Finite Group Databasebeta

← Group #307341

Character table — Group #307341

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80
size11111111222222222222222244444444444444444444444444888888888888888888161616161616161616163232
order12222222444444448888888844444488888888888888888888222244444488888888444444888822
χ111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111111111111111-1-1-1-111111111111111-1-1-1-1-1-1-1-1-1-1-1-1
χ31111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-1-11111-1-1-1-1111111-1-1-1-1-1-1
χ41111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1111111
χ51111111111111111111111111-1-1-1-11111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-11111-1-1
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
χ71111111111111111111111111-1-1-1-111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-11111-1-1-1-1111111-1-1-1-1-1-1-1-111
χ81111111111111111111111111-1-1-1-111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-11111-1-111111111-1-1
χ91111111111111111-1-1-1-1-1-1-1-1111111-1-1-1-111111111-1-1-1-1-1-1-1-111-1-1111111-1-1-1-1-1-1-1-11-111-1-111-1-11-1
χ101111111111111111-1-1-1-1-1-1-1-1111111-1-1-1-111111111-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-11-1-111-1-111-11
χ111111111111111111-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-11111111111-1-111-1-1-1-1-1-1-1-111111-111-1-1-1-111-11
χ121111111111111111-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-11111-1-1-1-1-1-1-1-11111-11-1-11111-1-11-1
χ131111111111111111-1-1-1-1-1-1-1-11-1-1-1-11-1-1-1-111111111-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1111111111-1-1-11111-1-1-11
χ141111111111111111-1-1-1-1-1-1-1-11-1-1-1-11-1-1-1-111111111-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-111111111-1111-1-1-1-1111-1
χ151111111111111111-1-1-1-1-1-1-1-11-1-1-1-11-1-1-1-1-1-1-1-1-1-1-1-11111111111-1-1-1-111111111-1-1-1-11-1-1-111-1-1111-1
χ161111111111111111-1-1-1-1-1-1-1-11-1-1-1-11-1-1-1-1-1-1-1-1-1-1-1-111111111-1-111-1-111111111-1-1-1-1-1111-1-111-1-1-11
χ17222222222-222-2-22-222222222-20000-2-2-2-2-20000000000000000222200000000000000-2-20000000000
χ18222222222-222-2-22-222222222-20000-2-2-2-2-20000000000000000-2-2-2-200000000000000220000000000
χ19222222222-222-2-22-2-2-2-2-2-2-2-2-2-20000-22222000000000000000022-2-200000000000000-220000000000
χ20222222222-222-2-22-2-2-2-2-2-2-2-2-2-20000-222220000000000000000-2-222000000000000002-20000000000
χ2122222222-22-2-222-2200000000-22222-200002222-2-2-2-2000000000000-2-222-2-200000000000000000000
χ2222222222-22-2-222-2200000000-22222-20000-2-2-2-22222000000000000-2-2-2-22200000000000000000000
χ2322222222-22-2-222-2200000000-2-2-2-2-2-200002222-2-2-2-200000000000022-2-22200000000000000000000
χ2422222222-22-2-222-2200000000-2-2-2-2-2-20000-2-2-2-222220000000000002222-2-200000000000000000000
χ2522-2-2-222-202002-20-22222−2−2−2−202i2i−2i−2i022−2−22i2i−2i−2i0000i2i2i2i2−i2−i2−i2−i20000002-200i2i2−i2−i222−2−2000000000000
χ2622-2-2-222-202002-20-22222−2−2−2−202i2i−2i−2i022−2−2−2i−2i2i2i0000−i2−i2−i2−i2i2i2i2i2000000-2200i2i2−i2−i2−2−222000000000000
χ2722-2-2-222-202002-20-22222−2−2−2−20−2i−2i2i2i022−2−22i2i−2i−2i0000i2i2i2i2−i2−i2−i2−i2000000-2200−i2−i2i2i2−2−222000000000000
χ2822-2-2-222-202002-20-22222−2−2−2−20−2i−2i2i2i022−2−2−2i−2i2i2i0000−i2−i2−i2−i2i2i2i2i20000002-200−i2−i2i2i222−2−2000000000000
χ2922-2-2-222-202002-20-2−2−2−2−2222202i2i−2i−2i0−2−2222i2i−2i−2i0000−i2−i2−i2−i2i2i2i2i20000002-200−i2−i2i2i2−2−222000000000000
χ3022-2-2-222-202002-20-2−2−2−2−2222202i2i−2i−2i0−2−222−2i−2i2i2i0000i2i2i2i2−i2−i2−i2−i2000000-2200−i2−i2i2i222−2−2000000000000
χ3122-2-2-222-202002-20-2−2−2−2−222220−2i−2i2i2i0−2−2222i2i−2i−2i0000−i2−i2−i2−i2i2i2i2i2000000-2200i2i2−i2−i222−2−2000000000000
χ3222-2-2-222-202002-20-2−2−2−2−222220−2i−2i2i2i0−2−222−2i−2i2i2i0000i2i2i2i2−i2−i2−i2−i20000002-200i2i2−i2−i2−2−222000000000000
χ332-22-2-2-2220-2002-20222−2−222−2−202-22-202−22−2000022-2-222−2−222−2−2000000002-22−22−22−22−2000000000000
χ342-22-2-2-2220-2002-20222−2−222−2−202-22-202−22−20000-2-222−2−222−2−22200000000-222−22−2−22−22000000000000
χ352-22-2-2-2220-2002-20222−2−222−2−20-22-2202−22−2000022-2-222−2−222−2−200000000-22−22−22−22−22000000000000
χ362-22-2-2-2220-2002-20222−2−222−2−20-22-2202−22−20000-2-222−2−222−2−222000000002-2−22−222−22−2000000000000
χ372-22-2-2-2220-2002-202−2−222−2−22202-22-20−22−22000022-2-2−2−222−2−222000000002-2−22−22−22−22000000000000
χ382-22-2-2-2220-2002-202−2−222−2−22202-22-20−22−220000-2-22222−2−222−2−200000000-22−22−222−22−2000000000000
χ392-22-2-2-2220-2002-202−2−222−2−2220-22-220−22−22000022-2-2−2−222−2−22200000000-222−22−22−22−2000000000000
χ402-22-2-2-2220-2002-202−2−222−2−2220-22-220−22−220000-2-22222−2−222−2−2000000002-22−22−2−22−22000000000000
χ412-2-222-22-22-2-2-2222-20000000022i−2i−2i2i-20000000000002i2i−2i−2i−2i−2i2i2i00002i−2i000000002-2-22000000000000
χ422-2-222-22-22-2-2-2222-20000000022i−2i−2i2i-2000000000000−2i−2i2i2i2i2i−2i−2i00002i−2i00000000-222-2000000000000
χ432-2-222-22-22-2-2-2222-2000000002−2i2i2i−2i-20000000000002i2i−2i−2i−2i−2i2i2i0000−2i2i00000000-222-2000000000000
χ442-2-222-22-22-2-2-2222-2000000002−2i2i2i−2i-2000000000000−2i−2i2i2i2i2i−2i−2i0000−2i2i000000002-2-22000000000000
χ452-2-222-22-2-2222-2-2-2222-2-2-2-22220000-2-222-20000000000000000000000000000000000002i−2i2i−2i000000
χ462-2-222-22-2-2222-2-2-2222-2-2-2-22220000-2-222-2000000000000000000000000000000000000−2i2i−2i2i000000
χ472-2-222-22-2-2222-2-2-22-2-22222-2-220000-22-2-220000000000000000000000000000000000002i−2i−2i2i000000
χ482-2-222-22-2-2222-2-2-22-2-22222-2-220000-22-2-22000000000000000000000000000000000000−2i2i2i−2i000000
χ492-2-222-22-2-2-22222-2-222-2-2-2-222-22i−2i−2i2i22-2-2200000000000000000000−2i2i00002i−2i−2i2i0000000000000000
χ502-2-222-22-2-2-22222-2-222-2-2-2-222-2−2i2i2i−2i22-2-22000000000000000000002i−2i0000−2i2i2i−2i0000000000000000
χ512-2-222-22-2-2-22222-2-2-2-22222-2-2-22i−2i−2i2i2-222-200000000000000000000−2i2i0000−2i2i2i−2i0000000000000000
χ522-2-222-22-2-2-22222-2-2-2-22222-2-2-2−2i2i2i−2i2-222-2000000000000000000002i−2i00002i−2i−2i2i0000000000000000
χ532-2-22-22-22-202-200202-22-22-22-200000000002−22−22−22−22−22−22−22−22-22-2000000000000000000002−22−200
χ542-2-22-22-22-202-200202-22-22-22-200000000002−22−22−22−22−22−22−22−2-22-2200000000000000000000−22−2200
χ552-2-22-22-22-202-200202-22-22-22-20000000000−22−22−22−22−22−22−22−222-22-200000000000000000000−22−2200
χ562-2-22-22-22-202-200202-22-22-22-20000000000−22−22−22−22−22−22−22−22-22-22000000000000000000002−22−200
χ572-2-22-22-22-202-20020-22-22-22-2200000000002−22−22−22−2−22−22−22−222-2-22000000000000000000002−2−2200
χ582-2-22-22-22-202-20020-22-22-22-2200000000002−22−22−22−2−22−22−22−22-222-200000000000000000000−222−200
χ592-2-22-22-22-202-20020-22-22-22-220000000000−22−22−22−222−22−22−22−22-2-2200000000000000000000−222−200
χ602-2-22-22-22-202-20020-22-22-22-220000000000−22−22−22−222−22−22−22−2-222-2000000000000000000002−2−2200
χ6144444444-4-4-4-4-4-4-4-40000000040000400000000000000000000000000000000000000000000000000
χ624444-4-4-4-4404-400-404-4-44-444-400000000000000000000000000000000000000000000000000000000
χ634444-4-4-4-4404-400-40-444-44-4-4400000000000000000000000000000000000000000000000000000000
χ644444-4-4-4-4-40-440040000000000000000000000000002i2−2i2−2i22i2−2i22i22i2−2i2000000000000000000000000000000
χ654444-4-4-4-4-40-44004000000000000000000000000000−2i22i22i2−2i22i2−2i2−2i22i2000000000000000000000000000000
χ6644-4-44-4-440000000022−22−222222−22−22220000000000000022−22−22222-2-222-2-22000000000000000000000000000000
χ6744-4-44-4-440000000022−22−222222−22−222200000000000000−222222−22-222-2-222-2000000000000000000000000000000
χ6844-4-44-4-4400000000−222222−22−222222−220000000000000022−22−2222-222-2-222-2000000000000000000000000000000
χ6944-4-44-4-4400000000−222222−22−222222−2200000000000000−222222−222-2-222-2-22000000000000000000000000000000
χ7044-4-4-444-40-400-440422222222−22−22−22−22000000−22−2222220000000000000000000000000000000000000000000000
χ7144-4-4-444-40-400-4404−22−22−22−22222222220000002222−22−220000000000000000000000000000000000000000000000
χ724-44-444-4-40000000022−2222−22−2222−222200000000002i2−2i2−2i22i200002i−2i2i−2i−2i2i−2i2i000000000000000000000000000000
χ734-44-444-4-40000000022−2222−22−2222−22220000000000−2i22i22i2−2i20000−2i2i−2i2i2i−2i2i−2i000000000000000000000000000000
χ744-44-444-4-400000000−2222−222222−2222−2200000000002i2−2i2−2i22i20000−2i2i−2i2i2i−2i2i−2i000000000000000000000000000000
χ754-44-444-4-400000000−2222−222222−2222−220000000000−2i22i22i2−2i200002i−2i2i−2i−2i2i−2i2i000000000000000000000000000000
χ764-44-4-4-4440400-440-42222−22−222222−22−22000000−2222−22220000000000000000000000000000000000000000000000
χ774-44-4-4-4440400-440-4−22−222222−22−22222200000022−2222−220000000000000000000000000000000000000000000000
χ784-4-444-44-444-4-4-4-44400000000-40000400000000000000000000000000000000000000000000000000
χ794-4-44-44-4440-4400-4000000000000000000022−2222−22−2222−222200000000000000000000000000000000000000
χ804-4-44-44-4440-4400-40000000000000000000−2222−222222−2222−2200000000000000000000000000000000000000

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