Finite Group Databasebeta

← Group #10798371

Character table — Group #10798371

Order 768.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96C97C98C99C100C101C102
size11111111222222222222444444444444444444444444666666668888888888888888888888881212121212121212121212121212121216161616242424242424
order12222222344446666666222244444444888812121212121212124444444444446666881212121212122424242424242424444444444444888812121212224488
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1
χ311111111111111111111111111111111-1-1-1-11111111111111111-1-1-1-11111-1-1111111-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ411111111111111111111111111111111-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1111111
χ5111111111111111111111111-1-1-1-1-1-1-1-1111111-1-1-1-11111111111-1-1111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-11111111111-1-111-1-1-1-1
χ6111111111111111111111111-1-1-1-1-1-1-1-1111111-1-1-1-111-1-1-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-11111-1-1-1-111111111-1-1-1-1-1-1-1-111-1-1-1-11111
χ7111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-1111111111111-1-1111111-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-11111-1-1-1-1-1-111-1-11111
χ8111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-111-1-1-1-1-1-1-1-111-1-1111111-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-11111-1-11111-1-1-1-1
χ911111111111111111111-1-1-1-11111-1-1-1-111111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-1111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-111
χ1011111111111111111111-1-1-1-11111-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-111111111-1-1-1-111111111-1-1-1-1-1-1-1-11111-1-1
χ1111111111111111111111-1-1-1-11111-1-1-1-1-1-1-1-111111111111111111111-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1
χ1211111111111111111111-1-1-1-11111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111111111-1-1-1-111
χ1311111111111111111111-1-1-1-1-1-1-1-11111111111-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-11111-1-1-1-11111-1-111-1-111-1-1
χ1411111111111111111111-1-1-1-1-1-1-1-11111111111-1-1-1-111-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-111111111-1-1-1-11111-1-1-1-11111-1-1-1-1-1-11111-1-111
χ1511111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-111-1-1-1-11111111111-1-111-1-1-1-111-1-11111-1-1-1-11111-1-1-1-11111-1-1-1-1-1-1-1-111-1-111-1-111
χ1611111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-111-1-1-1-111-1-1-1-1-1-1-1-1-1-111-1-1-1-111-1-11111-1-1-1-111111111-1-1-1-11111111111-1-1-1-111-1-1
χ17111-1-1-1-1111-11-11-1-111-1-111-1-1ii−i−iii−i−i11-1-11-1ii−i−i1-111-1-111-1-1i−i1-111-1-1i−ii−iii−i−i11-1-1ii−i−iii−i−iii−i−i11-1-111-1-11-1i−i1-1i−ii−i
χ18111-1-1-1-1111-11-11-1-111-1-111-1-1ii−i−iii−i−i11-1-11-1ii−i−i1-1-1-111-1-111i−i1-111-1-1i−ii−iii−i−i11-1-1ii−i−i−i−iii−i−iii-1-111-1-1111-1i−i-11−ii−ii
χ19111-1-1-1-1111-11-11-1-111-1-111-1-1ii−i−iii−i−i-1-1111-1ii−i−i1-111-1-111-1-1−ii-1111-1-1−iii−iii−i−i-1-111−i−iiiii−i−iii−i−i11-1-1-1-111-11−ii-11−ii−ii
χ20111-1-1-1-1111-11-11-1-111-1-111-1-1ii−i−iii−i−i-1-1111-1ii−i−i1-1-1-111-1-111−ii-1111-1-1−iii−iii−i−i-1-111−i−iii−i−iii−i−iii-1-11111-1-1-11−ii1-1i−ii−i
χ21111-1-1-1-1111-11-11-1-111-1-111-1-1−i−iii−i−iii11-1-11-1−i−iii1-111-1-111-1-1−ii1-111-1-1−ii−ii−i−iii11-1-1−i−iii−i−iii−i−iii11-1-111-1-11-1−ii1-1−ii−ii
χ22111-1-1-1-1111-11-11-1-111-1-111-1-1−i−iii−i−iii11-1-11-1−i−iii1-1-1-111-1-111−ii1-111-1-1−ii−ii−i−iii11-1-1−i−iiiii−i−iii−i−i-1-111-1-1111-1−ii-11i−ii−i
χ23111-1-1-1-1111-11-11-1-111-1-111-1-1−i−iii−i−iii-1-1111-1−i−iii1-111-1-111-1-1i−i-1111-1-1i−i−ii−i−iii-1-111ii−i−i−i−iii−i−iii11-1-1-1-111-11i−i-11i−ii−i
χ24111-1-1-1-1111-11-11-1-111-1-111-1-1−i−iii−i−iii-1-1111-1−i−iii1-1-1-111-1-111i−i-1111-1-1i−i−ii−i−iii-1-111ii−i−iii−i−iii−i−i-1-11111-1-1-11i−i1-1−ii−ii
χ25111-1-1-1-1111-11-11-1-111-1-1-1-111ii−i−i−i−iii11-1-11-1ii−i−i1-111-1-111-1-1−ii-11-1-111i−ii−i−i−iii11-1-1ii−i−iii−i−i−i−iii-1-11111-1-1-11−ii-11−iii−i
χ26111-1-1-1-1111-11-11-1-111-1-1-1-111ii−i−i−i−iii11-1-11-1ii−i−i1-1-1-111-1-111−ii-11-1-111i−ii−i−i−iii11-1-1ii−i−i−i−iiiii−i−i11-1-1-1-111-11−ii1-1i−i−ii
χ27111-1-1-1-1111-11-11-1-111-1-1-1-111ii−i−i−i−iii-1-1111-1ii−i−i1-111-1-111-1-1i−i1-1-1-111−iii−i−i−iii-1-111−i−iiiii−i−i−i−iii-1-111-1-1111-1i−i1-1i−i−ii
χ28111-1-1-1-1111-11-11-1-111-1-1-1-111ii−i−i−i−iii-1-1111-1ii−i−i1-1-1-111-1-111i−i1-1-1-111−iii−i−i−iii-1-111−i−iii−i−iiiii−i−i11-1-111-1-11-1i−i-11−iii−i
χ29111-1-1-1-1111-11-11-1-111-1-1-1-111−i−iiiii−i−i11-1-11-1−i−iii1-111-1-111-1-1i−i-11-1-111−ii−iiii−i−i11-1-1−i−iii−i−iiiii−i−i-1-11111-1-1-11i−i-11i−i−ii
χ30111-1-1-1-1111-11-11-1-111-1-1-1-111−i−iiiii−i−i11-1-11-1−i−iii1-1-1-111-1-111i−i-11-1-111−ii−iiii−i−i11-1-1−i−iiiii−i−i−i−iii11-1-1-1-111-11i−i1-1−iii−i
χ31111-1-1-1-1111-11-11-1-111-1-1-1-111−i−iiiii−i−i-1-1111-1−i−iii1-111-1-111-1-1−ii1-1-1-111i−i−iiii−i−i-1-111ii−i−i−i−iiiii−i−i-1-111-1-1111-1−ii1-1−iii−i
χ32111-1-1-1-1111-11-11-1-111-1-1-1-111−i−iiiii−i−i-1-1111-1−i−iii1-1-1-111-1-111−ii1-1-1-111i−i−iiii−i−i-1-111ii−i−iii−i−i−i−iii11-1-111-1-11-1−ii-11i−i−ii
χ33222222222-2-2-2-2222222200002-22-200000000-2-22222-2-22222-2-2-2-20000000000-2-20000000000002-22-20000000000000000000000
χ34222222222-2-2-2-2222222200002-22-200000000-2-22222-2-2-2-2-2-222220000000000-2-2000000000000-22-220000000000000000000000
χ35222222222-2-2-2-222222220000-22-2200000000-2-2-2-2-2-2-2-22222-2-2-2-2000000000022000000000000-22-220000000000000000000000
χ36222222222-2-2-2-222222220000-22-2200000000-2-2-2-2-2-2-2-2-2-2-2-222220000000000220000000000002-22-20000000000000000000000
χ3722222222-12222-1-1-1-1-1-1-12222222222222222-1-1-1-1-1-1-1-1000000002222-1-1-1-122-1-1-1-1-1-1-1-1-1-1-1-1-1-10000000000000000-1-1-1-1000000
χ3822222222-12222-1-1-1-1-1-1-1222222222222-2-2-2-2-1-1-1-1-1-1-1-100000000-2-2-2-2-1-1-1-1-2-2-1-1-1-1-1-11111111100000000000000001111000000
χ3922222222-12222-1-1-1-1-1-1-12222-2-2-2-2-2-2-2-22222-1-11111-1-100000000-2-222-1-1-1-1-2-2111111-1-1-1-111110000000000000000-1-111000000
χ4022222222-12222-1-1-1-1-1-1-12222-2-2-2-2-2-2-2-2-2-2-2-2-1-11111-1-10000000022-2-2-1-1-1-1221111111111-1-1-1-1000000000000000011-1-1000000
χ4122222222-12222-1-1-1-1-1-1-1-2-2-2-22222-2-2-2-22222-1-1-1-1-1-1-1-100000000-2-2-2-2111122-1-11111-1-1-1-1-1-1-1-100000000000000001111000000
χ4222222222-12222-1-1-1-1-1-1-1-2-2-2-22222-2-2-2-2-2-2-2-2-1-1-1-1-1-1-1-10000000022221111-2-2-1-11111111111110000000000000000-1-1-1-1000000
χ4322222222-12222-1-1-1-1-1-1-1-2-2-2-2-2-2-2-222222222-1-11111-1-10000000022-2-21111-2-211-1-1-1-1-1-1-1-11111000000000000000011-1-1000000
χ4422222222-12222-1-1-1-1-1-1-1-2-2-2-2-2-2-2-22222-2-2-2-2-1-11111-1-100000000-2-22211112211-1-1-1-11111-1-1-1-10000000000000000-1-111000000
χ45222-2-2-2-222-22-222-2-222-2-200002i−2i−2i2i00000000-222i2i−2i−2i-2222-2-2-2-2220000000000−2i2i0000000000002i−2i−2i2i0000000000000000000000
χ46222-2-2-2-222-22-222-2-222-2-200002i−2i−2i2i00000000-222i2i−2i−2i-22-2-22222-2-20000000000−2i2i000000000000−2i2i2i−2i0000000000000000000000
χ47222-2-2-2-222-22-222-2-222-2-20000−2i2i2i−2i00000000-22−2i−2i2i2i-2222-2-2-2-22200000000002i−2i000000000000−2i2i2i−2i0000000000000000000000
χ48222-2-2-2-222-22-222-2-222-2-20000−2i2i2i−2i00000000-22−2i−2i2i2i-22-2-22222-2-200000000002i−2i0000000000002i−2i−2i2i0000000000000000000000
χ49222-2-2-2-22-12-22-2-111-1-11122-2-22i2i−2i−2i2i2i−2i−2i22-2-2-11−i−iii-11000000002i−2i2-2-1-1112i−2i−ii−i−iii-1-111−i−iii0000000000000000-11−ii000000
χ50222-2-2-2-22-12-22-2-111-1-11122-2-22i2i−2i−2i2i2i−2i−2i-2-222-11−i−iii-1100000000−2i2i-22-1-111−2i2i−ii−i−iii11-1-1ii−i−i00000000000000001-1i−i000000
χ51222-2-2-2-22-12-22-2-111-1-11122-2-2−2i−2i2i2i−2i−2i2i2i22-2-2-11ii−i−i-1100000000−2i2i2-2-1-111−2i2ii−iii−i−i-1-111ii−i−i0000000000000000-11i−i000000
χ52222-2-2-2-22-12-22-2-111-1-11122-2-2−2i−2i2i2i−2i−2i2i2i-2-222-11ii−i−i-11000000002i−2i-22-1-1112i−2ii−iii−i−i11-1-1−i−iii00000000000000001-1−ii000000
χ53222-2-2-2-22-12-22-2-111-1-111-2-2222i2i−2i−2i−2i−2i2i2i22-2-2-11−i−iii-1100000000−2i2i-2211-1-12i−2i−iiii−i−i-1-111−i−iii00000000000000001-1i−i000000
χ54222-2-2-2-22-12-22-2-111-1-111-2-2222i2i−2i−2i−2i−2i2i2i-2-222-11−i−iii-11000000002i−2i2-211-1-1−2i2i−iiii−i−i11-1-1ii−i−i0000000000000000-11−ii000000
χ55222-2-2-2-22-12-22-2-111-1-111-2-222−2i−2i2i2i2i2i−2i−2i22-2-2-11ii−i−i-11000000002i−2i-2211-1-1−2i2ii−i−i−iii-1-111ii−i−i00000000000000001-1−ii000000
χ56222-2-2-2-22-12-22-2-111-1-111-2-222−2i−2i2i2i2i2i−2i−2i-2-222-11ii−i−i-1100000000−2i2i2-211-1-12i−2ii−i−i−iii11-1-1−i−iii0000000000000000-11i−i000000
χ5722-222-2-2-222-2-22-2-2-22-222000000002-22-20000-2200002-22i−2i2i−2i2i−2i2i−2i0000000000002-22-20000000000002i−2i2i−2i000000000000000000
χ5822-222-2-2-222-2-22-2-2-22-222000000002-22-20000-2200002-2−2i2i−2i2i−2i2i−2i2i0000000000002-22-2000000000000−2i2i−2i2i000000000000000000
χ5922-222-2-2-222-2-22-2-2-22-22200000000-22-220000-2200002-22i−2i2i−2i2i−2i2i−2i000000000000-22-22000000000000−2i2i−2i2i000000000000000000
χ6022-222-2-2-222-2-22-2-2-22-22200000000-22-220000-2200002-2−2i2i−2i2i−2i2i−2i2i000000000000-22-220000000000002i−2i2i−2i000000000000000000
χ6122-222-2-2-22-222-2-2-2-22-2222-22-20000000000002-20000-222i−2i2i−2i−2i2i−2i2i00002-22-20000000000000000000000002i−2i2i−2i00000000000000
χ6222-222-2-2-22-222-2-2-2-22-2222-22-20000000000002-20000-22−2i2i−2i2i2i−2i2i−2i00002-22-2000000000000000000000000−2i2i−2i2i00000000000000
χ6322-222-2-2-22-222-2-2-2-22-222-22-220000000000002-20000-222i−2i2i−2i−2i2i−2i2i0000-22-22000000000000000000000000−2i2i−2i2i00000000000000
χ6422-222-2-2-22-222-2-2-2-22-222-22-220000000000002-20000-22−2i2i−2i2i2i−2i2i−2i0000-22-220000000000000000000000002i−2i2i−2i00000000000000
χ6522-2-2-222-2222-2-2-2222-2-2-2000000002i−2i−2i2i0000-2-20000222i−2i−2i2i2i−2i−2i2i0000000000002i−2i−2i2i000000000000-222-2000000000000000000
χ6622-2-2-222-2222-2-2-2222-2-2-2000000002i−2i−2i2i0000-2-2000022−2i2i2i−2i−2i2i2i−2i0000000000002i−2i−2i2i0000000000002-2-22000000000000000000
χ6722-2-2-222-2222-2-2-2222-2-2-200000000−2i2i2i−2i0000-2-20000222i−2i−2i2i2i−2i−2i2i000000000000−2i2i2i−2i0000000000002-2-22000000000000000000
χ6822-2-2-222-2222-2-2-2222-2-2-200000000−2i2i2i−2i0000-2-2000022−2i2i2i−2i−2i2i2i−2i000000000000−2i2i2i−2i000000000000-222-2000000000000000000
χ6922-2-2-222-22-2-222-2222-2-2-22-2-22000000000000220000-2-22i−2i−2i2i−2i2i2i−2i00002-2-220000000000000000000000002i−2i−2i2i00000000000000
χ7022-2-2-222-22-2-222-2222-2-2-22-2-22000000000000220000-2-2−2i2i2i−2i2i−2i−2i2i00002-2-22000000000000000000000000−2i2i2i−2i00000000000000
χ7122-2-2-222-22-2-222-2222-2-2-2-222-2000000000000220000-2-22i−2i−2i2i−2i2i2i−2i0000-222-2000000000000000000000000−2i2i2i−2i00000000000000
χ7222-2-2-222-22-2-222-2222-2-2-2-222-2000000000000220000-2-2−2i2i2i−2i2i−2i−2i2i0000-222-20000000000000000000000002i−2i−2i2i00000000000000
χ7344444444-2-4-4-4-4-2-2-2-2-2-2-200004-44-40000000022-2-2-2-2220000000000000000002200000000000000000000000000000000000000
χ7444444444-2-4-4-4-4-2-2-2-2-2-2-20000-44-440000000022222222000000000000000000-2-200000000000000000000000000000000000000
χ75444-4-4-4-44-2-44-44-222-2-22200004i−4i−4i4i000000002-2−2i−2i2i2i2-20000000000000000002i−2i00000000000000000000000000000000000000
χ76444-4-4-4-44-2-44-44-222-2-2220000−4i4i4i−4i000000002-22i2i−2i−2i2-2000000000000000000−2i2i00000000000000000000000000000000000000
χ7744-444-4-4-4-24-4-44222-22-2-2000000004-44-400002-20000-2200000000000000000000-22-220000000000000000000000000000000000
χ7844-444-4-4-4-24-4-44222-22-2-200000000-44-4400002-20000-22000000000000000000002-22-20000000000000000000000000000000000
χ7944-444-4-4-4-2-444-4222-22-2-24-44-4000000000000-2200002-2000000000000-22-22000000000000000000000000000000000000000000
χ8044-444-4-4-4-2-444-4222-22-2-2-44-44000000000000-2200002-20000000000002-22-2000000000000000000000000000000000000000000
χ8144-4-4-444-4-244-4-42-2-2-2222000000004i−4i−4i4i0000220000-2-200000000000000000000−2i2i2i−2i0000000000000000000000000000000000
χ8244-4-4-444-4-244-4-42-2-2-222200000000−4i4i4i−4i0000220000-2-2000000000000000000002i−2i−2i2i0000000000000000000000000000000000
χ8344-4-4-444-4-2-4-4442-2-2-22224-4-44000000000000-2-2000022000000000000-222-2000000000000000000000000000000000000000000
χ8444-4-4-444-4-2-4-4442-2-2-2222-444-4000000000000-2-20000220000000000002-2-22000000000000000000000000000000000000000000
χ854-444-44-4-44000044-4-4-44-4000000000000−2i22i2−2i22i200000000000000000000000000000000−2i22i2−2i22i2000000000000000000000000000000
χ864-444-44-4-44000044-4-4-44-40000000000002i2−2i22i2−2i2000000000000000000000000000000002i2−2i22i2−2i2000000000000000000000000000000
χ874-444-44-4-4-20000-2-2222-22000000000000−2i22i2−2i22i200−2i32i3−2i32i300000000000000000000000000i2−i2i2−i26−66−600000000000000000000000000
χ884-444-44-4-4-20000-2-2222-22000000000000−2i22i2−2i22i2002i3−2i32i3−2i300000000000000000000000000i2−i2i2−i2−66−6600000000000000000000000000
χ894-444-44-4-4-20000-2-2222-220000000000002i2−2i22i2−2i200−2i32i3−2i32i300000000000000000000000000−i2i2−i2i2−66−6600000000000000000000000000
χ904-444-44-4-4-20000-2-2222-220000000000002i2−2i22i2−2i2002i3−2i32i3−2i300000000000000000000000000−i2i2−i2i26−66−600000000000000000000000000
χ914-44-44-44-4400004-44-4-4-44000000000000−2i22i22i2−2i200000000000000000000000000000000−2i22i22i2−2i2000000000000000000000000000000
χ924-44-44-44-4400004-44-4-4-440000000000002i2−2i2−2i22i2000000000000000000000000000000002i2−2i2−2i22i2000000000000000000000000000000
χ934-44-44-44-4-20000-22-2222-2000000000000−2i22i22i2−2i20023−23−232300000000000000000000000000i2−i2−i2i2i6−i6−i6i600000000000000000000000000
χ944-44-44-44-4-20000-22-2222-2000000000000−2i22i22i2−2i200−232323−2300000000000000000000000000i2−i2−i2i2−i6i6i6−i600000000000000000000000000
χ954-44-44-44-4-20000-22-2222-20000000000002i2−2i2−2i22i20023−23−232300000000000000000000000000−i2i2i2−i2−i6i6i6−i600000000000000000000000000
χ964-44-44-44-4-20000-22-2222-20000000000002i2−2i2−2i22i200−232323−2300000000000000000000000000−i2i2i2−i2i6−i6−i6i600000000000000000000000000
χ974-4-44-4-44440000-4-44-444-40000000000000000000000000000000000000000000000000000000000000000000022−2222−220000000000
χ984-4-44-4-44440000-4-44-444-400000000000000000000000000000000000000000000000000000000000000000000−2222−22220000000000
χ994-4-4-444-4440000-44-4-44-440000000000000000000000000000000000000000000000000000000000000000000022−22−22220000000000
χ1004-4-4-444-4440000-44-4-44-4400000000000000000000000000000000000000000000000000000000000000000000−222222−220000000000
χ1018-8-88-8-888-4000044-44-4-440000000000000000000000000000000000000000000000000000000000000000000000000000000000
χ1028-8-8-888-88-400004-444-44-40000000000000000000000000000000000000000000000000000000000000000000000000000000000

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