Finite Group Databasebeta

← Group #307351

Character table — Group #307351

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80
size11111111222222222222222244444444444444444444444444888888888888888888161616161616161616163232
order12222222444444448888888844444488888888888888888888222244444488888888444444888844
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
χ1722222222222-2-2-2-2200000000-22222-200002222-2-2-2-2000000000000-2-222-2-200000000000000000000
χ1822222222222-2-2-2-2200000000-22222-20000-2-2-2-22222000000000000-2-2-2-22200000000000000000000
χ1922222222222-2-2-2-2200000000-2-2-2-2-2-200002222-2-2-2-200000000000022-2-22200000000000000000000
χ2022222222222-2-2-2-2200000000-2-2-2-2-2-20000-2-2-2-222220000000000002222-2-200000000000000000000
χ2122222222-2-2-22222-222222222-20000-2-2-2-2-20000000000000000222200000000000000-2-20000000000
χ2222222222-2-2-22222-222222222-20000-2-2-2-2-20000000000000000-2-2-2-200000000000000220000000000
χ2322222222-2-2-22222-2-2-2-2-2-2-2-2-2-20000-22222000000000000000022-2-200000000000000-220000000000
χ2422222222-2-2-22222-2-2-2-2-2-2-2-2-2-20000-222220000000000000000-2-222000000000000002-20000000000
χ2522-2-2-222-22-2-222-2-222222-2-2-2-220000-222-2-20000000000000000000000000000000000002i−2i2i−2i000000
χ2622-2-2-222-22-2-222-2-222222-2-2-2-220000-222-2-2000000000000000000000000000000000000−2i2i−2i2i000000
χ2722-2-2-222-22-2-222-2-22-2-2-2-2222220000-2-2-2220000000000000000000000000000000000002i−2i−2i2i000000
χ2822-2-2-222-22-2-222-2-22-2-2-2-2222220000-2-2-222000000000000000000000000000000000000−2i2i2i−2i000000
χ2922-2-2-222-2-22222-2-2-22222-2-2-2-2-22i2i−2i−2i2-2-222000000000000000000002i−2i00002i2i−2i−2i0000000000000000
χ3022-2-2-222-2-22222-2-2-22222-2-2-2-2-2−2i−2i2i2i2-2-22200000000000000000000−2i2i0000−2i−2i2i2i0000000000000000
χ3122-2-2-222-2-22222-2-2-2-2-2-2-22222-22i2i−2i−2i222-2-2000000000000000000002i−2i0000−2i−2i2i2i0000000000000000
χ3222-2-2-222-2-22222-2-2-2-2-2-2-22222-2−2i−2i2i2i222-2-200000000000000000000−2i2i00002i2i−2i−2i0000000000000000
χ3322-2-2-222-2-222-2-222-20000000022i2i−2i−2i-20000000000002i2i2i2i−2i−2i−2i−2i0000−2i2i0000000022-2-2000000000000
χ3422-2-2-222-2-222-2-222-20000000022i2i−2i−2i-2000000000000−2i−2i−2i−2i2i2i2i2i0000−2i2i00000000-2-222000000000000
χ3522-2-2-222-2-222-2-222-2000000002−2i−2i2i2i-20000000000002i2i2i2i−2i−2i−2i−2i00002i−2i00000000-2-222000000000000
χ3622-2-2-222-2-222-2-222-2000000002−2i−2i2i2i-2000000000000−2i−2i−2i−2i2i2i2i2i00002i−2i0000000022-2-2000000000000
χ372-222-22-2-2-22-20000222−2−222−2−202i−2i2i−2i02−22−2000022-2-222−2−222−2−2000000002i−2ii2−i2i2−i2i2−i2i2−i2000000000000
χ382-222-22-2-2-22-20000222−2−222−2−202i−2i2i−2i02−22−20000-2-222−2−222−2−22200000000−2i2ii2−i2i2−i2−i2i2−i2i2000000000000
χ392-222-22-2-2-22-20000222−2−222−2−20−2i2i−2i2i02−22−2000022-2-222−2−222−2−200000000−2i2i−i2i2−i2i2−i2i2−i2i2000000000000
χ402-222-22-2-2-22-20000222−2−222−2−20−2i2i−2i2i02−22−20000-2-222−2−222−2−222000000002i−2i−i2i2−i2i2i2−i2i2−i2000000000000
χ412-222-22-2-2-22-200002−2−222−2−22202i−2i2i−2i0−22−22000022-2-2−2−222−2−222000000002i−2i−i2i2−i2i2−i2i2−i2i2000000000000
χ422-222-22-2-2-22-200002−2−222−2−22202i−2i2i−2i0−22−220000-2-22222−2−222−2−200000000−2i2i−i2i2−i2i2i2−i2i2−i2000000000000
χ432-222-22-2-2-22-200002−2−222−2−2220−2i2i−2i2i0−22−22000022-2-2−2−222−2−22200000000−2i2ii2−i2i2−i2i2−i2i2−i2000000000000
χ442-222-22-2-2-22-200002−2−222−2−2220−2i2i−2i2i0−22−220000-2-22222−2−222−2−2000000002i−2ii2−i2i2−i2−i2i2−i2i2000000000000
χ452-22-22-22-20002-22-202-22-22-22-20000000000i2i2−i2−i2i2−i2i2−i2i2−i2i2−i2i2−i2i2−i22-22-200000000000000000000i2−i2i2−i200
χ462-22-22-22-20002-22-202-22-22-22-20000000000i2i2−i2−i2i2−i2i2−i2i2−i2i2−i2i2−i2i2−i2-22-2200000000000000000000−i2i2−i2i200
χ472-22-22-22-20002-22-202-22-22-22-20000000000−i2−i2i2i2−i2i2−i2i2−i2i2−i2i2−i2i2−i2i22-22-200000000000000000000−i2i2−i2i200
χ482-22-22-22-20002-22-202-22-22-22-20000000000−i2−i2i2i2−i2i2−i2i2−i2i2−i2i2−i2i2−i2i2-22-2200000000000000000000i2−i2i2−i200
χ492-22-22-22-20002-22-20-22-22-22-220000000000i2i2−i2−i2i2−i2i2−i2−i2i2−i2i2−i2i2−i2i22-2-2200000000000000000000i2−i2−i2i200
χ502-22-22-22-20002-22-20-22-22-22-220000000000i2i2−i2−i2i2−i2i2−i2−i2i2−i2i2−i2i2−i2i2-222-200000000000000000000−i2i2i2−i200
χ512-22-22-22-20002-22-20-22-22-22-220000000000−i2−i2i2i2−i2i2−i2i2i2−i2i2−i2i2−i2i2−i22-2-2200000000000000000000−i2i2i2−i200
χ522-22-22-22-20002-22-20-22-22-22-220000000000−i2−i2i2i2−i2i2−i2i2i2−i2i2−i2i2−i2i2−i2-222-200000000000000000000i2−i2−i2i200
χ532-2-2-222-2222-20000-222−2−2−2−22202-2-220−222−22i−2i2i−2i0000i2i2−i2−i2−i2−i2i2i20000002i−2i002−2−22−i2i2i2−i2000000000000
χ542-2-2-222-2222-20000-222−2−2−2−22202-2-220−222−2−2i2i−2i2i0000−i2−i2i2i2i2i2−i2−i2000000−2i2i002−2−22i2−i2−i2i2000000000000
χ552-2-2-222-2222-20000-222−2−2−2−2220-222-20−222−22i−2i2i−2i0000i2i2−i2−i2−i2−i2i2i2000000−2i2i00−222−2i2−i2−i2i2000000000000
χ562-2-2-222-2222-20000-222−2−2−2−2220-222-20−222−2−2i2i−2i2i0000−i2−i2i2i2i2i2−i2−i20000002i−2i00−222−2−i2i2i2−i2000000000000
χ572-2-2-222-2222-20000-2−2−22222−2−202-2-2202−2−222i−2i2i−2i0000−i2−i2i2i2i2i2−i2−i20000002i−2i00−222−2i2−i2−i2i2000000000000
χ582-2-2-222-2222-20000-2−2−22222−2−202-2-2202−2−22−2i2i−2i2i0000i2i2−i2−i2−i2−i2i2i2000000−2i2i00−222−2−i2i2i2−i2000000000000
χ592-2-2-222-2222-20000-2−2−22222−2−20-222-202−2−222i−2i2i−2i0000−i2−i2i2i2i2i2−i2−i2000000−2i2i002−2−22−i2i2i2−i2000000000000
χ602-2-2-222-2222-20000-2−2−22222−2−20-222-202−2−22−2i2i−2i2i0000i2i2−i2−i2−i2−i2i2i20000002i−2i002−2−22i2−i2−i2i2000000000000
χ6144444444-4-4-4-4-4-4-4-40000000040000400000000000000000000000000000000000000000000000000
χ62444-4-4-4-440000000022−22−222222−22−2222000000000000002i2−2i2−2i22i22i−2i−2i2i2i−2i−2i2i000000000000000000000000000000
χ63444-4-4-4-440000000022−22−222222−22−222200000000000000−2i22i22i2−2i2−2i2i2i−2i−2i2i2i−2i000000000000000000000000000000
χ64444-4-4-4-4400000000−222222−22−222222−22000000000000002i2−2i2−2i22i2−2i2i2i−2i−2i2i2i−2i000000000000000000000000000000
χ65444-4-4-4-4400000000−222222−22−222222−2200000000000000−2i22i22i2−2i22i−2i−2i2i2i−2i−2i2i000000000000000000000000000000
χ6644-444-4-4-40000000022−22−2222−222222−22000000000022−22−222200002-2-22-222-2000000000000000000000000000000
χ6744-444-4-4-40000000022−22−2222−222222−220000000000−222222−220000-222-22-2-22000000000000000000000000000000
χ6844-444-4-4-400000000−222222−2222−22−2222000000000022−22−22220000-222-22-2-22000000000000000000000000000000
χ6944-444-4-4-400000000−222222−2222−22−22220000000000−222222−2200002-2-22-222-2000000000000000000000000000000
χ7044-4-4-444-44-4-4-4-444400000000-40000400000000000000000000000000000000000000000000000000
χ714-444-44-4-44-440000-42222−22−222222−22−22000000−2222−22220000000000000000000000000000000000000000000000
χ724-444-44-4-44-440000-4−22−222222−22−22222200000022−2222−220000000000000000000000000000000000000000000000
χ734-44-44-44-4000-44-4400000000000000000002i22i2−2i2−2i2−2i22i2−2i22i200000000000000000000000000000000000000
χ744-44-44-44-4000-44-440000000000000000000−2i2−2i22i22i22i2−2i22i2−2i200000000000000000000000000000000000000
χ754-4-44-4-4440004-4-4404-44-4-44-4400000000000000000000000000000000000000000000000000000000
χ764-4-44-4-4440004-4-440-44-444-44-400000000000000000000000000000000000000000000000000000000
χ774-4-44-4-444000-444-400000000000000000000000000022−2222−22−2222−2222000000000000000000000000000000
χ784-4-44-4-444000-444-4000000000000000000000000000−2222−222222−2222−22000000000000000000000000000000
χ794-4-4-444-44-4-44000042222−22−22−22−22222200000022−22−22220000000000000000000000000000000000000000000000
χ804-4-4-444-44-4-4400004−22−2222222222−22−22000000−222222−220000000000000000000000000000000000000000000000

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