Finite Group Databasebeta

← Group #312671

Character table — Group #312671

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80
size11111111222222222222222244444444444444444444444444888888888888888888161616161616161616163232
order12222222444444448888888844444488888888888888888888444444444488888888224444888844
χ111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111111111111111-1-111-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-1
χ3111111111111111111111111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-111-1-11111-1-11111-1-1-1-1111111-1-1-1-1-1-1
χ4111111111111111111111111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-11111-1-1-1-1-1-1-1-1-1-1111111
χ5111111111111111111111111-1-1-1-1111111111111111111111111-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-11111-1-1
χ6111111111111111111111111-1-1-1-11111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-111-1-1-1-111
χ7111111111111111111111111-1-1-1-111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1111111-1-111-1-1-1-11111-1-111-1-1-1-1-1-111
χ8111111111111111111111111-1-1-1-111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-111-1-1-1-1111111-1-1111111-1-1
χ91111111111111111-1-1-1-1-1-1-1-11111111111-1-1-1-11111-1-1-1-1-1-1-1-11111-1-11111-1-1-1-1-1-1-1-1111-1-1-1-1-111-11
χ101111111111111111-1-1-1-1-1-1-1-11111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-111111-1-11-1
χ111111111111111111-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-11111111111-1-1-1-111-1-1-1-1-1-11111111-1-1-111-1-11-1
χ121111111111111111-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-11111-1-1-1-1-1-11111-1-1-1111-1-111-11
χ131111111111111111-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-1-11111-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-111111111-1-11-111-1-1111-1
χ141111111111111111-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-11111111111-11-1-111-1-1-11
χ151111111111111111-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-1111111-1-1-1-1-1-11-11111-1-1-11
χ161111111111111111-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-11111-1-1111111-1-1-1-111-11-1-1-1-1111-1
χ17222222222-22-22-22-2222222220000-2-20000-2-2-2-200000000000022002200000000000000-2-200000000
χ18222222222-22-22-22-2222222220000-2-20000-2-2-2-2000000000000-2-200-2-2000000000000002200000000
χ19222222222-22-22-22-2-2-2-2-2-2-2-2-20000-2-2000022220000000000002200-2-200000000000000-2200000000
χ20222222222-22-22-22-2-2-2-2-2-2-2-2-20000-2-200002222000000000000-2-20022000000000000002-200000000
χ2122222222-22-22-22-22000000002222-2-222220000-2-2-2-200000000002200-2-2-2-200000000000000000000
χ2222222222-22-22-22-22000000002222-2-2-2-2-2-2000022220000000000-2-200-2-22200000000000000000000
χ2322222222-22-22-22-2200000000-2-2-2-2-2-222220000-2-2-2-20000000000-2-200222200000000000000000000
χ2422222222-22-22-22-2200000000-2-2-2-2-2-2-2-2-2-2000022220000000000220022-2-200000000000000000000
χ2522-22-2-2-22020-20-202i2i2i2i2−i2−i2−i2−i222-2-2000000i2i2−i2−i222-2-2i2i2i2i2−i2−i2−i2−i2000000002-2i2i2−i2−i2i2i2−i2−i2000000000000
χ2622-22-2-2-22020-20-202i2i2i2i2−i2−i2−i2−i222-2-2000000i2i2−i2−i2-2-222−i2−i2−i2−i2i2i2i2i200000000-22i2i2−i2−i2−i2−i2i2i2000000000000
χ2722-22-2-2-22020-20-202i2i2i2i2−i2−i2−i2−i2-2-222000000i2i2−i2−i222-2-2i2i2i2i2−i2−i2−i2−i200000000-22−i2−i2i2i2−i2−i2i2i2000000000000
χ2822-22-2-2-22020-20-202i2i2i2i2−i2−i2−i2−i2-2-222000000i2i2−i2−i2-2-222−i2−i2−i2−i2i2i2i2i2000000002-2−i2−i2i2i2i2i2−i2−i2000000000000
χ2922-22-2-2-22020-20-202−i2−i2−i2−i2i2i2i2i222-2-2000000−i2−i2i2i222-2-2−i2−i2−i2−i2i2i2i2i2000000002-2−i2−i2i2i2−i2−i2i2i2000000000000
χ3022-22-2-2-22020-20-202−i2−i2−i2−i2i2i2i2i222-2-2000000−i2−i2i2i2-2-222i2i2i2i2−i2−i2−i2−i200000000-22−i2−i2i2i2i2i2−i2−i2000000000000
χ3122-22-2-2-22020-20-202−i2−i2−i2−i2i2i2i2i2-2-222000000−i2−i2i2i222-2-2−i2−i2−i2−i2i2i2i2i200000000-22i2i2−i2−i2i2i2−i2−i2000000000000
χ3222-22-2-2-22020-20-202−i2−i2−i2−i2i2i2i2i2-2-222000000−i2−i2i2i2-2-222i2i2i2i2−i2−i2−i2−i2000000002-2i2i2−i2−i2−i2−i2i2i2000000000000
χ332-222-2-22-220-20-20202i2i−2i−2i2i2i−2i−2i000000i2i2−i2−i20000i2−i2i2−i222−2−222−2−22-2002i−2i0000000000000000002−2i2−i200
χ342-222-2-22-220-20-20202i2i−2i−2i2i2i−2i−2i000000i2i2−i2−i20000i2−i2i2−i222−2−222−2−2-2200−2i2i000000000000000000−22−i2i200
χ352-222-2-22-220-20-20202i2i−2i−2i2i2i−2i−2i000000−i2−i2i2i20000−i2i2−i2i2−2−222−2−2222-2002i−2i000000000000000000−22−i2i200
χ362-222-2-22-220-20-20202i2i−2i−2i2i2i−2i−2i000000−i2−i2i2i20000−i2i2−i2i2−2−222−2−222-2200−2i2i0000000000000000002−2i2−i200
χ372-222-2-22-220-20-2020−2i−2i2i2i−2i−2i2i2i000000i2i2−i2−i20000i2−i2i2−i2−2−222−2−2222-200−2i2i000000000000000000−22i2−i200
χ382-222-2-22-220-20-2020−2i−2i2i2i−2i−2i2i2i000000i2i2−i2−i20000i2−i2i2−i2−2−222−2−222-22002i−2i0000000000000000002−2−i2i200
χ392-222-2-22-220-20-2020−2i−2i2i2i−2i−2i2i2i000000−i2−i2i2i20000−i2i2−i2i222−2−222−2−22-200−2i2i0000000000000000002−2−i2i200
χ402-222-2-22-220-20-2020−2i−2i2i2i−2i−2i2i2i000000−i2−i2i2i20000−i2i2−i2i222−2−222−2−2-22002i−2i000000000000000000−22i2−i200
χ412-22-2-22-2222-2-222-2-22i−2i2i−2i2i−2i2i−2i2i−2i2i−2i-2200002i−2i2i−2i0000000000000000002i−2i002-22-20000000000000000
χ422-22-2-22-2222-2-222-2-22i−2i2i−2i2i−2i2i−2i−2i2i−2i2i-2200002i−2i2i−2i000000000000000000−2i2i00-22-220000000000000000
χ432-22-2-22-2222-2-222-2-2−2i2i−2i2i−2i2i−2i2i2i−2i2i−2i-220000−2i2i−2i2i0000000000000000002i−2i00-22-220000000000000000
χ442-22-2-22-2222-2-222-2-2−2i2i−2i2i−2i2i−2i2i−2i2i−2i2i-220000−2i2i−2i2i000000000000000000−2i2i002-22-20000000000000000
χ452-22-2-22-222-2-222-2-222i−2i2i−2i2i−2i2i−2i00002-20000−2i2i−2i2i0000000000000000000000000000002-2002i−2i000000
χ462-22-2-22-222-2-222-2-222i−2i2i−2i2i−2i2i−2i00002-20000−2i2i−2i2i000000000000000000000000000000-2200−2i2i000000
χ472-22-2-22-222-2-222-2-22−2i2i−2i2i−2i2i−2i2i00002-200002i−2i2i−2i0000000000000000000000000000002-200−2i2i000000
χ482-22-2-22-222-2-222-2-22−2i2i−2i2i−2i2i−2i2i00002-200002i−2i2i−2i000000000000000000000000000000-22002i−2i000000
χ492-22-2-22-22-222-2-222-2000000002i−2i2i−2i2-20000000000002i−2i2i−2i2i−2i2i−2i000000−2i2i0000002-22-2000000000000
χ502-22-2-22-22-222-2-222-2000000002i−2i2i−2i2-2000000000000−2i2i−2i2i−2i2i−2i2i000000−2i2i000000-22-22000000000000
χ512-22-2-22-22-222-2-222-200000000−2i2i−2i2i2-20000000000002i−2i2i−2i2i−2i2i−2i0000002i−2i000000-22-22000000000000
χ522-22-2-22-22-222-2-222-200000000−2i2i−2i2i2-2000000000000−2i2i−2i2i−2i2i−2i2i0000002i−2i0000002-22-2000000000000
χ532-2-2-22-22202020-20-22−22−2−22−222i−2i−2i2i002-22-22−2−2200002−22−2−22−22002i−2i000000−i2i2i2−i2−i2i2i2−i2000000000000
χ542-2-2-22-22202020-20-22−22−2−22−222i−2i−2i2i00-22-222−2−220000−22−222−22−200−2i2i000000−i2i2i2−i2i2−i2−i2i2000000000000
χ552-2-2-22-22202020-20-22−22−2−22−22−2i2i2i−2i002-22-22−2−2200002−22−2−22−2200−2i2i000000i2−i2−i2i2i2−i2−i2i2000000000000
χ562-2-2-22-22202020-20-22−22−2−22−22−2i2i2i−2i00-22-222−2−220000−22−222−22−2002i−2i000000i2−i2−i2i2−i2i2i2−i2000000000000
χ572-2-2-22-22202020-20-2−22−222−22−22i−2i−2i2i002-22-2−222−20000−22−222−22−2002i−2i000000i2−i2−i2i2i2−i2−i2i2000000000000
χ582-2-2-22-22202020-20-2−22−222−22−22i−2i−2i2i00-22-22−222−200002−22−2−22−2200−2i2i000000i2−i2−i2i2−i2i2i2−i2000000000000
χ592-2-2-22-22202020-20-2−22−222−22−2−2i2i2i−2i002-22-2−222−20000−22−222−22−200−2i2i000000−i2i2i2−i2−i2i2i2−i2000000000000
χ602-2-2-22-22202020-20-2−22−222−22−2−2i2i2i−2i00-22-22−222−200002−22−2−22−22002i−2i000000−i2i2i2−i2i2−i2−i2i2000000000000
χ6144444444-4-4-4-4-4-4-4-40000000000004400000000000000000000000000000000000000000000000000
χ62444-44-4-4-44040-40-404-4-444-4-4400000000000000000000000000000000000000000000000000000000
χ63444-44-4-4-44040-40-40-444-4-444-400000000000000000000000000000000000000000000000000000000
χ64444-44-4-4-4-40-404040000000000000000000000000002i2−2i2−2i22i22i2−2i2−2i22i2000000000000000000000000000000
χ65444-44-4-4-4-40-40404000000000000000000000000000−2i22i22i2−2i2−2i22i22i2−2i2000000000000000000000000000000
χ6644-44-4-4-440-404040-42i22i22i22i2−2i2−2i2−2i2−2i20000000000−2i2−2i22i22i2000000000000000000000000000000000000000000
χ6744-44-4-4-440-404040-4−2i2−2i2−2i2−2i22i22i22i22i200000000002i22i2−2i2−2i2000000000000000000000000000000000000000000
χ6844-4-4-444-4000000002i2−2i2−2i22i2−2i22i22i2−2i20000002i2−2i2−2i22i2000000002-2-22-222-2000000000000000000000000000000
χ6944-4-4-444-4000000002i2−2i2−2i22i2−2i22i22i2−2i2000000−2i22i22i2−2i200000000-222-22-2-22000000000000000000000000000000
χ7044-4-4-444-400000000−2i22i22i2−2i22i2−2i2−2i22i20000002i2−2i2−2i22i200000000-222-22-2-22000000000000000000000000000000
χ7144-4-4-444-400000000−2i22i22i2−2i22i2−2i2−2i22i2000000−2i22i22i2−2i2000000002-2-22-222-2000000000000000000000000000000
χ724-444-4-44-4-404040-40000000000000002i22i2−2i2−2i20000−2i22i2−2i22i200000000000000000000000000000000000000
χ734-444-4-44-4-404040-4000000000000000−2i2−2i22i22i200002i2−2i22i2−2i200000000000000000000000000000000000000
χ744-44-4-44-44-4-444-4-444000000000000-4400000000000000000000000000000000000000000000000000
χ754-4-4444-4-4000000002222−22−22−22−222222000000000000002i2−2i2−2i22i2−2i−2i2i2i2i2i−2i−2i000000000000000000000000000000
χ764-4-4444-4-4000000002222−22−22−22−22222200000000000000−2i22i22i2−2i22i2i−2i−2i−2i−2i2i2i000000000000000000000000000000
χ774-4-4444-4-400000000−22−2222222222−22−22000000000000002i2−2i2−2i22i22i2i−2i−2i−2i−2i2i2i000000000000000000000000000000
χ784-4-4444-4-400000000−22−2222222222−22−2200000000000000−2i22i22i2−2i2−2i−2i2i2i2i2i−2i−2i000000000000000000000000000000
χ794-4-4-44-4440-40-4040422−2222−22−2222−22220000000000−222222−22000000000000000000000000000000000000000000
χ804-4-4-44-4440-40-40404−2222−222222−2222−22000000000022−22−2222000000000000000000000000000000000000000000

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