Finite Group Databasebeta

← Group #313669

Character table — Group #313669

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80
size11111111222222222222222244444444444444444444444444888888888888888888161616161616161616163232
order12222222444444448888888844444488888888888888888888444444444488888888222444888844
χ111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111111111111111111111-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1
χ3111111111111111111111111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-11111-1-1-1-11111111111-1-1-1-1-1-1
χ4111111111111111111111111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1111111
χ51111111111111111111111111-1-1-1-1111111111111111111111-1-1-1-1-1-11111-1-1-1-1-1-1-1-11-1-11-1-11111-1-1
χ61111111111111111111111111-1-1-1-1111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-111-1-1-1-111
χ71111111111111111111111111-1-1-1-11-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-111-1-11111111111-1-1-1-11-1-11-1-1-1-1-1-111
χ81111111111111111111111111-1-1-1-11-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-111-1-111-1-1-1-11111-1-1-1-1-111-1111111-1-1
χ91111111111111111-1-1-1-1-1-1-1-11111111111-1-1-1-11111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1111-1-1111-1
χ101111111111111111-1-1-1-1-1-1-1-11111111111-1-1-1-11111-1-1-1-1-1-1-1-1111111-1-111-1-1-1-1-1-1-1-1111-1-1-111-1-1-11
χ111111111111111111-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-111-1-111-1-11111-1-1-1-1-1-1-111111-1-1-11
χ121111111111111111-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-111-1-1-1-1111111-1-1-1-1111-1-1-1-1-1111-1
χ131111111111111111-1-1-1-1-1-1-1-11-1-1-1-111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-111111111-1111-1-1-1-111-11
χ141111111111111111-1-1-1-1-1-1-1-11-1-1-1-111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111111-1-1-11111-1-11-1
χ151111111111111111-1-1-1-1-1-1-1-11-1-1-1-11-1-1-1-1-1-1-1-1-1-1-1-11111111111-1-11111-1-1-1-1-1-11111-1111-1-111-1-11-1
χ161111111111111111-1-1-1-1-1-1-1-11-1-1-1-11-1-1-1-1-1-1-1-1-1-1-1-11111111111-1-111-1-111-1-1-1-111111-1-1-111-1-111-11
χ17222222222-22-22-22-200000000-22222-222220000-2-2-2-200000000-2-2-2-222000000000000000000000000
χ18222222222-22-22-22-200000000-22222-2-2-2-2-2000022220000000022-2-2-2-2000000000000000000000000
χ19222222222-22-22-22-200000000-2-2-2-2-2-222220000-2-2-2-2000000002222-2-2000000000000000000000000
χ20222222222-22-22-22-200000000-2-2-2-2-2-2-2-2-2-20000222200000000-2-22222000000000000000000000000
χ2122222222-22-22-22-2222222222-20000-20000-2-2-2-2000000000000000000222200000000-200-200000000
χ2222222222-22-22-22-2222222222-20000-20000-2-2-2-2000000000000000000-2-2-2-200000000200200000000
χ2322222222-22-22-22-22-2-2-2-2-2-2-2-2-20000-20000222200000000000000000022-2-200000000200-200000000
χ2422222222-22-22-22-22-2-2-2-2-2-2-2-2-20000-200002222000000000000000000-2-22200000000-200200000000
χ2522-22-22-2-220-20-2020i2i2i2i2−i2−i2−i2−i2022-2-202i2i−2i−2ii2i2−i2−i200002222−2−2−2−200002i−2i000022−2−2i2i2−i2−i2000000000000
χ2622-22-22-2-220-20-2020i2i2i2i2−i2−i2−i2−i2022-2-20−2i−2i2i2ii2i2−i2−i20000−2−2−2−222220000−2i2i0000−2−222i2i2−i2−i2000000000000
χ2722-22-22-2-220-20-2020i2i2i2i2−i2−i2−i2−i20-2-22202i2i−2i−2ii2i2−i2−i200002222−2−2−2−20000−2i2i0000−2−222−i2−i2i2i2000000000000
χ2822-22-22-2-220-20-2020i2i2i2i2−i2−i2−i2−i20-2-2220−2i−2i2i2ii2i2−i2−i20000−2−2−2−2222200002i−2i000022−2−2−i2−i2i2i2000000000000
χ2922-22-22-2-220-20-2020−i2−i2−i2−i2i2i2i2i2022-2-202i2i−2i−2i−i2−i2i2i20000−2−2−2−2222200002i−2i0000−2−222−i2−i2i2i2000000000000
χ3022-22-22-2-220-20-2020−i2−i2−i2−i2i2i2i2i2022-2-20−2i−2i2i2i−i2−i2i2i200002222−2−2−2−20000−2i2i000022−2−2−i2−i2i2i2000000000000
χ3122-22-22-2-220-20-2020−i2−i2−i2−i2i2i2i2i20-2-22202i2i−2i−2i−i2−i2i2i20000−2−2−2−222220000−2i2i000022−2−2i2i2−i2−i2000000000000
χ3222-22-22-2-220-20-2020−i2−i2−i2−i2i2i2i2i20-2-2220−2i−2i2i2i−i2−i2i2i200002222−2−2−2−200002i−2i0000−2−222i2i2−i2−i2000000000000
χ332-22-2-222-222-2-222-2-22i2i−2i−2i2i2i−2i−2i-22-22-2200002i−2i2i−2i000000000000002-200000000002i−2i2i−2i000000000000
χ342-22-2-222-222-2-222-2-22i2i−2i−2i2i2i−2i−2i-2-22-22200002i−2i2i−2i00000000000000-220000000000−2i2i−2i2i000000000000
χ352-22-2-222-222-2-222-2-2−2i−2i2i2i−2i−2i2i2i-22-22-220000−2i2i−2i2i000000000000002-20000000000−2i2i−2i2i000000000000
χ362-22-2-222-222-2-222-2-2−2i−2i2i2i−2i−2i2i2i-2-22-2220000−2i2i−2i2i00000000000000-2200000000002i−2i2i−2i000000000000
χ372-22-2-222-22-2-222-2-220000000022-22-2-20000000000002i2i−2i−2i2i2i−2i−2i00-220000002i−2i2i−2i0000000000000000
χ382-22-2-222-22-2-222-2-220000000022-22-2-2000000000000−2i−2i2i2i−2i−2i2i2i00-22000000−2i2i−2i2i0000000000000000
χ392-22-2-222-22-2-222-2-22000000002-22-22-20000000000002i2i−2i−2i2i2i−2i−2i002-2000000−2i2i−2i2i0000000000000000
χ402-22-2-222-22-2-222-2-22000000002-22-22-2000000000000−2i−2i2i2i−2i−2i2i2i002-20000002i−2i2i−2i0000000000000000
χ412-22-2-222-2-222-2-222-22i2i−2i−2i2i2i−2i−2i20000-20000−2i2i−2i2i00000000000000000000000000000002-202i−2i000000
χ422-22-2-222-2-222-2-222-22i2i−2i−2i2i2i−2i−2i20000-20000−2i2i−2i2i0000000000000000000000000000000-220−2i2i000000
χ432-22-2-222-2-222-2-222-2−2i−2i2i2i−2i−2i2i2i20000-200002i−2i2i−2i00000000000000000000000000000002-20−2i2i000000
χ442-22-2-222-2-222-2-222-2−2i−2i2i2i−2i−2i2i2i20000-200002i−2i2i−2i0000000000000000000000000000000-2202i−2i000000
χ452-2-22-2-22202020-20-22-22-22-22-20000002−22−2000022−2−22−22−22−22−20000002i−2i2i−2i00000000000000i2−i2i2−i200
χ462-2-22-2-22202020-20-22-22-22-22-20000002−22−2000022−2−22−22−22−22−2000000−2i2i−2i2i00000000000000−i2i2−i2i200
χ472-2-22-2-22202020-20-22-22-22-22-2000000−22−220000−2−222−22−22−22−220000002i−2i2i−2i00000000000000−i2i2−i2i200
χ482-2-22-2-22202020-20-22-22-22-22-2000000−22−220000−2−222−22−22−22−22000000−2i2i−2i2i00000000000000i2−i2i2−i200
χ492-2-22-2-22202020-20-2-22-22-22-220000002−22−2000022−2−2−22−22−22−220000002i−2i−2i2i00000000000000−i2i2i2−i200
χ502-2-22-2-22202020-20-2-22-22-22-220000002−22−2000022−2−2−22−22−22−22000000−2i2i2i−2i00000000000000i2−i2−i2i200
χ512-2-22-2-22202020-20-2-22-22-22-22000000−22−220000−2−2222−22−22−22−20000002i−2i−2i2i00000000000000i2−i2−i2i200
χ522-2-22-2-22202020-20-2-22-22-22-22000000−22−220000−2−2222−22−22−22−2000000−2i2i2i−2i00000000000000−i2i2i2−i200
χ532-2-2-222-222020-20-2022−2−2−2−22202-2-22000002−2−222i−2i2i−2ii2i2−i2−i2−i2−i2i2i22i−2i00000000i2−i2−i2i22−2−22000000000000
χ542-2-2-222-222020-20-2022−2−2−2−22202-2-22000002−2−22−2i2i−2i2i−i2−i2i2i2i2i2−i2−i2−2i2i00000000−i2i2i2−i22−2−22000000000000
χ552-2-2-222-222020-20-2022−2−2−2−2220-222-2000002−2−222i−2i2i−2ii2i2−i2−i2−i2−i2i2i2−2i2i00000000−i2i2i2−i2−222−2000000000000
χ562-2-2-222-222020-20-2022−2−2−2−2220-222-2000002−2−22−2i2i−2i2i−i2−i2i2i2i2i2−i2−i22i−2i00000000i2−i2−i2i2−222−2000000000000
χ572-2-2-222-222020-20-20−2−22222−2−202-2-2200000−222−22i−2i2i−2i−i2−i2i2i2i2i2−i2−i22i−2i00000000−i2i2i2−i2−222−2000000000000
χ582-2-2-222-222020-20-20−2−22222−2−202-2-2200000−222−2−2i2i−2i2ii2i2−i2−i2−i2−i2i2i2−2i2i00000000i2−i2−i2i2−222−2000000000000
χ592-2-2-222-222020-20-20−2−22222−2−20-222-200000−222−22i−2i2i−2i−i2−i2i2i2i2i2−i2−i2−2i2i00000000i2−i2−i2i22−2−22000000000000
χ602-2-2-222-222020-20-20−2−22222−2−20-222-200000−222−2−2i2i−2i2ii2i2−i2−i2−i2−i2i2i22i−2i00000000−i2i2i2−i22−2−22000000000000
χ6144444444-4-4-4-4-4-4-4-40000000040000400000000000000000000000000000000000000000000000000
χ62444-4-4-4-440000000022−22−2222−222222−22000000000000002i2−2i2−2i22i22i−2i−2i2i−2i2i2i−2i000000000000000000000000000000
χ63444-4-4-4-440000000022−22−2222−222222−2200000000000000−2i22i22i2−2i2−2i2i2i−2i2i−2i−2i2i000000000000000000000000000000
χ64444-4-4-4-4400000000−222222−2222−22−2222000000000000002i2−2i2−2i22i2−2i2i2i−2i2i−2i−2i2i000000000000000000000000000000
χ65444-4-4-4-4400000000−222222−2222−22−222200000000000000−2i22i22i2−2i22i−2i−2i2i−2i2i2i−2i000000000000000000000000000000
χ6644-44-44-4-4-404040-402i22i22i22i2−2i2−2i2−2i2−2i20000000000−2i2−2i22i22i2000000000000000000000000000000000000000000
χ6744-44-44-4-4-404040-40−2i2−2i2−2i2−2i22i22i22i22i200000000002i22i2−2i2−2i2000000000000000000000000000000000000000000
χ6844-4-44-44-4040-40-4044i−4i−4i4i4i−4i−4i4i00000000000000000000000000000000000000000000000000000000
χ6944-4-44-44-4040-40-404−4i4i4i−4i−4i4i4i−4i00000000000000000000000000000000000000000000000000000000
χ7044-4-44-44-40-404040-4000000000000000000000000002i2−2i2−2i22i22i2−2i2−2i22i2000000000000000000000000000000
χ7144-4-44-44-40-404040-400000000000000000000000000−2i22i22i2−2i2−2i22i22i2−2i2000000000000000000000000000000
χ724-4444-4-4-4000000002i2−2i22i2−2i2−2i22i2−2i22i20000002i2−2i2−2i22i2000000002-22-2-22-22000000000000000000000000000000
χ734-4444-4-4-4000000002i2−2i22i2−2i2−2i22i2−2i22i2000000−2i22i22i2−2i200000000-22-222-22-2000000000000000000000000000000
χ744-4444-4-4-400000000−2i22i2−2i22i22i2−2i22i2−2i20000002i2−2i2−2i22i200000000-22-222-22-2000000000000000000000000000000
χ754-4444-4-4-400000000−2i22i2−2i22i22i2−2i22i2−2i2000000−2i22i22i2−2i2000000002-22-2-22-22000000000000000000000000000000
χ764-44-4-444-4-4-444-4-44400000000-40000400000000000000000000000000000000000000000000000000
χ774-4-44-4-4440-40-404040000000000000022−2222−220000−22−22222200000000000000000000000000000000000000
χ784-4-44-4-4440-40-4040400000000000000−2222−222200002222−22−2200000000000000000000000000000000000000
χ794-4-4-444-44-40-4040402222−22−22−22−2222220000000000−222222−22000000000000000000000000000000000000000000
χ804-4-4-444-44-40-404040−22−2222222222−22−22000000000022−22−2222000000000000000000000000000000000000000000

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