Finite Group Databasebeta

← Group #312573

Character table — Group #312573

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80
size11111111222222222222222244444444444444444444444444888888888888888888161616161616161616163232
order12222222444444448888888844444488888888888888888888224444444488888888444444888844
χ111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111111111111111-1-1-1-111111111111111-1-1-1-1-1-1-1-1-1-1-1-1
χ3111111111111111111111111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-1-11111-1-1-1-1111111-1-1-1-1-1-1
χ4111111111111111111111111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1111111
χ5111111111111111111111111-1-1-1-111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-11111-1-1
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
χ7111111111111111111111111-1-1-1-111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-11111-1-11111-1-1-1-1111111-1-1-1-1-1-1-1-111
χ8111111111111111111111111-1-1-1-111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-11111-1-111111111-1-1
χ91111111111111111-1-1-1-1-1-1-1-11111111111-1-1-1-11111-1-1-1-1-1-1-1-111-1-1111111-1-1-1-1-1-1-1-1-1111-1-111-1-11-1
χ101111111111111111-1-1-1-1-1-1-1-11111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-11-1-1-111-1-111-11
χ111111111111111111-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-11111111111-1-111-1-1-1-1-1-1-1-11111-1111-1-1-1-111-11
χ121111111111111111-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-11111-1-1-1-1-1-1-1-111111-1-1-11111-1-11-1
χ131111111111111111-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-1-11111-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-111111111-11-1-11111-1-1-11
χ141111111111111111-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-1111111111-111-1-1-1-1111-1
χ151111111111111111-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-11111111111-1-1-1-111111111-1-1-1-1-11-1-111-1-1111-1
χ161111111111111111-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-111-1-111111111-1-1-1-11-111-1-111-1-1-11
χ17222222222-22-22-22-2222222220000-2-20000-2-2-2-2000000000000222200000000000000-2-20000000000
χ18222222222-22-22-22-2222222220000-2-20000-2-2-2-2000000000000-2-2-2-200000000000000220000000000
χ19222222222-22-22-22-2-2-2-2-2-2-2-2-20000-2-20000222200000000000022-2-2000000000000002-20000000000
χ20222222222-22-22-22-2-2-2-2-2-2-2-2-20000-2-200002222000000000000-2-22200000000000000-220000000000
χ2122222222-22-22-22-22000000002222-2-222220000-2-2-2-2000000000000-2-222-2-200000000000000000000
χ2222222222-22-22-22-22000000002222-2-2-2-2-2-200002222000000000000-2-2-2-22200000000000000000000
χ2322222222-22-22-22-2200000000-2-2-2-2-2-222220000-2-2-2-200000000000022-2-22200000000000000000000
χ2422222222-22-22-22-2200000000-2-2-2-2-2-2-2-2-2-2000022220000000000002222-2-200000000000000000000
χ252222-2-2-2-22020-20-202222-2-2-2-200000022−2−2000022−2−22222−2−2−2−22-22-2000000000000000000002−22−200
χ262222-2-2-2-22020-20-202222-2-2-2-200000022−2−2000022−2−22222−2−2−2−2-22-2200000000000000000000−22−2200
χ272222-2-2-2-22020-20-202222-2-2-2-2000000−2−2220000−2−222−2−2−2−222222-22-200000000000000000000−22−2200
χ282222-2-2-2-22020-20-202222-2-2-2-2000000−2−2220000−2−222−2−2−2−22222-22-22000000000000000000002−22−200
χ292222-2-2-2-22020-20-20-2-2-2-2222200000022−2−2000022−2−2−2−2−2−222222-2-22000000000000000000002−2−2200
χ302222-2-2-2-22020-20-20-2-2-2-2222200000022−2−2000022−2−2−2−2−2−22222-222-200000000000000000000−222−200
χ312222-2-2-2-22020-20-20-2-2-2-22222000000−2−2220000−2−2222222−2−2−2−22-2-2200000000000000000000−222−200
χ322222-2-2-2-22020-20-20-2-2-2-22222000000−2−2220000−2−2222222−2−2−2−2-222-2000000000000000000002−2−2200
χ3322-2-2-222-20-202020-2i2i2−i2−i2i2i2−i2−i222-2-2002-22-2i2i2−i2−i20000i2i2−i2−i2i2i2−i2−i20000002-200i2i2−i2−i2i2i2−i2−i2000000000000
χ3422-2-2-222-20-202020-2i2i2−i2−i2i2i2−i2−i222-2-200-22-22i2i2−i2−i20000−i2−i2i2i2−i2−i2i2i2000000-2200i2i2−i2−i2−i2−i2i2i2000000000000
χ3522-2-2-222-20-202020-2i2i2−i2−i2i2i2−i2−i2-2-222002-22-2i2i2−i2−i20000i2i2−i2−i2i2i2−i2−i2000000-2200−i2−i2i2i2−i2−i2i2i2000000000000
χ3622-2-2-222-20-202020-2i2i2−i2−i2i2i2−i2−i2-2-22200-22-22i2i2−i2−i20000−i2−i2i2i2−i2−i2i2i20000002-200−i2−i2i2i2i2i2−i2−i2000000000000
χ3722-2-2-222-20-202020-2−i2−i2i2i2−i2−i2i2i222-2-2002-22-2−i2−i2i2i20000−i2−i2i2i2−i2−i2i2i20000002-200−i2−i2i2i2−i2−i2i2i2000000000000
χ3822-2-2-222-20-202020-2−i2−i2i2i2−i2−i2i2i222-2-200-22-22−i2−i2i2i20000i2i2−i2−i2i2i2−i2−i2000000-2200−i2−i2i2i2i2i2−i2−i2000000000000
χ3922-2-2-222-20-202020-2−i2−i2i2i2−i2−i2i2i2-2-222002-22-2−i2−i2i2i20000−i2−i2i2i2−i2−i2i2i2000000-2200i2i2−i2−i2i2i2−i2−i2000000000000
χ4022-2-2-222-20-202020-2−i2−i2i2i2−i2−i2i2i2-2-22200-22-22−i2−i2i2i20000i2i2−i2−i2i2i2−i2−i20000002-200i2i2−i2−i2−i2−i2i2i2000000000000
χ412-22-2-22-2222-2-222-2-22i−2i2i−2i2i−2i2i−2i2i−2i2i−2i-2200002i−2i2i−2i00000000000000002i−2i00002-22-20000000000000000
χ422-22-2-22-2222-2-222-2-22i−2i2i−2i2i−2i2i−2i−2i2i−2i2i-2200002i−2i2i−2i0000000000000000−2i2i0000-22-220000000000000000
χ432-22-2-22-2222-2-222-2-2−2i2i−2i2i−2i2i−2i2i2i−2i2i−2i-220000−2i2i−2i2i00000000000000002i−2i0000-22-220000000000000000
χ442-22-2-22-2222-2-222-2-2−2i2i−2i2i−2i2i−2i2i−2i2i−2i2i-220000−2i2i−2i2i0000000000000000−2i2i00002-22-20000000000000000
χ452-22-2-22-222-2-222-2-222i−2i2i−2i2i−2i2i−2i00002-20000−2i2i−2i2i000000000000000000000000000000002i−2i2-2000000
χ462-22-2-22-222-2-222-2-222i−2i2i−2i2i−2i2i−2i00002-20000−2i2i−2i2i00000000000000000000000000000000−2i2i-22000000
χ472-22-2-22-222-2-222-2-22−2i2i−2i2i−2i2i−2i2i00002-200002i−2i2i−2i000000000000000000000000000000002i−2i-22000000
χ482-22-2-22-222-2-222-2-22−2i2i−2i2i−2i2i−2i2i00002-200002i−2i2i−2i00000000000000000000000000000000−2i2i2-2000000
χ492-22-2-22-22-222-2-222-2000000002i−2i2i−2i2-20000000000002i−2i2i−2i2i−2i2i−2i0000−2i2i000000002-22-2000000000000
χ502-22-2-22-22-222-2-222-2000000002i−2i2i−2i2-2000000000000−2i2i−2i2i−2i2i−2i2i0000−2i2i00000000-22-22000000000000
χ512-22-2-22-22-222-2-222-200000000−2i2i−2i2i2-20000000000002i−2i2i−2i2i−2i2i−2i00002i−2i00000000-22-22000000000000
χ522-22-2-22-22-222-2-222-200000000−2i2i−2i2i2-2000000000000−2i2i−2i2i−2i2i−2i2i00002i−2i000000002-22-2000000000000
χ532-2-2222-2-20-20-202022−2−222−2−222i−2i−2i2i0000002−2−222-22-22−2−222−2−22000000002i−2i−i2i2i2−i2−i2i2i2−i2000000000000
χ542-2-2222-2-20-20-202022−2−222−2−222i−2i−2i2i0000002−2−22-22-22−222−2−222−200000000−2i2i−i2i2i2−i2i2−i2−i2i2000000000000
χ552-2-2222-2-20-20-202022−2−222−2−22−2i2i2i−2i0000002−2−222-22-22−2−222−2−2200000000−2i2ii2−i2−i2i2i2−i2−i2i2000000000000
χ562-2-2222-2-20-20-202022−2−222−2−22−2i2i2i−2i0000002−2−22-22-22−222−2−222−2000000002i−2ii2−i2−i2i2−i2i2i2−i2000000000000
χ572-2-2222-2-20-20-20202−222−2−222−22i−2i−2i2i000000−222−22-22-2−222−2−222−2000000002i−2ii2−i2−i2i2i2−i2−i2i2000000000000
χ582-2-2222-2-20-20-20202−222−2−222−22i−2i−2i2i000000−222−2-22-222−2−222−2−2200000000−2i2ii2−i2−i2i2−i2i2i2−i2000000000000
χ592-2-2222-2-20-20-20202−222−2−222−2−2i2i2i−2i000000−222−22-22-2−222−2−222−200000000−2i2i−i2i2i2−i2−i2i2i2−i2000000000000
χ602-2-2222-2-20-20-20202−222−2−222−2−2i2i2i−2i000000−222−2-22-222−2−222−2−22000000002i−2i−i2i2i2−i2i2−i2−i2i2000000000000
χ6144444444-4-4-4-4-4-4-4-40000000000004400000000000000000000000000000000000000000000000000
χ624444-4-4-4-4-40-404040000000000000002222−22−220000−22−22222200000000000000000000000000000000000000
χ634444-4-4-4-4-40-40404000000000000000−22−22222200002222−22−2200000000000000000000000000000000000000
χ6444-4-44-4-44000000002i22i2−2i2−2i2−2i2−2i22i22i200000022−22−2222000000002i2i−2i−2i−2i−2i2i2i000000000000000000000000000000
χ6544-4-44-4-44000000002i22i2−2i2−2i2−2i2−2i22i22i2000000−222222−2200000000−2i−2i2i2i2i2i−2i−2i000000000000000000000000000000
χ6644-4-44-4-4400000000−2i2−2i22i22i22i22i2−2i2−2i200000022−22−222200000000−2i−2i2i2i2i2i−2i−2i000000000000000000000000000000
χ6744-4-44-4-4400000000−2i2−2i22i22i22i22i2−2i2−2i2000000−222222−22000000002i2i−2i−2i−2i−2i2i2i000000000000000000000000000000
χ6844-4-4-444-4040-40-4042i22i2−2i2−2i22i22i2−2i2−2i20000000000−2i2−2i22i22i2000000000000000000000000000000000000000000
χ6944-4-4-444-4040-40-404−2i2−2i22i22i2−2i2−2i22i22i200000000002i22i2−2i2−2i2000000000000000000000000000000000000000000
χ704-44-44-44-440-40-40404i−4i4i−4i−4i4i−4i4i00000000000000000000000000000000000000000000000000000000
χ714-44-44-44-440-40-4040−4i4i−4i4i4i−4i4i−4i00000000000000000000000000000000000000000000000000000000
χ724-44-44-44-4-404040-40000000000000000000000000002i2−2i22i2−2i2−2i22i2−2i22i2000000000000000000000000000000
χ734-44-44-44-4-404040-4000000000000000000000000000−2i22i2−2i22i22i2−2i22i2−2i2000000000000000000000000000000
χ744-44-4-44-44-4-444-4-444000000000000-4400000000000000000000000000000000000000000000000000
χ754-4-4444-4-404040-40-422−22−222222−22−22220000000000−222222−22000000000000000000000000000000000000000000
χ764-4-4444-4-404040-40-4−222222−22−222222−22000000000022−22−2222000000000000000000000000000000000000000000
χ774-4-44-4-4440000000022−22−2222−222222−220000000000000022−22−22222-2-22-222-2000000000000000000000000000000
χ784-4-44-4-4440000000022−22−2222−222222−2200000000000000−222222−22-222-22-2-22000000000000000000000000000000
χ794-4-44-4-44400000000−222222−2222−22−22220000000000000022−22−2222-222-22-2-22000000000000000000000000000000
χ804-4-44-4-44400000000−222222−2222−22−222200000000000000−222222−222-2-22-222-2000000000000000000000000000000

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