Finite Group Databasebeta

← Group #10846257

Character table — Group #10846257

Order 768.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96
size111111112222222222222222444444444444444444666666668888888888888888888888121212121212121212121212161616161616242424244848
order1222222234444444466666664488888888121212121212121288888888444412121212121212121212242424242424242422444444888824661212224444
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111111111111111-1-1-1-111-1-1-1-1-1-1-1-111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1
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
χ4111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111
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
χ611111111111111111111111111-1-1-1-1-1-1-1-11111111111111111-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111-1-1-1-111
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
χ811111111111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-11111111111-1-1
χ9111111111-1-1-1-111111111111-1-11111-1-1-1-1-1-1-1-111111111111111-1-1-1-11111-1-1-1-11111-1-1-1-1-1-11111-1-1-1-1-1-1-11-1-111-1-1111-1
χ10111111111-1-1-1-111111111111-1-11111-1-1-1-1-1-1-1-1111111111111-1-111-1-1-1-1-1-111111111-1-1-1-1-1-11111-1-1-1-1-1-11-111-1-111-1-1-11
χ11111111111-1-1-1-111111111111-1-11111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-111-1-1-1-11111-1-1-1-11111-1-1-1-111-1-1-1-1111111-11-1-11111-1-1-11
χ12111111111-1-1-1-111111111111-1-11111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-111111111-1-1-1-111-1-1-1-11111111-111-1-1-1-1111-1
χ13111111111-1-1-1-111111111111-1-1-1-1-1-11111-1-1-1-111111111111111-1-1-1-11111-1-1-1-1-1-1-1-1111111-1-1-1-111-1-1-1-11-111-1-1-1-111-11
χ14111111111-1-1-1-111111111111-1-1-1-1-1-11111-1-1-1-1111111111111-1-111-1-1-1-1-1-11111-1-1-1-1111111-1-1-1-111-1-1-1-1-11-1-11111-1-11-1
χ15111111111-1-1-1-111111111111-1-1-1-1-1-11111-1-1-1-11111-1-1-1-1-1-1-1-111-1-1-1-11111-1-1-1-1-1-1-1-11111-1-11111-1-111111-111-1-111-1-11-1
χ16111111111-1-1-1-111111111111-1-1-1-1-1-11111-1-1-1-11111-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-11111-1-1-1-11111-1-11111-1-11111-11-1-111-1-111-11
χ172222222222222-2-2-2-22222222-2-2000000002222-2-2-2-2000000000000-2-200000000000000002222-2-2-2-20000000000000000
χ182222222222222-2-2-2-22222222-2-2000000002222-2-2-2-2000000000000-2-20000000000000000-2-2-2-222220000000000000000
χ19222222222-2-2-2-2-2-2-2-222222222200000000-2-2-2-2-2-2-2-200000000000022000000000000000022-2-222-2-20000000000000000
χ20222222222-2-2-2-2-2-2-2-222222222200000000-2-2-2-2-2-2-2-2000000000000220000000000000000-2-222-2-2220000000000000000
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
χ2222222222-122222222-1-1-1-1-1-1-12222222222-1-1-1-1-1-1-1-100000000-2-2-2-2-1-111111111-1-1-1-1-1-1-1-1000000000000-2-21111000000
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
χ2422222222-122222222-1-1-1-1-1-1-122-2-2-2-2-2-2-2-2-1-1-1-1-1-1-1-100000000-2-2-2-2-1-1111111111111111100000000000022-1-1-1-1000000
χ2522222222-1-2-2-2-22222-1-1-1-1-1-1-1-2-22222-2-2-2-21111-1-1-1-10000000022-2-211-1-1-1-11111-1-1-1-11111000000000000-2211-1-1000000
χ2622222222-1-2-2-2-22222-1-1-1-1-1-1-1-2-22222-2-2-2-21111-1-1-1-100000000-2-222111111-1-1-1-1-1-1-1-111110000000000002-2-1-111000000
χ2722222222-1-2-2-2-22222-1-1-1-1-1-1-1-2-2-2-2-2-222221111-1-1-1-10000000022-2-211-1-1-1-111111111-1-1-1-10000000000002-2-1-111000000
χ2822222222-1-2-2-2-22222-1-1-1-1-1-1-1-2-2-2-2-2-222221111-1-1-1-100000000-2-222111111-1-1-1-11111-1-1-1-1000000000000-2211-1-1000000
χ29222-2-2-2-2222i2i−2i−2i2-2-2222-2-2-22-22i−2i000000002i2i−2i−2i2-22-22222-2-2-2-200002i−2i0000000000000000000000002i2i−2i−2i000000000000
χ30222-2-2-2-2222i2i−2i−2i2-2-2222-2-2-22-22i−2i000000002i2i−2i−2i2-22-2-2-2-2-2222200002i−2i000000000000000000000000−2i−2i2i2i000000000000
χ31222-2-2-2-2222i2i−2i−2i-222-222-2-2-22-2−2i2i22-2-22i2i−2i−2i2i2i−2i−2i-22-22000000000000−2i2i0000000022-2-22i2i−2i−2i000000000000000000000000
χ32222-2-2-2-2222i2i−2i−2i-222-222-2-2-22-2−2i2i-2-222−2i−2i2i2i2i2i−2i−2i-22-22000000000000−2i2i00000000-2-222−2i−2i2i2i000000000000000000000000
χ33222-2-2-2-222−2i−2i2i2i2-2-2222-2-2-22-2−2i2i00000000−2i−2i2i2i2-22-22222-2-2-2-20000−2i2i000000000000000000000000−2i−2i2i2i000000000000
χ34222-2-2-2-222−2i−2i2i2i2-2-2222-2-2-22-2−2i2i00000000−2i−2i2i2i2-22-2-2-2-2-222220000−2i2i0000000000000000000000002i2i−2i−2i000000000000
χ35222-2-2-2-222−2i−2i2i2i-222-222-2-2-22-22i−2i22-2-2−2i−2i2i2i−2i−2i2i2i-22-220000000000002i−2i0000000022-2-2−2i−2i2i2i000000000000000000000000
χ36222-2-2-2-222−2i−2i2i2i-222-222-2-2-22-22i−2i-2-2222i2i−2i−2i−2i−2i2i2i-22-220000000000002i−2i00000000-2-2222i2i−2i−2i000000000000000000000000
χ37222-2-2-2-22-12i2i−2i−2i-222-2-1-1111-11−2i2i22-2-22i2i−2i−2i−i−iii1-11-1000000000000i−i33−3−3−i3−i3i3i3-1-111−i−iii00000000000000−i3i33−3000000
χ38222-2-2-2-22-12i2i−2i−2i-222-2-1-1111-11−2i2i22-2-22i2i−2i−2i−i−iii1-11-1000000000000i−i−3−333i3i3−i3−i3-1-111−i−iii00000000000000i3−i3−33000000
χ39222-2-2-2-22-12i2i−2i−2i-222-2-1-1111-11−2i2i-2-222−2i−2i2i2i−i−iii1-11-1000000000000i−i33−3−3−i3−i3i3i311-1-1ii−i−i00000000000000i3−i3−33000000
χ40222-2-2-2-22-12i2i−2i−2i-222-2-1-1111-11−2i2i-2-222−2i−2i2i2i−i−iii1-11-1000000000000i−i−3−333i3i3−i3−i311-1-1ii−i−i00000000000000−i3i33−3000000
χ41222-2-2-2-22-1−2i−2i2i2i-222-2-1-1111-112i−2i22-2-2−2i−2i2i2iii−i−i1-11-1000000000000−ii33−3−3i3i3−i3−i3-1-111ii−i−i00000000000000i3−i33−3000000
χ42222-2-2-2-22-1−2i−2i2i2i-222-2-1-1111-112i−2i22-2-2−2i−2i2i2iii−i−i1-11-1000000000000−ii−3−333−i3−i3i3i3-1-111ii−i−i00000000000000−i3i3−33000000
χ43222-2-2-2-22-1−2i−2i2i2i-222-2-1-1111-112i−2i-2-2222i2i−2i−2iii−i−i1-11-1000000000000−ii33−3−3i3i3−i3−i311-1-1−i−iii00000000000000−i3i3−33000000
χ44222-2-2-2-22-1−2i−2i2i2i-222-2-1-1111-112i−2i-2-2222i2i−2i−2iii−i−i1-11-1000000000000−ii−3−333−i3−i3i3i311-1-1−i−iii00000000000000i3−i33−3000000
χ4522-22-2-22-222i−2i2i−2i00002-22-2-2-2200−i2i2−i2i22−22−22i−2i2i−2i0000−i2−i2i2i2−i2−i2i2i200000000000000−i2i2−i2i22−22−200002-22i−2i2−22−2000000000000
χ4622-22-2-22-222i−2i2i−2i00002-22-2-2-2200−i2i2−i2i22−22−22i−2i2i−2i0000i2i2−i2−i2i2i2−i2−i200000000000000−i2i2−i2i22−22−20000-22−2i2i−22−22000000000000
χ4722-22-2-22-222i−2i2i−2i00002-22-2-2-2200i2−i2i2−i2−22−222i−2i2i−2i0000−i2−i2i2i2−i2−i2i2i200000000000000i2−i2i2−i2−22−220000-22−2i2i2−22−2000000000000
χ4822-22-2-22-222i−2i2i−2i00002-22-2-2-2200i2−i2i2−i2−22−222i−2i2i−2i0000i2i2−i2−i2i2i2−i2−i200000000000000i2−i2i2−i2−22−2200002-22i−2i−22−22000000000000
χ4922-22-2-22-22−2i2i−2i2i00002-22-2-2-2200−i2i2−i2i2−22−22−2i2i−2i2i0000−i2−i2i2i2−i2−i2i2i200000000000000−i2i2−i2i2−22−2200002-2−2i2i−22−22000000000000
χ5022-22-2-22-22−2i2i−2i2i00002-22-2-2-2200−i2i2−i2i2−22−22−2i2i−2i2i0000i2i2−i2−i2i2i2−i2−i200000000000000−i2i2−i2i2−22−220000-222i−2i2−22−2000000000000
χ5122-22-2-22-22−2i2i−2i2i00002-22-2-2-2200i2−i2i2−i22−22−2−2i2i−2i2i0000−i2−i2i2i2−i2−i2i2i200000000000000i2−i2i2−i22−22−20000-222i−2i−22−22000000000000
χ5222-22-2-22-22−2i2i−2i2i00002-22-2-2-2200i2−i2i2−i22−22−2−2i2i−2i2i0000i2i2−i2−i2i2i2−i2−i200000000000000i2−i2i2−i22−22−200002-2−2i2i2−22−2000000000000
χ5322-2-222-2-222-2-2200002-2-222-2-200−i2i2i2−i2−i2i2i2−i22-2-220000−i2−i2i2i2i2i2−i2−i200000000000000−i2i2i2−i2−i2i2i2−i22-22-20000−i2i2i2−i2000000000000
χ5422-2-222-2-222-2-2200002-2-222-2-200−i2i2i2−i2−i2i2i2−i22-2-220000i2i2−i2−i2−i2−i2i2i200000000000000−i2i2i2−i2−i2i2i2−i2-22-220000i2−i2−i2i2000000000000
χ5522-2-222-2-222-2-2200002-2-222-2-200i2−i2−i2i2i2−i2−i2i22-2-220000−i2−i2i2i2i2i2−i2−i200000000000000i2−i2−i2i2i2−i2−i2i2-22-220000−i2i2i2−i2000000000000
χ5622-2-222-2-222-2-2200002-2-222-2-200i2−i2−i2i2i2−i2−i2i22-2-220000i2i2−i2−i2−i2−i2i2i200000000000000i2−i2−i2i2i2−i2−i2i22-22-20000i2−i2−i2i2000000000000
χ5722-2-222-2-22-222-200002-2-222-2-200−i2i2i2−i2i2−i2−i2i2-222-20000−i2−i2i2i2i2i2−i2−i200000000000000−i2i2i2−i2i2−i2−i2i2-222-20000i2−i2−i2i2000000000000
χ5822-2-222-2-22-222-200002-2-222-2-200−i2i2i2−i2i2−i2−i2i2-222-20000i2i2−i2−i2−i2−i2i2i200000000000000−i2i2i2−i2i2−i2−i2i22-2-220000−i2i2i2−i2000000000000
χ5922-2-222-2-22-222-200002-2-222-2-200i2−i2−i2i2−i2i2i2−i2-222-20000−i2−i2i2i2i2i2−i2−i200000000000000i2−i2−i2i2−i2i2i2−i22-2-220000i2−i2−i2i2000000000000
χ6022-2-222-2-22-222-200002-2-222-2-200i2−i2−i2i2−i2i2i2−i2-222-20000i2i2−i2−i2−i2−i2i2i200000000000000i2−i2−i2i2−i2i2i2−i2-222-20000−i2i2i2−i2000000000000
χ612-2-22-22-2220000-2-222-2-2-22-22200000000000000-222-22-22-22-22-22-200002-22-2000000000000000000000000000000002-200
χ622-2-22-22-2220000-2-222-2-2-22-22200000000000000-222-22-22-22-22-2-220000-22-2200000000000000000000000000000000-2200
χ632-2-22-22-2220000-2-222-2-2-22-22200000000000000-222-2-22-22-22-222-200002-22-200000000000000000000000000000000-2200
χ642-2-22-22-2220000-2-222-2-2-22-22200000000000000-222-2-22-22-22-22-220000-22-22000000000000000000000000000000002-200
χ652-2-2-22-22220000-22-22-2-22-222-200000000000000-2-2222-22-2-22-22002-20000002-22-2000000000000000000000000002-20000
χ662-2-2-22-22220000-22-22-2-22-222-200000000000000-2-2222-22-2-22-2200-22000000-22-2200000000000000000000000000-220000
χ672-2-2-22-22220000-22-22-2-22-222-200000000000000-2-222-22-222-22-2002-20000002-22-200000000000000000000000000-220000
χ682-2-2-22-22220000-22-22-2-22-222-200000000000000-2-222-22-222-22-200-22000000-22-22000000000000000000000000002-20000
χ6944444444-24444-4-4-4-4-2-2-2-2-2-2-2-4-400000000-2-2-2-22222000000000000220000000000000000000000000000000000000000
χ7044444444-2-4-4-4-4-4-4-4-4-2-2-2-2-2-2-2440000000022222222000000000000-2-20000000000000000000000000000000000000000
χ71444-4-4-4-44-24i4i−4i−4i4-4-44-2-2222-224i−4i00000000−2i−2i2i2i-22-22000000000000−2i2i0000000000000000000000000000000000000000
χ72444-4-4-4-44-2−4i−4i4i4i4-4-44-2-2222-22−4i4i000000002i2i−2i−2i-22-220000000000002i−2i0000000000000000000000000000000000000000
χ7344-44-4-44-4-24i−4i4i−4i0000-22-2222-200−2i22i2−2i22i222−2222−22−2i2i−2i2i00000000000000000000000000i2−i2i2−i2−22−22000000000000000000000000
χ7444-44-4-44-4-24i−4i4i−4i0000-22-2222-2002i2−2i22i2−2i2−2222−2222−2i2i−2i2i00000000000000000000000000−i2i2−i2i22−22−2000000000000000000000000
χ7544-44-4-44-4-2−4i4i−4i4i0000-22-2222-200−2i22i2−2i22i2−2222−22222i−2i2i−2i00000000000000000000000000i2−i2i2−i22−22−2000000000000000000000000
χ7644-44-4-44-4-2−4i4i−4i4i0000-22-2222-2002i2−2i22i2−2i222−2222−222i−2i2i−2i00000000000000000000000000−i2i2−i2i2−22−22000000000000000000000000
χ7744-4-444-4-4-24-4-440000-222-2-22200−2i22i22i2−2i2−2i22i22i2−2i2-222-200000000000000000000000000i2−i2−i2i2i2−i2−i2i2000000000000000000000000
χ7844-4-444-4-4-24-4-440000-222-2-222002i2−2i2−2i22i22i2−2i2−2i22i2-222-200000000000000000000000000−i2i2i2−i2−i2i2i2−i2000000000000000000000000
χ7944-4-444-4-4-2-444-40000-222-2-22200−2i22i22i2−2i22i2−2i2−2i22i22-2-2200000000000000000000000000i2−i2−i2i2−i2i2i2−i2000000000000000000000000
χ8044-4-444-4-4-2-444-40000-222-2-222002i2−2i2−2i22i2−2i22i22i2−2i22-2-2200000000000000000000000000−i2i2i2−i2i2−i2−i2i2000000000000000000000000
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
χ854-4-44-44-444000044-4-4-4-4-44-444000000000000004-4-44000000000000000000000000000000000000000000000000000000
χ864-4-44-44-44-2000044-4-4222-22-2-200000000000000-222-2000000000000000000−2i32i32i3−2i300000000000000000000000000000000
χ874-4-44-44-44-2000044-4-4222-22-2-200000000000000-222-20000000000000000002i3−2i3−2i32i300000000000000000000000000000000
χ884-4-44-44-44-20000-4-444222-22-2-2000000000000002-2-22000000004-40000-22-22000000000000000000000000000000000000
χ894-4-44-44-44-20000-4-444222-22-2-2000000000000002-2-2200000000-4400002-22-2000000000000000000000000000000000000
χ904-4-4-44-444400004-44-4-4-44-444-40000000000000044-4-4000000000000000000000000000000000000000000000000000000
χ914-4-4-44-444-200004-44-422-22-2-2200000000000000-2-2220000000000000023−23−2323000000000000000000000000000000000000
χ924-4-4-44-444-200004-44-422-22-2-2200000000000000-2-22200000000000000−232323−23000000000000000000000000000000000000
χ934-4-4-44-444-20000-44-4422-22-2-220000000000000022-2-200000000004-4000000-22-2200000000000000000000000000000000
χ944-4-4-44-444-20000-44-4422-22-2-220000000000000022-2-20000000000-440000002-22-200000000000000000000000000000000
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).