Finite Group Databasebeta

← Group #72242726

Character table — Group #72242726

Order 3456.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96C97C98C99C100C101C102C103C104C105C106C107C108C109C110C111C112
size1122333366666666612121212121212121212121212121212121236363636363672727272727272727296969696969611223333666666666121212121212121212121212121212121212363636363636727272727272727272969696969696
order1236336624466121212122666666666661212121212124412121212266882424242433366622666666244661212121226666666666612121212121244121212122668824242424666666
χ11111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111
χ31111−1+i32−1−i32−1+i32−1−i32111−1+i32−1−i32−1+i32−1+i32−1−i32−1−i321111−1+i32−1+i32−1+i32−1+i32−1−i32−1−i32−1−i32−1−i3211−1+i32−1+i32−1−i32−1−i3211−1+i32−1+i32−1−i32−1−i321−1+i32−1−i3211−1+i32−1+i32−1−i32−1−i321−1+i32−1−i321−1+i32−1−i321111−1+i32−1−i32−1+i32−1−i32111−1+i32−1−i32−1+i32−1+i32−1−i32−1−i321111−1+i32−1+i32−1+i32−1+i32−1−i32−1−i32−1−i32−1−i3211−1+i32−1+i32−1−i32−1−i3211−1+i32−1+i32−1−i32−1−i321−1+i32−1−i3211−1+i32−1+i32−1−i32−1−i321−1+i32−1−i321−1+i32−1−i32
χ41111−1+i32−1−i32−1+i32−1−i32111−1+i32−1−i32−1+i32−1+i32−1−i32−1−i321111−1+i32−1+i32−1+i32−1+i32−1−i32−1−i32−1−i32−1−i3211−1+i32−1+i32−1−i32−1−i32-1-11−i321−i321+i321+i32-11−i321+i32-1-11−i321−i321+i321+i321−1+i32−1−i321−1+i32−1−i321111−1+i32−1−i32−1+i32−1−i32111−1+i32−1−i32−1+i32−1+i32−1−i32−1−i321111−1+i32−1+i32−1+i32−1+i32−1−i32−1−i32−1−i32−1−i3211−1+i32−1+i32−1−i32−1−i32-1-11−i321−i321+i321+i32-11−i321+i32-1-11−i321−i321+i321+i321−1+i32−1−i321−1+i32−1−i32
χ51111−1−i32−1+i32−1−i32−1+i32111−1−i32−1+i32−1−i32−1−i32−1+i32−1+i321111−1−i32−1−i32−1−i32−1−i32−1+i32−1+i32−1+i32−1+i3211−1−i32−1−i32−1+i32−1+i3211−1−i32−1−i32−1+i32−1+i321−1−i32−1+i3211−1−i32−1−i32−1+i32−1+i321−1−i32−1+i321−1−i32−1+i321111−1−i32−1+i32−1−i32−1+i32111−1−i32−1+i32−1−i32−1−i32−1+i32−1+i321111−1−i32−1−i32−1−i32−1−i32−1+i32−1+i32−1+i32−1+i3211−1−i32−1−i32−1+i32−1+i3211−1−i32−1−i32−1+i32−1+i321−1−i32−1+i3211−1−i32−1−i32−1+i32−1+i321−1−i32−1+i321−1−i32−1+i32
χ61111−1−i32−1+i32−1−i32−1+i32111−1−i32−1+i32−1−i32−1−i32−1+i32−1+i321111−1−i32−1−i32−1−i32−1−i32−1+i32−1+i32−1+i32−1+i3211−1−i32−1−i32−1+i32−1+i32-1-11+i321+i321−i321−i32-11+i321−i32-1-11+i321+i321−i321−i321−1−i32−1+i321−1−i32−1+i321111−1−i32−1+i32−1−i32−1+i32111−1−i32−1+i32−1−i32−1−i32−1+i32−1+i321111−1−i32−1−i32−1−i32−1−i32−1+i32−1+i32−1+i32−1+i3211−1−i32−1−i32−1+i32−1+i32-1-11+i321+i321−i321−i32-11+i321−i32-1-11+i321+i321−i321−i321−1−i32−1+i321−1−i32−1+i32
χ722222222222222222222222222222222222000000000000000-1-1-1-1-1-122222222222222222222222222222222222000000000000000-1-1-1-1-1-1
χ82222−1+i3−1−i3−1+i3−1−i3222−1+i3−1−i3−1+i3−1+i3−1−i3−1−i32222−1+i3−1+i3−1+i3−1+i3−1−i3−1−i3−1−i3−1−i322−1+i3−1+i3−1−i3−1−i3000000000000000-11−i321+i32-11−i321+i322222−1+i3−1−i3−1+i3−1−i3222−1+i3−1−i3−1+i3−1+i3−1−i3−1−i32222−1+i3−1+i3−1+i3−1+i3−1−i3−1−i3−1−i3−1−i322−1+i3−1+i3−1−i3−1−i3000000000000000-11−i321+i32-11−i321+i32
χ92222−1−i3−1+i3−1−i3−1+i3222−1−i3−1+i3−1−i3−1−i3−1+i3−1+i32222−1−i3−1−i3−1−i3−1−i3−1+i3−1+i3−1+i3−1+i322−1−i3−1−i3−1+i3−1+i3000000000000000-11+i321−i32-11+i321−i322222−1−i3−1+i3−1−i3−1+i3222−1−i3−1+i3−1−i3−1−i3−1+i3−1+i32222−1−i3−1−i3−1−i3−1−i3−1+i3−1+i3−1+i3−1+i322−1−i3−1−i3−1+i3−1+i3000000000000000-11+i321−i32-11+i321−i32
χ10333333333-1-133-1-1-1-1-13-1-13-1-1-13-1-1-1-1-1-1-1-1-1111111111-1-1-1-1-1-1000000333333333-1-133-1-1-1-1-13-1-13-1-1-13-1-1-1-1-1-1-1-1-1111111111-1-1-1-1-1-1000000
χ11333333333-1-133-1-1-1-1-13-1-13-1-1-13-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111000000333333333-1-133-1-1-1-1-13-1-13-1-1-13-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111000000
χ1233333333-13-1-1-13-13-1-1-1-1-1-1-1-1-1-1-1-1-13-13-13-1111111-1-1-11-11-11-100000033333333-13-1-1-13-13-1-1-1-1-1-1-1-1-1-1-1-1-13-13-13-1111111-1-1-11-11-11-1000000
χ1333333333-13-1-1-13-13-1-1-1-1-1-1-1-1-1-1-1-1-13-13-13-1-1-1-1-1-1-1111-11-11-1100000033333333-13-1-1-13-13-1-1-1-1-1-1-1-1-1-1-1-1-13-13-13-1-1-1-1-1-1-1111-11-11-11000000
χ1433333333-1-13-1-1-13-13-1-1-1-1-1-1-1-1-1-1-1-1-13-13-13111111-1-1-1-11-11-1100000033333333-1-13-1-1-13-13-1-1-1-1-1-1-1-1-1-1-1-1-13-13-13111111-1-1-1-11-11-11000000
χ1533333333-1-13-1-1-13-13-1-1-1-1-1-1-1-1-1-1-1-1-13-13-13-1-1-1-1-1-11111-11-11-100000033333333-1-13-1-1-13-13-1-1-1-1-1-1-1-1-1-1-1-1-13-13-13-1-1-1-1-1-11111-11-11-1000000
χ163333−3+3i32−3−3i32−3+3i32−3−3i323-1-1−3+3i32−3−3i321−i321−i321+i321+i32-13-1-1−3+3i321−i321−i321−i32−3−3i321+i321+i321+i32-1-11−i321−i321+i321+i3211−1+i32−1+i32−1−i32−1−i321−1+i32−1−i32-1-11−i321−i321+i321+i320000003333−3+3i32−3−3i32−3+3i32−3−3i323-1-1−3+3i32−3−3i321−i321−i321+i321+i32-13-1-1−3+3i321−i321−i321−i32−3−3i321+i321+i321+i32-1-11−i321−i321+i321+i3211−1+i32−1+i32−1−i32−1−i321−1+i32−1−i32-1-11−i321−i321+i321+i32000000
χ173333−3+3i32−3−3i32−3+3i32−3−3i323-1-1−3+3i32−3−3i321−i321−i321+i321+i32-13-1-1−3+3i321−i321−i321−i32−3−3i321+i321+i321+i32-1-11−i321−i321+i321+i32-1-11−i321−i321+i321+i32-11−i321+i3211−1+i32−1+i32−1−i32−1−i320000003333−3+3i32−3−3i32−3+3i32−3−3i323-1-1−3+3i32−3−3i321−i321−i321+i321+i32-13-1-1−3+3i321−i321−i321−i32−3−3i321+i321+i321+i32-1-11−i321−i321+i321+i32-1-11−i321−i321+i321+i32-11−i321+i3211−1+i32−1+i32−1−i32−1−i32000000
χ183333−3+3i32−3−3i32−3+3i32−3−3i32-13-11−i321+i32−3+3i321−i32−3−3i321+i32-1-1-1-11−i321−i321−i321−i321+i321+i321+i321+i323-1−3+3i321−i32−3−3i321+i3211−1+i32−1+i32−1−i32−1−i32-11−i321+i321-1−1+i321−i32−1−i321+i320000003333−3+3i32−3−3i32−3+3i32−3−3i32-13-11−i321+i32−3+3i321−i32−3−3i321+i32-1-1-1-11−i321−i321−i321−i321+i321+i321+i321+i323-1−3+3i321−i32−3−3i321+i3211−1+i32−1+i32−1−i32−1−i32-11−i321+i321-1−1+i321−i32−1−i321+i32000000
χ193333−3+3i32−3−3i32−3+3i32−3−3i32-13-11−i321+i32−3+3i321−i32−3−3i321+i32-1-1-1-11−i321−i321−i321−i321+i321+i321+i321+i323-1−3+3i321−i32−3−3i321+i32-1-11−i321−i321+i321+i321−1+i32−1−i32-111−i32−1+i321+i32−1−i320000003333−3+3i32−3−3i32−3+3i32−3−3i32-13-11−i321+i32−3+3i321−i32−3−3i321+i32-1-1-1-11−i321−i321−i321−i321+i321+i321+i321+i323-1−3+3i321−i32−3−3i321+i32-1-11−i321−i321+i321+i321−1+i32−1−i32-111−i32−1+i321+i32−1−i32000000
χ203333−3+3i32−3−3i32−3+3i32−3−3i32-1-131−i321+i321−i32−3+3i321+i32−3−3i32-1-1-1-11−i321−i321−i321−i321+i321+i321+i321+i32-131−i32−3+3i321+i32−3−3i3211−1+i32−1+i32−1−i32−1−i32-11−i321+i32-111−i32−1+i321+i32−1−i320000003333−3+3i32−3−3i32−3+3i32−3−3i32-1-131−i321+i321−i32−3+3i321+i32−3−3i32-1-1-1-11−i321−i321−i321−i321+i321+i321+i321+i32-131−i32−3+3i321+i32−3−3i3211−1+i32−1+i32−1−i32−1−i32-11−i321+i32-111−i32−1+i321+i32−1−i32000000
χ213333−3+3i32−3−3i32−3+3i32−3−3i32-1-131−i321+i321−i32−3+3i321+i32−3−3i32-1-1-1-11−i321−i321−i321−i321+i321+i321+i321+i32-131−i32−3+3i321+i32−3−3i32-1-11−i321−i321+i321+i321−1+i32−1−i321-1−1+i321−i32−1−i321+i320000003333−3+3i32−3−3i32−3+3i32−3−3i32-1-131−i321+i321−i32−3+3i321+i32−3−3i32-1-1-1-11−i321−i321−i321−i321+i321+i321+i321+i32-131−i32−3+3i321+i32−3−3i32-1-11−i321−i321+i321+i321−1+i32−1−i321-1−1+i321−i32−1−i321+i32000000
χ223333−3−3i32−3+3i32−3−3i32−3+3i323-1-1−3−3i32−3+3i321+i321+i321−i321−i32-13-1-1−3−3i321+i321+i321+i32−3+3i321−i321−i321−i32-1-11+i321+i321−i321−i3211−1−i32−1−i32−1+i32−1+i321−1−i32−1+i32-1-11+i321+i321−i321−i320000003333−3−3i32−3+3i32−3−3i32−3+3i323-1-1−3−3i32−3+3i321+i321+i321−i321−i32-13-1-1−3−3i321+i321+i321+i32−3+3i321−i321−i321−i32-1-11+i321+i321−i321−i3211−1−i32−1−i32−1+i32−1+i321−1−i32−1+i32-1-11+i321+i321−i321−i32000000
χ233333−3−3i32−3+3i32−3−3i32−3+3i323-1-1−3−3i32−3+3i321+i321+i321−i321−i32-13-1-1−3−3i321+i321+i321+i32−3+3i321−i321−i321−i32-1-11+i321+i321−i321−i32-1-11+i321+i321−i321−i32-11+i321−i3211−1−i32−1−i32−1+i32−1+i320000003333−3−3i32−3+3i32−3−3i32−3+3i323-1-1−3−3i32−3+3i321+i321+i321−i321−i32-13-1-1−3−3i321+i321+i321+i32−3+3i321−i321−i321−i32-1-11+i321+i321−i321−i32-1-11+i321+i321−i321−i32-11+i321−i3211−1−i32−1−i32−1+i32−1+i32000000
χ243333−3−3i32−3+3i32−3−3i32−3+3i32-13-11+i321−i32−3−3i321+i32−3+3i321−i32-1-1-1-11+i321+i321+i321+i321−i321−i321−i321−i323-1−3−3i321+i32−3+3i321−i3211−1−i32−1−i32−1+i32−1+i32-11+i321−i321-1−1−i321+i32−1+i321−i320000003333−3−3i32−3+3i32−3−3i32−3+3i32-13-11+i321−i32−3−3i321+i32−3+3i321−i32-1-1-1-11+i321+i321+i321+i321−i321−i321−i321−i323-1−3−3i321+i32−3+3i321−i3211−1−i32−1−i32−1+i32−1+i32-11+i321−i321-1−1−i321+i32−1+i321−i32000000
χ253333−3−3i32−3+3i32−3−3i32−3+3i32-13-11+i321−i32−3−3i321+i32−3+3i321−i32-1-1-1-11+i321+i321+i321+i321−i321−i321−i321−i323-1−3−3i321+i32−3+3i321−i32-1-11+i321+i321−i321−i321−1−i32−1+i32-111+i32−1−i321−i32−1+i320000003333−3−3i32−3+3i32−3−3i32−3+3i32-13-11+i321−i32−3−3i321+i32−3+3i321−i32-1-1-1-11+i321+i321+i321+i321−i321−i321−i321−i323-1−3−3i321+i32−3+3i321−i32-1-11+i321+i321−i321−i321−1−i32−1+i32-111+i32−1−i321−i32−1+i32000000
χ263333−3−3i32−3+3i32−3−3i32−3+3i32-1-131+i321−i321+i32−3−3i321−i32−3+3i32-1-1-1-11+i321+i321+i321+i321−i321−i321−i321−i32-131+i32−3−3i321−i32−3+3i3211−1−i32−1−i32−1+i32−1+i32-11+i321−i32-111+i32−1−i321−i32−1+i320000003333−3−3i32−3+3i32−3−3i32−3+3i32-1-131+i321−i321+i32−3−3i321−i32−3+3i32-1-1-1-11+i321+i321+i321+i321−i321−i321−i321−i32-131+i32−3−3i321−i32−3+3i3211−1−i32−1−i32−1+i32−1+i32-11+i321−i32-111+i32−1−i321−i32−1+i32000000
χ273333−3−3i32−3+3i32−3−3i32−3+3i32-1-131+i321−i321+i32−3−3i321−i32−3+3i32-1-1-1-11+i321+i321+i321+i321−i321−i321−i321−i32-131+i32−3−3i321−i32−3+3i32-1-11+i321+i321−i321−i321−1−i32−1+i321-1−1−i321+i32−1+i321−i320000003333−3−3i32−3+3i32−3−3i32−3+3i32-1-131+i321−i321+i32−3−3i321−i32−3+3i32-1-1-1-11+i321+i321+i321+i321−i321−i321−i321−i32-131+i32−3−3i321−i32−3+3i32-1-11+i321+i321−i321−i321−1−i32−1+i321-1−1−i321+i32−1+i321−i32000000
χ284-44-444-4-40000000000000000000000000002-22-22-2000000000111-1-1-14-44-444-4-40000000000000000000000000002-22-22-2000000000111-1-1-1
χ294-44-444-4-4000000000000000000000000000-22-22-22000000000111-1-1-14-44-444-4-4000000000000000000000000000-22-22-22000000000111-1-1-1
χ304-44-4−2+2i3−2−2i32−2i32+2i30000000000000000000000000002-2−1+i31−i3−1−i31+i30000000001−1+i32−1−i32-11−i321+i324-44-4−2+2i3−2−2i32−2i32+2i30000000000000000000000000002-2−1+i31−i3−1−i31+i30000000001−1+i32−1−i32-11−i321+i32
χ314-44-4−2+2i3−2−2i32−2i32+2i3000000000000000000000000000-221−i3−1+i31+i3−1−i30000000001−1+i32−1−i32-11−i321+i324-44-4−2+2i3−2−2i32−2i32+2i3000000000000000000000000000-221−i3−1+i31+i3−1−i30000000001−1+i32−1−i32-11−i321+i32
χ324-44-4−2−2i3−2+2i32+2i32−2i30000000000000000000000000002-2−1−i31+i3−1+i31−i30000000001−1−i32−1+i32-11+i321−i324-44-4−2−2i3−2+2i32+2i32−2i30000000000000000000000000002-2−1−i31+i3−1+i31−i30000000001−1−i32−1+i32-11+i321−i32
χ334-44-4−2−2i3−2+2i32+2i32−2i3000000000000000000000000000-221+i3−1−i31−i3−1+i30000000001−1−i32−1+i32-11+i321−i324-44-4−2−2i3−2+2i32+2i32−2i3000000000000000000000000000-221+i3−1−i31−i3−1+i30000000001−1−i32−1+i32-11+i321−i32
χ3466666666-2-2-2-2-2-2-2-2-22-222-2222-2222-2-2-2-2-2-200000000000000000000066666666-2-2-2-2-2-2-2-2-22-222-2222-2222-2-2-2-2-2-2000000000000000000000
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χ11224-24-12120000000000000000000000000000000000000000000000000000-242412-120000000000000000000000000000000000000000000000000000

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