Finite Group Databasebeta

← Group #10846247

Character table — Group #10846247

Order 768.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96
size111111112222222222222222444444444444444444666666668888888888888888888888121212121212121212121212161616161616242424244848
order1222222234444444466666662244444444121212121212121288888888224466666612121212121212121212121288888888888824661212444444
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111111111111111-1-1-1-111-1-1-1-111111111-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-1
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
χ4111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111
χ5111111111111111111111111-1-1-1-111-1-1-1-111111111111111111111-1-1111111-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1
χ6111111111111111111111111-1-1-1-111-1-1-1-11111111111111111-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1111111-1-1-1-111
χ7111111111111111111111111-1-1-1-111-1-1-1-111111111-1-1-1-1-1-1-1-11111-1-1111111-1-1-1-1-1-11111-1-1-1-111111111-1-1-1-1-1-1-1-1-1-111
χ8111111111111111111111111-1-1-1-111-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111111111-1-1
χ9111111111-1-1-1-11111111111111-1-1-1-1-1-1111111-1-1-1-11111111111-1-1111111-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-11-1-111-1-1111-1
χ10111111111-1-1-1-11111111111111-1-1-1-1-1-1111111-1-1-1-111111111-1-11111-1-1-1-1-1-1-1-111-1-11111-1-1-1-1-1-1-1-111111-111-1-111-1-1-11
χ11111111111-1-1-1-11111111111111-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-111-1-1111111-1-1-1-111-1-1-1-1-1-111111111-1-1-1-1-11-1-11111-1-1-11
χ12111111111-1-1-1-11111111111111-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-111-1-1111111111111-1-1-1-11-111-1-1-1-1111-1
χ13111111111-1-1-1-111111111111-1-111-1-111-1-11111-1-1-1-11111111111-1-1-1-11111-1-111-1-111-1-1-1-1-1-1-1-11111-1-1-1-11-111-1-1-1-111-11
χ14111111111-1-1-1-111111111111-1-111-1-111-1-11111-1-1-1-111111111-1-111-1-1-1-1-1-1-1-111-1-1111111-1-1-1-11111-1-1-1-1-11-1-11111-1-11-1
χ15111111111-1-1-1-111111111111-1-111-1-111-1-11111-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-11111-1-111-1-111-1-1-1-11111-1-1-1-111111-111-1-111-1-11-1
χ16111111111-1-1-1-111111111111-1-111-1-111-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-111-1-11111111111-1-1-1-11111-11-1-111-1-111-11
χ172222222222222-2-2-2-222222222222-2-2-2-2-2-2-2-2-2-22222000000000000220000-2-2-2-2-2-2220000000000000000000000000000
χ182222222222222-2-2-2-22222222-2-2-2-2-2-22222-2-2-2-22222000000000000-2-20000-2-22222-2-20000000000000000000000000000
χ19222222222-2-2-2-2-2-2-2-2222222222-2-22222-2-2-2-2-2-2-2-2-2-20000000000002200002222-2-2-2-20000000000000000000000000000
χ20222222222-2-2-2-2-2-2-2-22222222-2-22222-2-222-2-2-2-2-2-2-2-2000000000000-2-2000022-2-222220000000000000000000000000000
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
χ2222222222-122222222-1-1-1-1-1-1-12222222222-1-1-1-1-1-1-1-100000000-2-2-2-2-1-11111-1-1-1-1-1-1-1-11111000000000000-2-21111000000
χ2322222222-122222222-1-1-1-1-1-1-1-2-2-2-222-2-2-2-2-1-1-1-1-1-1-1-100000000222211-1-1-1-1-1-1111111-1-1-1-1000000000000-2-21111000000
χ2422222222-122222222-1-1-1-1-1-1-1-2-2-2-222-2-2-2-2-1-1-1-1-1-1-1-100000000-2-2-2-2111111-1-1111111111100000000000022-1-1-1-1000000
χ2522222222-12222-2-2-2-2-1-1-1-1-1-1-12222-2-2-2-2-2-21111-1-1-1-1000000000000-1-1−i3−i3i3i3111111-1-1−i3−i3i3i300000000000000−i3i3−i3i3000000
χ2622222222-12222-2-2-2-2-1-1-1-1-1-1-12222-2-2-2-2-2-21111-1-1-1-1000000000000-1-1i3i3−i3−i3111111-1-1i3i3−i3−i300000000000000i3−i3i3−i3000000
χ2722222222-12222-2-2-2-2-1-1-1-1-1-1-1-2-2-2-2-2-222221111-1-1-1-100000000000011−i3−i3i3i311-1-1-1-111−i3−i3i3i300000000000000i3−i3i3−i3000000
χ2822222222-12222-2-2-2-2-1-1-1-1-1-1-1-2-2-2-2-2-222221111-1-1-1-100000000000011i3i3−i3−i311-1-1-1-111i3i3−i3−i300000000000000−i3i3−i3i3000000
χ2922222222-1-2-2-2-22222-1-1-1-1-1-1-122-2-2-2-2-2-222-1-1-1-111110000000022-2-2-1-1-1-1-1-11111-1-1111111000000000000-2211-1-1000000
χ3022222222-1-2-2-2-22222-1-1-1-1-1-1-122-2-2-2-2-2-222-1-1-1-1111100000000-2-222-1-111111111-1-111-1-1-1-10000000000002-2-1-111000000
χ3122222222-1-2-2-2-22222-1-1-1-1-1-1-1-2-222-2-222-2-2-1-1-1-111110000000022-2-211-1-1-1-111-1-111-1-111110000000000002-2-1-111000000
χ3222222222-1-2-2-2-22222-1-1-1-1-1-1-1-2-222-2-222-2-2-1-1-1-1111100000000-2-22211111111-1-111-1-1-1-1-1-1000000000000-2211-1-1000000
χ3322222222-1-2-2-2-2-2-2-2-2-1-1-1-1-1-1-122-2-22222-2-211111111000000000000-1-1−i3−i3i3i3-1-1-1-11111i3i3−i3−i300000000000000i3−i3−i3i3000000
χ3422222222-1-2-2-2-2-2-2-2-2-1-1-1-1-1-1-122-2-22222-2-211111111000000000000-1-1i3i3−i3−i3-1-1-1-11111−i3−i3i3i300000000000000−i3i3i3−i3000000
χ3522222222-1-2-2-2-2-2-2-2-2-1-1-1-1-1-1-1-2-22222-2-2221111111100000000000011−i3−i3i3i3-1-111-1-1-1-1i3i3−i3−i300000000000000−i3i3i3−i3000000
χ3622222222-1-2-2-2-2-2-2-2-2-1-1-1-1-1-1-1-2-22222-2-2221111111100000000000011i3i3−i3−i3-1-111-1-1-1-1−i3−i3i3i300000000000000i3−i3−i3i3000000
χ37222-2-2-2-2222i2i−2i−2i2-2-2222-2-22-2-200002i−2i000022-2-22i2i−2i−2i2222-2-2-2-200000000002i−2i00000000002i2i−2i−2i00000000000000000000
χ38222-2-2-2-2222i2i−2i−2i2-2-2222-2-22-2-200002i−2i000022-2-22i2i−2i−2i-2-2-2-2222200000000002i−2i0000000000−2i−2i2i2i00000000000000000000
χ39222-2-2-2-2222i2i−2i−2i-222-222-2-22-2-20000−2i2i0000-2-2222i2i−2i−2i000000000000000000−2i2i0000000000000022-2-22i2i−2i−2i000000000000
χ40222-2-2-2-2222i2i−2i−2i-222-222-2-22-2-20000−2i2i0000-2-2222i2i−2i−2i000000000000000000−2i2i00000000000000-2-222−2i−2i2i2i000000000000
χ41222-2-2-2-222−2i−2i2i2i2-2-2222-2-22-2-20000−2i2i000022-2-2−2i−2i2i2i2222-2-2-2-20000000000−2i2i0000000000−2i−2i2i2i00000000000000000000
χ42222-2-2-2-222−2i−2i2i2i2-2-2222-2-22-2-20000−2i2i000022-2-2−2i−2i2i2i-2-2-2-222220000000000−2i2i00000000002i2i−2i−2i00000000000000000000
χ43222-2-2-2-222−2i−2i2i2i-222-222-2-22-2-200002i−2i0000-2-222−2i−2i2i2i0000000000000000002i−2i0000000000000022-2-2−2i−2i2i2i000000000000
χ44222-2-2-2-222−2i−2i2i2i-222-222-2-22-2-200002i−2i0000-2-222−2i−2i2i2i0000000000000000002i−2i00000000000000-2-2222i2i−2i−2i000000000000
χ4522-222-2-2-222-22-200002-2-2-2-2222-22-200000000002-22-2−i2−i2i2i2−i2−i2i2i200002-200000000002-20000−i2i2−i2i2−i2i2−i2i2−i2i2−i2i2000000000000
χ4622-222-2-2-222-22-200002-2-2-2-2222-22-200000000002-22-2i2i2−i2−i2i2i2−i2−i200002-200000000002-20000i2−i2i2−i2i2−i2i2−i2i2−i2i2−i2000000000000
χ4722-222-2-2-222-22-200002-2-2-2-222-22-2200000000002-22-2−i2−i2i2i2−i2−i2i2i20000-220000000000-220000−i2i2−i2i2i2−i2i2−i2i2−i2i2−i2000000000000
χ4822-222-2-2-222-22-200002-2-2-2-222-22-2200000000002-22-2i2i2−i2−i2i2i2−i2−i20000-220000000000-220000i2−i2i2−i2−i2i2−i2i2−i2i2−i2i2000000000000
χ4922-222-2-2-22-22-2200002-2-2-2-2222-2-220000000000-22-22−i2−i2i2i2−i2−i2i2i200002-20000000000-220000i2−i2i2−i2i2−i2i2−i2−i2i2−i2i2000000000000
χ5022-222-2-2-22-22-2200002-2-2-2-2222-2-220000000000-22-22i2i2−i2−i2i2i2−i2−i200002-20000000000-220000−i2i2−i2i2−i2i2−i2i2i2−i2i2−i2000000000000
χ5122-222-2-2-22-22-2200002-2-2-2-222-222-20000000000-22-22−i2−i2i2i2−i2−i2i2i20000-2200000000002-20000i2−i2i2−i2−i2i2−i2i2i2−i2i2−i2000000000000
χ5222-222-2-2-22-22-2200002-2-2-2-222-222-20000000000-22-22i2i2−i2−i2i2i2−i2−i20000-2200000000002-20000−i2i2−i2i2i2−i2i2−i2−i2i2−i2i2000000000000
χ5322-2-2-222-222i−2i−2i2i00002-222-2-2-20000002-22i−2i00002i−2i−2i2i−i2−i2i2i2i2i2−i2−i20000000000002-22i−2i0000002−2−22−i2i2i2−i22−2−22000000000000
χ5422-2-2-222-222i−2i−2i2i00002-222-2-2-20000002-22i−2i00002i−2i−2i2ii2i2−i2−i2−i2−i2i2i20000000000002-22i−2i000000−222−2i2−i2−i2i2−222−2000000000000
χ5522-2-2-222-222i−2i−2i2i00002-222-2-2-2000000-22−2i2i00002i−2i−2i2i−i2−i2i2i2i2i2−i2−i2000000000000-22−2i2i0000002−2−22i2−i2−i2i2−222−2000000000000
χ5622-2-2-222-222i−2i−2i2i00002-222-2-2-2000000-22−2i2i00002i−2i−2i2ii2i2−i2−i2−i2−i2i2i2000000000000-22−2i2i000000−222−2−i2i2i2−i22−2−22000000000000
χ5722-2-2-222-22−2i2i2i−2i00002-222-2-2-20000002-2−2i2i0000−2i2i2i−2i−i2−i2i2i2i2i2−i2−i20000000000002-2−2i2i000000−222−2−i2i2i2−i2−222−2000000000000
χ5822-2-2-222-22−2i2i2i−2i00002-222-2-2-20000002-2−2i2i0000−2i2i2i−2ii2i2−i2−i2−i2−i2i2i20000000000002-2−2i2i0000002−2−22i2−i2−i2i22−2−22000000000000
χ5922-2-2-222-22−2i2i2i−2i00002-222-2-2-2000000-222i−2i0000−2i2i2i−2i−i2−i2i2i2i2i2−i2−i2000000000000-222i−2i000000−222−2i2−i2−i2i22−2−22000000000000
χ6022-2-2-222-22−2i2i2i−2i00002-222-2-2-2000000-222i−2i0000−2i2i2i−2ii2i2−i2−i2−i2−i2i2i2000000000000-222i−2i0000002−2−22−i2i2i2−i2−222−2000000000000
χ612-2-22-22-2220000-22-22-2-22-222-200000000002-22-200002-22-22-22-2002-2000000000000002-22-20000000000000000002-20000
χ622-2-22-22-2220000-22-22-2-22-222-200000000002-22-200002-22-22-22-200-2200000000000000-22-22000000000000000000-220000
χ632-2-22-22-2220000-22-22-2-22-222-200000000002-22-20000-22-22-22-22002-2000000000000002-22-2000000000000000000-220000
χ642-2-22-22-2220000-22-22-2-22-222-200000000002-22-20000-22-22-22-2200-2200000000000000-22-220000000000000000002-20000
χ652-2-2-22-22220000-2-222-2-2-222-2200000000002-2-2200002-22-2-22-222-200002-22-2000000000000000000000000000000002-200
χ662-2-2-22-22220000-2-222-2-2-222-2200000000002-2-2200002-22-2-22-22-220000-22-2200000000000000000000000000000000-2200
χ672-2-2-22-22220000-2-222-2-2-222-2200000000002-2-220000-22-222-22-22-200002-22-200000000000000000000000000000000-2200
χ682-2-2-22-22220000-2-222-2-2-222-2200000000002-2-220000-22-222-22-2-220000-22-22000000000000000000000000000000002-200
χ69444-4-4-4-44-24i4i−4i−4i4-4-44-2-222-22200004i−4i0000-2-222−2i−2i2i2i000000000000000000−2i2i0000000000000000000000000000000000
χ70444-4-4-4-44-24i4i−4i−4i-444-4-2-222-2220000−4i4i000022-2-2−2i−2i2i2i0000000000000000002i−2i0000000000000000000000000000000000
χ71444-4-4-4-44-2−4i−4i4i4i4-4-44-2-222-2220000−4i4i0000-2-2222i2i−2i−2i0000000000000000002i−2i0000000000000000000000000000000000
χ72444-4-4-4-44-2−4i−4i4i4i-444-4-2-222-22200004i−4i000022-2-22i2i−2i−2i000000000000000000−2i2i0000000000000000000000000000000000
χ7344-444-4-4-4-24-44-40000-22222-2-24-44-40000000000-22-22000000000000-220000000000-220000000000000000000000000000
χ7444-444-4-4-4-24-44-40000-22222-2-2-44-440000000000-22-220000000000002-200000000002-20000000000000000000000000000
χ7544-444-4-4-4-2-44-440000-22222-2-24-4-4400000000002-22-2000000000000-2200000000002-20000000000000000000000000000
χ7644-444-4-4-4-2-44-440000-22222-2-2-444-400000000002-22-20000000000002-20000000000-220000000000000000000000000000
χ7744-4-4-444-4-24i−4i−4i4i0000-22-2-22220000004-44i−4i0000−2i2i2i−2i00000000000000000000-22−2i2i000000000000000000000000000000
χ7844-4-4-444-4-24i−4i−4i4i0000-22-2-2222000000-44−4i4i0000−2i2i2i−2i000000000000000000002-22i−2i000000000000000000000000000000
χ7944-4-4-444-4-2−4i4i4i−4i0000-22-2-22220000004-4−4i4i00002i−2i−2i2i00000000000000000000-222i−2i000000000000000000000000000000
χ8044-4-4-444-4-2−4i4i4i−4i0000-22-2-2222000000-444i−4i00002i−2i−2i2i000000000000000000002-2−2i2i000000000000000000000000000000
χ814-444-4-44-4400000000-44-44-44-4000000000000000000−2i22i22i2−2i2−2i22i22i2−2i20000000000000000000000000000000000000000000000
χ824-444-4-44-4400000000-44-44-44-40000000000000000002i2−2i2−2i22i22i2−2i2−2i22i20000000000000000000000000000000000000000000000
χ834-44-444-4-4400000000-444-4-4-44000000000000000000−2i22i22i2−2i22i2−2i2−2i22i20000000000000000000000000000000000000000000000
χ844-44-444-4-4400000000-444-4-4-440000000000000000002i2−2i2−2i22i2−2i22i22i2−2i20000000000000000000000000000000000000000000000
χ854-4-44-44-44400004-44-4-4-44-444-40000000000-44-440000000000000000000000000000000000000000000000000000000000
χ864-4-44-44-44-200004-44-422-22-2-2200000000002-22-2000000000000000000000000000000−2i32i32i3−2i3000000000000000000000000
χ874-4-44-44-44-200004-44-422-22-2-2200000000002-22-20000000000000000000000000000002i3−2i3−2i32i3000000000000000000000000
χ884-4-44-44-44-20000-44-4422-22-2-220000000000-22-22000000000000004-400000000000000-22-22000000000000000000000000
χ894-4-44-44-44-20000-44-4422-22-2-220000000000-22-2200000000000000-44000000000000002-22-2000000000000000000000000
χ904-4-4-44-4444000044-4-4-4-4-444-440000000000-444-40000000000000000000000000000000000000000000000000000000000
χ914-4-4-44-444-2000044-4-4222-2-22-200000000002-2-22000000000000000000−2i32i32i3−2i3000000000000000000000000000000000000
χ924-4-4-44-444-2000044-4-4222-2-22-200000000002-2-220000000000000000002i3−2i3−2i32i3000000000000000000000000000000000000
χ934-4-4-44-444-20000-4-444222-2-22-20000000000-222-20000000000004-40000-22-22000000000000000000000000000000000000
χ944-4-4-44-444-20000-4-444222-2-22-20000000000-222-2000000000000-4400002-22-2000000000000000000000000000000000000
χ958-888-8-88-8-4000000004-44-44-44000000000000000000000000000000000000000000000000000000000000000000000000
χ968-88-888-8-8-4000000004-4-4444-4000000000000000000000000000000000000000000000000000000000000000000000000

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