Finite Group Databasebeta

← Group #313658

Character table — Group #313658

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80
size11111111222222222222222244444444444444444444444444888888888888888888161616161616161616163232
order12222222444444448888888844444488888888888888888888444444444488888888244444888844
χ111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111111111111111-1-11111-1-11111111111-1-1-1-1-1-1-1-1-1-1-1-1
χ3111111111111111111111111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-111-1-11111-1-1-1-1-1-11111111111-1-1-1-1-1-1
χ4111111111111111111111111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1111111
χ51111111111111111111111111-1-1-1-111111111111111111111111-1-1-1-111-1-1-1-1-1-1-1-1-1-111-1-1-1-11111-1-1
χ61111111111111111111111111-1-1-1-1111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-111
χ71111111111111111111111111-1-1-1-11-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-11111-1-111111111-1-1-1-111-1-1-1-1-1-1-1-111
χ81111111111111111111111111-1-1-1-11-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-1111111-1-1-1-1-1-111111111-1-1
χ91111111111111111-1-1-1-1-1-1-1-11111111111-1-1-1-11111-1-1-1-1-1-1-1-1111111-1-111-1-1-1-1-1-1-1-1-11-1-111-1-1111-1
χ101111111111111111-1-1-1-1-1-1-1-11111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-11-111-1-111-1-1-11
χ111111111111111111-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-11111111111-1-111-1-1-1-11111-1-1-1-1-11-1-11111-1-1-11
χ121111111111111111-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-11111-1-11111-1-1-1-11-111-1-1-1-1111-1
χ131111111111111111-1-1-1-1-1-1-1-11-1-1-1-111111-1-1-1-11111-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-111111111-1111-1-1-1-111-11
χ141111111111111111-1-1-1-1-1-1-1-11-1-1-1-111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1111111111-1-1-11111-1-11-1
χ151111111111111111-1-1-1-1-1-1-1-11-1-1-1-11-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-111-1-1-1-11111-1111-1-111-1-11-1
χ161111111111111111-1-1-1-1-1-1-1-11-1-1-1-11-1-1-1-1-1-1-1-1-1-1-1-111111111-1-111-1-11111-1-1-1-111111-1-1-111-1-111-11
χ17222222222-22-22-22-200000000-22222-222220000-2-2-2-2000000000022-2-200-2-200000000000000000000
χ18222222222-22-22-22-200000000-22222-2-2-2-2-2000022220000000000-2-2-2-2002200000000000000000000
χ19222222222-22-22-22-200000000-2-2-2-2-2-222220000-2-2-2-20000000000-2-222002200000000000000000000
χ20222222222-22-22-22-200000000-2-2-2-2-2-2-2-2-2-2000022220000000000222200-2-200000000000000000000
χ2122222222-22-22-22-2222222222-20000-20000-2-2-2-2000000000000220000220000000000-2-20000000000
χ2222222222-22-22-22-2222222222-20000-20000-2-2-2-2000000000000-2-20000-2-20000000000220000000000
χ2322222222-22-22-22-22-2-2-2-2-2-2-2-2-20000-200002222000000000000220000-2-200000000002-20000000000
χ2422222222-22-22-22-22-2-2-2-2-2-2-2-2-20000-200002222000000000000-2-20000220000000000-220000000000
χ25222-22-2-2-2-20-2020202222−2−2−2−202i2i−2i−2i0000022−2−222-2-22222−2−2−2−2000000002i−2ii2i2−i2−i2i2i2−i2−i2000000000000
χ26222-22-2-2-2-20-2020202222−2−2−2−202i2i−2i−2i0000022−2−2-2-222−2−2−2−2222200000000−2i2i−i2−i2i2i2i2i2−i2−i2000000000000
χ27222-22-2-2-2-20-2020202222−2−2−2−20−2i−2i2i2i0000022−2−222-2-22222−2−2−2−200000000−2i2i−i2−i2i2i2−i2−i2i2i2000000000000
χ28222-22-2-2-2-20-2020202222−2−2−2−20−2i−2i2i2i0000022−2−2-2-222−2−2−2−22222000000002i−2ii2i2−i2−i2−i2−i2i2i2000000000000
χ29222-22-2-2-2-20-202020−2−2−2−2222202i2i−2i−2i00000−2−22222-2-2−2−2−2−22222000000002i−2i−i2−i2i2i2−i2−i2i2i2000000000000
χ30222-22-2-2-2-20-202020−2−2−2−2222202i2i−2i−2i00000−2−222-2-2222222−2−2−2−200000000−2i2ii2i2−i2−i2−i2−i2i2i2000000000000
χ31222-22-2-2-2-20-202020−2−2−2−222220−2i−2i2i2i00000−2−22222-2-2−2−2−2−2222200000000−2i2ii2i2−i2−i2i2i2−i2−i2000000000000
χ32222-22-2-2-2-20-202020−2−2−2−222220−2i−2i2i2i00000−2−222-2-2222222−2−2−2−2000000002i−2i−i2−i2i2i2i2i2−i2−i2000000000000
χ332-22-2-222-20-202020-222-2-222-2-2000000i2i2−i2−i20000i2−i2i2−i2i2i2−i2−i2i2i2−i2−i22i−2i00002i−2i00000000000000002−22−200
χ342-22-2-222-20-202020-222-2-222-2-2000000i2i2−i2−i20000i2−i2i2−i2i2i2−i2−i2i2i2−i2−i2−2i2i0000−2i2i0000000000000000−22−2200
χ352-22-2-222-20-202020-222-2-222-2-2000000−i2−i2i2i20000−i2i2−i2i2−i2−i2i2i2−i2−i2i2i22i−2i00002i−2i0000000000000000−22−2200
χ362-22-2-222-20-202020-222-2-222-2-2000000−i2−i2i2i20000−i2i2−i2i2−i2−i2i2i2−i2−i2i2i2−2i2i0000−2i2i00000000000000002−22−200
χ372-22-2-222-20-202020-2-2-222-2-222000000i2i2−i2−i20000i2−i2i2−i2−i2−i2i2i2−i2−i2i2i22i−2i0000−2i2i0000000000000000−222−200
χ382-22-2-222-20-202020-2-2-222-2-222000000i2i2−i2−i20000i2−i2i2−i2−i2−i2i2i2−i2−i2i2i2−2i2i00002i−2i00000000000000002−2−2200
χ392-22-2-222-20-202020-2-2-222-2-222000000−i2−i2i2i20000−i2i2−i2i2i2i2−i2−i2i2i2−i2−i22i−2i0000−2i2i00000000000000002−2−2200
χ402-22-2-222-20-202020-2-2-222-2-222000000−i2−i2i2i20000−i2i2−i2i2i2i2−i2−i2i2i2−i2−i2−2i2i00002i−2i0000000000000000−222−200
χ412-2-222-22-2-202020-20i2−i2i2−i2i2−i2i2−i202i−2i2i−2i02-22-2i2−i2i2−i20000i2−i2i2−i2i2−i2i2−i2002i−2i0000002−22−22−22−2000000000000
χ422-2-222-22-2-202020-20i2−i2i2−i2i2−i2i2−i202i−2i2i−2i0-22-22i2−i2i2−i20000−i2i2−i2i2−i2i2−i2i200−2i2i000000−22−222−22−2000000000000
χ432-2-222-22-2-202020-20i2−i2i2−i2i2−i2i2−i20−2i2i−2i2i02-22-2i2−i2i2−i20000i2−i2i2−i2i2−i2i2−i200−2i2i000000−22−22−22−22000000000000
χ442-2-222-22-2-202020-20i2−i2i2−i2i2−i2i2−i20−2i2i−2i2i0-22-22i2−i2i2−i20000−i2i2−i2i2−i2i2−i2i2002i−2i0000002−22−2−22−22000000000000
χ452-2-222-22-2-202020-20−i2i2−i2i2−i2i2−i2i202i−2i2i−2i02-22-2−i2i2−i2i20000−i2i2−i2i2−i2i2−i2i2002i−2i000000−22−22−22−22000000000000
χ462-2-222-22-2-202020-20−i2i2−i2i2−i2i2−i2i202i−2i2i−2i0-22-22−i2i2−i2i20000i2−i2i2−i2i2−i2i2−i200−2i2i0000002−22−2−22−22000000000000
χ472-2-222-22-2-202020-20−i2i2−i2i2−i2i2−i2i20−2i2i−2i2i02-22-2−i2i2−i2i20000−i2i2−i2i2−i2i2−i2i200−2i2i0000002−22−22−22−2000000000000
χ482-2-222-22-2-202020-20−i2i2−i2i2−i2i2−i2i20−2i2i−2i2i0-22-22−i2i2−i2i20000i2−i2i2−i2i2−i2i2−i2002i−2i000000−22−222−22−2000000000000
χ492-2-2-222-2222-2-222-2-22i−2i2i−2i−2i2i−2i2i-22-2-22200002i−2i−2i2i00000000000000002-200000000−2i2i2i−2i000000000000
χ502-2-2-222-2222-2-222-2-22i−2i2i−2i−2i2i−2i2i-2-222-2200002i−2i−2i2i0000000000000000-22000000002i−2i−2i2i000000000000
χ512-2-2-222-2222-2-222-2-2−2i2i−2i2i2i−2i2i−2i-22-2-2220000−2i2i2i−2i00000000000000002-2000000002i−2i−2i2i000000000000
χ522-2-2-222-2222-2-222-2-2−2i2i−2i2i2i−2i2i−2i-2-222-220000−2i2i2i−2i0000000000000000-2200000000−2i2i2i−2i000000000000
χ532-2-2-222-222-2-222-2-220000000022-2-22-20000000000002i−2i2i−2i−2i2i−2i2i0000-220000−2i2i2i−2i0000000000000000
χ542-2-2-222-222-2-222-2-220000000022-2-22-2000000000000−2i2i−2i2i2i−2i2i−2i0000-2200002i−2i−2i2i0000000000000000
χ552-2-2-222-222-2-222-2-22000000002-222-2-20000000000002i−2i2i−2i−2i2i−2i2i00002-200002i−2i−2i2i0000000000000000
χ562-2-2-222-222-2-222-2-22000000002-222-2-2000000000000−2i2i−2i2i2i−2i2i−2i00002-20000−2i2i2i−2i0000000000000000
χ572-2-2-222-22-222-2-222-22i−2i2i−2i−2i2i−2i2i20000-20000−2i2i2i−2i000000000000000000000000000000002-22i−2i000000
χ582-2-2-222-22-222-2-222-22i−2i2i−2i−2i2i−2i2i20000-20000−2i2i2i−2i00000000000000000000000000000000-22−2i2i000000
χ592-2-2-222-22-222-2-222-2−2i2i−2i2i2i−2i2i−2i20000-200002i−2i−2i2i000000000000000000000000000000002-2−2i2i000000
χ602-2-2-222-22-222-2-222-2−2i2i−2i2i2i−2i2i−2i20000-200002i−2i−2i2i00000000000000000000000000000000-222i−2i000000
χ6144444444-4-4-4-4-4-4-4-40000000040000400000000000000000000000000000000000000000000000000
χ62444-44-4-4-44040-40-4022222222−22−22−22−220000000000−22−222222000000000000000000000000000000000000000000
χ63444-44-4-4-44040-40-40−22−22−22−222222222200000000002222−22−22000000000000000000000000000000000000000000
χ6444-44-44-4-404040-40-40000000000000000000000000022−22−2222−222222−22000000000000000000000000000000
χ6544-44-44-4-404040-40-400000000000000000000000000−222222−2222−22−2222000000000000000000000000000000
χ6644-44-44-4-40-40-404044i−4i−4i4i−4i4i4i−4i00000000000000000000000000000000000000000000000000000000
χ6744-44-44-4-40-40-40404−4i4i4i−4i4i−4i−4i4i00000000000000000000000000000000000000000000000000000000
χ6844-4-4-4-444000000002i2−2i2−2i22i22i2−2i2−2i22i20000002i2−2i2−2i22i200000000-222-2-222-2000000000000000000000000000000
χ6944-4-4-4-444000000002i2−2i2−2i22i22i2−2i2−2i22i2000000−2i22i22i2−2i2000000002-2-222-2-22000000000000000000000000000000
χ7044-4-4-4-44400000000−2i22i22i2−2i2−2i22i22i2−2i20000002i2−2i2−2i22i2000000002-2-222-2-22000000000000000000000000000000
χ7144-4-4-4-44400000000−2i22i22i2−2i2−2i22i22i2−2i2000000−2i22i22i2−2i200000000-222-2-222-2000000000000000000000000000000
χ724-444-4-4-44000000002222−22−22−22−222222000000000000002i2−2i2−2i22i22i2i−2i−2i−2i−2i2i2i000000000000000000000000000000
χ734-444-4-4-44000000002222−22−22−22−22222200000000000000−2i22i22i2−2i2−2i−2i2i2i2i2i−2i−2i000000000000000000000000000000
χ744-444-4-4-4400000000−22−2222222222−22−22000000000000002i2−2i2−2i22i2−2i−2i2i2i2i2i−2i−2i000000000000000000000000000000
χ754-444-4-4-4400000000−22−2222222222−22−2200000000000000−2i22i22i2−2i22i2i−2i−2i−2i−2i2i2i000000000000000000000000000000
χ764-44-4-444-4040-40-404000000000000002i22i2−2i2−2i20000−2i22i2−2i22i200000000000000000000000000000000000000
χ774-44-4-444-4040-40-40400000000000000−2i2−2i22i22i200002i2−2i22i2−2i200000000000000000000000000000000000000
χ784-4-444-44-440-40-40402i2−2i22i2−2i22i2−2i22i2−2i20000000000−2i22i2−2i22i2000000000000000000000000000000000000000000
χ794-4-444-44-440-40-4040−2i22i2−2i22i2−2i22i2−2i22i200000000002i2−2i22i2−2i2000000000000000000000000000000000000000000
χ804-4-4-444-44-4-444-4-44400000000-40000400000000000000000000000000000000000000000000000000

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