Finite Group Databasebeta

← Group #10846249

Character table — Group #10846249

Order 768.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96
size111111112222222222222222444444444444444444666666668888888888888888888888121212121212121212121212161616161616242424244848
order12222222344444444666666644888888881212121212121212888888882244666612121212121224242424242424242244444488884412121212444424
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-111-1-1-1-111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1
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
χ4111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111
χ511111111111111111111111111-1-1-1-1-1-1-1-1111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-11111-1-1
χ611111111111111111111111111-1-1-1-1-1-1-1-11111111111111111-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111-1-1-1-111
χ711111111111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-111
χ811111111111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-11111111111-1-1
χ9111111111-1-1-1-111111111111-1-11111-1-1-1-111-1-1-1-1111111111111-1-11111-1-1-1-1-1-11111-1-1-1-1-1-11111-1-1-1-1-1-1-11-1-111-1-1111-1
χ10111111111-1-1-1-111111111111-1-11111-1-1-1-111-1-1-1-11111111111-1-111-1-1-1-1-1-111111111-1-1-1-1-1-11111-1-1-1-1-1-11-111-1-111-1-1-11
χ11111111111-1-1-1-111111111111-1-11111-1-1-1-111-1-1-1-111-1-1-1-1-1-1-1-111-1-11111-1-1-1-1-1-11111-1-1-1-111-1-1-1-1111111-11-1-11111-1-1-11
χ12111111111-1-1-1-111111111111-1-11111-1-1-1-111-1-1-1-111-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-111111111-1-1-1-111-1-1-1-11111111-111-1-1-1-1111-1
χ13111111111-1-1-1-111111111111-1-1-1-1-1-1111111-1-1-1-1111111111111-1-11111-1-1-1-1-1-1-1-1-1-1111111-1-1-1-111-1-1-1-11-111-1-1-1-111-11
χ14111111111-1-1-1-111111111111-1-1-1-1-1-1111111-1-1-1-11111111111-1-111-1-1-1-1-1-11111-1-1-1-1111111-1-1-1-111-1-1-1-1-11-1-11111-1-11-1
χ15111111111-1-1-1-111111111111-1-1-1-1-1-1111111-1-1-1-111-1-1-1-1-1-1-1-111-1-11111-1-1-1-1-1-1-1-1-1-11111-1-11111-1-111111-111-1-111-1-11-1
χ16111111111-1-1-1-111111111111-1-1-1-1-1-1111111-1-1-1-111-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-11111-1-1-1-11111-1-11111-1-11111-11-1-111-1-111-11
χ172222222222222-2-2-2-22222222-2-200000000-2-22222-2-20000000000000000-2-200000000000022-2-222-2-20000000000000000
χ182222222222222-2-2-2-22222222-2-200000000-2-22222-2-20000000000000000-2-2000000000000-2-222-2-2220000000000000000
χ19222222222-2-2-2-2-2-2-2-222222222200000000-2-2-2-2-2-2-2-20000000000000000220000000000002222-2-2-2-20000000000000000
χ20222222222-2-2-2-2-2-2-2-222222222200000000-2-2-2-2-2-2-2-2000000000000000022000000000000-2-2-2-222220000000000000000
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
χ2222222222-122222222-1-1-1-1-1-1-12222222222-1-1-1-1-1-1-1-100000000-2-2-2-21111-1-11111-1-1-1-1-1-1-1-1000000000000-2-21111000000
χ2322222222-122222222-1-1-1-1-1-1-122-2-2-2-2-2-2-2-2-1-1-1-1-1-1-1-1000000002222-1-1-1-1-1-1-1-1-1-111111111000000000000-2-21111000000
χ2422222222-122222222-1-1-1-1-1-1-122-2-2-2-2-2-2-2-2-1-1-1-1-1-1-1-100000000-2-2-2-21111-1-111111111111100000000000022-1-1-1-1000000
χ2522222222-1-2-2-2-22222-1-1-1-1-1-1-1-2-22222-2-2-2-2-1-11111-1-10000000022-2-2-1-1-1-1111111-1-1-1-11111000000000000-2211-1-1000000
χ2622222222-1-2-2-2-22222-1-1-1-1-1-1-1-2-22222-2-2-2-2-1-11111-1-100000000-2-222111111-1-1-1-1-1-1-1-111110000000000002-2-1-111000000
χ2722222222-1-2-2-2-22222-1-1-1-1-1-1-1-2-2-2-2-2-22222-1-11111-1-10000000022-2-2-1-1-1-11111111111-1-1-1-10000000000002-2-1-111000000
χ2822222222-1-2-2-2-22222-1-1-1-1-1-1-1-2-2-2-2-2-22222-1-11111-1-100000000-2-222111111-1-1-1-11111-1-1-1-1000000000000-2211-1-1000000
χ29222-2-2-2-2222i2i−2i−2i2-2-2222-2-2-22-22i−2i000000002-22i2i−2i−2i2-22222-2-2-2-2000000002i−2i000000000000000000002i2i−2i−2i000000000000
χ30222-2-2-2-2222i2i−2i−2i2-2-2222-2-2-22-22i−2i000000002-22i2i−2i−2i2-2-2-2-2-22222000000002i−2i00000000000000000000−2i−2i2i2i000000000000
χ31222-2-2-2-2222i2i−2i−2i-222-222-2-2-22-2−2i2i22-2-22i2i−2i−2i-222i2i−2i−2i-220000000000000000−2i2i000022-2-22i2i−2i−2i000000000000000000000000
χ32222-2-2-2-2222i2i−2i−2i-222-222-2-2-22-2−2i2i-2-222−2i−2i2i2i-222i2i−2i−2i-220000000000000000−2i2i0000-2-222−2i−2i2i2i000000000000000000000000
χ33222-2-2-2-222−2i−2i2i2i2-2-2222-2-2-22-2−2i2i000000002-2−2i−2i2i2i2-22222-2-2-2-200000000−2i2i00000000000000000000−2i−2i2i2i000000000000
χ34222-2-2-2-222−2i−2i2i2i2-2-2222-2-2-22-2−2i2i000000002-2−2i−2i2i2i2-2-2-2-2-2222200000000−2i2i000000000000000000002i2i−2i−2i000000000000
χ35222-2-2-2-222−2i−2i2i2i-222-222-2-2-22-22i−2i22-2-2−2i−2i2i2i-22−2i−2i2i2i-2200000000000000002i−2i000022-2-2−2i−2i2i2i000000000000000000000000
χ36222-2-2-2-222−2i−2i2i2i-222-222-2-2-22-22i−2i-2-2222i2i−2i−2i-22−2i−2i2i2i-2200000000000000002i−2i0000-2-2222i2i−2i−2i000000000000000000000000
χ37222-2-2-2-22-12i2i−2i−2i-222-2-1-1111-11−2i2i22-2-22i2i−2i−2i1-1−i−iii1-1000000000000−i3−i3i3i3i−i33−3−3-1-111−i−iii000000000000003−3−i3i3000000
χ38222-2-2-2-22-12i2i−2i−2i-222-2-1-1111-11−2i2i22-2-22i2i−2i−2i1-1−i−iii1-1000000000000i3i3−i3−i3i−i−3−333-1-111−i−iii00000000000000−33i3−i3000000
χ39222-2-2-2-22-12i2i−2i−2i-222-2-1-1111-11−2i2i-2-222−2i−2i2i2i1-1−i−iii1-1000000000000−i3−i3i3i3i−i33−3−311-1-1ii−i−i00000000000000−33i3−i3000000
χ40222-2-2-2-22-12i2i−2i−2i-222-2-1-1111-11−2i2i-2-222−2i−2i2i2i1-1−i−iii1-1000000000000i3i3−i3−i3i−i−3−33311-1-1ii−i−i000000000000003−3−i3i3000000
χ41222-2-2-2-22-1−2i−2i2i2i-222-2-1-1111-112i−2i22-2-2−2i−2i2i2i1-1ii−i−i1-1000000000000−i3−i3i3i3−ii−3−333-1-111ii−i−i00000000000000−33−i3i3000000
χ42222-2-2-2-22-1−2i−2i2i2i-222-2-1-1111-112i−2i22-2-2−2i−2i2i2i1-1ii−i−i1-1000000000000i3i3−i3−i3−ii33−3−3-1-111ii−i−i000000000000003−3i3−i3000000
χ43222-2-2-2-22-1−2i−2i2i2i-222-2-1-1111-112i−2i-2-2222i2i−2i−2i1-1ii−i−i1-1000000000000−i3−i3i3i3−ii−3−33311-1-1−i−iii000000000000003−3i3−i3000000
χ44222-2-2-2-22-1−2i−2i2i2i-222-2-1-1111-112i−2i-2-2222i2i−2i−2i1-1ii−i−i1-1000000000000i3i3−i3−i3−ii33−3−311-1-1−i−iii00000000000000−33−i3i3000000
χ4522-22-2-22-222-22-200002-22-2-2-2200−i2i2−i2i2−i2i2−i2i2002-22-200−i2−i2i2i2−i2−i2i2i200000000000000−i2i2−i2i2−i2i2−i2i22-2002-200−i2i2−i2i2000000000000
χ4622-22-2-22-222-22-200002-22-2-2-2200−i2i2−i2i2−i2i2−i2i2002-22-200i2i2−i2−i2i2i2−i2−i200000000000000−i2i2−i2i2−i2i2−i2i2-2200-2200i2−i2i2−i2000000000000
χ4722-22-2-22-222-22-200002-22-2-2-2200i2−i2i2−i2i2−i2i2−i2002-22-200−i2−i2i2i2−i2−i2i2i200000000000000i2−i2i2−i2i2−i2i2−i2-2200-2200−i2i2−i2i2000000000000
χ4822-22-2-22-222-22-200002-22-2-2-2200i2−i2i2−i2i2−i2i2−i2002-22-200i2i2−i2−i2i2i2−i2−i200000000000000i2−i2i2−i2i2−i2i2−i22-2002-200i2−i2i2−i2000000000000
χ4922-22-2-22-22-22-2200002-22-2-2-2200−i2i2−i2i2i2−i2i2−i200-22-2200−i2−i2i2i2−i2−i2i2i200000000000000−i2i2−i2i2i2−i2i2−i2-22002-200i2−i2i2−i2000000000000
χ5022-22-2-22-22-22-2200002-22-2-2-2200−i2i2−i2i2i2−i2i2−i200-22-2200i2i2−i2−i2i2i2−i2−i200000000000000−i2i2−i2i2i2−i2i2−i22-200-2200−i2i2−i2i2000000000000
χ5122-22-2-22-22-22-2200002-22-2-2-2200i2−i2i2−i2−i2i2−i2i200-22-2200−i2−i2i2i2−i2−i2i2i200000000000000i2−i2i2−i2−i2i2−i2i22-200-2200i2−i2i2−i2000000000000
χ5222-22-2-22-22-22-2200002-22-2-2-2200i2−i2i2−i2−i2i2−i2i200-22-2200i2i2−i2−i2i2i2−i2−i200000000000000i2−i2i2−i2−i2i2−i2i2-22002-200−i2i2−i2i2000000000000
χ5322-2-222-2-222i−2i−2i2i00002-2-222-2-200−i2i2i2−i22−2−22002i−2i−2i2i00−i2−i2i2i2i2i2−i2−i200000000000000−i2i2i2−i22−2−22002-2002i−2i2−2−22000000000000
χ5422-2-222-2-222i−2i−2i2i00002-2-222-2-200−i2i2i2−i22−2−22002i−2i−2i2i00i2i2−i2−i2−i2−i2i2i200000000000000−i2i2i2−i22−2−2200-2200−2i2i−222−2000000000000
χ5522-2-222-2-222i−2i−2i2i00002-2-222-2-200i2−i2−i2i2−222−2002i−2i−2i2i00−i2−i2i2i2i2i2−i2−i200000000000000i2−i2−i2i2−222−200-2200−2i2i2−2−22000000000000
χ5622-2-222-2-222i−2i−2i2i00002-2-222-2-200i2−i2−i2i2−222−2002i−2i−2i2i00i2i2−i2−i2−i2−i2i2i200000000000000i2−i2−i2i2−222−2002-2002i−2i−222−2000000000000
χ5722-2-222-2-22−2i2i2i−2i00002-2-222-2-200−i2i2i2−i2−222−200−2i2i2i−2i00−i2−i2i2i2i2i2−i2−i200000000000000−i2i2i2−i2−222−2002-200−2i2i−222−2000000000000
χ5822-2-222-2-22−2i2i2i−2i00002-2-222-2-200−i2i2i2−i2−222−200−2i2i2i−2i00i2i2−i2−i2−i2−i2i2i200000000000000−i2i2i2−i2−222−200-22002i−2i2−2−22000000000000
χ5922-2-222-2-22−2i2i2i−2i00002-2-222-2-200i2−i2−i2i22−2−2200−2i2i2i−2i00−i2−i2i2i2i2i2−i2−i200000000000000i2−i2−i2i22−2−2200-22002i−2i−222−2000000000000
χ6022-2-222-2-22−2i2i2i−2i00002-2-222-2-200i2−i2−i2i22−2−2200−2i2i2i−2i00i2i2−i2−i2−i2−i2i2i200000000000000i2−i2−i2i22−2−22002-200−2i2i2−2−22000000000000
χ612-2-22-22-2220000-2-222-2-2-22-2220000000000-2200002-22-22-22-22-2002-20000002-22-2000000000000000000000000002-20000
χ622-2-22-22-2220000-2-222-2-2-22-2220000000000-2200002-22-22-22-22-200-22000000-22-2200000000000000000000000000-220000
χ632-2-22-22-2220000-2-222-2-2-22-2220000000000-2200002-2-22-22-22-22002-20000002-22-200000000000000000000000000-220000
χ642-2-22-22-2220000-2-222-2-2-22-2220000000000-2200002-2-22-22-22-2200-22000000-22-22000000000000000000000000002-20000
χ652-2-2-22-22220000-22-22-2-22-222-20000000000-2-20000222-22-2-22-222-2002-22-200000000000000000000000000000000002-200
χ662-2-2-22-22220000-22-22-2-22-222-20000000000-2-20000222-22-2-22-22-2200-22-220000000000000000000000000000000000-2200
χ672-2-2-22-22220000-22-22-2-22-222-20000000000-2-2000022-22-222-22-22-2002-22-20000000000000000000000000000000000-2200
χ682-2-2-22-22220000-22-22-2-22-222-20000000000-2-2000022-22-222-22-2-2200-22-2200000000000000000000000000000000002-200
χ6944444444-24444-4-4-4-4-2-2-2-2-2-2-2-4-40000000022-2-2-2-222000000000000000022000000000000000000000000000000000000
χ7044444444-2-4-4-4-4-4-4-4-4-2-2-2-2-2-2-24400000000222222220000000000000000-2-2000000000000000000000000000000000000
χ71444-4-4-4-44-24i4i−4i−4i4-4-44-2-2222-224i−4i00000000-22−2i−2i2i2i-220000000000000000−2i2i000000000000000000000000000000000000
χ72444-4-4-4-44-2−4i−4i4i4i4-4-44-2-2222-22−4i4i00000000-222i2i−2i−2i-2200000000000000002i−2i000000000000000000000000000000000000
χ7344-44-4-44-4-24-44-40000-22-2222-200−2i22i2−2i22i2−2i22i2−2i22i200-22-22000000000000000000000000i2−i2i2−i2i2−i2i2−i2000000000000000000000000
χ7444-44-4-44-4-24-44-40000-22-2222-2002i2−2i22i2−2i22i2−2i22i2−2i200-22-22000000000000000000000000−i2i2−i2i2−i2i2−i2i2000000000000000000000000
χ7544-44-4-44-4-2-44-440000-22-2222-200−2i22i2−2i22i22i2−2i22i2−2i2002-22-2000000000000000000000000i2−i2i2−i2−i2i2−i2i2000000000000000000000000
χ7644-44-4-44-4-2-44-440000-22-2222-2002i2−2i22i2−2i2−2i22i2−2i22i2002-22-2000000000000000000000000−i2i2−i2i2i2−i2i2−i2000000000000000000000000
χ7744-4-444-4-4-24i−4i−4i4i0000-222-2-22200−2i22i22i2−2i222−22−222200−2i2i2i−2i000000000000000000000000i2−i2−i2i2−222−2000000000000000000000000
χ7844-4-444-4-4-24i−4i−4i4i0000-222-2-222002i2−2i2−2i22i2−222222−2200−2i2i2i−2i000000000000000000000000−i2i2i2−i22−2−22000000000000000000000000
χ7944-4-444-4-4-2−4i4i4i−4i0000-222-2-22200−2i22i22i2−2i2−222222−22002i−2i−2i2i000000000000000000000000i2−i2−i2i22−2−22000000000000000000000000
χ8044-4-444-4-4-2−4i4i4i−4i0000-222-2-222002i2−2i2−2i22i222−22−2222002i−2i−2i2i000000000000000000000000−i2i2i2−i2−222−2000000000000000000000000
χ814-4444-4-4-4400000000-44-4-44-44000000000000000000−2i22i22i2−2i2−2i22i22i2−2i20000000000000000000000000000000000000000000000
χ824-4444-4-4-4400000000-44-4-44-440000000000000000002i2−2i2−2i22i22i2−2i2−2i22i20000000000000000000000000000000000000000000000
χ834-44-4-444-4400000000-4444-4-4-4000000000000000000−2i22i22i2−2i22i2−2i2−2i22i20000000000000000000000000000000000000000000000
χ844-44-4-444-4400000000-4444-4-4-40000000000000000002i2−2i2−2i22i2−2i22i22i2−2i20000000000000000000000000000000000000000000000
χ854-4-44-44-444000044-4-4-4-4-44-44400000000004-40000-44000000000000000000000000000000000000000000000000000000
χ864-4-44-44-44-2000044-4-4222-22-2-20000000000-2200002-2000000000000−2i32i32i3−2i300000000000000000000000000000000000000
χ874-4-44-44-44-2000044-4-4222-22-2-20000000000-2200002-20000000000002i3−2i3−2i32i300000000000000000000000000000000000000
χ884-4-44-44-44-20000-4-444222-22-2-200000000002-20000-2200000000004-4000000-22-2200000000000000000000000000000000
χ894-4-44-44-44-20000-4-444222-22-2-200000000002-20000-220000000000-440000002-22-200000000000000000000000000000000
χ904-4-4-44-444400004-44-4-4-44-444-40000000000440000-4-4000000000000000000000000000000000000000000000000000000
χ914-4-4-44-444-200004-44-422-22-2-220000000000-2-200002200000000000000000023−23−232300000000000000000000000000000000
χ924-4-4-44-444-200004-44-422-22-2-220000000000-2-2000022000000000000000000−232323−2300000000000000000000000000000000
χ934-4-4-44-444-20000-44-4422-22-2-220000000000220000-2-2000000004-400-22-2200000000000000000000000000000000000000
χ944-4-4-44-444-20000-44-4422-22-2-220000000000220000-2-200000000-44002-22-200000000000000000000000000000000000000
χ958-8888-8-8-8-4000000004-444-44-4000000000000000000000000000000000000000000000000000000000000000000000000
χ968-88-8-888-8-4000000004-4-4-4444000000000000000000000000000000000000000000000000000000000000000000000000

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