Finite Group Databasebeta

← Group #10823309

Character table — Group #10823309

Order 768.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90
size1111222222222222222222222244444444444488888888888888888888888888888888888824242424242424242424242424242424
order1222222222344444444666121212126666661212121212124444444444441212121212121212121212121212121212121212121212124444444488888888
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ31111111111111111111111111111111111111111-1-1-1-111-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1
χ41111111111111111111111111111111111111111-1-1-1-111-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111
χ511111111111111111111111111111111111111-1-111-1-1-1-111-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1-1-1
χ611111111111111111111111111111111111111-1-111-1-1-1-111-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-11111
χ711111111111111111111111111111111111111-1-1-1-111-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-11111
χ811111111111111111111111111111111111111-1-1-1-111-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-111111111-1-1-1-1
χ911111-1-1-1-11111-1-1-1-111111-1-1-1-111-1-1-1-11111-1-1111-11-1-1-11-11-11111-1-1-1-11111-1-1-1-11111-1-1-1-111-1-111-1-111-1-111-1-1
χ1011111-1-1-1-11111-1-1-1-111111-1-1-1-111-1-1-1-11111-1-1111-11-1-1-11-11-11111-1-1-1-11111-1-1-1-11111-1-1-1-1-1-111-1-111-1-111-1-111
χ1111111-1-1-1-11111-1-1-1-111111-1-1-1-111-1-1-1-11111-1-111-11-11-1-1-11-111111-1-1-1-1-1-1-1-11111-1-1-1-1111111-1-111-1-1-1-111-1-111
χ1211111-1-1-1-11111-1-1-1-111111-1-1-1-111-1-1-1-11111-1-111-11-11-1-1-11-111111-1-1-1-1-1-1-1-11111-1-1-1-11111-1-111-1-11111-1-111-1-1
χ1311111-1-1-1-11111-1-1-1-111111-1-1-1-111-1-1-1-11111-1-1-1-11-1-11111-1-11-1-1-1-111111111-1-1-1-1-1-1-1-1111111-1-1-1-11111-1-1-1-111
χ1411111-1-1-1-11111-1-1-1-111111-1-1-1-111-1-1-1-11111-1-1-1-11-1-11111-1-11-1-1-1-111111111-1-1-1-1-1-1-1-11111-1-11111-1-1-1-11111-1-1
χ1511111-1-1-1-11111-1-1-1-111111-1-1-1-111-1-1-1-11111-1-1-1-1-111-111-111-1-1-1-1-11111-1-1-1-111111111-1-1-1-111-1-1-1-111-1-11111-1-1
χ1611111-1-1-1-11111-1-1-1-111111-1-1-1-111-1-1-1-11111-1-1-1-1-111-111-111-1-1-1-1-11111-1-1-1-111111111-1-1-1-1-1-11111-1-111-1-1-1-111
χ1722222222222-2-2-2-2-2-2-2-2222-2-2-2-2222222-2-2-2-2-2-22-200002-2000022-2-222-2-200000000000000000000000000000000
χ1822222222222-2-2-2-2-2-2-2-2222-2-2-2-2222222-2-2-2-2-2-2-220000-220000-2-222-2-22200000000000000000000000000000000
χ192222222222-122222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1222222222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-10000000000000000
χ202222222222-122222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-122-2-2-2-222-2-2-2-2-1-1-1-1-1-1-1-111111111111111110000000000000000
χ212222222222-122222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-2-222-2-2-2-222-2-211111111-1-1-1-1-1-1-1-1111111110000000000000000
χ222222222222-122222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-2-2-2-222-2-2-2-2221111111111111111-1-1-1-1-1-1-1-10000000000000000
χ232222222222-1-2-2-2-2-2-2-2-2-1-1-11111-1-1-1-1-1-11111112-200002-20000-1-111-1-111−i3−i3i3i3−i3−i3i3i3−i3−i3i3i3−i3−i3i3i30000000000000000
χ242222222222-1-2-2-2-2-2-2-2-2-1-1-11111-1-1-1-1-1-11111112-200002-20000-1-111-1-111i3i3−i3−i3i3i3−i3−i3i3i3−i3−i3i3i3−i3−i30000000000000000
χ252222222222-1-2-2-2-2-2-2-2-2-1-1-11111-1-1-1-1-1-1111111-220000-22000011-1-111-1-1−i3−i3i3i3−i3−i3i3i3i3i3−i3−i3i3i3−i3−i30000000000000000
χ262222222222-1-2-2-2-2-2-2-2-2-1-1-11111-1-1-1-1-1-1111111-220000-22000011-1-111-1-1i3i3−i3−i3i3i3−i3−i3−i3−i3i3i3−i3−i3i3i30000000000000000
χ2722222-2-2-2-222-2-22222-2-2222222222-2-2-2-2-2-2-2-2222-20000-22000022-2-2-2-22200000000000000000000000000000000
χ2822222-2-2-2-222-2-22222-2-2222222222-2-2-2-2-2-2-2-222-2200002-20000-2-22222-2-200000000000000000000000000000000
χ2922222-2-2-2-22-122-2-2-2-222-1-1-11111-1-11111-1-1-1-111222-22-2-2-22-22-2-1-1-1-11111-1-1-1-11111-1-1-1-111110000000000000000
χ3022222-2-2-2-22-122-2-2-2-222-1-1-11111-1-11111-1-1-1-11122-22-22-2-2-22-22-1-1-1-111111111-1-1-1-11111-1-1-1-10000000000000000
χ3122222-2-2-2-22-122-2-2-2-222-1-1-11111-1-11111-1-1-1-111-2-22-2-22222-2-221111-1-1-1-1-1-1-1-111111111-1-1-1-10000000000000000
χ3222222-2-2-2-22-122-2-2-2-222-1-1-11111-1-11111-1-1-1-111-2-2-222-222-222-21111-1-1-1-11111-1-1-1-1-1-1-1-111110000000000000000
χ3322222-2-2-2-22-1-2-22222-2-2-1-1-1-1-1-1-1-1-111111111-1-12-20000-220000-1-11111-1-1−i3−i3i3i3i3i3−i3−i3−i3−i3i3i3i3i3−i3−i30000000000000000
χ3422222-2-2-2-22-1-2-22222-2-2-1-1-1-1-1-1-1-1-111111111-1-12-20000-220000-1-11111-1-1i3i3−i3−i3−i3−i3i3i3i3i3−i3−i3−i3−i3i3i30000000000000000
χ3522222-2-2-2-22-1-2-22222-2-2-1-1-1-1-1-1-1-1-111111111-1-1-2200002-2000011-1-1-1-111−i3−i3i3i3i3i3−i3−i3i3i3−i3−i3−i3−i3i3i30000000000000000
χ3622222-2-2-2-22-1-2-22222-2-2-1-1-1-1-1-1-1-1-111111111-1-1-2200002-2000011-1-1-1-111i3i3−i3−i3−i3−i3i3i3−i3−i3i3i3i3i3−i3−i30000000000000000
χ372222-222-2-2-222-222-2-22-22222222-2-222-2-222-2-2-2-200002-20000-2200000000000000002-22-22-22-20000000000000000
χ382222-222-2-2-222-222-2-22-22222222-2-222-2-222-2-2-2-20000-2200002-20000000000000000-22-22-22-220000000000000000
χ392222-222-2-2-22-22-2-222-22222-2-2-2-2-2-222-2-2-2-2222200220000-2-200000000002-22-22-22-2000000000000000000000000
χ402222-222-2-2-22-22-2-222-22222-2-2-2-2-2-222-2-2-2-2222200-2-20000220000000000-22-22-22-22000000000000000000000000
χ412222-222-2-2-2-12-222-2-22-2-1-1-1-1-1-1-111-1-111-1-1111100002-20000-22−i3i3−i3i3−i3i3−i3i3−i3i3i3−i3−i3i3i3−i3-11-11-11-110000000000000000
χ422222-222-2-2-2-12-222-2-22-2-1-1-1-1-1-1-111-1-111-1-1111100002-20000-22i3−i3i3−i3i3−i3i3−i3i3−i3−i3i3i3−i3−i3i3-11-11-11-110000000000000000
χ432222-222-2-2-2-12-222-2-22-2-1-1-1-1-1-1-111-1-111-1-111110000-2200002-2−i3i3−i3i3−i3i3−i3i3i3−i3−i3i3i3−i3−i3i31-11-11-11-10000000000000000
χ442222-222-2-2-2-12-222-2-22-2-1-1-1-1-1-1-111-1-111-1-111110000-2200002-2i3−i3i3−i3i3−i3i3−i3−i3i3i3−i3−i3i3i3−i31-11-11-11-10000000000000000
χ452222-222-2-2-2-1-22-2-222-22-1-1-1111111-1-11111-1-1-1-100220000-2-200−i3i3i3−i3−i3i3i3−i3-11-11-11-11−i3i3i3−i3−i3i3i3−i30000000000000000
χ462222-222-2-2-2-1-22-2-222-22-1-1-1111111-1-11111-1-1-1-100220000-2-200i3−i3−i3i3i3−i3−i3i3-11-11-11-11i3−i3−i3i3i3−i3−i3i30000000000000000
χ472222-222-2-2-2-1-22-2-222-22-1-1-1111111-1-11111-1-1-1-100-2-200002200−i3i3i3−i3−i3i3i3−i31-11-11-11-1i3−i3−i3i3i3−i3−i3i30000000000000000
χ482222-222-2-2-2-1-22-2-222-22-1-1-1111111-1-11111-1-1-1-100-2-200002200i3−i3−i3i3i3−i3−i3i31-11-11-11-1−i3i3i3−i3−i3i3i3−i30000000000000000
χ492222-2-2-222-222-2-2-2222-2222-2-2-2-2-2-2-2-22222-2-2220000220000-2-200000000000000002-22-2-22-220000000000000000
χ502222-2-2-222-222-2-2-2222-2222-2-2-2-2-2-2-2-22222-2-2220000-2-20000220000000000000000-22-222-22-20000000000000000
χ512222-2-2-222-22-2222-2-2-222222222-2-2-2-222-2-222-2-2002-20000-2200000000002-22-2-22-22000000000000000000000000
χ522222-2-2-222-22-2222-2-2-222222222-2-2-2-222-2-222-2-200-2200002-20000000000-22-222-22-2000000000000000000000000
χ532222-2-2-222-2-12-2-2-2222-2-1-1-111111111-1-1-1-111-1-10000220000-2-2−i3i3−i3i3i3−i3i3−i3−i3i3i3−i3i3−i3−i3i3-11-111-11-10000000000000000
χ542222-2-2-222-2-12-2-2-2222-2-1-1-111111111-1-1-1-111-1-10000220000-2-2i3−i3i3−i3−i3i3−i3i3i3−i3−i3i3−i3i3i3−i3-11-111-11-10000000000000000
χ552222-2-2-222-2-12-2-2-2222-2-1-1-111111111-1-1-1-111-1-10000-2-2000022−i3i3−i3i3i3−i3i3−i3i3−i3−i3i3−i3i3i3−i31-11-1-11-110000000000000000
χ562222-2-2-222-2-12-2-2-2222-2-1-1-111111111-1-1-1-111-1-10000-2-2000022i3−i3i3−i3−i3i3−i3i3−i3i3i3−i3i3−i3−i3i31-11-1-11-110000000000000000
χ572222-2-2-222-2-1-2222-2-2-22-1-1-1-1-1-1-11111-1-111-1-111002-20000-2200−i3i3i3−i3i3−i3−i3i3-11-111-11-1−i3i3i3−i3i3−i3−i3i30000000000000000
χ582222-2-2-222-2-1-2222-2-2-22-1-1-1-1-1-1-11111-1-111-1-111002-20000-2200i3−i3−i3i3−i3i3i3−i3-11-111-11-1i3−i3−i3i3−i3i3i3−i30000000000000000
χ592222-2-2-222-2-1-2222-2-2-22-1-1-1-1-1-1-11111-1-111-1-11100-2200002-200−i3i3i3−i3i3−i3−i3i31-11-1-11-11i3−i3−i3i3−i3i3i3−i30000000000000000
χ602222-2-2-222-2-1-2222-2-2-22-1-1-1-1-1-1-11111-1-111-1-11100-2200002-200i3−i3−i3i3−i3i3i3−i31-11-1-11-11−i3i3i3−i3i3−i3−i3i30000000000000000
χ6122-2-222-22-2-222-22-22-2-222-2-222-2-22-22-22-22-22-22-2000000000000000000000000000000000000000000002-22-20000
χ6222-2-222-22-2-222-22-22-2-222-2-222-2-22-22-22-22-22-22-200000000000000000000000000000000000000000000-22-220000
χ6322-2-222-22-2-22-22-22-222-22-2-2-2-2222-22-22-2-22-22-220000000000000000000000000000000000000000000000002-22-2
χ6422-2-222-22-2-22-22-22-222-22-2-2-2-2222-22-22-2-22-22-22000000000000000000000000000000000000000000000000-22-22
χ6522-2-22-22-22-222-2-22-22-222-2-2-2-2222-2-22-222-22-2-22000000000000000000000000000000000000000000002-2-220000
χ6622-2-22-22-22-222-2-22-22-222-2-2-2-2222-2-22-222-22-2-2200000000000000000000000000000000000000000000-222-20000
χ6722-2-22-22-22-22-222-22-22-22-2-222-2-22-2-22-22-22-222-20000000000000000000000000000000000000000000000002-2-22
χ6822-2-22-22-22-22-222-22-22-22-2-222-2-22-2-22-22-22-222-2000000000000000000000000000000000000000000000000-222-2
χ6922-2-2-22-2-2222222-2-22-2-22-2-222-2-2-222-2-222-2-22-2200000000000000000000000000000000000000002-22-200000000
χ7022-2-2-22-2-2222222-2-22-2-22-2-222-2-2-222-2-222-2-22-220000000000000000000000000000000000000000-22-2200000000
χ7122-2-2-22-2-2222-2-2-222-2222-2-2-2-222-222-2-22-222-22-20000000000000000000000000000000000002i−2i2i−2i000000000000
χ7222-2-2-22-2-2222-2-2-222-2222-2-2-2-222-222-2-22-222-22-2000000000000000000000000000000000000−2i2i−2i2i000000000000
χ7322-2-2-2-222-22222-222-2-2-22-2-2-2-222-22-222-22-2-222-200000000000000000000000000000000000000002-2-2200000000
χ7422-2-2-2-222-22222-222-2-2-22-2-2-2-222-22-222-22-2-222-20000000000000000000000000000000000000000-222-200000000
χ7522-2-2-2-222-222-2-22-2-22222-2-222-2-2-22-222-2-222-2-220000000000000000000000000000000000002i−2i−2i2i000000000000
χ7622-2-2-2-222-222-2-22-2-22222-2-222-2-2-22-222-2-222-2-22000000000000000000000000000000000000−2i2i2i−2i000000000000
χ7744-4-444-44-4-4-24-44-44-4-44-222-2-222-22-22-22-22-22-220000000000000000000000000000000000000000000000000000
χ7844-4-444-44-4-4-2-44-44-444-4-22222-2-2-22-22-222-22-22-20000000000000000000000000000000000000000000000000000
χ7944-4-44-44-44-4-24-4-44-44-44-22222-2-2-222-22-2-22-222-20000000000000000000000000000000000000000000000000000
χ8044-4-44-44-44-4-2-444-44-44-4-222-2-222-222-22-22-22-2-220000000000000000000000000000000000000000000000000000
χ8144-4-4-44-4-444-2444-4-44-4-4-222-2-2222-2-222-2-222-22-20000000000000000000000000000000000000000000000000000
χ8244-4-4-44-4-444-2-4-4-444-444-22222-2-22-2-222-22-2-22-220000000000000000000000000000000000000000000000000000
χ8344-4-4-4-444-44-244-444-4-4-4-22222-2-22-22-2-22-222-2-220000000000000000000000000000000000000000000000000000
χ8444-4-4-4-444-44-2-4-44-4-4444-222-2-2222-22-2-222-2-222-20000000000000000000000000000000000000000000000000000
χ858-88-8000000800000000-88-800000000000000000000000000000000000000000000000000000000000000000000
χ868-88-8000000-4000000004-4443−4343−430000000000000000000000000000000000000000000000000000000000000000
χ878-88-8000000-4000000004-44−4343−43430000000000000000000000000000000000000000000000000000000000000000
χ888-8-88000000800000000-8-8800000000000000000000000000000000000000000000000000000000000000000000
χ898-8-88000000-40000000044-443−43−43430000000000000000000000000000000000000000000000000000000000000000
χ908-8-88000000-40000000044-4−434343−430000000000000000000000000000000000000000000000000000000000000000

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