Finite Group Databasebeta

← Group #72342863

Character table — Group #72342863

Order 3072.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96C97C98C99C100C101C102C103C104C105C106C107C108C109C110C111C112
size112222233444444444666668888888888888888881212121212121212121616161616161616161616162424242424242424242432323232323232323232323232323232323232323232323296969696969696969696969696969696
order122448822448881616161624488361212161624242424323232323232323244888161616166122424484848484848484816163232323232323232121224244848484896969696969696969696969696969696888888881616161616161616
χ11111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ3111111111111111111111111111111111-1-1-1-1-1-1-1-111111111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1
χ4111111111111111111111111111111111-1-1-1-1-1-1-1-111111111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111
χ5111111111-1-11-1-11111111111111-1-111111111-1-1-1-1-1-11-1-11111111111111111-1-11111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1ii−i−iii−i−iii−i−iii−i−i
χ6111111111-1-11-1-11111111111111-1-111111111-1-1-1-1-1-11-1-11111111111111111-1-11111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1−i−iii−i−iii−i−iii−i−iii
χ7111111111-1-11-1-11111111111111-1-11111-1-1-1-11111-1-11-1-11111111111111111-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111ii−i−iii−i−i−i−iii−i−iii
χ8111111111-1-11-1-11111111111111-1-11111-1-1-1-11111-1-11-1-11111111111111111-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111−i−iii−i−iiiii−i−iii−i−i
χ911-11-11111i−i-1i−i11-1-1-11-1111111i−i111111-1-1ii−i−ii−i-1i−i11-1-1-1-1-1-11111-1-1-1-1i−i11-1-1ii−i−ii−ii−iii−i−i1111-1-1-1-1iiii−i−i−i−iζ7+ζ23−ζ7−ζ23−ζ5−ζ13ζ5+ζ13ζ7+ζ23−ζ7−ζ23−ζ5−ζ13ζ5+ζ13ζ7+ζ23−ζ7−ζ23−ζ5−ζ13ζ5+ζ13ζ7+ζ23−ζ7−ζ23−ζ5−ζ13ζ5+ζ13
χ1011-11-11111i−i-1i−i11-1-1-11-1111111i−i111111-1-1ii−i−ii−i-1i−i11-1-1-1-1-1-11111-1-1-1-1i−i11-1-1ii−i−ii−ii−iii−i−i1111-1-1-1-1iiii−i−i−i−i−ζ7−ζ23ζ7+ζ23ζ5+ζ13−ζ5−ζ13−ζ7−ζ23ζ7+ζ23ζ5+ζ13−ζ5−ζ13−ζ7−ζ23ζ7+ζ23ζ5+ζ13−ζ5−ζ13−ζ7−ζ23ζ7+ζ23ζ5+ζ13−ζ5−ζ13
χ1111-11-11111i−i-1i−i11-1-1-11-1111111i−i1111-1-111−i−iiii−i-1i−i11-1-1-1-1-1-11111-1-1-1-1i−i-1-111−i−iiii−ii−iii−i−i-1-1-1-11111−i−i−i−iiiiiζ7+ζ23−ζ7−ζ23−ζ5−ζ13ζ5+ζ13ζ7+ζ23−ζ7−ζ23−ζ5−ζ13ζ5+ζ13−ζ7−ζ23ζ7+ζ23ζ5+ζ13−ζ5−ζ13−ζ7−ζ23ζ7+ζ23ζ5+ζ13−ζ5−ζ13
χ1211-11-11111i−i-1i−i11-1-1-11-1111111i−i1111-1-111−i−iiii−i-1i−i11-1-1-1-1-1-11111-1-1-1-1i−i-1-111−i−iiii−ii−iii−i−i-1-1-1-11111−i−i−i−iiiii−ζ7−ζ23ζ7+ζ23ζ5+ζ13−ζ5−ζ13−ζ7−ζ23ζ7+ζ23ζ5+ζ13−ζ5−ζ13ζ7+ζ23−ζ7−ζ23−ζ5−ζ13ζ5+ζ13ζ7+ζ23−ζ7−ζ23−ζ5−ζ13ζ5+ζ13
χ1311-11-11111−ii-1−ii11-1-1-11-1111111−ii111111-1-1−i−iii−ii-1−ii11-1-1-1-1-1-11111-1-1-1-1−ii11-1-1−i−iii−ii−ii−i−iii1111-1-1-1-1−i−i−i−iiiii−ζ5−ζ13ζ5+ζ13ζ7+ζ23−ζ7−ζ23−ζ5−ζ13ζ5+ζ13ζ7+ζ23−ζ7−ζ23−ζ5−ζ13ζ5+ζ13ζ7+ζ23−ζ7−ζ23−ζ5−ζ13ζ5+ζ13ζ7+ζ23−ζ7−ζ23
χ1411-11-11111−ii-1−ii11-1-1-11-1111111−ii111111-1-1−i−iii−ii-1−ii11-1-1-1-1-1-11111-1-1-1-1−ii11-1-1−i−iii−ii−ii−i−iii1111-1-1-1-1−i−i−i−iiiiiζ5+ζ13−ζ5−ζ13−ζ7−ζ23ζ7+ζ23ζ5+ζ13−ζ5−ζ13−ζ7−ζ23ζ7+ζ23ζ5+ζ13−ζ5−ζ13−ζ7−ζ23ζ7+ζ23ζ5+ζ13−ζ5−ζ13−ζ7−ζ23ζ7+ζ23
χ1511-11-11111−ii-1−ii11-1-1-11-1111111−ii1111-1-111ii−i−i−ii-1−ii11-1-1-1-1-1-11111-1-1-1-1−ii-1-111ii−i−i−ii−ii−i−iii-1-1-1-11111iiii−i−i−i−i−ζ5−ζ13ζ5+ζ13ζ7+ζ23−ζ7−ζ23−ζ5−ζ13ζ5+ζ13ζ7+ζ23−ζ7−ζ23ζ5+ζ13−ζ5−ζ13−ζ7−ζ23ζ7+ζ23ζ5+ζ13−ζ5−ζ13−ζ7−ζ23ζ7+ζ23
χ1611-11-11111−ii-1−ii11-1-1-11-1111111−ii1111-1-111ii−i−i−ii-1−ii11-1-1-1-1-1-11111-1-1-1-1−ii-1-111ii−i−i−ii−ii−i−iii-1-1-1-11111iiii−i−i−i−iζ5+ζ13−ζ5−ζ13−ζ7−ζ23ζ7+ζ23ζ5+ζ13−ζ5−ζ13−ζ7−ζ23ζ7+ζ23−ζ5−ζ13ζ5+ζ13ζ7+ζ23−ζ7−ζ23−ζ5−ζ13ζ5+ζ13ζ7+ζ23−ζ7−ζ23
χ1722222222222222222222222-1-1-1-122-1-1-1-122222222222222222-1-1-1-1-1-1-1-1-1-1-1-12222222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-10000000000000000
χ1822222222222222222222222-1-1-1-122-1-1-1-1-2-2-2-2-2-2-2-2222222222-1-1-1-1-1-1-1-1-1-1-1-122-2-2-2-2-2-2-2-2-1-1-1-1-1-1-1-111111111111111110000000000000000
χ1922222222222222-2-2-2-2222222222-2-222220000000022222-2-2-2-22222-2-2-2-2-2-2-2-2-2-2000000002222-2-2-2-200000000000000000000000000000000
χ2022222222222222-2-2-2-222222-1-1-1-1-2-2-1-1-1-10000000022222-2-2-2-2-1-1-1-111111111-2-200000000-1-1-1-1111133−3−333−3−333−3−333−3−30000000000000000
χ2122222222222222-2-2-2-222222-1-1-1-1-2-2-1-1-1-10000000022222-2-2-2-2-1-1-1-111111111-2-200000000-1-1-1-11111−3−333−3−333−3−333−3−3330000000000000000
χ22222222222-2-22-2-2222222222-1-1-1-1-2-2-1-1-1-12222-2-2-2-2-2-22-2-22222-1-1-1-1-1-1-1-1-1-1-1-1-2-22222-2-2-2-211111111-1-1-1-1-1-1-1-1111111110000000000000000
χ23222222222-2-22-2-2222222222-1-1-1-1-2-2-1-1-1-1-2-2-2-22222-2-22-2-22222-1-1-1-1-1-1-1-1-1-1-1-1-2-2-2-2-2-222221111111111111111-1-1-1-1-1-1-1-10000000000000000
χ24222222222-2-22-2-2-2-2-2-222222222222222200000000-2-22-2-2-2-2-2-22222-2-2-2-2-2-2-2-22200000000-2-2-2-2222200000000000000000000000000000000
χ25222222222-2-22-2-2-2-2-2-222222-1-1-1-122-1-1-1-100000000-2-22-2-2-2-2-2-2-1-1-1-11111111122000000001111-1-1-1-133−3−333−3−3−3−333−3−3330000000000000000
χ26222222222-2-22-2-2-2-2-2-222222-1-1-1-122-1-1-1-100000000-2-22-2-2-2-2-2-2-1-1-1-11111111122000000001111-1-1-1-1−3−333−3−33333−3−333−3−30000000000000000
χ2722222-2-22222-2-2-20000222-2-2222200-2-2-2-2−i2i2−i2i2−i2i2−i2i222-2-2-2000022-2-20000000000−i2i2−i2i2−i2i2−i2i222-2-20000−i2i2−i2i2−i2i2−i2i2−i2i2−i2i2−i2i2−i2i20000000000000000
χ2822222-2-22222-2-2-20000222-2-2222200-2-2-2-2i2−i2i2−i2i2−i2i2−i222-2-2-2000022-2-20000000000i2−i2i2−i2i2−i2i2−i222-2-20000i2−i2i2−i2i2−i2i2−i2i2−i2i2−i2i2−i2i2−i20000000000000000
χ2922222-2-22222-2-2-20000222-2-2-1-1-1-1001111−i2i2−i2i2−i2i2−i2i222-2-2-20000-1-11133−3−333−3−300−i2i2−i2i2−i2i2−i2i2-1-1113−33−3ζ5+ζ7−ζ5−ζ7ζ13+ζ23−ζ13−ζ23ζ5+ζ7−ζ5−ζ7ζ13+ζ23−ζ13−ζ23ζ5+ζ7−ζ5−ζ7ζ13+ζ23−ζ13−ζ23ζ5+ζ7−ζ5−ζ7ζ13+ζ23−ζ13−ζ230000000000000000
χ3022222-2-22222-2-2-20000222-2-2-1-1-1-1001111−i2i2−i2i2−i2i2−i2i222-2-2-20000-1-111−3−333−3−33300−i2i2−i2i2−i2i2−i2i2-1-111−33−33ζ13+ζ23−ζ13−ζ23ζ5+ζ7−ζ5−ζ7ζ13+ζ23−ζ13−ζ23ζ5+ζ7−ζ5−ζ7ζ13+ζ23−ζ13−ζ23ζ5+ζ7−ζ5−ζ7ζ13+ζ23−ζ13−ζ23ζ5+ζ7−ζ5−ζ70000000000000000
χ3122222-2-22222-2-2-20000222-2-2-1-1-1-1001111i2−i2i2−i2i2−i2i2−i222-2-2-20000-1-11133−3−333−3−300i2−i2i2−i2i2−i2i2−i2-1-1113−33−3−ζ5−ζ7ζ5+ζ7−ζ13−ζ23ζ13+ζ23−ζ5−ζ7ζ5+ζ7−ζ13−ζ23ζ13+ζ23−ζ5−ζ7ζ5+ζ7−ζ13−ζ23ζ13+ζ23−ζ5−ζ7ζ5+ζ7−ζ13−ζ23ζ13+ζ230000000000000000
χ3222222-2-22222-2-2-20000222-2-2-1-1-1-1001111i2−i2i2−i2i2−i2i2−i222-2-2-20000-1-111−3−333−3−33300i2−i2i2−i2i2−i2i2−i2-1-111−33−33−ζ13−ζ23ζ13+ζ23−ζ5−ζ7ζ5+ζ7−ζ13−ζ23ζ13+ζ23−ζ5−ζ7ζ5+ζ7−ζ13−ζ23ζ13+ζ23−ζ5−ζ7ζ5+ζ7−ζ13−ζ23ζ13+ζ23−ζ5−ζ7ζ5+ζ70000000000000000
χ3322222-2-222-2-2-2220000222-2-2222200-2-2-2-2−i2i2−i2i2i2−i2i2−i2-2-2-222000022-2-20000000000−i2i2−i2i2i2−i2i2−i2-2-2220000−i2i2−i2i2−i2i2−i2i2i2−i2i2−i2i2−i2i2−i20000000000000000
χ3422222-2-222-2-2-2220000222-2-2222200-2-2-2-2i2−i2i2−i2−i2i2−i2i2-2-2-222000022-2-20000000000i2−i2i2−i2−i2i2−i2i2-2-2220000i2−i2i2−i2i2−i2i2−i2−i2i2−i2i2−i2i2−i2i20000000000000000
χ3522222-2-222-2-2-2220000222-2-2-1-1-1-1001111−i2i2−i2i2i2−i2i2−i2-2-2-2220000-1-11133−3−333−3−300−i2i2−i2i2i2−i2i2−i211-1-1−33−33ζ5+ζ7−ζ5−ζ7ζ13+ζ23−ζ13−ζ23ζ5+ζ7−ζ5−ζ7ζ13+ζ23−ζ13−ζ23−ζ5−ζ7ζ5+ζ7−ζ13−ζ23ζ13+ζ23−ζ5−ζ7ζ5+ζ7−ζ13−ζ23ζ13+ζ230000000000000000
χ3622222-2-222-2-2-2220000222-2-2-1-1-1-1001111−i2i2−i2i2i2−i2i2−i2-2-2-2220000-1-111−3−333−3−33300−i2i2−i2i2i2−i2i2−i211-1-13−33−3ζ13+ζ23−ζ13−ζ23ζ5+ζ7−ζ5−ζ7ζ13+ζ23−ζ13−ζ23ζ5+ζ7−ζ5−ζ7−ζ13−ζ23ζ13+ζ23−ζ5−ζ7ζ5+ζ7−ζ13−ζ23ζ13+ζ23−ζ5−ζ7ζ5+ζ70000000000000000
χ3722222-2-222-2-2-2220000222-2-2-1-1-1-1001111i2−i2i2−i2−i2i2−i2i2-2-2-2220000-1-11133−3−333−3−300i2−i2i2−i2−i2i2−i2i211-1-1−33−33−ζ5−ζ7ζ5+ζ7−ζ13−ζ23ζ13+ζ23−ζ5−ζ7ζ5+ζ7−ζ13−ζ23ζ13+ζ23ζ5+ζ7−ζ5−ζ7ζ13+ζ23−ζ13−ζ23ζ5+ζ7−ζ5−ζ7ζ13+ζ23−ζ13−ζ230000000000000000
χ3822222-2-222-2-2-2220000222-2-2-1-1-1-1001111i2−i2i2−i2−i2i2−i2i2-2-2-2220000-1-111−3−333−3−33300i2−i2i2−i2−i2i2−i2i211-1-13−33−3−ζ13−ζ23ζ13+ζ23−ζ5−ζ7ζ5+ζ7−ζ13−ζ23ζ13+ζ23−ζ5−ζ7ζ5+ζ7ζ13+ζ23−ζ13−ζ23ζ5+ζ7−ζ5−ζ7ζ13+ζ23−ζ13−ζ23ζ5+ζ7−ζ5−ζ70000000000000000
χ3922-22-222222i−2i-22i−2i22-2-2-22-222-1-1-1-12i−2i-1-1-1-122-2-22i2i−2i−2i2i−2i-22i−2i22-2-21111-1-1-1-111112i−2i22-2-22i2i−2i−2i−ii−ii−i−iii-1-1-1-11111−i−i−i−iiiii0000000000000000
χ4022-22-222222i−2i-22i−2i22-2-2-22-222-1-1-1-12i−2i-1-1-1-1-2-222−2i−2i2i2i2i−2i-22i−2i22-2-21111-1-1-1-111112i−2i-2-222−2i−2i2i2i−ii−ii−i−iii1111-1-1-1-1iiii−i−i−i−i0000000000000000
χ4122-22-222222i−2i-22i−2i-2-222-22-2222222−2i2i2222000000002i−2i-22i−2i-2-222-2-2-2-2-2-2-2-22222−2i2i000000002i−2i2i−2i−2i−2i2i2i00000000000000000000000000000000
χ4222-22-222222i−2i-22i−2i-2-222-22-222-1-1-1-1−2i2i-1-1-1-1000000002i−2i-22i−2i-2-22211111111-1-1-1-1−2i2i00000000−ii−iiii−i−i33−3−3−3−333i3i3−i3−i3−i3−i3i3i30000000000000000
χ4322-22-222222i−2i-22i−2i-2-222-22-222-1-1-1-1−2i2i-1-1-1-1000000002i−2i-22i−2i-2-22211111111-1-1-1-1−2i2i00000000−ii−iiii−i−i−3−33333−3−3−i3−i3i3i3i3i3−i3−i30000000000000000
χ4422-22-22222−2i2i-2−2i2i22-2-2-22-222-1-1-1-1−2i2i-1-1-1-122-2-2−2i−2i2i2i−2i2i-2−2i2i22-2-21111-1-1-1-11111−2i2i22-2-2−2i−2i2i2ii−ii−iii−i−i-1-1-1-11111iiii−i−i−i−i0000000000000000
χ4522-22-22222−2i2i-2−2i2i22-2-2-22-222-1-1-1-1−2i2i-1-1-1-1-2-2222i2i−2i−2i−2i2i-2−2i2i22-2-21111-1-1-1-11111−2i2i-2-2222i2i−2i−2ii−ii−iii−i−i1111-1-1-1-1−i−i−i−iiiii0000000000000000
χ4622-22-22222−2i2i-2−2i2i-2-222-22-22222222i−2i222200000000−2i2i-2−2i2i-2-222-2-2-2-2-2-2-2-222222i−2i00000000−2i2i−2i2i2i2i−2i−2i00000000000000000000000000000000
χ4722-22-22222−2i2i-2−2i2i-2-222-22-222-1-1-1-12i−2i-1-1-1-100000000−2i2i-2−2i2i-2-22211111111-1-1-1-12i−2i00000000i−ii−i−i−iii33−3−3−3−333−i3−i3i3i3i3i3−i3−i30000000000000000
χ4822-22-22222−2i2i-2−2i2i-2-222-22-222-1-1-1-12i−2i-1-1-1-100000000−2i2i-2−2i2i-2-22211111111-1-1-1-12i−2i00000000i−ii−i−i−iii−3−33333−3−3i3i3−i3−i3−i3−i3i3i30000000000000000
χ4922-22-2-2-2222i−2i2−2i2i0000-22-2-2-2222200-2-2-2-2−i2i2i2−i22−2−222i−2i2−2i2i0000-2-2220000000000−i2i2i2−i22−2−222i−2i−2i2i0000−i2i2−i2i2i2−i2i2−i22−22−2−22−220000000000000000
χ5022-22-2-2-2222i−2i2−2i2i0000-22-2-2-2222200-2-2-2-2i2−i2−i2i2−222−22i−2i2−2i2i0000-2-2220000000000i2−i2−i2i2−222−22i−2i−2i2i0000i2−i2i2−i2−i2i2−i2i2−22−222−22−20000000000000000
χ5122-22-2-2-2222i−2i2−2i2i0000-22-2-2-2-1-1-1-1001111−i2i2i2−i22−2−222i−2i2−2i2i000011-1-133−3−3−3−33300−i2i2i2−i22−2−22−iii−ii3−i3−i3i3ζ5+ζ7−ζ5−ζ7ζ13+ζ23−ζ13−ζ23−ζ5−ζ7ζ5+ζ7−ζ13−ζ23ζ13+ζ23ζ13−ζ23−ζ13+ζ23ζ5−ζ7−ζ5+ζ7−ζ13+ζ23ζ13−ζ23−ζ5+ζ7ζ5−ζ70000000000000000
χ5222-22-2-2-2222i−2i2−2i2i0000-22-2-2-2-1-1-1-1001111−i2i2i2−i22−2−222i−2i2−2i2i000011-1-1−3−33333−3−300−i2i2i2−i22−2−22−iii−i−i3i3i3−i3ζ13+ζ23−ζ13−ζ23ζ5+ζ7−ζ5−ζ7−ζ13−ζ23ζ13+ζ23−ζ5−ζ7ζ5+ζ7ζ5−ζ7−ζ5+ζ7ζ13−ζ23−ζ13+ζ23−ζ5+ζ7ζ5−ζ7−ζ13+ζ23ζ13−ζ230000000000000000
χ5322-22-2-2-2222i−2i2−2i2i0000-22-2-2-2-1-1-1-1001111i2−i2−i2i2−222−22i−2i2−2i2i000011-1-133−3−3−3−33300i2−i2−i2i2−222−2−iii−ii3−i3−i3i3−ζ5−ζ7ζ5+ζ7−ζ13−ζ23ζ13+ζ23ζ5+ζ7−ζ5−ζ7ζ13+ζ23−ζ13−ζ23−ζ13+ζ23ζ13−ζ23−ζ5+ζ7ζ5−ζ7ζ13−ζ23−ζ13+ζ23ζ5−ζ7−ζ5+ζ70000000000000000
χ5422-22-2-2-2222i−2i2−2i2i0000-22-2-2-2-1-1-1-1001111i2−i2−i2i2−222−22i−2i2−2i2i000011-1-1−3−33333−3−300i2−i2−i2i2−222−2−iii−i−i3i3i3−i3−ζ13−ζ23ζ13+ζ23−ζ5−ζ7ζ5+ζ7ζ13+ζ23−ζ13−ζ23ζ5+ζ7−ζ5−ζ7−ζ5+ζ7ζ5−ζ7−ζ13+ζ23ζ13−ζ23ζ5−ζ7−ζ5+ζ7ζ13−ζ23−ζ13+ζ230000000000000000
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Here ζ is a primitive root of unity of order 24 (ζ24 = 1); i = ζ6.