Finite Group Databasebeta

← Group #10827354

Character table — Group #10827354

Order 768.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96C97C98C99C100C101C102C103C104C105C106C107C108
size1111111122222222222222222222222244444444444444444444444444444444444444888888888888888888888812121212242424242424242424244848
order122222222222344446666666121212121212121222444466668888888812121212242424242424242424242424242424244466888812121212121224242424242424244444224444444444
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ3111111111111111111111111111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1111111-1-1-1-1-1-1-1-1111111-1-1-1-11111-1-1
χ4111111111111111111111111111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-111
χ511111111111111111111111111111111-1-111-1-111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1111111-1-1-1-1
χ611111111111111111111111111111111-1-111-1-111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-11111
χ711111111111111111111111111111111-1-111-1-11111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1111111111111-1-1-1-1-1-111-1-111
χ811111111111111111111111111111111-1-111-1-11111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-111111111-1-1-1-1111111-1-111-1-1
χ911111111-1-1-1-11111111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-111111-1-1-1-1-1-1111111-1-1-1-11111-1-111-1-1-1-1111-1
χ1011111111-1-1-1-11111111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-111111-1-1-1-1-1-1111111-1-1-1-1-1-1-1-111-1-11111-1-1-11
χ1111111111-1-1-1-11111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-111111111-1111-1-111-1-1-1-111-1-1-1-111111111-1-1-1-111-1-111-11
χ1211111111-1-1-1-11111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-111111111-1111-1-111-1-1-1-111-1-1-1-11111-1-1-1-11111-1-111-1-11-1
χ1311111111-1-1-1-111111111111111111111-1-1-1-111-1-1-1-11111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-11-1-1-1-1-1111111-1-1-1-1-1-1111111111111-1-1-1-1-1-1-11
χ1411111111-1-1-1-111111111111111111111-1-1-1-111-1-1-1-11111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-11-1-1-1-1-1111111-1-1-1-1-1-11111-1-1-1-1-1-1-1-11111111-1
χ1511111111-1-1-1-111111111111111111111-1-1-1-111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1111111111-1-1-111-1-11111-1-11111-1-1-1-1111111-1-111-1-1-1-11-1
χ1611111111-1-1-1-111111111111111111111-1-1-1-111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1111111111-1-1-111-1-11111-1-11111-1-1-1-1-1-1-1-1-1-111-1-11111-11
χ172222222222222-2-2-2-22222222-2-2-2-2-2-2-2-222-2-222222200000000-2-2-2-20000000000000000-2-222000022-2-2-2-2000000000000000000000000
χ182222222222222-2-2-2-22222222-2-2-2-2-2-2-2-2-2-2-2-2-2-2222200000000-2-2-2-2000000000000000022-2-20000-2-22222000000000000000000000000
χ19222222222222-12222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1222222-1-1-1-122222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-122-1-12222-1-1-1-1-1-1-1-1-1-1-1-1-1-10000000000000000
χ20222222222222-12222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1222222-1-1-1-1-2-2-2-2-2-2-2-2-1-1-1-1111111111111111122-1-1-2-2-2-2-1-1-1-1-1-1111111110000000000000000
χ21222222222222-12222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-2-222-2-2-1-1-1-122222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-2-211-2-2-2-2111111111111110000000000000000
χ22222222222222-12222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-2-222-2-2-1-1-1-1-2-2-2-2-2-2-2-2-1-1-1-11111111111111111-2-2112222111111-1-1-1-1-1-1-1-10000000000000000
χ23222222222222-1-2-2-2-2-1-1-1-1-1-1-11111111122-2-222-1-1-1-10000000011113333−3−3−3−33333−3−3−3−3-2-2-1-10000-1-1111133−3−333−3−30000000000000000
χ24222222222222-1-2-2-2-2-1-1-1-1-1-1-11111111122-2-222-1-1-1-1000000001111−3−3−3−33333−3−3−3−33333-2-2-1-10000-1-11111−3−333−3−3330000000000000000
χ25222222222222-1-2-2-2-2-1-1-1-1-1-1-111111111-2-2-2-2-2-2-1-1-1-10000000011113333−3−3−3−33333−3−3−3−32211000011-1-1-1-1−3−333−3−3330000000000000000
χ26222222222222-1-2-2-2-2-1-1-1-1-1-1-111111111-2-2-2-2-2-2-1-1-1-1000000001111−3−3−3−33333−3−3−3−333332211000011-1-1-1-133−3−333−3−30000000000000000
χ2722222222-2-2-2-22-2-2-2-22222222-2-2-2-2-2-2-2-22222-2-2-2-2-2-200000000222200000000000000002-2220000-2-222-2-2000000000000000000000000
χ2822222222-2-2-2-22-2-2-2-22222222-2-2-2-2-2-2-2-2-2-22222-2-2-2-20000000022220000000000000000-22-2-2000022-2-222000000000000000000000000
χ2922222222-2-2-2-2-12222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-122-2-2-2-211112222-2-2-2-21111-1-1-1-1-1-1-1-111111111-22-1-122-2-21111-1-1-1-1-1-111110000000000000000
χ3022222222-2-2-2-2-12222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-122-2-2-2-21111-2-2-2-22222111111111111-1-1-1-1-1-1-1-1-22-1-1-2-2221111-1-11111-1-1-1-10000000000000000
χ3122222222-2-2-2-2-12222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-2-2-2-22211112222-2-2-2-21111-1-1-1-1-1-1-1-1111111112-211-2-222-1-1-1-1111111-1-1-1-10000000000000000
χ3222222222-2-2-2-2-12222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-2-2-2-2221111-2-2-2-22222111111111111-1-1-1-1-1-1-1-12-21122-2-2-1-1-1-111-1-1-1-111110000000000000000
χ3322222222-2-2-2-2-1-2-2-2-2-1-1-1-1-1-1-1111111112222-2-2111100000000-1-1-1-13333−3−3−3−3−3−3−3−333332-2-1-1000011-1-11133−3−3−3−3330000000000000000
χ3422222222-2-2-2-2-1-2-2-2-2-1-1-1-1-1-1-1111111112222-2-2111100000000-1-1-1-1−3−3−3−333333333−3−3−3−32-2-1-1000011-1-111−3−33333−3−30000000000000000
χ3522222222-2-2-2-2-1-2-2-2-2-1-1-1-1-1-1-111111111-2-22222111100000000-1-1-1-13333−3−3−3−3−3−3−3−33333-22110000-1-111-1-1−3−33333−3−30000000000000000
χ3622222222-2-2-2-2-1-2-2-2-2-1-1-1-1-1-1-111111111-2-22222111100000000-1-1-1-1−3−3−3−333333333−3−3−3−3-22110000-1-111-1-133−3−3−3−3330000000000000000
χ37222-2-2-2-2222-2-22000022-2-22-2-2000000002-2002-222-2-2−i2−i2i2i2−i2−i2i2i20000−i2−i2i2i2−i2−i2i2i2−i2−i2i2i2−i2−i2i2i2002-2−i2i2−i2i22-20000−i2i2−i2i2−i2i2−i2i20000000000000000
χ38222-2-2-2-2222-2-22000022-2-22-2-2000000002-2002-222-2-2i2i2−i2−i2i2i2−i2−i20000i2i2−i2−i2i2i2−i2−i2i2i2−i2−i2i2i2−i2−i2002-2i2−i2i2−i22-20000i2−i2i2−i2i2−i2i2−i20000000000000000
χ39222-2-2-2-2222-2-22000022-2-22-2-200000000-2200-2222-2-2−i2−i2i2i2−i2−i2i2i20000−i2−i2i2i2−i2−i2i2i2−i2−i2i2i2−i2−i2i2i200-22i2−i2i2−i2-220000i2−i2i2−i2i2−i2i2−i20000000000000000
χ40222-2-2-2-2222-2-22000022-2-22-2-200000000-2200-2222-2-2i2i2−i2−i2i2i2−i2−i20000i2i2−i2−i2i2i2−i2−i2i2i2−i2−i2i2i2−i2−i200-22−i2i2−i2i2-220000−i2i2−i2i2−i2i2−i2i20000000000000000
χ41222-2-2-2-2222-2-2-10000-1-111-1113−333−3−33−32-2002-2-1-111−i2−i2i2i2−i2−i2i2i233−3−3ζ5+ζ7ζ5+ζ7−ζ5−ζ7−ζ5−ζ7ζ13+ζ23ζ13+ζ23−ζ13−ζ23−ζ13−ζ23ζ5+ζ7ζ5+ζ7−ζ5−ζ7−ζ5−ζ7ζ13+ζ23ζ13+ζ23−ζ13−ζ23−ζ13−ζ2300-11−i2i2−i2i2-113−33−3ζ5+ζ7−ζ5−ζ7ζ13+ζ23−ζ13−ζ23ζ5+ζ7−ζ5−ζ7ζ13+ζ23−ζ13−ζ230000000000000000
χ42222-2-2-2-2222-2-2-10000-1-111-1113−333−3−33−32-2002-2-1-111i2i2−i2−i2i2i2−i2−i233−3−3−ζ5−ζ7−ζ5−ζ7ζ5+ζ7ζ5+ζ7−ζ13−ζ23−ζ13−ζ23ζ13+ζ23ζ13+ζ23−ζ5−ζ7−ζ5−ζ7ζ5+ζ7ζ5+ζ7−ζ13−ζ23−ζ13−ζ23ζ13+ζ23ζ13+ζ2300-11i2−i2i2−i2-113−33−3−ζ5−ζ7ζ5+ζ7−ζ13−ζ23ζ13+ζ23−ζ5−ζ7ζ5+ζ7−ζ13−ζ23ζ13+ζ230000000000000000
χ43222-2-2-2-2222-2-2-10000-1-111-1113−333−3−33−3-2200-22-1-111−i2−i2i2i2−i2−i2i2i233−3−3ζ5+ζ7ζ5+ζ7−ζ5−ζ7−ζ5−ζ7ζ13+ζ23ζ13+ζ23−ζ13−ζ23−ζ13−ζ23ζ5+ζ7ζ5+ζ7−ζ5−ζ7−ζ5−ζ7ζ13+ζ23ζ13+ζ23−ζ13−ζ23−ζ13−ζ23001-1i2−i2i2−i21-1−33−33−ζ5−ζ7ζ5+ζ7−ζ13−ζ23ζ13+ζ23−ζ5−ζ7ζ5+ζ7−ζ13−ζ23ζ13+ζ230000000000000000
χ44222-2-2-2-2222-2-2-10000-1-111-1113−333−3−33−3-2200-22-1-111i2i2−i2−i2i2i2−i2−i233−3−3−ζ5−ζ7−ζ5−ζ7ζ5+ζ7ζ5+ζ7−ζ13−ζ23−ζ13−ζ23ζ13+ζ23ζ13+ζ23−ζ5−ζ7−ζ5−ζ7ζ5+ζ7ζ5+ζ7−ζ13−ζ23−ζ13−ζ23ζ13+ζ23ζ13+ζ23001-1−i2i2−i2i21-1−33−33ζ5+ζ7−ζ5−ζ7ζ13+ζ23−ζ13−ζ23ζ5+ζ7−ζ5−ζ7ζ13+ζ23−ζ13−ζ230000000000000000
χ45222-2-2-2-2222-2-2-10000-1-111-111−33−3−333−332-2002-2-1-111−i2−i2i2i2−i2−i2i2i2−3−333ζ13+ζ23ζ13+ζ23−ζ13−ζ23−ζ13−ζ23ζ5+ζ7ζ5+ζ7−ζ5−ζ7−ζ5−ζ7ζ13+ζ23ζ13+ζ23−ζ13−ζ23−ζ13−ζ23ζ5+ζ7ζ5+ζ7−ζ5−ζ7−ζ5−ζ700-11−i2i2−i2i2-11−33−33ζ13+ζ23−ζ13−ζ23ζ5+ζ7−ζ5−ζ7ζ13+ζ23−ζ13−ζ23ζ5+ζ7−ζ5−ζ70000000000000000
χ46222-2-2-2-2222-2-2-10000-1-111-111−33−3−333−332-2002-2-1-111i2i2−i2−i2i2i2−i2−i2−3−333−ζ13−ζ23−ζ13−ζ23ζ13+ζ23ζ13+ζ23−ζ5−ζ7−ζ5−ζ7ζ5+ζ7ζ5+ζ7−ζ13−ζ23−ζ13−ζ23ζ13+ζ23ζ13+ζ23−ζ5−ζ7−ζ5−ζ7ζ5+ζ7ζ5+ζ700-11i2−i2i2−i2-11−33−33−ζ13−ζ23ζ13+ζ23−ζ5−ζ7ζ5+ζ7−ζ13−ζ23ζ13+ζ23−ζ5−ζ7ζ5+ζ70000000000000000
χ47222-2-2-2-2222-2-2-10000-1-111-111−33−3−333−33-2200-22-1-111−i2−i2i2i2−i2−i2i2i2−3−333ζ13+ζ23ζ13+ζ23−ζ13−ζ23−ζ13−ζ23ζ5+ζ7ζ5+ζ7−ζ5−ζ7−ζ5−ζ7ζ13+ζ23ζ13+ζ23−ζ13−ζ23−ζ13−ζ23ζ5+ζ7ζ5+ζ7−ζ5−ζ7−ζ5−ζ7001-1i2−i2i2−i21-13−33−3−ζ13−ζ23ζ13+ζ23−ζ5−ζ7ζ5+ζ7−ζ13−ζ23ζ13+ζ23−ζ5−ζ7ζ5+ζ70000000000000000
χ48222-2-2-2-2222-2-2-10000-1-111-111−33−3−333−33-2200-22-1-111i2i2−i2−i2i2i2−i2−i2−3−333−ζ13−ζ23−ζ13−ζ23ζ13+ζ23ζ13+ζ23−ζ5−ζ7−ζ5−ζ7ζ5+ζ7ζ5+ζ7−ζ13−ζ23−ζ13−ζ23ζ13+ζ23ζ13+ζ23−ζ5−ζ7−ζ5−ζ7ζ5+ζ7ζ5+ζ7001-1−i2i2−i2i21-13−33−3ζ13+ζ23−ζ13−ζ23ζ5+ζ7−ζ5−ζ7ζ13+ζ23−ζ13−ζ23ζ5+ζ7−ζ5−ζ70000000000000000
χ49222-2-2-2-22-2-2222000022-2-22-2-2000000002-200-22-2-222−i2−i2i2i2i2i2−i2−i20000−i2−i2i2i2−i2−i2i2i2i2i2−i2−i2i2i2−i2−i2002-2−i2i2i2−i2-220000−i2i2−i2i2i2−i2i2−i20000000000000000
χ50222-2-2-2-22-2-2222000022-2-22-2-2000000002-200-22-2-222i2i2−i2−i2−i2−i2i2i20000i2i2−i2−i2i2i2−i2−i2−i2−i2i2i2−i2−i2i2i2002-2i2−i2−i2i2-220000i2−i2i2−i2−i2i2−i2i20000000000000000
χ51222-2-2-2-22-2-2222000022-2-22-2-200000000-22002-2-2-222−i2−i2i2i2i2i2−i2−i20000−i2−i2i2i2−i2−i2i2i2i2i2−i2−i2i2i2−i2−i200-22i2−i2−i2i22-20000i2−i2i2−i2−i2i2−i2i20000000000000000
χ52222-2-2-2-22-2-2222000022-2-22-2-200000000-22002-2-2-222i2i2−i2−i2−i2−i2i2i20000i2i2−i2−i2i2i2−i2−i2−i2−i2i2i2−i2−i2i2i200-22−i2i2i2−i22-20000−i2i2−i2i2i2−i2i2−i20000000000000000
χ53222-2-2-2-22-2-222-10000-1-111-1113−333−3−33−32-200-2211-1-1−i2−i2i2i2i2i2−i2−i2−3−333ζ5+ζ7ζ5+ζ7−ζ5−ζ7−ζ5−ζ7ζ13+ζ23ζ13+ζ23−ζ13−ζ23−ζ13−ζ23−ζ5−ζ7−ζ5−ζ7ζ5+ζ7ζ5+ζ7−ζ13−ζ23−ζ13−ζ23ζ13+ζ23ζ13+ζ2300-11−i2i2i2−i21-1−333−3ζ5+ζ7−ζ5−ζ7ζ13+ζ23−ζ13−ζ23−ζ5−ζ7ζ5+ζ7−ζ13−ζ23ζ13+ζ230000000000000000
χ54222-2-2-2-22-2-222-10000-1-111-1113−333−3−33−32-200-2211-1-1i2i2−i2−i2−i2−i2i2i2−3−333−ζ5−ζ7−ζ5−ζ7ζ5+ζ7ζ5+ζ7−ζ13−ζ23−ζ13−ζ23ζ13+ζ23ζ13+ζ23ζ5+ζ7ζ5+ζ7−ζ5−ζ7−ζ5−ζ7ζ13+ζ23ζ13+ζ23−ζ13−ζ23−ζ13−ζ2300-11i2−i2−i2i21-1−333−3−ζ5−ζ7ζ5+ζ7−ζ13−ζ23ζ13+ζ23ζ5+ζ7−ζ5−ζ7ζ13+ζ23−ζ13−ζ230000000000000000
χ55222-2-2-2-22-2-222-10000-1-111-1113−333−3−33−3-22002-211-1-1−i2−i2i2i2i2i2−i2−i2−3−333ζ5+ζ7ζ5+ζ7−ζ5−ζ7−ζ5−ζ7ζ13+ζ23ζ13+ζ23−ζ13−ζ23−ζ13−ζ23−ζ5−ζ7−ζ5−ζ7ζ5+ζ7ζ5+ζ7−ζ13−ζ23−ζ13−ζ23ζ13+ζ23ζ13+ζ23001-1i2−i2−i2i2-113−3−33−ζ5−ζ7ζ5+ζ7−ζ13−ζ23ζ13+ζ23ζ5+ζ7−ζ5−ζ7ζ13+ζ23−ζ13−ζ230000000000000000
χ56222-2-2-2-22-2-222-10000-1-111-1113−333−3−33−3-22002-211-1-1i2i2−i2−i2−i2−i2i2i2−3−333−ζ5−ζ7−ζ5−ζ7ζ5+ζ7ζ5+ζ7−ζ13−ζ23−ζ13−ζ23ζ13+ζ23ζ13+ζ23ζ5+ζ7ζ5+ζ7−ζ5−ζ7−ζ5−ζ7ζ13+ζ23ζ13+ζ23−ζ13−ζ23−ζ13−ζ23001-1−i2i2i2−i2-113−3−33ζ5+ζ7−ζ5−ζ7ζ13+ζ23−ζ13−ζ23−ζ5−ζ7ζ5+ζ7−ζ13−ζ23ζ13+ζ230000000000000000
χ57222-2-2-2-22-2-222-10000-1-111-111−33−3−333−332-200-2211-1-1−i2−i2i2i2i2i2−i2−i233−3−3ζ13+ζ23ζ13+ζ23−ζ13−ζ23−ζ13−ζ23ζ5+ζ7ζ5+ζ7−ζ5−ζ7−ζ5−ζ7−ζ13−ζ23−ζ13−ζ23ζ13+ζ23ζ13+ζ23−ζ5−ζ7−ζ5−ζ7ζ5+ζ7ζ5+ζ700-11−i2i2i2−i21-13−3−33ζ13+ζ23−ζ13−ζ23ζ5+ζ7−ζ5−ζ7−ζ13−ζ23ζ13+ζ23−ζ5−ζ7ζ5+ζ70000000000000000
χ58222-2-2-2-22-2-222-10000-1-111-111−33−3−333−332-200-2211-1-1i2i2−i2−i2−i2−i2i2i233−3−3−ζ13−ζ23−ζ13−ζ23ζ13+ζ23ζ13+ζ23−ζ5−ζ7−ζ5−ζ7ζ5+ζ7ζ5+ζ7ζ13+ζ23ζ13+ζ23−ζ13−ζ23−ζ13−ζ23ζ5+ζ7ζ5+ζ7−ζ5−ζ7−ζ5−ζ700-11i2−i2−i2i21-13−3−33−ζ13−ζ23ζ13+ζ23−ζ5−ζ7ζ5+ζ7ζ13+ζ23−ζ13−ζ23ζ5+ζ7−ζ5−ζ70000000000000000
χ59222-2-2-2-22-2-222-10000-1-111-111−33−3−333−33-22002-211-1-1−i2−i2i2i2i2i2−i2−i233−3−3ζ13+ζ23ζ13+ζ23−ζ13−ζ23−ζ13−ζ23ζ5+ζ7ζ5+ζ7−ζ5−ζ7−ζ5−ζ7−ζ13−ζ23−ζ13−ζ23ζ13+ζ23ζ13+ζ23−ζ5−ζ7−ζ5−ζ7ζ5+ζ7ζ5+ζ7001-1i2−i2−i2i2-11−333−3−ζ13−ζ23ζ13+ζ23−ζ5−ζ7ζ5+ζ7ζ13+ζ23−ζ13−ζ23ζ5+ζ7−ζ5−ζ70000000000000000
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Here ζ is a primitive root of unity of order 24 (ζ24 = 1); i = ζ6.