Finite Group Databasebeta

← Group #72222293

Character table — Group #72222293

Order 6048.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96C97C98C99C100C101C102C103C104C105
size16777773182121212121636424242424263642424242428485656565656212141414141463642424242421272848484848412728484848484169611211211211211231821212121219546363636363181081261261261261261810812612612612612624144168168168168168
order1723366214266662142666642841212121232163366321633666426666664266666128412121212123216336621426666214266662142666642841212121264266666
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ2111−1+i32−1−i32−1+i32−1−i32111−1+i32−1−i32−1+i32−1−i32111−1+i32−1−i32−1+i32−1−i32111−1+i32−1−i32−1+i32−1−i32111−1+i32−1−i32−1+i32−1−i32111−1+i32−1−i32−1+i32−1−i32111−1+i32−1−i32−1+i32−1−i32111−1+i32−1−i32−1+i32−1−i32111−1+i32−1−i32−1+i32−1−i32111−1+i32−1−i32−1+i32−1−i32111−1+i32−1−i32−1+i32−1−i32111−1+i32−1−i32−1+i32−1−i32111−1+i32−1−i32−1+i32−1−i32111−1+i32−1−i32−1+i32−1−i32111−1+i32−1−i32−1+i32−1−i32
χ3111−1−i32−1+i32−1−i32−1+i32111−1−i32−1+i32−1−i32−1+i32111−1−i32−1+i32−1−i32−1+i32111−1−i32−1+i32−1−i32−1+i32111−1−i32−1+i32−1−i32−1+i32111−1−i32−1+i32−1−i32−1+i32111−1−i32−1+i32−1−i32−1+i32111−1−i32−1+i32−1−i32−1+i32111−1−i32−1+i32−1−i32−1+i32111−1−i32−1+i32−1−i32−1+i32111−1−i32−1+i32−1−i32−1+i32111−1−i32−1+i32−1−i32−1+i32111−1−i32−1+i32−1−i32−1+i32111−1−i32−1+i32−1−i32−1+i32111−1−i32−1+i32−1−i32−1+i32
χ411-111-1-111-111-1-111-111-1-111-111-1-111-111-1-111-111-1-111-111-1-111-111-1-111-111-1-111-111-1-111-111-1-111-111-1-111-111-1-111-111-1-111-111-1-1
χ511-1−1+i32−1−i321−i321+i3211-1−1+i32−1−i321−i321+i3211-1−1+i32−1−i321−i321+i3211-1−1+i32−1−i321−i321+i3211-1−1+i32−1−i321−i321+i3211-1−1+i32−1−i321−i321+i3211-1−1+i32−1−i321−i321+i3211-1−1+i32−1−i321−i321+i3211-1−1+i32−1−i321−i321+i3211-1−1+i32−1−i321−i321+i3211-1−1+i32−1−i321−i321+i3211-1−1+i32−1−i321−i321+i3211-1−1+i32−1−i321−i321+i3211-1−1+i32−1−i321−i321+i3211-1−1+i32−1−i321−i321+i32
χ611-1−1−i32−1+i321+i321−i3211-1−1−i32−1+i321+i321−i3211-1−1−i32−1+i321+i321−i3211-1−1−i32−1+i321+i321−i3211-1−1−i32−1+i321+i321−i3211-1−1−i32−1+i321+i321−i3211-1−1−i32−1+i321+i321−i3211-1−1−i32−1+i321+i321−i3211-1−1−i32−1+i321+i321−i3211-1−1−i32−1+i321+i321−i3211-1−1−i32−1+i321+i321−i3211-1−1−i32−1+i321+i321−i3211-1−1−i32−1+i321+i321−i3211-1−1−i32−1+i321+i321−i3211-1−1−i32−1+i321+i321−i32
χ76-1000006-1000006-1000006-1000006-1000006-1000006-1000006-1000006-1000006-1000006-1000006-1000006-1000006-1000006-100000
χ811111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111
χ9111−1+i32−1−i32−1+i32−1−i32111−1+i32−1−i32−1+i32−1−i32-1-1-11−i321+i321−i321+i32-1-1-11−i321+i321−i321+i32111−1+i32−1−i32−1+i32−1−i32111−1+i32−1−i32−1+i32−1−i32111−1+i32−1−i32−1+i32−1−i32-1-1-11−i321+i321−i321+i32-1-1-11−i321+i321−i321+i32111−1+i32−1−i32−1+i32−1−i32111−1+i32−1−i32−1+i32−1−i32111−1+i32−1−i32−1+i32−1−i32-1-1-11−i321+i321−i321+i32-1-1-11−i321+i321−i321+i32111−1+i32−1−i32−1+i32−1−i32
χ10111−1−i32−1+i32−1−i32−1+i32111−1−i32−1+i32−1−i32−1+i32-1-1-11+i321−i321+i321−i32-1-1-11+i321−i321+i321−i32111−1−i32−1+i32−1−i32−1+i32111−1−i32−1+i32−1−i32−1+i32111−1−i32−1+i32−1−i32−1+i32-1-1-11+i321−i321+i321−i32-1-1-11+i321−i321+i321−i32111−1−i32−1+i32−1−i32−1+i32111−1−i32−1+i32−1−i32−1+i32111−1−i32−1+i32−1−i32−1+i32-1-1-11+i321−i321+i321−i32-1-1-11+i321−i321+i321−i32111−1−i32−1+i32−1−i32−1+i32
χ1111-111-1-111-111-1-1-1-11-1-111-1-11-1-11111-111-1-111-111-1-111-111-1-1-1-11-1-111-1-11-1-11111-111-1-111-111-1-111-111-1-1-1-11-1-111-1-11-1-11111-111-1-1
χ1211-1−1+i32−1−i321−i321+i3211-1−1+i32−1−i321−i321+i32-1-111−i321+i32−1+i32−1−i32-1-111−i321+i32−1+i32−1−i3211-1−1+i32−1−i321−i321+i3211-1−1+i32−1−i321−i321+i3211-1−1+i32−1−i321−i321+i32-1-111−i321+i32−1+i32−1−i32-1-111−i321+i32−1+i32−1−i3211-1−1+i32−1−i321−i321+i3211-1−1+i32−1−i321−i321+i3211-1−1+i32−1−i321−i321+i32-1-111−i321+i32−1+i32−1−i32-1-111−i321+i32−1+i32−1−i3211-1−1+i32−1−i321−i321+i32
χ1311-1−1−i32−1+i321+i321−i3211-1−1−i32−1+i321+i321−i32-1-111+i321−i32−1−i32−1+i32-1-111+i321−i32−1−i32−1+i3211-1−1−i32−1+i321+i321−i3211-1−1−i32−1+i321+i321−i3211-1−1−i32−1+i321+i321−i32-1-111+i321−i32−1−i32−1+i32-1-111+i321−i32−1−i32−1+i3211-1−1−i32−1+i321+i321−i3211-1−1−i32−1+i321+i321−i3211-1−1−i32−1+i321+i321−i32-1-111+i321−i32−1−i32−1+i32-1-111+i321−i32−1−i32−1+i3211-1−1−i32−1+i321+i321−i32
χ146-1000006-100000-6100000-61000006-1000006-1000006-100000-6100000-61000006-1000006-1000006-100000-6100000-61000006-100000
χ152222222222222200000000000000-1-1-1-1-1-1-12222222222222200000000000000-1-1-1-1-1-1-12222222222222200000000000000-1-1-1-1-1-1-1
χ16222−1+i3−1−i3−1+i3−1−i3222−1+i3−1−i3−1+i3−1−i300000000000000-1-1-11−i321+i321−i321+i32222−1+i3−1−i3−1+i3−1−i3222−1+i3−1−i3−1+i3−1−i300000000000000-1-1-11−i321+i321−i321+i32222−1+i3−1−i3−1+i3−1−i3222−1+i3−1−i3−1+i3−1−i300000000000000-1-1-11−i321+i321−i321+i32
χ17222−1−i3−1+i3−1−i3−1+i3222−1−i3−1+i3−1−i3−1+i300000000000000-1-1-11+i321−i321+i321−i32222−1−i3−1+i3−1−i3−1+i3222−1−i3−1+i3−1−i3−1+i300000000000000-1-1-11+i321−i321+i321−i32222−1−i3−1+i3−1−i3−1+i3222−1−i3−1+i3−1−i3−1+i300000000000000-1-1-11+i321−i321+i321−i32
χ1822-222-2-222-222-2-200000000000000-1-11-1-11122-222-2-222-222-2-200000000000000-1-11-1-11122-222-2-222-222-2-200000000000000-1-11-1-111
χ1922-2−1+i3−1−i31−i31+i322-2−1+i3−1−i31−i31+i300000000000000-1-111−i321+i32−1+i32−1−i3222-2−1+i3−1−i31−i31+i322-2−1+i3−1−i31−i31+i300000000000000-1-111−i321+i32−1+i32−1−i3222-2−1+i3−1−i31−i31+i322-2−1+i3−1−i31−i31+i300000000000000-1-111−i321+i32−1+i32−1−i32
χ2022-2−1−i3−1+i31+i31−i322-2−1−i3−1+i31+i31−i300000000000000-1-111+i321−i32−1−i32−1+i3222-2−1−i3−1+i31+i31−i322-2−1−i3−1+i31+i31−i300000000000000-1-111+i321−i32−1−i32−1+i3222-2−1−i3−1+i31+i31−i322-2−1−i3−1+i31+i31−i300000000000000-1-111+i321−i32−1−i32−1+i32
χ2112-20000012-20000000000000000000-610000012-20000012-20000000000000000000-610000012-20000012-20000000000000000000-6100000
χ223333333-1-1-1-1-1-1-11111111-1-1-1-1-1-1-100000003333333-1-1-1-1-1-1-11111111-1-1-1-1-1-1-100000003333333-1-1-1-1-1-1-11111111-1-1-1-1-1-1-10000000
χ23333−3+3i32−3−3i32−3+3i32−3−3i32-1-1-11−i321+i321−i321+i32111−1+i32−1−i32−1+i32−1−i32-1-1-11−i321+i321−i321+i320000000333−3+3i32−3−3i32−3+3i32−3−3i32-1-1-11−i321+i321−i321+i32111−1+i32−1−i32−1+i32−1−i32-1-1-11−i321+i321−i321+i320000000333−3+3i32−3−3i32−3+3i32−3−3i32-1-1-11−i321+i321−i321+i32111−1+i32−1−i32−1+i32−1−i32-1-1-11−i321+i321−i321+i320000000
χ24333−3−3i32−3+3i32−3−3i32−3+3i32-1-1-11+i321−i321+i321−i32111−1−i32−1+i32−1−i32−1+i32-1-1-11+i321−i321+i321−i320000000333−3−3i32−3+3i32−3−3i32−3+3i32-1-1-11+i321−i321+i321−i32111−1−i32−1+i32−1−i32−1+i32-1-1-11+i321−i321+i321−i320000000333−3−3i32−3+3i32−3−3i32−3+3i32-1-1-11+i321−i321+i321−i32111−1−i32−1+i32−1−i32−1+i32-1-1-11+i321−i321+i321−i320000000
χ2533-333-3-3-1-11-1-11111-111-1-1-1-11-1-111000000033-333-3-3-1-11-1-11111-111-1-1-1-11-1-111000000033-333-3-3-1-11-1-11111-111-1-1-1-11-1-1110000000
χ2633-3−3+3i32−3−3i323−3i323+3i32-1-111−i321+i32−1+i32−1−i3211-1−1+i32−1−i321−i321+i32-1-111−i321+i32−1+i32−1−i32000000033-3−3+3i32−3−3i323−3i323+3i32-1-111−i321+i32−1+i32−1−i3211-1−1+i32−1−i321−i321+i32-1-111−i321+i32−1+i32−1−i32000000033-3−3+3i32−3−3i323−3i323+3i32-1-111−i321+i32−1+i32−1−i3211-1−1+i32−1−i321−i321+i32-1-111−i321+i32−1+i32−1−i320000000
χ2733-3−3−3i32−3+3i323+3i323−3i32-1-111+i321−i32−1−i32−1+i3211-1−1−i32−1+i321+i321−i32-1-111+i321−i32−1−i32−1+i32000000033-3−3−3i32−3+3i323+3i323−3i32-1-111+i321−i32−1−i32−1+i3211-1−1−i32−1+i321+i321−i32-1-111+i321−i32−1−i32−1+i32000000033-3−3−3i32−3+3i323+3i323−3i32-1-111+i321−i32−1−i32−1+i3211-1−1−i32−1+i321+i321−i32-1-111+i321−i32−1−i32−1+i320000000
χ2818-300000-61000006-100000-6100000000000018-300000-61000006-100000-6100000000000018-300000-61000006-100000-61000000000000
χ293333333-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111100000003333333-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111100000003333333-1-1-1-1-1-1-1-1-1-1-1-1-1-111111110000000
χ30333−3+3i32−3−3i32−3+3i32−3−3i32-1-1-11−i321+i321−i321+i32-1-1-11−i321+i321−i321+i32111−1+i32−1−i32−1+i32−1−i320000000333−3+3i32−3−3i32−3+3i32−3−3i32-1-1-11−i321+i321−i321+i32-1-1-11−i321+i321−i321+i32111−1+i32−1−i32−1+i32−1−i320000000333−3+3i32−3−3i32−3+3i32−3−3i32-1-1-11−i321+i321−i321+i32-1-1-11−i321+i321−i321+i32111−1+i32−1−i32−1+i32−1−i320000000
χ31333−3−3i32−3+3i32−3−3i32−3+3i32-1-1-11+i321−i321+i321−i32-1-1-11+i321−i321+i321−i32111−1−i32−1+i32−1−i32−1+i320000000333−3−3i32−3+3i32−3−3i32−3+3i32-1-1-11+i321−i321+i321−i32-1-1-11+i321−i321+i321−i32111−1−i32−1+i32−1−i32−1+i320000000333−3−3i32−3+3i32−3−3i32−3+3i32-1-1-11+i321−i321+i321−i32-1-1-11+i321−i321+i321−i32111−1−i32−1+i32−1−i32−1+i320000000
χ3233-333-3-3-1-11-1-111-1-11-1-11111-111-1-1000000033-333-3-3-1-11-1-111-1-11-1-11111-111-1-1000000033-333-3-3-1-11-1-111-1-11-1-11111-111-1-10000000
χ3333-3−3+3i32−3−3i323−3i323+3i32-1-111−i321+i32−1+i32−1−i32-1-111−i321+i32−1+i32−1−i3211-1−1+i32−1−i321−i321+i32000000033-3−3+3i32−3−3i323−3i323+3i32-1-111−i321+i32−1+i32−1−i32-1-111−i321+i32−1+i32−1−i3211-1−1+i32−1−i321−i321+i32000000033-3−3+3i32−3−3i323−3i323+3i32-1-111−i321+i32−1+i32−1−i32-1-111−i321+i32−1+i32−1−i3211-1−1+i32−1−i321−i321+i320000000
χ3433-3−3−3i32−3+3i323+3i323−3i32-1-111+i321−i32−1−i32−1+i32-1-111+i321−i32−1−i32−1+i3211-1−1−i32−1+i321+i321−i32000000033-3−3−3i32−3+3i323+3i323−3i32-1-111+i321−i32−1−i32−1+i32-1-111+i321−i32−1−i32−1+i3211-1−1−i32−1+i321+i321−i32000000033-3−3−3i32−3+3i323+3i323−3i32-1-111+i321−i32−1−i32−1+i32-1-111+i321−i32−1−i32−1+i3211-1−1−i32−1+i321+i321−i320000000
χ3518-300000-6100000-61000006-100000000000018-300000-6100000-61000006-100000000000018-300000-6100000-61000006-1000000000000
χ361111111111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ37111−1+i32−1−i32−1+i32−1−i32111−1+i32−1−i32−1+i32−1−i32111−1+i32−1−i32−1+i32−1−i32111−1+i32−1−i32−1+i32−1−i32111−1+i32−1−i32−1+i32−1−i32111−1+i32−1−i32−1+i32−1−i32111−1+i32−1−i32−1+i32−1−i32111−1+i32−1−i32−1+i32−1−i32111−1+i32−1−i32−1+i32−1−i32111−1+i32−1−i32−1+i32−1−i32-1-1-11−i321+i321−i321+i32-1-1-11−i321+i321−i321+i32-1-1-11−i321+i321−i321+i32-1-1-11−i321+i321−i321+i32-1-1-11−i321+i321−i321+i32
χ38111−1−i32−1+i32−1−i32−1+i32111−1−i32−1+i32−1−i32−1+i32111−1−i32−1+i32−1−i32−1+i32111−1−i32−1+i32−1−i32−1+i32111−1−i32−1+i32−1−i32−1+i32111−1−i32−1+i32−1−i32−1+i32111−1−i32−1+i32−1−i32−1+i32111−1−i32−1+i32−1−i32−1+i32111−1−i32−1+i32−1−i32−1+i32111−1−i32−1+i32−1−i32−1+i32-1-1-11+i321−i321+i321−i32-1-1-11+i321−i321+i321−i32-1-1-11+i321−i321+i321−i32-1-1-11+i321−i321+i321−i32-1-1-11+i321−i321+i321−i32
χ3911-111-1-111-111-1-111-111-1-111-111-1-111-111-1-111-111-1-111-111-1-111-111-1-111-111-1-111-111-1-1-1-11-1-111-1-11-1-111-1-11-1-111-1-11-1-111-1-11-1-111
χ4011-1−1+i32−1−i321−i321+i3211-1−1+i32−1−i321−i321+i3211-1−1+i32−1−i321−i321+i3211-1−1+i32−1−i321−i321+i3211-1−1+i32−1−i321−i321+i3211-1−1+i32−1−i321−i321+i3211-1−1+i32−1−i321−i321+i3211-1−1+i32−1−i321−i321+i3211-1−1+i32−1−i321−i321+i3211-1−1+i32−1−i321−i321+i32-1-111−i321+i32−1+i32−1−i32-1-111−i321+i32−1+i32−1−i32-1-111−i321+i32−1+i32−1−i32-1-111−i321+i32−1+i32−1−i32-1-111−i321+i32−1+i32−1−i32
χ4111-1−1−i32−1+i321+i321−i3211-1−1−i32−1+i321+i321−i3211-1−1−i32−1+i321+i321−i3211-1−1−i32−1+i321+i321−i3211-1−1−i32−1+i321+i321−i3211-1−1−i32−1+i321+i321−i3211-1−1−i32−1+i321+i321−i3211-1−1−i32−1+i321+i321−i3211-1−1−i32−1+i321+i321−i3211-1−1−i32−1+i321+i321−i32-1-111+i321−i32−1−i32−1+i32-1-111+i321−i32−1−i32−1+i32-1-111+i321−i32−1−i32−1+i32-1-111+i321−i32−1−i32−1+i32-1-111+i321−i32−1−i32−1+i32
χ426-1000006-1000006-1000006-1000006-1000006-1000006-1000006-1000006-1000006-100000-6100000-6100000-6100000-6100000-6100000
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χ926666666-2-2-2-2-2-2-22222222-2-2-2-2-2-2-20000000-3-3-3-3-3-3-31111111-1-1-1-1-1-1-11111111000000000000000000000000000000000000000000
χ93666−3+3i3−3−3i3−3+3i3−3−3i3-2-2-21−i31+i31−i31+i3222−1+i3−1−i3−1+i3−1−i3-2-2-21−i31+i31−i31+i30000000-3-3-33−3i323+3i323−3i323+3i32111−1+i32−1−i32−1+i32−1−i32-1-1-11−i321+i321−i321+i32111−1+i32−1−i32−1+i32−1−i32000000000000000000000000000000000000000000
χ94666−3−3i3−3+3i3−3−3i3−3+3i3-2-2-21+i31−i31+i31−i3222−1−i3−1+i3−1−i3−1+i3-2-2-21+i31−i31+i31−i30000000-3-3-33+3i323−3i323+3i323−3i32111−1−i32−1+i32−1−i32−1+i32-1-1-11+i321−i321+i321−i32111−1−i32−1+i32−1−i32−1+i32000000000000000000000000000000000000000000
χ9566-666-6-6-2-22-2-22222-222-2-2-2-22-2-2220000000-3-33-3-33311-111-1-1-1-11-1-11111-111-1-1000000000000000000000000000000000000000000
χ9666-6−3+3i3−3−3i33−3i33+3i3-2-221−i31+i3−1+i3−1−i322-2−1+i3−1−i31−i31+i3-2-221−i31+i3−1+i3−1−i30000000-3-333−3i323+3i32−3+3i32−3−3i3211-1−1+i32−1−i321−i321+i32-1-111−i321+i32−1+i32−1−i3211-1−1+i32−1−i321−i321+i32000000000000000000000000000000000000000000
χ9766-6−3−3i3−3+3i33+3i33−3i3-2-221+i31−i3−1−i3−1+i322-2−1−i3−1+i31+i31−i3-2-221+i31−i3−1−i3−1+i30000000-3-333+3i323−3i32−3−3i32−3+3i3211-1−1−i32−1+i321+i321−i32-1-111+i321−i32−1−i32−1+i3211-1−1−i32−1+i321+i321−i32000000000000000000000000000000000000000000
χ9836-600000-1220000012-200000-122000000000000-183000006-100000-61000006-100000000000000000000000000000000000000000000000
χ996666666-2-2-2-2-2-2-2-2-2-2-2-2-2-222222220000000-3-3-3-3-3-3-311111111111111-1-1-1-1-1-1-1000000000000000000000000000000000000000000
χ100666−3+3i3−3−3i3−3+3i3−3−3i3-2-2-21−i31+i31−i31+i3-2-2-21−i31+i31−i31+i3222−1+i3−1−i3−1+i3−1−i30000000-3-3-33−3i323+3i323−3i323+3i32111−1+i32−1−i32−1+i32−1−i32111−1+i32−1−i32−1+i32−1−i32-1-1-11−i321+i321−i321+i32000000000000000000000000000000000000000000
χ101666−3−3i3−3+3i3−3−3i3−3+3i3-2-2-21+i31−i31+i31−i3-2-2-21+i31−i31+i31−i3222−1−i3−1+i3−1−i3−1+i30000000-3-3-33+3i323−3i323+3i323−3i32111−1−i32−1+i32−1−i32−1+i32111−1−i32−1+i32−1−i32−1+i32-1-1-11+i321−i321+i321−i32000000000000000000000000000000000000000000
χ10266-666-6-6-2-22-2-222-2-22-2-22222-222-2-20000000-3-33-3-33311-111-1-111-111-1-1-1-11-1-111000000000000000000000000000000000000000000
χ10366-6−3+3i3−3−3i33−3i33+3i3-2-221−i31+i3−1+i3−1−i3-2-221−i31+i3−1+i3−1−i322-2−1+i3−1−i31−i31+i30000000-3-333−3i323+3i32−3+3i32−3−3i3211-1−1+i32−1−i321−i321+i3211-1−1+i32−1−i321−i321+i32-1-111−i321+i32−1+i32−1−i32000000000000000000000000000000000000000000
χ10466-6−3−3i3−3+3i33+3i33−3i3-2-221+i31−i3−1−i3−1+i3-2-221+i31−i3−1−i3−1+i322-2−1−i3−1+i31+i31−i30000000-3-333+3i323−3i32−3−3i32−3+3i3211-1−1−i32−1+i321+i321−i3211-1−1−i32−1+i321+i321−i32-1-111+i321−i32−1−i32−1+i32000000000000000000000000000000000000000000
χ10536-600000-12200000-1220000012-2000000000000-183000006-1000006-100000-6100000000000000000000000000000000000000000000000

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