Finite Group Databasebeta

← Group #72213068

Character table — Group #72213068

Order 1536.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96C97C98C99C100C101C102C103C104C105C106C107C108C109C110C111C112
size1111111122223333333333333333333333336666666666666666666666666666242424242424242424242424242424242424242424242424242424242424242432323232323232323232323232323232
order122222224444222222224444444444444444444444444444444444444444444444444444444444448888888888888888366666661212121212121212
χ11111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111111111
χ311111111-1-1-1-1111111111111111111111111-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1-1-111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1
χ411111111-1-1-1-1111111111111111111111111-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1-1-1-1-1-1-11111111111111111-1-1-1-1-1-1-1-1
χ5111-1-11-1-111-1-111-1-111-1-111111111-1-1-1-1-1-1-1-111-1-11111-1-1-1-111111111-1-1-1-1-1-1-1-1ii−i−iii−i−iii−i−iii−i−iiiii−i−i−i−iiiii−i−i−i−i111-1-1-1-111111-1-1-1-1
χ6111-1-11-1-111-1-111-1-111-1-111111111-1-1-1-1-1-1-1-111-1-11111-1-1-1-111111111-1-1-1-1-1-1-1-1−i−iii−i−iii−i−iii−i−iii−i−i−i−iiiii−i−i−i−iiiii111-1-1-1-111111-1-1-1-1
χ7111-1-11-1-1-1-11111-1-111-1-111111111-1-1-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-111111111ii−i−i−i−iiiii−i−i−i−iiiiiii−i−i−i−i−i−i−i−iiiii111-1-1-1-11-1-1-1-11111
χ8111-1-11-1-1-1-11111-1-111-1-111111111-1-1-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-111111111−i−iiiii−i−i−i−iiiii−i−i−i−i−i−iiiiiiiii−i−i−i−i111-1-1-1-11-1-1-1-11111
χ911-11-1-11-1i−ii−i1-11-11-11-11111-1-1-1-111-1-111-1-1i−ii−i11-1-111-1-1iiii−i−i−i−iiiii−i−i−i−i1-11-1i−ii−i1-11-1i−ii−i11-1-111-1-1ii−i−iii−i−i11-111-1-1-1ii−i−iii−i−i
χ1011-11-1-11-1i−ii−i1-11-11-11-11111-1-1-1-111-1-111-1-1i−ii−i11-1-111-1-1iiii−i−i−i−iiiii−i−i−i−i-11-11−ii−ii-11-11−ii−ii-1-111-1-111−i−iii−i−iii11-111-1-1-1ii−i−iii−i−i
χ1111-11-1-11-1−ii−ii1-11-11-11-11111-1-1-1-111-1-111-1-1−ii−ii11-1-111-1-1−i−i−i−iiiii−i−i−i−iiiii1-11-1−ii−ii1-11-1−ii−ii11-1-111-1-1−i−iii−i−iii11-111-1-1-1−i−iii−i−iii
χ1211-11-1-11-1−ii−ii1-11-11-11-11111-1-1-1-111-1-111-1-1−ii−ii11-1-111-1-1−i−i−i−iiiii−i−i−i−iiiii-11-11i−ii−i-11-11i−ii−i-1-111-1-111ii−i−iii−i−i11-111-1-1-1−i−iii−i−iii
χ1311-1-11-1-11i−i−ii1-1-111-1-111111-1-1-1-1-1-111-1-111i−i−ii11-1-1-1-111iiii−i−i−i−i−i−i−i−iiiiii−i−ii-111-1i−i−ii-111-1ii−i−i−i−iii-1-11111-1-111-1-1-111-1ii−i−i−i−iii
χ1411-1-11-1-11i−i−ii1-1-111-1-111111-1-1-1-1-1-111-1-111i−i−ii11-1-1-1-111iiii−i−i−i−i−i−i−i−iiiii−iii−i1-1-11−iii−i1-1-11−i−iiiii−i−i11-1-1-1-11111-1-1-111-1ii−i−i−i−iii
χ1511-1-11-1-11−iii−i1-1-111-1-111111-1-1-1-1-1-111-1-111−iii−i11-1-1-1-111−i−i−i−iiiiiiiii−i−i−i−ii−i−ii1-1-11i−i−ii1-1-11ii−i−i−i−iii11-1-1-1-11111-1-1-111-1−i−iiiii−i−i
χ1611-1-11-1-11−iii−i1-1-111-1-111111-1-1-1-1-1-111-1-111−iii−i11-1-1-1-111−i−i−i−iiiiiiiii−i−i−i−i−iii−i-111-1−iii−i-111-1−i−iiiii−i−i-1-11111-1-111-1-1-111-1−i−iiiii−i−i
χ17222222222222222222222222222222222222222222222222222222222222222200000000000000000000000000000000-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ1822222222-2-2-2-2222222222222222222222222-2-2-2-222222222-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-200000000000000000000000000000000-1-1-1-1-1-1-1-111111111
χ19222-2-22-2-222-2-222-2-222-2-222222222-2-2-2-2-2-2-2-222-2-22222-2-2-2-222222222-2-2-2-2-2-2-2-200000000000000000000000000000000-1-1-11111-1-1-1-1-11111
χ20222-2-22-2-2-2-22222-2-222-2-222222222-2-2-2-2-2-2-2-2-2-2222222-2-2-2-2-2-2-2-2-2-2-2-22222222200000000000000000000000000000000-1-1-11111-11111-1-1-1-1
χ2122-22-2-22-22i−2i2i−2i2-22-22-22-22222-2-2-2-222-2-222-2-22i−2i2i−2i22-2-222-2-22i2i2i2i−2i−2i−2i−2i2i2i2i2i−2i−2i−2i−2i00000000000000000000000000000000-1-11-1-1111−i−iii−i−iii
χ2222-22-2-22-2−2i2i−2i2i2-22-22-22-22222-2-2-2-222-2-222-2-2−2i2i−2i2i22-2-222-2-2−2i−2i−2i−2i2i2i2i2i−2i−2i−2i−2i2i2i2i2i00000000000000000000000000000000-1-11-1-1111ii−i−iii−i−i
χ2322-2-22-2-222i−2i−2i2i2-2-222-2-222222-2-2-2-2-2-222-2-2222i−2i−2i2i22-2-2-2-2222i2i2i2i−2i−2i−2i−2i−2i−2i−2i−2i2i2i2i2i00000000000000000000000000000000-1-1111-1-11−i−iiiii−i−i
χ2422-2-22-2-22−2i2i2i−2i2-2-222-2-222222-2-2-2-2-2-222-2-222−2i2i2i−2i22-2-2-2-222−2i−2i−2i−2i2i2i2i2i2i2i2i2i−2i−2i−2i−2i00000000000000000000000000000000-1-1111-1-11ii−i−i−i−iii
χ252-2222-2-2-20000-22222-2-2-222-2-222-2-22222-2-2-2-200002-22-22-22-20000000000000000000000000000000000000000000000002-222-22-2-200000000
χ262-2222-2-2-20000-22222-2-2-222-2-222-2-22222-2-2-2-200002-22-22-22-2000000000000000000000000000000000000000000000000-11-1-11-1113−33−33−33−3
χ272-2222-2-2-20000-22222-2-2-222-2-222-2-22222-2-2-2-200002-22-22-22-2000000000000000000000000000000000000000000000000-11-1-11-111−33−33−33−33
χ282-22-2-2-2220000-22-2-22-22222-2-222-2-2-2-2-2-2222200002-22-2-22-220000000000000000000000000000000000000000000000002-22-22-22-200000000
χ292-22-2-2-2220000-22-2-22-22222-2-222-2-2-2-2-2-2222200002-22-2-22-22000000000000000000000000000000000000000000000000-11-11-11-113−33−3−33−33
χ302-22-2-2-2220000-22-2-22-22222-2-222-2-2-2-2-2-2222200002-22-2-22-22000000000000000000000000000000000000000000000000-11-11-11-11−33−333−33−3
χ312-2-22-22-220000-2-22-222-2222-2-2-2-22222-2-2-2-22200002-2-222-2-220000000000000000000000000000000000000000000000002-2-22-2-22200000000
χ322-2-22-22-220000-2-22-222-2222-2-2-2-22222-2-2-2-22200002-2-222-2-22000000000000000000000000000000000000000000000000-111-111-1-1−i3i3i3−i3−i3i3i3−i3
χ332-2-22-22-220000-2-22-222-2222-2-2-2-22222-2-2-2-22200002-2-222-2-22000000000000000000000000000000000000000000000000-111-111-1-1i3−i3−i3i3i3−i3−i3i3
χ342-2-2-2222-20000-2-2-22222-222-2-2-2-222-2-22222-2-200002-2-22-222-20000000000000000000000000000000000000000000000002-2-2-222-2200000000
χ352-2-2-2222-20000-2-2-22222-222-2-2-2-222-2-22222-2-200002-2-22-222-2000000000000000000000000000000000000000000000000-1111-1-11-1−i3i3i3−i3i3−i3−i3i3
χ362-2-2-2222-20000-2-2-22222-222-2-2-2-222-2-22222-2-200002-2-22-222-2000000000000000000000000000000000000000000000000-1111-1-11-1i3−i3−i3i3−i3i3i3−i3
χ3733333333333333333333-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-13333-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-10000000000000000
χ3833333333333333333333-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-13333-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111111111110000000000000000
χ39333333333333-1-1-1-1-1-1-1-1−1+2i−1−2i−1+2i−1−2i−1+2i−1−2i−1+2i−1−2i−1+2i−1−2i−1+2i−1−2i−1+2i−1−2i−1+2i−1−2i-1-1-1-11111111111−1+2i−1−2i11−1+2i−1−2i11−1+2i−1−2i11−1+2i−1−2i11111111-1-1-1-1-1-1-1-1i−ii−ii−ii−ii−ii−ii−ii−i0000000000000000
χ40333333333333-1-1-1-1-1-1-1-1−1+2i−1−2i−1+2i−1−2i−1+2i−1−2i−1+2i−1−2i−1+2i−1−2i−1+2i−1−2i−1+2i−1−2i−1+2i−1−2i-1-1-1-11111111111−1+2i−1−2i11−1+2i−1−2i11−1+2i−1−2i11−1+2i−1−2i-1-1-1-1-1-1-1-111111111−ii−ii−ii−ii−ii−ii−ii−ii0000000000000000
χ41333333333333-1-1-1-1-1-1-1-1−1−2i−1+2i−1−2i−1+2i−1−2i−1+2i−1−2i−1+2i−1−2i−1+2i−1−2i−1+2i−1−2i−1+2i−1−2i−1+2i-1-1-1-11111111111−1−2i−1+2i11−1−2i−1+2i11−1−2i−1+2i11−1−2i−1+2i11111111-1-1-1-1-1-1-1-1−ii−ii−ii−ii−ii−ii−ii−ii0000000000000000
χ42333333333333-1-1-1-1-1-1-1-1−1−2i−1+2i−1−2i−1+2i−1−2i−1+2i−1−2i−1+2i−1−2i−1+2i−1−2i−1+2i−1−2i−1+2i−1−2i−1+2i-1-1-1-11111111111−1−2i−1+2i11−1−2i−1+2i11−1−2i−1+2i11−1−2i−1+2i-1-1-1-1-1-1-1-111111111i−ii−ii−ii−ii−ii−ii−ii−i0000000000000000
χ4333333333-3-3-3-333333333-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-3-3-3-3-1-1-1-1-1-1-1-111111111111111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1111111110000000000000000
χ4433333333-3-3-3-333333333-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-3-3-3-3-1-1-1-1-1-1-1-11111111111111111-1-1-1-11111-1-1-1-1111111111111-1-1-1-1-1-1-1-10000000000000000
χ4533333333-3-3-3-3-1-1-1-1-1-1-1-1−1+2i−1−2i−1+2i−1−2i−1+2i−1−2i−1+2i−1−2i−1+2i−1−2i−1+2i−1−2i−1+2i−1−2i−1+2i−1−2i111111111111-1-11−2i1+2i-1-11−2i1+2i-1-11−2i1+2i-1-11−2i1+2i1111-1-1-1-1-1-1-1-11111i−ii−ii−ii−i−ii−ii−ii−ii0000000000000000
χ4633333333-3-3-3-3-1-1-1-1-1-1-1-1−1+2i−1−2i−1+2i−1−2i−1+2i−1−2i−1+2i−1−2i−1+2i−1−2i−1+2i−1−2i−1+2i−1−2i−1+2i−1−2i111111111111-1-11−2i1+2i-1-11−2i1+2i-1-11−2i1+2i-1-11−2i1+2i-1-1-1-111111111-1-1-1-1−ii−ii−ii−iii−ii−ii−ii−i0000000000000000
χ4733333333-3-3-3-3-1-1-1-1-1-1-1-1−1−2i−1+2i−1−2i−1+2i−1−2i−1+2i−1−2i−1+2i−1−2i−1+2i−1−2i−1+2i−1−2i−1+2i−1−2i−1+2i111111111111-1-11+2i1−2i-1-11+2i1−2i-1-11+2i1−2i-1-11+2i1−2i1111-1-1-1-1-1-1-1-11111−ii−ii−ii−iii−ii−ii−ii−i0000000000000000
χ4833333333-3-3-3-3-1-1-1-1-1-1-1-1−1−2i−1+2i−1−2i−1+2i−1−2i−1+2i−1−2i−1+2i−1−2i−1+2i−1−2i−1+2i−1−2i−1+2i−1−2i−1+2i111111111111-1-11+2i1−2i-1-11+2i1−2i-1-11+2i1−2i-1-11+2i1−2i-1-1-1-111111111-1-1-1-1i−ii−ii−ii−i−ii−ii−ii−ii0000000000000000
χ49333-3-33-3-333-3-333-3-333-3-3-1-1-1-1-1-1-1-11111111133-3-3-1-1-1-11111-1-1-1-1-1-1-1-111111111ii−i−iii−i−iii−i−iii−i−i−i−i−i−iiiii−i−i−i−iiiii0000000000000000
χ50333-3-33-3-333-3-333-3-333-3-3-1-1-1-1-1-1-1-11111111133-3-3-1-1-1-11111-1-1-1-1-1-1-1-111111111−i−iii−i−iii−i−iii−i−iiiiiii−i−i−i−iiiii−i−i−i−i0000000000000000
χ51333-3-33-3-333-3-3-1-111-1-111−1+2i−1−2i−1+2i−1−2i−1+2i−1−2i−1+2i−1−2i1−2i1+2i1−2i1+2i1−2i1+2i1−2i1+2i-1-1111111-1-1-1-111−1+2i−1−2i11−1+2i−1−2i-1-11−2i1+2i-1-11−2i1+2iii−i−iii−i−i−i−iii−i−iii-11-111-11-1-11-111-11-10000000000000000
χ52333-3-33-3-333-3-3-1-111-1-111−1+2i−1−2i−1+2i−1−2i−1+2i−1−2i−1+2i−1−2i1−2i1+2i1−2i1+2i1−2i1+2i1−2i1+2i-1-1111111-1-1-1-111−1+2i−1−2i11−1+2i−1−2i-1-11−2i1+2i-1-11−2i1+2i−i−iii−i−iiiii−i−iii−i−i1-11-1-11-111-11-1-11-110000000000000000
χ53333-3-33-3-333-3-3-1-111-1-111−1−2i−1+2i−1−2i−1+2i−1−2i−1+2i−1−2i−1+2i1+2i1−2i1+2i1−2i1+2i1−2i1+2i1−2i-1-1111111-1-1-1-111−1−2i−1+2i11−1−2i−1+2i-1-11+2i1−2i-1-11+2i1−2iii−i−iii−i−i−i−iii−i−iii1-11-1-11-111-11-1-11-110000000000000000
χ54333-3-33-3-333-3-3-1-111-1-111−1−2i−1+2i−1−2i−1+2i−1−2i−1+2i−1−2i−1+2i1+2i1−2i1+2i1−2i1+2i1−2i1+2i1−2i-1-1111111-1-1-1-111−1−2i−1+2i11−1−2i−1+2i-1-11+2i1−2i-1-11+2i1−2i−i−iii−i−iiiii−i−iii−i−i-11-111-11-1-11-111-11-10000000000000000
χ55333-3-33-3-3-3-33333-3-333-3-3-1-1-1-1-1-1-1-111111111-3-333-1-1-1-1111111111111-1-1-1-1-1-1-1-1ii−i−i−i−iiiii−i−i−i−iii−i−i−i−iiiiiiiii−i−i−i−i0000000000000000
χ56333-3-33-3-3-3-33333-3-333-3-3-1-1-1-1-1-1-1-111111111-3-333-1-1-1-1111111111111-1-1-1-1-1-1-1-1−i−iiiii−i−i−i−iiiii−i−iiiii−i−i−i−i−i−i−i−iiiii0000000000000000
χ57333-3-33-3-3-3-333-1-111-1-111−1+2i−1−2i−1+2i−1−2i−1+2i−1−2i−1+2i−1−2i1−2i1+2i1−2i1+2i1−2i1+2i1−2i1+2i11-1-11111-1-1-1-1-1-11−2i1+2i-1-11−2i1+2i11−1+2i−1−2i11−1+2i−1−2iii−i−i−i−iii−i−iiiii−i−i-11-111-11-11-11-1-11-110000000000000000
χ58333-3-33-3-3-3-333-1-111-1-111−1+2i−1−2i−1+2i−1−2i−1+2i−1−2i−1+2i−1−2i1−2i1+2i1−2i1+2i1−2i1+2i1−2i1+2i11-1-11111-1-1-1-1-1-11−2i1+2i-1-11−2i1+2i11−1+2i−1−2i11−1+2i−1−2i−i−iiiii−i−iii−i−i−i−iii1-11-1-11-11-11-111-11-10000000000000000
χ59333-3-33-3-3-3-333-1-111-1-111−1−2i−1+2i−1−2i−1+2i−1−2i−1+2i−1−2i−1+2i1+2i1−2i1+2i1−2i1+2i1−2i1+2i1−2i11-1-11111-1-1-1-1-1-11+2i1−2i-1-11+2i1−2i11−1−2i−1+2i11−1−2i−1+2iii−i−i−i−iii−i−iiiii−i−i1-11-1-11-11-11-111-11-10000000000000000
χ60333-3-33-3-3-3-333-1-111-1-111−1−2i−1+2i−1−2i−1+2i−1−2i−1+2i−1−2i−1+2i1+2i1−2i1+2i1−2i1+2i1−2i1+2i1−2i11-1-11111-1-1-1-1-1-11+2i1−2i-1-11+2i1−2i11−1−2i−1+2i11−1−2i−1+2i−i−iiiii−i−iii−i−i−i−iii-11-111-11-11-11-1-11-110000000000000000
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χ6233-33-3-33-33i−3i3i−3i3-33-33-33-3-1-1-1-11111-1-111-1-1113i−3i3i−3i-1-111-1-111−i−i−i−iiiii−i−i−i−iiiii-11-11−ii−ii-11-11−ii−ii11-1-111-1-1ii−i−iii−i−i0000000000000000
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χ1126-6-6-6666-60000-6-6-66666-6-2-22222-2-222-2-2-2-2220000-222-22-2-220000000000000000000000000000000000000000000000000000000000000000

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