Finite Group Databasebeta

← Group #72277433

Character table — Group #72277433

Order 4374.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96C97C98C99C100C101C102
size111111111666666666666999999999999999999545454545454545454545454545454545454545454545454545454545454545454545454818181818181818181818181818181818181818181818181818181
order133999999333399999999333333999999999999333999999999999999999999999999999999266666666181818181818181818181818181818181818
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ3111−1+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−i32−1+i32−1+i32−1+i32−1−i32−1−i32−1−i32111111−1+i32−1+i32−1+i32−1−i32−1−i32−1−i32111−1+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−i32111−1+i32−1+i32−1+i32−1−i32−1−i32−1−i32−1+i32−1+i32−1+i32−1−i32−1−i32−1−i32111111−1+i32−1+i32−1+i32−1−i32−1−i32−1−i32
χ4111−1+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−i32−1+i32−1+i32−1+i32−1−i32−1−i32−1−i32111111−1+i32−1+i32−1+i32−1−i32−1−i32−1−i32111−1+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−i32-1-1-11−i321−i321−i321+i321+i321+i321−i321−i321−i321+i321+i321+i32-1-1-1-1-1-11−i321−i321−i321+i321+i321+i32
χ5111−1−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+i32−1−i32−1−i32−1−i32−1+i32−1+i32−1+i32111111−1−i32−1−i32−1−i32−1+i32−1+i32−1+i32111−1−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+i32111−1−i32−1−i32−1−i32−1+i32−1+i32−1+i32−1−i32−1−i32−1−i32−1+i32−1+i32−1+i32111111−1−i32−1−i32−1−i32−1+i32−1+i32−1+i32
χ6111−1−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+i32−1−i32−1−i32−1−i32−1+i32−1+i32−1+i32111111−1−i32−1−i32−1−i32−1+i32−1+i32−1+i32111−1−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+i32-1-1-11+i321+i321+i321−i321−i321−i321+i321+i321+i321−i321−i321−i32-1-1-1-1-1-11+i321+i321+i321−i321−i321−i32
χ7222222222222222222222222222222222222222222222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1000000000000000000000000000
χ8222222222222222222222222222222222222222-1-1-1-1-1-1-1-1-1222-1-1-1-1-1-1222-1-1-1-1-1-1222-1-1-1-1-1-1000000000000000000000000000
χ9222222222222222222222222222222222222222-1-1-1-1-1-1-1-1-1-1-1-1222-1-1-1-1-1-1222-1-1-1-1-1-1222-1-1-1000000000000000000000000000
χ10222222222222222222222222222222222222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1222-1-1-1-1-1-1222-1-1-1-1-1-1222000000000000000000000000000
χ11222−1+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−i3−1+i3−1+i3−1+i3−1−i3−1−i3−1−i3222222−1+i3−1+i3−1+i3−1−i3−1−i3−1−i3222−1+i3−1+i3−1+i3−1−i3−1−i3−1−i3-1-1-1-1-1-1-1-1-11−i321−i321−i321−i321−i321−i321−i321−i321−i321+i321+i321+i321+i321+i321+i321+i321+i321+i32000000000000000000000000000
χ12222−1+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−i3−1+i3−1+i3−1+i3−1−i3−1−i3−1−i3222222−1+i3−1+i3−1+i3−1−i3−1−i3−1−i3-1-1-11−i321−i321−i321+i321+i321+i32222-1-1-1-1-1-1−1+i3−1+i3−1+i31−i321−i321−i321−i321−i321−i32−1−i3−1−i3−1−i31+i321+i321+i321+i321+i321+i32000000000000000000000000000
χ13222−1+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−i3−1+i3−1+i3−1+i3−1−i3−1−i3−1−i3222222−1+i3−1+i3−1+i3−1−i3−1−i3−1−i3-1-1-11−i321−i321−i321+i321+i321+i32-1-1-1222-1-1-11−i321−i321−i32−1+i3−1+i3−1+i31−i321−i321−i321+i321+i321+i32−1−i3−1−i3−1−i31+i321+i321+i32000000000000000000000000000
χ14222−1+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−i3−1+i3−1+i3−1+i3−1−i3−1−i3−1−i3222222−1+i3−1+i3−1+i3−1−i3−1−i3−1−i3-1-1-11−i321−i321−i321+i321+i321+i32-1-1-1-1-1-12221−i321−i321−i321−i321−i321−i32−1+i3−1+i3−1+i31+i321+i321+i321+i321+i321+i32−1−i3−1−i3−1−i3000000000000000000000000000
χ15222−1−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+i3−1−i3−1−i3−1−i3−1+i3−1+i3−1+i3222222−1−i3−1−i3−1−i3−1+i3−1+i3−1+i3222−1−i3−1−i3−1−i3−1+i3−1+i3−1+i3-1-1-1-1-1-1-1-1-11+i321+i321+i321+i321+i321+i321+i321+i321+i321−i321−i321−i321−i321−i321−i321−i321−i321−i32000000000000000000000000000
χ16222−1−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+i3−1−i3−1−i3−1−i3−1+i3−1+i3−1+i3222222−1−i3−1−i3−1−i3−1+i3−1+i3−1+i3-1-1-11+i321+i321+i321−i321−i321−i32222-1-1-1-1-1-1−1−i3−1−i3−1−i31+i321+i321+i321+i321+i321+i32−1+i3−1+i3−1+i31−i321−i321−i321−i321−i321−i32000000000000000000000000000
χ17222−1−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+i3−1−i3−1−i3−1−i3−1+i3−1+i3−1+i3222222−1−i3−1−i3−1−i3−1+i3−1+i3−1+i3-1-1-11+i321+i321+i321−i321−i321−i32-1-1-1222-1-1-11+i321+i321+i32−1−i3−1−i3−1−i31+i321+i321+i321−i321−i321−i32−1+i3−1+i3−1+i31−i321−i321−i32000000000000000000000000000
χ18222−1−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+i3−1−i3−1−i3−1−i3−1+i3−1+i3−1+i3222222−1−i3−1−i3−1−i3−1+i3−1+i3−1+i3-1-1-11+i321+i321+i321−i321−i321−i32-1-1-1-1-1-12221+i321+i321+i321+i321+i321+i32−1−i3−1−i3−1−i31−i321−i321−i321−i321−i321−i32−1+i3−1+i3−1+i3000000000000000000000000000
χ19333333333333333333333−3+3i32−3+3i32−3+3i32−3−3i32−3−3i32−3−3i32−3+3i32−3+3i32−3+3i32−3−3i32−3−3i32−3−3i32−3−3i32−3−3i32−3−3i32−3+3i32−3+3i32−3+3i32000000000000000000000000000000000000111−1+i32−1+i32−1+i32−1−i32−1−i32−1−i32111111−1+i32−1+i32−1+i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1+i32−1+i32−1+i32
χ20333333333333333333333−3+3i32−3+3i32−3+3i32−3−3i32−3−3i32−3−3i32−3+3i32−3+3i32−3+3i32−3−3i32−3−3i32−3−3i32−3−3i32−3−3i32−3−3i32−3+3i32−3+3i32−3+3i32000000000000000000000000000000000000-1-1-11−i321−i321−i321+i321+i321+i32-1-1-1-1-1-11−i321−i321−i321+i321+i321+i321+i321+i321+i321−i321−i321−i32
χ21333333333333333333333−3−3i32−3−3i32−3−3i32−3+3i32−3+3i32−3+3i32−3−3i32−3−3i32−3−3i32−3+3i32−3+3i32−3+3i32−3+3i32−3+3i32−3+3i32−3−3i32−3−3i32−3−3i32000000000000000000000000000000000000111−1−i32−1−i32−1−i32−1+i32−1+i32−1+i32111111−1−i32−1−i32−1−i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1−i32−1−i32−1−i32
χ22333333333333333333333−3−3i32−3−3i32−3−3i32−3+3i32−3+3i32−3+3i32−3−3i32−3−3i32−3−3i32−3+3i32−3+3i32−3+3i32−3+3i32−3+3i32−3+3i32−3−3i32−3−3i32−3−3i32000000000000000000000000000000000000-1-1-11+i321+i321+i321−i321−i321−i32-1-1-1-1-1-11+i321+i321+i321−i321−i321−i321−i321−i321−i321+i321+i321+i32
χ23333−3+3i32−3+3i32−3+3i32−3−3i32−3−3i32−3−3i323333−3+3i32−3+3i32−3+3i32−3+3i32−3−3i32−3−3i32−3−3i32−3−3i32333333−3−3i32−3−3i32−3−3i32−3+3i32−3+3i32−3+3i32−3−3i32−3−3i32−3−3i32−3+3i32−3+3i32−3+3i32000000000000000000000000000000000000111111111−1+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
χ24333−3+3i32−3+3i32−3+3i32−3−3i32−3−3i32−3−3i323333−3+3i32−3+3i32−3+3i32−3+3i32−3−3i32−3−3i32−3−3i32−3−3i32333333−3−3i32−3−3i32−3−3i32−3+3i32−3+3i32−3+3i32−3−3i32−3−3i32−3−3i32−3+3i32−3+3i32−3+3i32000000000000000000000000000000000000-1-1-1-1-1-1-1-1-11−i321−i321−i321+i321+i321+i321+i321+i321+i321−i321−i321−i321+i321+i321+i321−i321−i321−i32
χ25333−3+3i32−3+3i32−3+3i32−3−3i32−3−3i32−3−3i323333−3+3i32−3+3i32−3+3i32−3+3i32−3−3i32−3−3i32−3−3i32−3−3i32−3−3i32−3−3i32−3−3i32−3+3i32−3+3i32−3+3i32−3+3i32−3+3i32−3+3i32−3−3i32−3−3i32−3−3i32333333000000000000000000000000000000000000111−1−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−i32111111
χ26333−3+3i32−3+3i32−3+3i32−3−3i32−3−3i32−3−3i323333−3+3i32−3+3i32−3+3i32−3+3i32−3−3i32−3−3i32−3−3i32−3−3i32−3−3i32−3−3i32−3−3i32−3+3i32−3+3i32−3+3i32−3+3i32−3+3i32−3+3i32−3−3i32−3−3i32−3−3i32333333000000000000000000000000000000000000-1-1-11+i321+i321+i321−i321−i321−i321−i321−i321−i321+i321+i321+i321−i321−i321−i321+i321+i321+i32-1-1-1-1-1-1
χ27333−3−3i32−3−3i32−3−3i32−3+3i32−3+3i32−3+3i323333−3−3i32−3−3i32−3−3i32−3−3i32−3+3i32−3+3i32−3+3i32−3+3i32333333−3+3i32−3+3i32−3+3i32−3−3i32−3−3i32−3−3i32−3+3i32−3+3i32−3+3i32−3−3i32−3−3i32−3−3i32000000000000000000000000000000000000111111111−1−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
χ28333−3−3i32−3−3i32−3−3i32−3+3i32−3+3i32−3+3i323333−3−3i32−3−3i32−3−3i32−3−3i32−3+3i32−3+3i32−3+3i32−3+3i32333333−3+3i32−3+3i32−3+3i32−3−3i32−3−3i32−3−3i32−3+3i32−3+3i32−3+3i32−3−3i32−3−3i32−3−3i32000000000000000000000000000000000000-1-1-1-1-1-1-1-1-11+i321+i321+i321−i321−i321−i321−i321−i321−i321+i321+i321+i321−i321−i321−i321+i321+i321+i32
χ29333−3−3i32−3−3i32−3−3i32−3+3i32−3+3i32−3+3i323333−3−3i32−3−3i32−3−3i32−3−3i32−3+3i32−3+3i32−3+3i32−3+3i32−3+3i32−3+3i32−3+3i32−3−3i32−3−3i32−3−3i32−3−3i32−3−3i32−3−3i32−3+3i32−3+3i32−3+3i32333333000000000000000000000000000000000000111−1+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+i32111111
χ30333−3−3i32−3−3i32−3−3i32−3+3i32−3+3i32−3+3i323333−3−3i32−3−3i32−3−3i32−3−3i32−3+3i32−3+3i32−3+3i32−3+3i32−3+3i32−3+3i32−3+3i32−3−3i32−3−3i32−3−3i32−3−3i32−3−3i32−3−3i32−3+3i32−3+3i32−3+3i32333333000000000000000000000000000000000000-1-1-11−i321−i321−i321+i321+i321+i321+i321+i321+i321−i321−i321−i321+i321+i321+i321−i321−i321−i32-1-1-1-1-1-1
χ316666666666-3-3-36-3-3-36-3-3-30000000000000000000000000000000002ζ−2ζ2+ζ4−ζ5−ζ+ζ2+ζ4+2ζ5−ζ+ζ2−2ζ4−ζ50000002ζ−2ζ2+ζ4−ζ5−ζ+ζ2+ζ4+2ζ5−ζ+ζ2−2ζ4−ζ50000002ζ−2ζ2+ζ4−ζ5−ζ+ζ2+ζ4+2ζ5−ζ+ζ2−2ζ4−ζ5000000000000000000000000000
χ326666666666-3-3-36-3-3-36-3-3-3000000000000000000000000000000000−ζ+ζ2+ζ4+2ζ5−ζ+ζ2−2ζ4−ζ52ζ−2ζ2+ζ4−ζ5000000−ζ+ζ2+ζ4+2ζ5−ζ+ζ2−2ζ4−ζ52ζ−2ζ2+ζ4−ζ5000000−ζ+ζ2+ζ4+2ζ5−ζ+ζ2−2ζ4−ζ52ζ−2ζ2+ζ4−ζ5000000000000000000000000000
χ336666666666-3-3-36-3-3-36-3-3-3000000000000000000000000000000000−ζ+ζ2−2ζ4−ζ52ζ−2ζ2+ζ4−ζ5−ζ+ζ2+ζ4+2ζ5000000−ζ+ζ2−2ζ4−ζ52ζ−2ζ2+ζ4−ζ5−ζ+ζ2+ζ4+2ζ5000000−ζ+ζ2−2ζ4−ζ52ζ−2ζ2+ζ4−ζ5−ζ+ζ2+ζ4+2ζ5000000000000000000000000000
χ34666666666-36-3-3-36-3-3-36-3-300000000000000000000000000003-300000003-300000003-3000000000000000000000000000000000
χ35666666666-36-3-3-36-3-3-36-3-30000000000000000000000000003-300000003-300000003-30000000000000000000000000000000000
χ36666666666-36-3-3-36-3-3-36-3-3000000000000000000000000000-303000000-303000000-303000000000000000000000000000000000
χ37666666666-3-36-3-3-36-3-3-36-300000000000000000000000000000003-300000003-300000003-3000000000000000000000000000000
χ38666666666-3-36-3-3-36-3-3-36-30000000000000000000000000000003-300000003-300000003-30000000000000000000000000000000
χ39666666666-3-36-3-3-36-3-3-36-3000000000000000000000000000000-303000000-303000000-303000000000000000000000000000000
χ40666666666-3-3-36-3-3-36-3-3-3600000000000000000003-303-303-3000000000000000000000000000000000000000000000000000000
χ41666666666-3-3-36-3-3-36-3-3-360000000000000000003-303-303-30000000000000000000000000000000000000000000000000000000
χ42666666666-3-3-36-3-3-36-3-3-36000000000000000000-303-303-303000000000000000000000000000000000000000000000000000000
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χ989−9−9i32−9+9i329ζ89ζ59ζ29ζ79ζ49ζ0000000000003−3−3i32−3+3i323−3−3i32−3+3i323ζ73ζ43ζ3ζ83ζ53ζ23ζ73ζ43ζ3ζ83ζ53ζ2000000000000000000000000000000000000-11+i321−i32-11+i321−i32-11+i321−i32−ζ8−ζ5−ζ2−ζ7−ζ4−ζ−ζ7−ζ4−ζ−ζ8−ζ5−ζ2−ζ7−ζ4−ζ−ζ8−ζ5−ζ2
χ999−9−9i32−9+9i329ζ89ζ59ζ29ζ79ζ49ζ000000000000−3+3i323−3−3i32−3−3i32−3+3i3233ζ3ζ73ζ43ζ53ζ23ζ83ζ43ζ3ζ73ζ23ζ83ζ50000000000000000000000000000000000001−1−i32−1+i32−1+i321−1−i32−1−i32−1+i321ζ8ζ5ζ2ζ7ζ4ζζζ7ζ4ζ5ζ2ζ8ζ4ζζ7ζ2ζ8ζ5
χ1009−9−9i32−9+9i329ζ89ζ59ζ29ζ79ζ49ζ000000000000−3+3i323−3−3i32−3−3i32−3+3i3233ζ3ζ73ζ43ζ53ζ23ζ83ζ43ζ3ζ73ζ23ζ83ζ5000000000000000000000000000000000000-11+i321−i321−i32-11+i321+i321−i32-1−ζ8−ζ5−ζ2−ζ7−ζ4−ζ−ζ−ζ7−ζ4−ζ5−ζ2−ζ8−ζ4−ζ−ζ7−ζ2−ζ8−ζ5
χ1019−9−9i32−9+9i329ζ89ζ59ζ29ζ79ζ49ζ000000000000−3−3i32−3+3i323−3+3i323−3−3i323ζ43ζ3ζ73ζ23ζ83ζ53ζ3ζ73ζ43ζ53ζ23ζ80000000000000000000000000000000000001−1−i32−1+i32−1−i32−1+i321−1+i321−1−i32ζ8ζ5ζ2ζ7ζ4ζζ4ζζ7ζ2ζ8ζ5ζζ7ζ4ζ5ζ2ζ8
χ1029−9−9i32−9+9i329ζ89ζ59ζ29ζ79ζ49ζ000000000000−3−3i32−3+3i323−3+3i323−3−3i323ζ43ζ3ζ73ζ23ζ83ζ53ζ3ζ73ζ43ζ53ζ23ζ8000000000000000000000000000000000000-11+i321−i321+i321−i32-11−i32-11+i32−ζ8−ζ5−ζ2−ζ7−ζ4−ζ−ζ4−ζ−ζ7−ζ2−ζ8−ζ5−ζ−ζ7−ζ4−ζ5−ζ2−ζ8

Here ζ is a primitive root of unity of order 9 (ζ9 = 1); i = ζ2.