2−2i200000000002i2−2i2−2i22i20000-2-22222-2-2000000000000000000000000000000
χ6944-4-4-444-400000000−2i2−2i22i22i22i22i2−2i2−2i20000000000−2i22i22i2−2i2000022-2-2-2-222000000000000000000000000000000
χ704-44-44-44-440-40-4040000000000000000000000000002i2−2i22i2−2i2−2i22i2−2i22i2000000000000000000000000000000
χ714-44-44-44-440-40-404000000000000000000000000000−2i22i2−2i22i22i2−2i22i2−2i2000000000000000000000000000000
χ724-44-44-44-4-404040-404i−4i4i−4i−4i4i−4i4i00000000000000000000000000000000000000000000000000000000
χ734-44-44-44-4-404040-40−4i4i−4i4i4i−4i4i−4i00000000000000000000000000000000000000000000000000000000
χ744-44-4-44-44-4-444-4-444000000000000-4400000000000000000000000000000000000000000000000000
χ754-4-4444-4-40000000022−22−2222−222222−22000000000000002i2−2i2−2i22i22i−2i−2i2i−2i2i2i−2i000000000000000000000000000000
χ764-4-4444-4-40000000022−22−2222−222222−2200000000000000−2i22i22i2−2i2−2i2i2i−2i2i−2i−2i2i000000000000000000000000000000
χ774-4-4444-4-400000000−222222−2222−22−2222000000000000002i2−2i2−2i22i2−2i2i2i−2i2i−2i−2i2i000000000000000000000000000000
χ784-4-4444-4-400000000−222222−2222−22−222200000000000000−2i22i22i2−2i22i−2i−2i2i−2i2i2i−2i000000000000000000000000000000
χ794-4-44-4-4440-40-4040422−22−222222−22−2222000000−222222−220000000000000000000000000000000000000000000000
χ804-4-44-4-4440-40-40404−222222−22−222222−2200000022−22−22220000000000000000000000000000000000000000000000

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