Finite Group Databasebeta

← Group #13048129

Character table — Group #13048129

Order 1296.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96
size111222333666666666666666999121212121212242424242424272727363636363636111222333666666666666666999121212121212242424242424272727363636363636
order133333266666999181818181818181818266999999999999266181818181818266666266666181818181818181818181818266181818181818181818181818266181818181818
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111−1+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−i32111111111111111111111111111−1+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
χ3111111111111111111111111111−1−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+i32111111111111111111111111111−1−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
χ4111111111111111111111111-1-1-1111111111111-1-1-1-1-1-1-1-1-1111111111111111111111111-1-1-1111111111111-1-1-1-1-1-1-1-1-1
χ5111111111111111111111111-1-1-1−1+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+i32111111111111111111111111-1-1-1−1+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+i32
χ6111111111111111111111111-1-1-1−1−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−i32111111111111111111111111-1-1-1−1−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−i32
χ71−1+i32−1−i321−1+i32−1−i321−1+i32−1−i321−1+i32−1−i321−1+i32−1−i32111−1+i32−1+i32−1+i32−1−i32−1−i32−1−i321−1+i32−1−i32ζζ4ζ7ζ2ζ5ζ8ζζ4ζ7ζ2ζ5ζ81−1+i32−1−i32ζζ4ζ7ζ2ζ5ζ81−1+i32−1−i321−1+i32−1−i321−1+i32−1−i321−1+i32−1−i321−1+i32−1−i32111−1+i32−1+i32−1+i32−1−i32−1−i32−1−i321−1+i32−1−i32ζζ4ζ7ζ2ζ5ζ8ζζ4ζ7ζ2ζ5ζ81−1+i32−1−i32ζζ4ζ7ζ2ζ5ζ8
χ81−1+i32−1−i321−1+i32−1−i321−1+i32−1−i321−1+i32−1−i321−1+i32−1−i32111−1+i32−1+i32−1+i32−1−i32−1−i32−1−i321−1+i32−1−i32ζ4ζ7ζζ8ζ2ζ5ζ4ζ7ζζ8ζ2ζ51−1+i32−1−i32ζ4ζ7ζζ8ζ2ζ51−1+i32−1−i321−1+i32−1−i321−1+i32−1−i321−1+i32−1−i321−1+i32−1−i32111−1+i32−1+i32−1+i32−1−i32−1−i32−1−i321−1+i32−1−i32ζ4ζ7ζζ8ζ2ζ5ζ4ζ7ζζ8ζ2ζ51−1+i32−1−i32ζ4ζ7ζζ8ζ2ζ5
χ91−1+i32−1−i321−1+i32−1−i321−1+i32−1−i321−1+i32−1−i321−1+i32−1−i32111−1+i32−1+i32−1+i32−1−i32−1−i32−1−i321−1+i32−1−i32ζ7ζζ4ζ5ζ8ζ2ζ7ζζ4ζ5ζ8ζ21−1+i32−1−i32ζ7ζζ4ζ5ζ8ζ21−1+i32−1−i321−1+i32−1−i321−1+i32−1−i321−1+i32−1−i321−1+i32−1−i32111−1+i32−1+i32−1+i32−1−i32−1−i32−1−i321−1+i32−1−i32ζ7ζζ4ζ5ζ8ζ2ζ7ζζ4ζ5ζ8ζ21−1+i32−1−i32ζ7ζζ4ζ5ζ8ζ2
χ101−1+i32−1−i321−1+i32−1−i321−1+i32−1−i321−1+i32−1−i321−1+i32−1−i32111−1+i32−1+i32−1+i32−1−i32−1−i32−1−i32-11−i321+i32ζζ4ζ7ζ2ζ5ζ8ζζ4ζ7ζ2ζ5ζ8-11−i321+i32−ζ−ζ4−ζ7−ζ2−ζ5−ζ81−1+i32−1−i321−1+i32−1−i321−1+i32−1−i321−1+i32−1−i321−1+i32−1−i32111−1+i32−1+i32−1+i32−1−i32−1−i32−1−i32-11−i321+i32ζζ4ζ7ζ2ζ5ζ8ζζ4ζ7ζ2ζ5ζ8-11−i321+i32−ζ−ζ4−ζ7−ζ2−ζ5−ζ8
χ111−1+i32−1−i321−1+i32−1−i321−1+i32−1−i321−1+i32−1−i321−1+i32−1−i32111−1+i32−1+i32−1+i32−1−i32−1−i32−1−i32-11−i321+i32ζ4ζ7ζζ8ζ2ζ5ζ4ζ7ζζ8ζ2ζ5-11−i321+i32−ζ4−ζ7−ζ−ζ8−ζ2−ζ51−1+i32−1−i321−1+i32−1−i321−1+i32−1−i321−1+i32−1−i321−1+i32−1−i32111−1+i32−1+i32−1+i32−1−i32−1−i32−1−i32-11−i321+i32ζ4ζ7ζζ8ζ2ζ5ζ4ζ7ζζ8ζ2ζ5-11−i321+i32−ζ4−ζ7−ζ−ζ8−ζ2−ζ5
χ121−1+i32−1−i321−1+i32−1−i321−1+i32−1−i321−1+i32−1−i321−1+i32−1−i32111−1+i32−1+i32−1+i32−1−i32−1−i32−1−i32-11−i321+i32ζ7ζζ4ζ5ζ8ζ2ζ7ζζ4ζ5ζ8ζ2-11−i321+i32−ζ7−ζ−ζ4−ζ5−ζ8−ζ21−1+i32−1−i321−1+i32−1−i321−1+i32−1−i321−1+i32−1−i321−1+i32−1−i32111−1+i32−1+i32−1+i32−1−i32−1−i32−1−i32-11−i321+i32ζ7ζζ4ζ5ζ8ζ2ζ7ζζ4ζ5ζ8ζ2-11−i321+i32−ζ7−ζ−ζ4−ζ5−ζ8−ζ2
χ131−1−i32−1+i321−1−i32−1+i321−1−i32−1+i321−1−i32−1+i321−1−i32−1+i32111−1−i32−1−i32−1−i32−1+i32−1+i32−1+i321−1−i32−1+i32ζ2ζ8ζ5ζ4ζζ7ζ2ζ8ζ5ζ4ζζ71−1−i32−1+i32ζ2ζ8ζ5ζ4ζζ71−1−i32−1+i321−1−i32−1+i321−1−i32−1+i321−1−i32−1+i321−1−i32−1+i32111−1−i32−1−i32−1−i32−1+i32−1+i32−1+i321−1−i32−1+i32ζ2ζ8ζ5ζ4ζζ7ζ2ζ8ζ5ζ4ζζ71−1−i32−1+i32ζ2ζ8ζ5ζ4ζζ7
χ141−1−i32−1+i321−1−i32−1+i321−1−i32−1+i321−1−i32−1+i321−1−i32−1+i32111−1−i32−1−i32−1−i32−1+i32−1+i32−1+i321−1−i32−1+i32ζ5ζ2ζ8ζζ7ζ4ζ5ζ2ζ8ζζ7ζ41−1−i32−1+i32ζ5ζ2ζ8ζζ7ζ41−1−i32−1+i321−1−i32−1+i321−1−i32−1+i321−1−i32−1+i321−1−i32−1+i32111−1−i32−1−i32−1−i32−1+i32−1+i32−1+i321−1−i32−1+i32ζ5ζ2ζ8ζζ7ζ4ζ5ζ2ζ8ζζ7ζ41−1−i32−1+i32ζ5ζ2ζ8ζζ7ζ4
χ151−1−i32−1+i321−1−i32−1+i321−1−i32−1+i321−1−i32−1+i321−1−i32−1+i32111−1−i32−1−i32−1−i32−1+i32−1+i32−1+i321−1−i32−1+i32ζ8ζ5ζ2ζ7ζ4ζζ8ζ5ζ2ζ7ζ4ζ1−1−i32−1+i32ζ8ζ5ζ2ζ7ζ4ζ1−1−i32−1+i321−1−i32−1+i321−1−i32−1+i321−1−i32−1+i321−1−i32−1+i32111−1−i32−1−i32−1−i32−1+i32−1+i32−1+i321−1−i32−1+i32ζ8ζ5ζ2ζ7ζ4ζζ8ζ5ζ2ζ7ζ4ζ1−1−i32−1+i32ζ8ζ5ζ2ζ7ζ4ζ
χ161−1−i32−1+i321−1−i32−1+i321−1−i32−1+i321−1−i32−1+i321−1−i32−1+i32111−1−i32−1−i32−1−i32−1+i32−1+i32−1+i32-11+i321−i32ζ2ζ8ζ5ζ4ζζ7ζ2ζ8ζ5ζ4ζζ7-11+i321−i32−ζ2−ζ8−ζ5−ζ4−ζ−ζ71−1−i32−1+i321−1−i32−1+i321−1−i32−1+i321−1−i32−1+i321−1−i32−1+i32111−1−i32−1−i32−1−i32−1+i32−1+i32−1+i32-11+i321−i32ζ2ζ8ζ5ζ4ζζ7ζ2ζ8ζ5ζ4ζζ7-11+i321−i32−ζ2−ζ8−ζ5−ζ4−ζ−ζ7
χ171−1−i32−1+i321−1−i32−1+i321−1−i32−1+i321−1−i32−1+i321−1−i32−1+i32111−1−i32−1−i32−1−i32−1+i32−1+i32−1+i32-11+i321−i32ζ5ζ2ζ8ζζ7ζ4ζ5ζ2ζ8ζζ7ζ4-11+i321−i32−ζ5−ζ2−ζ8−ζ−ζ7−ζ41−1−i32−1+i321−1−i32−1+i321−1−i32−1+i321−1−i32−1+i321−1−i32−1+i32111−1−i32−1−i32−1−i32−1+i32−1+i32−1+i32-11+i321−i32ζ5ζ2ζ8ζζ7ζ4ζ5ζ2ζ8ζζ7ζ4-11+i321−i32−ζ5−ζ2−ζ8−ζ−ζ7−ζ4
χ181−1−i32−1+i321−1−i32−1+i321−1−i32−1+i321−1−i32−1+i321−1−i32−1+i32111−1−i32−1−i32−1−i32−1+i32−1+i32−1+i32-11+i321−i32ζ8ζ5ζ2ζ7ζ4ζζ8ζ5ζ2ζ7ζ4ζ-11+i321−i32−ζ8−ζ5−ζ2−ζ7−ζ4−ζ1−1−i32−1+i321−1−i32−1+i321−1−i32−1+i321−1−i32−1+i321−1−i32−1+i32111−1−i32−1−i32−1−i32−1+i32−1+i32−1+i32-11+i321−i32ζ8ζ5ζ2ζ7ζ4ζζ8ζ5ζ2ζ7ζ4ζ-11+i321−i32−ζ8−ζ5−ζ2−ζ7−ζ4−ζ
χ19222222222222-1-1-1-1-1-1-1-1-1-1-1-1000222222-1-1-1-1-1-1000000000222222222222-1-1-1-1-1-1-1-1-1-1-1-1000222222-1-1-1-1-1-1000000000
χ20222222222222-1-1-1-1-1-1-1-1-1-1-1-1000−1+i3−1+i3−1+i3−1−i3−1−i3−1−i31−i321−i321−i321+i321+i321+i32000000000222222222222-1-1-1-1-1-1-1-1-1-1-1-1000−1+i3−1+i3−1+i3−1−i3−1−i3−1−i31−i321−i321−i321+i321+i321+i32000000000
χ21222222222222-1-1-1-1-1-1-1-1-1-1-1-1000−1−i3−1−i3−1−i3−1+i3−1+i3−1+i31+i321+i321+i321−i321−i321−i32000000000222222222222-1-1-1-1-1-1-1-1-1-1-1-1000−1−i3−1−i3−1−i3−1+i3−1+i3−1+i31+i321+i321+i321−i321−i321−i32000000000
χ222−1+i3−1−i32−1+i3−1−i32−1+i3−1−i32−1+i3−1−i3-11−i321+i32-1-1-11−i321−i321−i321+i321+i321+i320002ζ2ζ42ζ72ζ22ζ52ζ8−ζ−ζ4−ζ7−ζ2−ζ5−ζ80000000002−1+i3−1−i32−1+i3−1−i32−1+i3−1−i32−1+i3−1−i3-11−i321+i32-1-1-11−i321−i321−i321+i321+i321+i320002ζ2ζ42ζ72ζ22ζ52ζ8−ζ−ζ4−ζ7−ζ2−ζ5−ζ8000000000
χ232−1+i3−1−i32−1+i3−1−i32−1+i3−1−i32−1+i3−1−i3-11−i321+i32-1-1-11−i321−i321−i321+i321+i321+i320002ζ42ζ72ζ2ζ82ζ22ζ5−ζ4−ζ7−ζ−ζ8−ζ2−ζ50000000002−1+i3−1−i32−1+i3−1−i32−1+i3−1−i32−1+i3−1−i3-11−i321+i32-1-1-11−i321−i321−i321+i321+i321+i320002ζ42ζ72ζ2ζ82ζ22ζ5−ζ4−ζ7−ζ−ζ8−ζ2−ζ5000000000
χ242−1+i3−1−i32−1+i3−1−i32−1+i3−1−i32−1+i3−1−i3-11−i321+i32-1-1-11−i321−i321−i321+i321+i321+i320002ζ72ζ2ζ42ζ52ζ82ζ2−ζ7−ζ−ζ4−ζ5−ζ8−ζ20000000002−1+i3−1−i32−1+i3−1−i32−1+i3−1−i32−1+i3−1−i3-11−i321+i32-1-1-11−i321−i321−i321+i321+i321+i320002ζ72ζ2ζ42ζ52ζ82ζ2−ζ7−ζ−ζ4−ζ5−ζ8−ζ2000000000
χ252−1−i3−1+i32−1−i3−1+i32−1−i3−1+i32−1−i3−1+i3-11+i321−i32-1-1-11+i321+i321+i321−i321−i321−i320002ζ22ζ82ζ52ζ42ζ2ζ7−ζ2−ζ8−ζ5−ζ4−ζ−ζ70000000002−1−i3−1+i32−1−i3−1+i32−1−i3−1+i32−1−i3−1+i3-11+i321−i32-1-1-11+i321+i321+i321−i321−i321−i320002ζ22ζ82ζ52ζ42ζ2ζ7−ζ2−ζ8−ζ5−ζ4−ζ−ζ7000000000
χ262−1−i3−1+i32−1−i3−1+i32−1−i3−1+i32−1−i3−1+i3-11+i321−i32-1-1-11+i321+i321+i321−i321−i321−i320002ζ52ζ22ζ82ζ2ζ72ζ4−ζ5−ζ2−ζ8−ζ−ζ7−ζ40000000002−1−i3−1+i32−1−i3−1+i32−1−i3−1+i32−1−i3−1+i3-11+i321−i32-1-1-11+i321+i321+i321−i321−i321−i320002ζ52ζ22ζ82ζ2ζ72ζ4−ζ5−ζ2−ζ8−ζ−ζ7−ζ4000000000
χ272−1−i3−1+i32−1−i3−1+i32−1−i3−1+i32−1−i3−1+i3-11+i321−i32-1-1-11+i321+i321+i321−i321−i321−i320002ζ82ζ52ζ22ζ72ζ42ζ−ζ8−ζ5−ζ2−ζ7−ζ4−ζ0000000002−1−i3−1+i32−1−i3−1+i32−1−i3−1+i32−1−i3−1+i3-11+i321−i32-1-1-11+i321+i321+i321−i321−i321−i320002ζ82ζ52ζ22ζ72ζ42ζ−ζ8−ζ5−ζ2−ζ7−ζ4−ζ000000000
χ28333333-1-1-1-1-1-1333-1-1-1-1-1-1-1-1-1333000000000000-1-1-1000000333333-1-1-1-1-1-1333-1-1-1-1-1-1-1-1-1333000000000000-1-1-1000000
χ29333333-1-1-1-1-1-1333-1-1-1-1-1-1-1-1-1-3-3-3000000000000111000000333333-1-1-1-1-1-1333-1-1-1-1-1-1-1-1-1-3-3-3000000000000111000000
χ303−3+3i32−3−3i323−3+3i32−3−3i32-11−i321+i32-11−i321+i323−3+3i32−3−3i32-1-1-11−i321−i321−i321+i321+i321+i323−3+3i32−3−3i32000000000000-11−i321+i320000003−3+3i32−3−3i323−3+3i32−3−3i32-11−i321+i32-11−i321+i323−3+3i32−3−3i32-1-1-11−i321−i321−i321+i321+i321+i323−3+3i32−3−3i32000000000000-11−i321+i32000000
χ313−3+3i32−3−3i323−3+3i32−3−3i32-11−i321+i32-11−i321+i323−3+3i32−3−3i32-1-1-11−i321−i321−i321+i321+i321+i32-33−3i323+3i320000000000001−1+i32−1−i320000003−3+3i32−3−3i323−3+3i32−3−3i32-11−i321+i32-11−i321+i323−3+3i32−3−3i32-1-1-11−i321−i321−i321+i321+i321+i32-33−3i323+3i320000000000001−1+i32−1−i32000000
χ323−3−3i32−3+3i323−3−3i32−3+3i32-11+i321−i32-11+i321−i323−3−3i32−3+3i32-1-1-11+i321+i321+i321−i321−i321−i323−3−3i32−3+3i32000000000000-11+i321−i320000003−3−3i32−3+3i323−3−3i32−3+3i32-11+i321−i32-11+i321−i323−3−3i32−3+3i32-1-1-11+i321+i321+i321−i321−i321−i323−3−3i32−3+3i32000000000000-11+i321−i32000000
χ333−3−3i32−3+3i323−3−3i32−3+3i32-11+i321−i32-11+i321−i323−3−3i32−3+3i32-1-1-11+i321+i321+i321−i321−i321−i32-33+3i323−3i320000000000001−1−i32−1+i320000003−3−3i32−3+3i323−3−3i32−3+3i32-11+i321−i32-11+i321−i323−3−3i32−3+3i32-1-1-11+i321+i321+i321−i321−i321−i32-33+3i323−3i320000000000001−1−i32−1+i32000000
χ34666666-2-2-2-2-2-2-3-3-3111111111000000000000000000000000666666-2-2-2-2-2-2-3-3-3111111111000000000000000000000000
χ35666-3-3-3666-3-3-3000000000000000000000000000000000000666-3-3-3666-3-3-3000000000000000000000000000000000000
χ36666-3-3-3-2-2-21110002ζ+2ζ82ζ2+2ζ72ζ4+2ζ52ζ+2ζ82ζ2+2ζ72ζ4+2ζ52ζ+2ζ82ζ2+2ζ72ζ4+2ζ5000000000000000000000000666-3-3-3-2-2-21110002ζ+2ζ82ζ2+2ζ72ζ4+2ζ52ζ+2ζ82ζ2+2ζ72ζ4+2ζ52ζ+2ζ82ζ2+2ζ72ζ4+2ζ5000000000000000000000000
χ37666-3-3-3-2-2-21110002ζ2+2ζ72ζ4+2ζ52ζ+2ζ82ζ2+2ζ72ζ4+2ζ52ζ+2ζ82ζ2+2ζ72ζ4+2ζ52ζ+2ζ8000000000000000000000000666-3-3-3-2-2-21110002ζ2+2ζ72ζ4+2ζ52ζ+2ζ82ζ2+2ζ72ζ4+2ζ52ζ+2ζ82ζ2+2ζ72ζ4+2ζ52ζ+2ζ8000000000000000000000000
χ38666-3-3-3-2-2-21110002ζ4+2ζ52ζ+2ζ82ζ2+2ζ72ζ4+2ζ52ζ+2ζ82ζ2+2ζ72ζ4+2ζ52ζ+2ζ82ζ2+2ζ7000000000000000000000000666-3-3-3-2-2-21110002ζ4+2ζ52ζ+2ζ82ζ2+2ζ72ζ4+2ζ52ζ+2ζ82ζ2+2ζ72ζ4+2ζ52ζ+2ζ82ζ2+2ζ7000000000000000000000000
χ396−3+3i3−3−3i36−3+3i3−3−3i3-21−i31+i3-21−i31+i3-33−3i323+3i32111−1+i32−1+i32−1+i32−1−i32−1−i32−1−i320000000000000000000000006−3+3i3−3−3i36−3+3i3−3−3i3-21−i31+i3-21−i31+i3-33−3i323+3i32111−1+i32−1+i32−1+i32−1−i32−1−i32−1−i32000000000000000000000000
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Here ζ is a primitive root of unity of order 9 (ζ9 = 1); i = ζ2.