Finite Group Databasebeta

← Group #10844753

Character table — Group #10844753

Order 768.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96
size111111112222222222222222444444444444444444666666668888888888888888888888121212121212121212121212161616161616242424244848
order1222222234444444466666664444444444121212121212121288888888444412121212121212121212121212121212121288888888888824661212444444
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-11111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1
χ3111111111111111111111111111111111111111111-1-1-1-1-1-1-1-11111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1
χ4111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111
χ5111111111111111111111111-1-1-1-111-1-1-1-1111111111111111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1
χ6111111111111111111111111-1-1-1-111-1-1-1-11111111111111111-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1111111-1-1-1-111
χ7111111111111111111111111-1-1-1-111-1-1-1-111111111-1-1-1-1-1-1-1-111111111111111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-111
χ8111111111111111111111111-1-1-1-111-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1111111111111111111-1-1
χ9111111111-1-1-1-11111111111111-1-1-1-111-1-11111-1-1-1-11111111111-1-11111-1-1-1-1-1-11111-1-1-1-1-1-1-1-11111-1-1-1-11-111-1-111-1-11-1
χ10111111111-1-1-1-11111111111111-1-1-1-111-1-11111-1-1-1-111111111-1-111-1-1-1-11111-1-11111-1-1-1-1-1-1-1-11111-1-1-1-1-11-1-111-1-111-11
χ11111111111-1-1-1-11111111111111-1-1-1-111-1-11111-1-1-1-1-1-1-1-1-1-1-1-111-1-11111-1-1-1-1-1-11111-1-1-1-11111-1-1-1-111111-111-1-1-1-111-11
χ12111111111-1-1-1-11111111111111-1-1-1-111-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-11111-1-11111-1-1-1-11111-1-1-1-11111-11-1-11111-1-11-1
χ13111111111-1-1-1-111111111111-1-111-1-1-1-1111111-1-1-1-11111111111-1-11111-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-11111-11-1-11111-1-1-11
χ14111111111-1-1-1-111111111111-1-111-1-1-1-1111111-1-1-1-111111111-1-111-1-1-1-11111-1-1-1-1-1-11111-1-1-1-1-1-1-1-111111-111-1-1-1-1111-1
χ15111111111-1-1-1-111111111111-1-111-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-111-1-11111-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-1-11-1-111-1-1111-1
χ16111111111-1-1-1-111111111111-1-111-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-11111-1-1-1-1-1-1111111111111-1-1-1-11-111-1-111-1-1-11
χ172222222222222-2-2-2-2222222222-2-2-2-2-2-222-2-2-2-2222200000000000000000000-2-222-2-222-2-2000000000000000000000000
χ182222222222222-2-2-2-22222222-2-222-2-222-2-2-2-2-2-2222200000000000000000000-2-2-2-222-2-222000000000000000000000000
χ19222222222-2-2-2-2-2-2-2-22222222222222-2-2-2-2-2-2-2-2-2-2-2-2000000000000000000002222-2-2-2-222000000000000000000000000
χ20222222222-2-2-2-2-2-2-2-22222222-2-2-2-2222222-2-2-2-2-2-2-2-20000000000000000000022-2-22222-2-2000000000000000000000000
χ2122222222-122222222-1-1-1-1-1-1-12222222222-1-1-1-1-1-1-1-1000000002222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-100000000000022-1-1-1-1000000
χ2222222222-122222222-1-1-1-1-1-1-12222222222-1-1-1-1-1-1-1-100000000-2-2-2-211111111-1-1-1-1-1-1-1-1-1-1000000000000-2-21111000000
χ2322222222-122222222-1-1-1-1-1-1-1-2-2-2-222-2-2-2-2-1-1-1-1-1-1-1-1000000002222-1-1-1-1-1-1-1-1-1-111111111000000000000-2-21111000000
χ2422222222-122222222-1-1-1-1-1-1-1-2-2-2-222-2-2-2-2-1-1-1-1-1-1-1-100000000-2-2-2-211111111-1-11111111100000000000022-1-1-1-1000000
χ2522222222-12222-2-2-2-2-1-1-1-1-1-1-122-2-2-2-2-2-2221111-1-1-1-1000000000000−i3−i3i3i3−i3−i3i3i311-1-111-1-11100000000000000−i3i3−i3i3000000
χ2622222222-12222-2-2-2-2-1-1-1-1-1-1-122-2-2-2-2-2-2221111-1-1-1-1000000000000i3i3−i3−i3i3i3−i3−i311-1-111-1-11100000000000000i3−i3i3−i3000000
χ2722222222-12222-2-2-2-2-1-1-1-1-1-1-1-2-222-2-222-2-21111-1-1-1-1000000000000−i3−i3i3i3−i3−i3i3i31111-1-111-1-100000000000000i3−i3i3−i3000000
χ2822222222-12222-2-2-2-2-1-1-1-1-1-1-1-2-222-2-222-2-21111-1-1-1-1000000000000i3i3−i3−i3i3i3−i3−i31111-1-111-1-100000000000000−i3i3−i3i3000000
χ2922222222-1-2-2-2-22222-1-1-1-1-1-1-122-2-2-2-222-2-2-1-1-1-111110000000022-2-2-1-1-1-1111111-1-1-1-111110000000000002-2-1-111000000
χ3022222222-1-2-2-2-22222-1-1-1-1-1-1-122-2-2-2-222-2-2-1-1-1-1111100000000-2-2221111-1-1-1-111-1-1-1-11111000000000000-2211-1-1000000
χ3122222222-1-2-2-2-22222-1-1-1-1-1-1-1-2-222-2-2-2-222-1-1-1-111110000000022-2-2-1-1-1-11111111111-1-1-1-1000000000000-2211-1-1000000
χ3222222222-1-2-2-2-22222-1-1-1-1-1-1-1-2-222-2-2-2-222-1-1-1-1111100000000-2-2221111-1-1-1-1111111-1-1-1-10000000000002-2-1-111000000
χ3322222222-1-2-2-2-2-2-2-2-2-1-1-1-1-1-1-1222222-2-2-2-211111111000000000000−i3−i3i3i3i3i3−i3−i3-1-1-1-11111-1-100000000000000−i3i3i3−i3000000
χ3422222222-1-2-2-2-2-2-2-2-2-1-1-1-1-1-1-1222222-2-2-2-211111111000000000000i3i3−i3−i3−i3−i3i3i3-1-1-1-11111-1-100000000000000i3−i3−i3i3000000
χ3522222222-1-2-2-2-2-2-2-2-2-1-1-1-1-1-1-1-2-2-2-222222211111111000000000000−i3−i3i3i3i3i3−i3−i3-1-111-1-1-1-11100000000000000i3−i3−i3i3000000
χ3622222222-1-2-2-2-2-2-2-2-2-1-1-1-1-1-1-1-2-2-2-222222211111111000000000000i3i3−i3−i3−i3−i3i3i3-1-111-1-1-1-11100000000000000−i3i3i3−i3000000
χ37222-2-2-22-2200002-2-222-22-22-2-2000000000022-2-200002i2i2i2i−2i−2i−2i−2i002i−2i00002i−2i2i−2i0000000000000000000000000000002-200
χ38222-2-2-22-2200002-2-222-22-22-2-2000000000022-2-200002i2i2i2i−2i−2i−2i−2i00−2i2i0000−2i2i−2i2i000000000000000000000000000000-2200
χ39222-2-2-22-2200002-2-222-22-22-2-2000000000022-2-20000−2i−2i−2i−2i2i2i2i2i002i−2i00002i−2i2i−2i000000000000000000000000000000-2200
χ40222-2-2-22-2200002-2-222-22-22-2-2000000000022-2-20000−2i−2i−2i−2i2i2i2i2i00−2i2i0000−2i2i−2i2i0000000000000000000000000000002-200
χ4122-2-2-22-2222i2i−2i−2i00002-2-22-22-22i−2i0000002-200002i2i−2i−2i−i2−i2i2i2−i2−i2i2i2000000000000002i−2i002-20022−2−222−2−2−i2−i2i2i2000000000000
χ4222-2-2-22-2222i2i−2i−2i00002-2-22-22-22i−2i0000002-200002i2i−2i−2ii2i2−i2−i2i2i2−i2−i2000000000000002i−2i002-200−2−222−2−222i2i2−i2−i2000000000000
χ4322-2-2-22-2222i2i−2i−2i00002-2-22-22-2−2i2i000000-2200002i2i−2i−2i−i2−i2i2i2−i2−i2i2i200000000000000−2i2i00-220022−2−2−2−222i2i2−i2−i2000000000000
χ4422-2-2-22-2222i2i−2i−2i00002-2-22-22-2−2i2i000000-2200002i2i−2i−2ii2i2−i2−i2i2i2−i2−i200000000000000−2i2i00-2200−2−22222−2−2−i2−i2i2i2000000000000
χ4522-2-2-22-222−2i−2i2i2i00002-2-22-22-22i−2i000000-220000−2i−2i2i2i−i2−i2i2i2−i2−i2i2i2000000000000002i−2i00-2200−2−22222−2−2i2i2−i2−i2000000000000
χ4622-2-2-22-222−2i−2i2i2i00002-2-22-22-22i−2i000000-220000−2i−2i2i2ii2i2−i2−i2i2i2−i2−i2000000000000002i−2i00-220022−2−2−2−222−i2−i2i2i2000000000000
χ4722-2-2-22-222−2i−2i2i2i00002-2-22-22-2−2i2i0000002-20000−2i−2i2i2i−i2−i2i2i2−i2−i2i2i200000000000000−2i2i002-200−2−222−2−222−i2−i2i2i2000000000000
χ4822-2-2-22-222−2i−2i2i2i00002-2-22-22-2−2i2i0000002-20000−2i−2i2i2ii2i2−i2−i2i2i2−i2−i200000000000000−2i2i002-20022−2−222−2−2i2i2−i2−i2000000000000
χ492-22-22-2-2222i−2i2i−2i0000-222-2-22-2002i−2i002-20000002i−2i2i−2i2−22−22−22−200000000000000002-2002i−2i−i2i2−i2i22−22−2−i2i2−i2i2000000000000
χ502-22-22-2-2222i−2i2i−2i0000-222-2-22-2002i−2i002-20000002i−2i2i−2i−22−22−22−2200000000000000002-2002i−2ii2−i2i2−i2−22−22i2−i2i2−i2000000000000
χ512-22-22-2-2222i−2i2i−2i0000-222-2-22-200−2i2i00-220000002i−2i2i−2i2−22−22−22−20000000000000000-2200−2i2i−i2i2−i2i2−22−22i2−i2i2−i2000000000000
χ522-22-22-2-2222i−2i2i−2i0000-222-2-22-200−2i2i00-220000002i−2i2i−2i−22−22−22−220000000000000000-2200−2i2ii2−i2i2−i22−22−2−i2i2−i2i2000000000000
χ532-22-22-2-222−2i2i−2i2i0000-222-2-22-2002i−2i00-22000000−2i2i−2i2i2−22−22−22−20000000000000000-22002i−2ii2−i2i2−i2−22−22−i2i2−i2i2000000000000
χ542-22-22-2-222−2i2i−2i2i0000-222-2-22-2002i−2i00-22000000−2i2i−2i2i−22−22−22−220000000000000000-22002i−2i−i2i2−i2i22−22−2i2−i2i2−i2000000000000
χ552-22-22-2-222−2i2i−2i2i0000-222-2-22-200−2i2i002-2000000−2i2i−2i2i2−22−22−22−200000000000000002-200−2i2ii2−i2i2−i22−22−2i2−i2i2−i2000000000000
χ562-22-22-2-222−2i2i−2i2i0000-222-2-22-200−2i2i002-2000000−2i2i−2i2i−22−22−22−2200000000000000002-200−2i2i−i2i2−i2i2−22−22−i2i2−i2i2000000000000
χ572-2-22-2-22222-2-2222-2-2-2-2-2-222200002-200002-22-22-2-222i−2i−2i2i2i−2i−2i2i0000000000002-200000000−2i2i2i−2i00000000000000000000
χ582-2-22-2-22222-2-2222-2-2-2-2-2-222200002-200002-22-22-2-22−2i2i2i−2i−2i2i2i−2i0000000000002-2000000002i−2i−2i2i00000000000000000000
χ592-2-22-2-22222-2-22-2-222-2-2-2-22220000-220000-22-222-2-2200000000000000000000-220000000000002-2-222-2-22000000000000
χ602-2-22-2-22222-2-22-2-222-2-2-2-22220000-220000-22-222-2-2200000000000000000000-22000000000000-222-2-222-2000000000000
χ612-2-22-2-2222-222-222-2-2-2-2-2-22220000-2200002-22-2-222-22i−2i−2i2i2i−2i−2i2i000000000000-22000000002i−2i−2i2i00000000000000000000
χ622-2-22-2-2222-222-222-2-2-2-2-2-22220000-2200002-22-2-222-2−2i2i2i−2i−2i2i2i−2i000000000000-2200000000−2i2i2i−2i00000000000000000000
χ632-2-22-2-2222-222-2-2-222-2-2-2-222200002-20000-22-22-222-2000000000000000000002-20000000000002-2-22-222-2000000000000
χ642-2-22-2-2222-222-2-2-222-2-2-2-222200002-20000-22-22-222-2000000000000000000002-2000000000000-222-22-2-22000000000000
χ652-2-2-2222-2200002-22-2-22-222-2-200000000002-2-2200002-2-22-222-22i−2i002i−2i2i−2i000000000000000000000000000000002i−2i0000
χ662-2-2-2222-2200002-22-2-22-222-2-200000000002-2-2200002-2-22-222-2−2i2i00−2i2i−2i2i00000000000000000000000000000000−2i2i0000
χ672-2-2-2222-2200002-22-2-22-222-2-200000000002-2-220000-222-22-2-222i−2i002i−2i2i−2i00000000000000000000000000000000−2i2i0000
χ682-2-2-2222-2200002-22-2-22-222-2-200000000002-2-220000-222-22-2-22−2i2i00−2i2i−2i2i000000000000000000000000000000002i−2i0000
χ69444-4-4-44-440000-444-44-44-44-4-40000000000-4-4440000000000000000000000000000000000000000000000000000000000
χ70444-4-4-44-4-200004-4-44-22-22-2220000000000-2-222000000000000004i−4i0000−2i2i−2i2i0000000000000000000000000000000000
χ71444-4-4-44-4-200004-4-44-22-22-2220000000000-2-22200000000000000−4i4i00002i−2i2i−2i0000000000000000000000000000000000
χ72444-4-4-44-4-20000-444-4-22-22-222000000000022-2-20000000000000000000023−23−23230000000000000000000000000000000000
χ73444-4-4-44-4-20000-444-4-22-22-222000000000022-2-200000000000000000000−232323−230000000000000000000000000000000000
χ7444-444-4-4-440000000044-4-4-4-440000000000000000002222−22−22−22−2222220000000000000000000000000000000000000000000000
χ7544-444-4-4-440000000044-4-4-4-44000000000000000000−22−2222222222−22−220000000000000000000000000000000000000000000000
χ7644-4-4-44-44-24i4i−4i−4i0000-222-22-224i−4i0000004-40000−2i−2i2i2i0000000000000000000000−2i2i00-2200000000000000000000000000
χ7744-4-4-44-44-24i4i−4i−4i0000-222-22-22−4i4i000000-440000−2i−2i2i2i00000000000000000000002i−2i002-200000000000000000000000000
χ7844-4-4-44-44-2−4i−4i4i4i0000-222-22-224i−4i000000-4400002i2i−2i−2i0000000000000000000000−2i2i002-200000000000000000000000000
χ7944-4-4-44-44-2−4i−4i4i4i0000-222-22-22−4i4i0000004-400002i2i−2i−2i00000000000000000000002i−2i00-2200000000000000000000000000
χ804-444-44-4-4400000000-4-444-4-44000000000000000000−2i22i2−2i22i22i2−2i22i2−2i20000000000000000000000000000000000000000000000
χ814-444-44-4-4400000000-4-444-4-440000000000000000002i2−2i22i2−2i2−2i22i2−2i22i20000000000000000000000000000000000000000000000
χ824-44-44-4-44-24i−4i4i−4i00002-2-222-22004i−4i004-4000000−2i2i−2i2i000000000000000000000000-2200−2i2i000000000000000000000000
χ834-44-44-4-44-24i−4i4i−4i00002-2-222-2200−4i4i00-44000000−2i2i−2i2i0000000000000000000000002-2002i−2i000000000000000000000000
χ844-44-44-4-44-2−4i4i−4i4i00002-2-222-22004i−4i00-440000002i−2i2i−2i0000000000000000000000002-200−2i2i000000000000000000000000
χ854-44-44-4-44-2−4i4i−4i4i00002-2-222-2200−4i4i004-40000002i−2i2i−2i000000000000000000000000-22002i−2i000000000000000000000000
χ864-4-44-4-444-24-4-4444-4-42222-2-2-200004-40000-22-22-222-200000000000000000000-2200000000000000000000000000000000
χ874-4-44-4-444-24-4-44-4-4442222-2-2-20000-4400002-22-2-222-2000000000000000000002-200000000000000000000000000000000
χ884-4-44-4-444-2-444-444-4-42222-2-2-20000-440000-22-222-2-22000000000000000000002-200000000000000000000000000000000
χ894-4-44-4-444-2-444-4-4-4442222-2-2-200004-400002-22-22-2-2200000000000000000000-2200000000000000000000000000000000
χ904-4-4-4444-440000-44-44-44-444-4-40000000000-444-40000000000000000000000000000000000000000000000000000000000
χ914-4-4-4444-4-200004-44-42-22-2-2220000000000-222-20000000000004i−4i00−2i2i−2i2i00000000000000000000000000000000000000
χ924-4-4-4444-4-200004-44-42-22-2-2220000000000-222-2000000000000−4i4i002i−2i2i−2i00000000000000000000000000000000000000
χ934-4-4-4444-4-20000-44-442-22-2-22200000000002-2-22000000000000000023−23−232300000000000000000000000000000000000000
χ944-4-4-4444-4-20000-44-442-22-2-22200000000002-2-220000000000000000−232323−2300000000000000000000000000000000000000
χ9588-888-8-8-8-400000000-4-44444-4000000000000000000000000000000000000000000000000000000000000000000000000
χ968-888-88-8-8-40000000044-4-444-4000000000000000000000000000000000000000000000000000000000000000000000000

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