Finite Group Databasebeta

← Group #72277356

Character table — Group #72277356

Order 4032.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85
size1344412121212161616161616161639121212363636364848484848484848391212123636363648484848484848487212828288484848411211211211211211211211272128282884848484112112112112112112112112
order122222444336666667141414141428282821214242424242427141414141428282821214242424242423666661212123366666636666612121233666666
χ11111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ2111111111−1+i32−1−i32−1+i32−1+i32−1+i32−1−i32−1−i32−1−i32111111111−1+i32−1−i32−1+i32−1+i32−1+i32−1−i32−1−i32−1−i32111111111−1+i32−1−i32−1+i32−1+i32−1+i32−1−i32−1−i32−1−i32111111111−1+i32−1−i32−1+i32−1+i32−1+i32−1−i32−1−i32−1−i32111111111−1+i32−1−i32−1+i32−1+i32−1+i32−1−i32−1−i32−1−i32
χ3111111111−1−i32−1+i32−1−i32−1−i32−1−i32−1+i32−1+i32−1+i32111111111−1−i32−1+i32−1−i32−1−i32−1−i32−1+i32−1+i32−1+i32111111111−1−i32−1+i32−1−i32−1−i32−1−i32−1+i32−1+i32−1+i32111111111−1−i32−1+i32−1−i32−1−i32−1−i32−1+i32−1+i32−1+i32111111111−1−i32−1+i32−1−i32−1−i32−1−i32−1+i32−1+i32−1+i32
χ4111-1-111-1-1111-1-11-1-1111-1-111-1-1111-1-11-1-1111-1-111-1-1111-1-11-1-1111-1-111-1-1111-1-11-1-1111-1-111-1-1111-1-11-1-1
χ5111-1-111-1-1−1+i32−1−i32−1+i321−i321−i32−1−i321+i321+i32111-1-111-1-1−1+i32−1−i32−1+i321−i321−i32−1−i321+i321+i32111-1-111-1-1−1+i32−1−i32−1+i321−i321−i32−1−i321+i321+i32111-1-111-1-1−1+i32−1−i32−1+i321−i321−i32−1−i321+i321+i32111-1-111-1-1−1+i32−1−i32−1+i321−i321−i32−1−i321+i321+i32
χ6111-1-111-1-1−1−i32−1+i32−1−i321+i321+i32−1+i321−i321−i32111-1-111-1-1−1−i32−1+i32−1−i321+i321+i32−1+i321−i321−i32111-1-111-1-1−1−i32−1+i32−1−i321+i321+i32−1+i321−i321−i32111-1-111-1-1−1−i32−1+i32−1−i321+i321+i32−1+i321−i321−i32111-1-111-1-1−1−i32−1+i32−1−i321+i321+i32−1+i321−i321−i32
χ711-11-11-11-111-11-1-11-111-11-11-11-111-11-1-11-111-11-11-11-111-11-1-11-111-11-11-11-111-11-1-11-111-11-11-11-111-11-1-11-1
χ811-11-11-11-1−1+i32−1−i321−i32−1+i321−i321+i32−1−i321+i3211-11-11-11-1−1+i32−1−i321−i32−1+i321−i321+i32−1−i321+i3211-11-11-11-1−1+i32−1−i321−i32−1+i321−i321+i32−1−i321+i3211-11-11-11-1−1+i32−1−i321−i32−1+i321−i321+i32−1−i321+i3211-11-11-11-1−1+i32−1−i321−i32−1+i321−i321+i32−1−i321+i32
χ911-11-11-11-1−1−i32−1+i321+i32−1−i321+i321−i32−1+i321−i3211-11-11-11-1−1−i32−1+i321+i32−1−i321+i321−i32−1+i321−i3211-11-11-11-1−1−i32−1+i321+i32−1−i321+i321−i32−1+i321−i3211-11-11-11-1−1−i32−1+i321+i32−1−i321+i321−i32−1+i321−i3211-11-11-11-1−1−i32−1+i321+i32−1−i321+i321−i32−1+i321−i32
χ1011-1-111-1-1111-1-11-1-1111-1-111-1-1111-1-11-1-1111-1-111-1-1111-1-11-1-1111-1-111-1-1111-1-11-1-1111-1-111-1-1111-1-11-1-11
χ1111-1-111-1-11−1+i32−1−i321−i321−i32−1+i321+i321+i32−1−i3211-1-111-1-11−1+i32−1−i321−i321−i32−1+i321+i321+i32−1−i3211-1-111-1-11−1+i32−1−i321−i321−i32−1+i321+i321+i32−1−i3211-1-111-1-11−1+i32−1−i321−i321−i32−1+i321+i321+i32−1−i3211-1-111-1-11−1+i32−1−i321−i321−i32−1+i321+i321+i32−1−i32
χ1211-1-111-1-11−1−i32−1+i321+i321+i32−1−i321−i321−i32−1+i3211-1-111-1-11−1−i32−1+i321+i321+i32−1−i321−i321−i32−1+i3211-1-111-1-11−1−i32−1+i321+i321+i32−1−i321−i321−i32−1+i3211-1-111-1-11−1−i32−1+i321+i321+i32−1−i321−i321−i32−1+i3211-1-111-1-11−1−i32−1+i321+i321+i32−1−i321−i321−i32−1+i32
χ1333333-1-1-1-10000000033333-1-1-1-10000000033333-1-1-1-10000000033333-1-1-1-10000000033333-1-1-1-100000000
χ14333-3-3-1-11100000000333-3-3-1-11100000000333-3-3-1-11100000000333-3-3-1-11100000000333-3-3-1-11100000000
χ1533-33-3-11-110000000033-33-3-11-110000000033-33-3-11-110000000033-33-3-11-110000000033-33-3-11-1100000000
χ1633-3-33-111-10000000033-3-33-111-10000000033-3-33-111-10000000033-3-33-111-10000000033-3-33-111-100000000
χ1712-400000000000000012-400000000000000012-400000000000000012-400000000000000012-4000000000000000
χ18111111111111111111111111111111111111111111111111111−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32
χ19111111111−1+i32−1−i32−1+i32−1+i32−1+i32−1−i32−1−i32−1−i32111111111−1+i32−1−i32−1+i32−1+i32−1+i32−1−i32−1−i32−1−i32111111111−1+i32−1−i32−1+i32−1+i32−1+i32−1−i32−1−i32−1−i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1−i321−1−i32−1−i32−1−i32111−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i321−1+i32111−1+i32−1+i32−1+i32
χ20111111111−1−i32−1+i32−1−i32−1−i32−1−i32−1+i32−1+i32−1+i32111111111−1−i32−1+i32−1−i32−1−i32−1−i32−1+i32−1+i32−1+i32111111111−1−i32−1+i32−1−i32−1−i32−1−i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i321−1−i32111−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1+i321−1+i32−1+i32−1+i32111
χ21111-1-111-1-1111-1-11-1-1111-1-111-1-1111-1-11-1-1111-1-111-1-1111-1-11-1-1−1+i32−1+i32−1+i321−i321−i32−1+i32−1+i321−i321−i32−1+i32−1+i32−1+i321−i321−i32−1+i321−i321−i32−1−i32−1−i32−1−i321+i321+i32−1−i32−1−i321+i321+i32−1−i32−1−i32−1−i321+i321+i32−1−i321+i321+i32
χ22111-1-111-1-1−1+i32−1−i32−1+i321−i321−i32−1−i321+i321+i32111-1-111-1-1−1+i32−1−i32−1+i321−i321−i32−1−i321+i321+i32111-1-111-1-1−1+i32−1−i32−1+i321−i321−i32−1−i321+i321+i32−1+i32−1+i32−1+i321−i321−i32−1+i32−1+i321−i321−i32−1−i321−1−i321+i321+i321-1-1−1−i32−1−i32−1−i321+i321+i32−1−i32−1−i321+i321+i321−1+i321-1-1−1+i321−i321−i32
χ23111-1-111-1-1−1−i32−1+i32−1−i321+i321+i32−1+i321−i321−i32111-1-111-1-1−1−i32−1+i32−1−i321+i321+i32−1+i321−i321−i32111-1-111-1-1−1−i32−1+i32−1−i321+i321+i32−1+i321−i321−i32−1+i32−1+i32−1+i321−i321−i32−1+i32−1+i321−i321−i321−1−i321-1-1−1−i321+i321+i32−1−i32−1−i32−1−i321+i321+i32−1−i32−1−i321+i321+i32−1+i321−1+i321−i321−i321-1-1
χ2411-11-11-11-111-11-1-11-111-11-11-11-111-11-1-11-111-11-11-11-111-11-1-11-1−1+i32−1+i321−i32−1+i321−i32−1+i321−i32−1+i321−i32−1+i32−1+i321−i32−1+i321−i321−i32−1+i321−i32−1−i32−1−i321+i32−1−i321+i32−1−i321+i32−1−i321+i32−1−i32−1−i321+i32−1−i321+i321+i32−1−i321+i32
χ2511-11-11-11-1−1+i32−1−i321−i32−1+i321−i321+i32−1−i321+i3211-11-11-11-1−1+i32−1−i321−i32−1+i321−i321+i32−1−i321+i3211-11-11-11-1−1+i32−1−i321−i32−1+i321−i321+i32−1−i321+i32−1+i32−1+i321−i32−1+i321−i32−1+i321−i32−1+i321−i32−1−i3211+i32−1−i321+i32-11-1−1−i32−1−i321+i32−1−i321+i32−1−i321+i32−1−i321+i321−1+i32-11-11−i32−1+i321−i32
χ2611-11-11-11-1−1−i32−1+i321+i32−1−i321+i321−i32−1+i321−i3211-11-11-11-1−1−i32−1+i321+i32−1−i321+i321−i32−1+i321−i3211-11-11-11-1−1−i32−1+i321+i32−1−i321+i321−i32−1+i321−i32−1+i32−1+i321−i32−1+i321−i32−1+i321−i32−1+i321−i321−1−i32-11-11+i32−1−i321+i32−1−i32−1−i321+i32−1−i321+i32−1−i321+i32−1−i321+i32−1+i3211−i32−1+i321−i32-11-1
χ2711-1-111-1-1111-1-11-1-1111-1-111-1-1111-1-11-1-1111-1-111-1-1111-1-11-1-11−1+i32−1+i321−i321−i32−1+i32−1+i321−i321−i32−1+i32−1+i32−1+i321−i321−i32−1+i321−i321−i32−1+i32−1−i32−1−i321+i321+i32−1−i32−1−i321+i321+i32−1−i32−1−i32−1−i321+i321+i32−1−i321+i321+i32−1−i32
χ2811-1-111-1-11−1+i32−1−i321−i321−i32−1+i321+i321+i32−1−i3211-1-111-1-11−1+i32−1−i321−i321−i32−1+i321+i321+i32−1−i3211-1-111-1-11−1+i32−1−i321−i321−i32−1+i321+i321+i32−1−i32−1+i32−1+i321−i321−i32−1+i32−1+i321−i321−i32−1+i32−1−i3211+i321+i32−1−i32-1-11−1−i32−1−i321+i321+i32−1−i32−1−i321+i321+i32−1−i321−1+i32-1-111−i321−i32−1+i32
χ2911-1-111-1-11−1−i32−1+i321+i321+i32−1−i321−i321−i32−1+i3211-1-111-1-11−1−i32−1+i321+i321+i32−1−i321−i321−i32−1+i3211-1-111-1-11−1−i32−1+i321+i321+i32−1−i321−i321−i32−1+i32−1+i32−1+i321−i321−i32−1+i32−1+i321−i321−i32−1+i321−1−i32-1-111+i321+i32−1−i32−1−i32−1−i321+i321+i32−1−i32−1−i321+i321+i32−1−i32−1+i3211−i321−i32−1+i32-1-11
χ3033333-1-1-1-10000000033333-1-1-1-10000000033333-1-1-1-100000000−3+3i32−3+3i32−3+3i32−3+3i32−3+3i321−i321−i321−i321−i3200000000−3−3i32−3−3i32−3−3i32−3−3i32−3−3i321+i321+i321+i321+i3200000000
χ31333-3-3-1-11100000000333-3-3-1-11100000000333-3-3-1-11100000000−3+3i32−3+3i32−3+3i323−3i323−3i321−i321−i32−1+i32−1+i3200000000−3−3i32−3−3i32−3−3i323+3i323+3i321+i321+i32−1−i32−1−i3200000000
χ3233-33-3-11-110000000033-33-3-11-110000000033-33-3-11-1100000000−3+3i32−3+3i323−3i32−3+3i323−3i321−i32−1+i321−i32−1+i3200000000−3−3i32−3−3i323+3i32−3−3i323+3i321+i32−1−i321+i32−1−i3200000000
χ3333-3-33-111-10000000033-3-33-111-10000000033-3-33-111-100000000−3+3i32−3+3i323−3i323−3i32−3+3i321−i32−1+i32−1+i321−i3200000000−3−3i32−3−3i323+3i323+3i32−3−3i321+i32−1−i32−1−i321+i3200000000
χ3412-400000000000000012-400000000000000012-4000000000000000−6+6i32−2i3000000000000000−6−6i32+2i3000000000000000
χ35111111111111111111111111111111111111111111111111111−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32
χ36111111111−1+i32−1−i32−1+i32−1+i32−1+i32−1−i32−1−i32−1−i32111111111−1+i32−1−i32−1+i32−1+i32−1+i32−1−i32−1−i32−1−i32111111111−1+i32−1−i32−1+i32−1+i32−1+i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i321−1+i32111−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1−i321−1−i32−1−i32−1−i32111
χ37111111111−1−i32−1+i32−1−i32−1−i32−1−i32−1+i32−1+i32−1+i32111111111−1−i32−1+i32−1−i32−1−i32−1−i32−1+i32−1+i32−1+i32111111111−1−i32−1+i32−1−i32−1−i32−1−i32−1+i32−1+i32−1+i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1+i321−1+i32−1+i32−1+i32111−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i321−1−i32111−1−i32−1−i32−1−i32
χ38111-1-111-1-1111-1-11-1-1111-1-111-1-1111-1-11-1-1111-1-111-1-1111-1-11-1-1−1−i32−1−i32−1−i321+i321+i32−1−i32−1−i321+i321+i32−1−i32−1−i32−1−i321+i321+i32−1−i321+i321+i32−1+i32−1+i32−1+i321−i321−i32−1+i32−1+i321−i321−i32−1+i32−1+i32−1+i321−i321−i32−1+i321−i321−i32
χ39111-1-111-1-1−1+i32−1−i32−1+i321−i321−i32−1−i321+i321+i32111-1-111-1-1−1+i32−1−i32−1+i321−i321−i32−1−i321+i321+i32111-1-111-1-1−1+i32−1−i32−1+i321−i321−i32−1−i321+i321+i32−1−i32−1−i32−1−i321+i321+i32−1−i32−1−i321+i321+i321−1+i321-1-1−1+i321−i321−i32−1+i32−1+i32−1+i321−i321−i32−1+i32−1+i321−i321−i32−1−i321−1−i321+i321+i321-1-1
χ40111-1-111-1-1−1−i32−1+i32−1−i321+i321+i32−1+i321−i321−i32111-1-111-1-1−1−i32−1+i32−1−i321+i321+i32−1+i321−i321−i32111-1-111-1-1−1−i32−1+i32−1−i321+i321+i32−1+i321−i321−i32−1−i32−1−i32−1−i321+i321+i32−1−i32−1−i321+i321+i32−1+i321−1+i321−i321−i321-1-1−1+i32−1+i32−1+i321−i321−i32−1+i32−1+i321−i321−i321−1−i321-1-1−1−i321+i321+i32
χ4111-11-11-11-111-11-1-11-111-11-11-11-111-11-1-11-111-11-11-11-111-11-1-11-1−1−i32−1−i321+i32−1−i321+i32−1−i321+i32−1−i321+i32−1−i32−1−i321+i32−1−i321+i321+i32−1−i321+i32−1+i32−1+i321−i32−1+i321−i32−1+i321−i32−1+i321−i32−1+i32−1+i321−i32−1+i321−i321−i32−1+i321−i32
χ4211-11-11-11-1−1+i32−1−i321−i32−1+i321−i321+i32−1−i321+i3211-11-11-11-1−1+i32−1−i321−i32−1+i321−i321+i32−1−i321+i3211-11-11-11-1−1+i32−1−i321−i32−1+i321−i321+i32−1−i321+i32−1−i32−1−i321+i32−1−i321+i32−1−i321+i32−1−i321+i321−1+i32-11-11−i32−1+i321−i32−1+i32−1+i321−i32−1+i321−i32−1+i321−i32−1+i321−i32−1−i3211+i32−1−i321+i32-11-1
χ4311-11-11-11-1−1−i32−1+i321+i32−1−i321+i321−i32−1+i321−i3211-11-11-11-1−1−i32−1+i321+i32−1−i321+i321−i32−1+i321−i3211-11-11-11-1−1−i32−1+i321+i32−1−i321+i321−i32−1+i321−i32−1−i32−1−i321+i32−1−i321+i32−1−i321+i32−1−i321+i32−1+i3211−i32−1+i321−i32-11-1−1+i32−1+i321−i32−1+i321−i32−1+i321−i32−1+i321−i321−1−i32-11-11+i32−1−i321+i32
χ4411-1-111-1-1111-1-11-1-1111-1-111-1-1111-1-11-1-1111-1-111-1-1111-1-11-1-11−1−i32−1−i321+i321+i32−1−i32−1−i321+i321+i32−1−i32−1−i32−1−i321+i321+i32−1−i321+i321+i32−1−i32−1+i32−1+i321−i321−i32−1+i32−1+i321−i321−i32−1+i32−1+i32−1+i321−i321−i32−1+i321−i321−i32−1+i32
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χ8536-12000000000000000−6+6i72−2i7000000000000000−6−6i72+2i70000000000000000000000000000000000000000000000000

Here ζ is a primitive root of unity of order 21 (ζ21 = 1); i = ζ5.