Finite Group Databasebeta

← Group #13157030

Character table — Group #13157030

Order 1728.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96C97C98C99C100C101C102C103C104C105C106C107C108
size112233666666666666661212161616163232323236364848484811223366666666666666121216161616323232323636484848481122336666666666666612121616161632323232363648484848
order1236224444661212121212121212443366336644121212123636661212121266121212121212121212123366336612121212121236366612121212661212121212121212121233663366121212121212
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111−1−i32−1+i32−1−i32−1+i32−1−i32−1+i32−1−i32−1+i3211−1−i32−1−i32−1+i32−1+i321111111111111111111111−1−i32−1+i32−1−i32−1+i32−1−i32−1+i32−1−i32−1+i3211−1−i32−1−i32−1+i32−1+i321111111111111111111111−1−i32−1+i32−1−i32−1+i32−1−i32−1+i32−1−i32−1+i3211−1−i32−1−i32−1+i32−1+i32
χ31111111111111111111111−1+i32−1−i32−1+i32−1−i32−1+i32−1−i32−1+i32−1−i3211−1+i32−1+i32−1−i32−1−i321111111111111111111111−1+i32−1−i32−1+i32−1−i32−1+i32−1−i32−1+i32−1−i3211−1+i32−1+i32−1−i32−1−i321111111111111111111111−1+i32−1−i32−1+i32−1−i32−1+i32−1−i32−1+i32−1−i3211−1+i32−1+i32−1−i32−1−i32
χ411111111111111111111-1-111111111-1-1-1-1-1-111111111111111111111-1-111111111-1-1-1-1-1-111111111111111111111-1-111111111-1-1-1-1-1-1
χ511111111111111111111-1-1−1−i32−1+i32−1−i32−1+i32−1−i32−1+i32−1−i32−1+i32-1-11+i321+i321−i321−i3211111111111111111111-1-1−1−i32−1+i32−1−i32−1+i32−1−i32−1+i32−1−i32−1+i32-1-11+i321+i321−i321−i3211111111111111111111-1-1−1−i32−1+i32−1−i32−1+i32−1−i32−1+i32−1−i32−1+i32-1-11+i321+i321−i321−i32
χ611111111111111111111-1-1−1+i32−1−i32−1+i32−1−i32−1+i32−1−i32−1+i32−1−i32-1-11−i321−i321+i321+i3211111111111111111111-1-1−1+i32−1−i32−1+i32−1−i32−1+i32−1−i32−1+i32−1−i32-1-11−i321−i321+i321+i3211111111111111111111-1-1−1+i32−1−i32−1+i32−1−i32−1+i32−1−i32−1+i32−1−i32-1-11−i321−i321+i321+i32
χ71-11-1-1111-1-1-111111-1-1-1-1i−i11-1-111-1-1i−ii−ii−i1-11-1-1111-1-1-111111-1-1-1-1i−i11-1-111-1-1i−ii−ii−i1-11-1-1111-1-1-111111-1-1-1-1i−i11-1-111-1-1i−ii−ii−i
χ81-11-1-1111-1-1-111111-1-1-1-1i−i−1−i32−1+i321+i321−i32−1−i32−1+i321+i321−i32i−iζ11−ζ11ζ7−ζ71-11-1-1111-1-1-111111-1-1-1-1i−i−1−i32−1+i321+i321−i32−1−i32−1+i321+i321−i32i−iζ11−ζ11ζ7−ζ71-11-1-1111-1-1-111111-1-1-1-1i−i−1−i32−1+i321+i321−i32−1−i32−1+i321+i321−i32i−iζ11−ζ11ζ7−ζ7
χ91-11-1-1111-1-1-111111-1-1-1-1i−i−1+i32−1−i321−i321+i32−1+i32−1−i321−i321+i32i−iζ7−ζ7ζ11−ζ111-11-1-1111-1-1-111111-1-1-1-1i−i−1+i32−1−i321−i321+i32−1+i32−1−i321−i321+i32i−iζ7−ζ7ζ11−ζ111-11-1-1111-1-1-111111-1-1-1-1i−i−1+i32−1−i321−i321+i32−1+i32−1−i321−i321+i32i−iζ7−ζ7ζ11−ζ11
χ101-11-1-1111-1-1-111111-1-1-1-1−ii11-1-111-1-1−ii−ii−ii1-11-1-1111-1-1-111111-1-1-1-1−ii11-1-111-1-1−ii−ii−ii1-11-1-1111-1-1-111111-1-1-1-1−ii11-1-111-1-1−ii−ii−ii
χ111-11-1-1111-1-1-111111-1-1-1-1−ii−1−i32−1+i321+i321−i32−1−i32−1+i321+i321−i32−ii−ζ11ζ11−ζ7ζ71-11-1-1111-1-1-111111-1-1-1-1−ii−1−i32−1+i321+i321−i32−1−i32−1+i321+i321−i32−ii−ζ11ζ11−ζ7ζ71-11-1-1111-1-1-111111-1-1-1-1−ii−1−i32−1+i321+i321−i32−1−i32−1+i321+i321−i32−ii−ζ11ζ11−ζ7ζ7
χ121-11-1-1111-1-1-111111-1-1-1-1−ii−1+i32−1−i321−i321+i32−1+i32−1−i321−i321+i32−ii−ζ7ζ7−ζ11ζ111-11-1-1111-1-1-111111-1-1-1-1−ii−1+i32−1−i321−i321+i32−1+i32−1−i321−i321+i32−ii−ζ7ζ7−ζ11ζ111-11-1-1111-1-1-111111-1-1-1-1−ii−1+i32−1−i321−i321+i32−1+i32−1−i321−i321+i32−ii−ζ7ζ7−ζ11ζ11
χ1322-1-1222222-1-1-1-1-1-1-1-1-1-1002222-1-1-1-100000022-1-1222222-1-1-1-1-1-1-1-1-1-1002222-1-1-1-100000022-1-1222222-1-1-1-1-1-1-1-1-1-1002222-1-1-1-1000000
χ1422-1-1222222-1-1-1-1-1-1-1-1-1-100−1−i3−1+i3−1−i3−1+i31+i321−i321+i321−i3200000022-1-1222222-1-1-1-1-1-1-1-1-1-100−1−i3−1+i3−1−i3−1+i31+i321−i321+i321−i3200000022-1-1222222-1-1-1-1-1-1-1-1-1-100−1−i3−1+i3−1−i3−1+i31+i321−i321+i321−i32000000
χ1522-1-1222222-1-1-1-1-1-1-1-1-1-100−1+i3−1−i3−1+i3−1−i31−i321+i321−i321+i3200000022-1-1222222-1-1-1-1-1-1-1-1-1-100−1+i3−1−i3−1+i3−1−i31−i321+i321−i321+i3200000022-1-1222222-1-1-1-1-1-1-1-1-1-100−1+i3−1−i3−1+i3−1−i31−i321+i321−i321+i32000000
χ162-2-11-2222-2-21-1-1-1-1-111110022-2-2-1-1110000002-2-11-2222-2-21-1-1-1-1-111110022-2-2-1-1110000002-2-11-2222-2-21-1-1-1-1-111110022-2-2-1-111000000
χ172-2-11-2222-2-21-1-1-1-1-1111100−1−i3−1+i31+i31−i31+i321−i32−1−i32−1+i320000002-2-11-2222-2-21-1-1-1-1-1111100−1−i3−1+i31+i31−i31+i321−i32−1−i32−1+i320000002-2-11-2222-2-21-1-1-1-1-1111100−1−i3−1+i31+i31−i31+i321−i32−1−i32−1+i32000000
χ182-2-11-2222-2-21-1-1-1-1-1111100−1+i3−1−i31−i31+i31−i321+i32−1+i32−1−i320000002-2-11-2222-2-21-1-1-1-1-1111100−1+i3−1−i31−i31+i31−i321+i32−1+i32−1−i320000002-2-11-2222-2-21-1-1-1-1-1111100−1+i3−1−i31−i31+i31−i321+i32−1+i32−1−i32000000
χ19333333-1-1-1-133-1-1-1-1-1-1-1-13300000000-1-10000333333-1-1-1-133-1-1-1-1-1-1-1-13300000000-1-10000333333-1-1-1-133-1-1-1-1-1-1-1-13300000000-1-10000
χ20333333-1-1-1-133-1-1-1-1-1-1-1-1-3-300000000110000333333-1-1-1-133-1-1-1-1-1-1-1-1-3-300000000110000333333-1-1-1-133-1-1-1-1-1-1-1-1-3-300000000110000
χ213-33-3-33-1-111-33-1-1-1-111113i−3i00000000−ii00003-33-3-33-1-111-33-1-1-1-111113i−3i00000000−ii00003-33-3-33-1-111-33-1-1-1-111113i−3i00000000−ii0000
χ223-33-3-33-1-111-33-1-1-1-11111−3i3i00000000i−i00003-33-3-33-1-111-33-1-1-1-11111−3i3i00000000i−i00003-33-3-33-1-111-33-1-1-1-11111−3i3i00000000i−i0000
χ236666-2-22-22-2-2-222-2-222-2-200000000000000006666-2-22-22-2-2-222-2-222-2-200000000000000006666-2-22-22-2-2-222-2-222-2-20000000000000000
χ246666-2-2-22-22-2-2-2-222-2-22200000000000000006666-2-2-22-22-2-2-2-222-2-22200000000000000006666-2-2-22-22-2-2-2-222-2-2220000000000000000
χ2566-3-366-2-2-2-2-3-311111111000000000000000066-3-366-2-2-2-2-3-311111111000000000000000066-3-366-2-2-2-2-3-3111111110000000000000000
χ2666-3-3-2-22-22-211-1-11+231−23-1-11+231−23000000000000000066-3-3-2-22-22-211-1-11+231−23-1-11+231−23000000000000000066-3-3-2-22-22-211-1-11+231−23-1-11+231−230000000000000000
χ2766-3-3-2-22-22-211-1-11−231+23-1-11−231+23000000000000000066-3-3-2-22-22-211-1-11−231+23-1-11−231+23000000000000000066-3-3-2-22-22-211-1-11−231+23-1-11−231+230000000000000000
χ2866-3-3-2-2-22-22111+231−23-1-11+231−23-1-1000000000000000066-3-3-2-2-22-22111+231−23-1-11+231−23-1-1000000000000000066-3-3-2-2-22-22111+231−23-1-11+231−23-1-10000000000000000
χ2966-3-3-2-2-22-22111−231+23-1-11−231+23-1-1000000000000000066-3-3-2-2-22-22111−231+23-1-11−231+23-1-1000000000000000066-3-3-2-2-22-22111−231+23-1-11−231+23-1-10000000000000000
χ306-66-62-22-2-222-222-2-2-2-22200000000000000006-66-62-22-2-222-222-2-2-2-22200000000000000006-66-62-22-2-222-222-2-2-2-2220000000000000000
χ316-66-62-2-222-22-2-2-22222-2-200000000000000006-66-62-2-222-22-2-2-22222-2-200000000000000006-66-62-2-222-22-2-2-22222-2-20000000000000000
χ326-6-332-22-2-22-11-1-11+231−2311−1−23−1+2300000000000000006-6-332-22-2-22-11-1-11+231−2311−1−23−1+2300000000000000006-6-332-22-2-22-11-1-11+231−2311−1−23−1+230000000000000000
χ336-6-332-22-2-22-11-1-11−231+2311−1+23−1−2300000000000000006-6-332-22-2-22-11-1-11−231+2311−1+23−1−2300000000000000006-6-332-22-2-22-11-1-11−231+2311−1+23−1−230000000000000000
χ346-6-332-2-222-2-111+231−23-1-1−1−23−1+231100000000000000006-6-332-2-222-2-111+231−23-1-1−1−23−1+231100000000000000006-6-332-2-222-2-111+231−23-1-1−1−23−1+23110000000000000000
χ356-6-332-2-222-2-111−231+23-1-1−1+23−1−231100000000000000006-6-332-2-222-2-111−231+23-1-1−1+23−1−231100000000000000006-6-332-2-222-2-111−231+23-1-1−1+23−1−23110000000000000000
χ366-6-33-66-2-2223-31111-1-1-1-100000000000000006-6-33-66-2-2223-31111-1-1-1-100000000000000006-6-33-66-2-2223-31111-1-1-1-10000000000000000
χ37111111111111111111111111111111111111−1+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+i32−1+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−i32−1−i32−1−i32−1−i32−1−i32
χ381111111111111111111111−1−i32−1+i32−1−i32−1+i32−1−i32−1+i32−1−i32−1+i3211−1−i32−1−i32−1+i32−1+i32−1+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+i321−1−i321−1−i321−1−i321−1−i32−1+i32−1+i3211−1−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+i321−1+i321−1+i321−1+i321−1−i32−1−i32−1+i32−1+i3211
χ391111111111111111111111−1+i32−1−i32−1+i32−1−i32−1+i32−1−i32−1+i32−1−i3211−1+i32−1+i32−1−i32−1−i32−1+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−i321−1−i321−1−i321−1−i321−1+i32−1+i32−1−i32−1−i3211−1−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−i321−1+i321−1+i321−1+i321−1+i32−1−i32−1−i3211−1+i32−1+i32
χ4011111111111111111111-1-111111111-1-1-1-1-1-1−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i321−i321−i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i321−i321−i321−i321−i321−i321−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−i321+i321+i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i321+i321+i321+i321+i321+i321+i32
χ4111111111111111111111-1-1−1−i32−1+i32−1−i32−1+i32−1−i32−1+i32−1−i32−1+i32-1-11+i321+i321−i321−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+i321−i321−i321−1−i321−1−i321−1−i321−1−i321−i321−i32-1-11+i321+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−i321+i321+i32−1+i321−1+i321−1+i321−1+i3211+i321+i321−i321−i32-1-1
χ4211111111111111111111-1-1−1+i32−1−i32−1+i32−1−i32−1+i32−1−i32−1+i32−1−i32-1-11−i321−i321+i321+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+i321−i321−i32−1−i321−1−i321−1−i321−1−i3211−i321−i321+i321+i32-1-1−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i321+i321+i321−1+i321−1+i321−1+i321−1+i321+i321+i32-1-11−i321−i32
χ431-11-1-1111-1-1-111111-1-1-1-1i−i11-1-111-1-1i−ii−ii−i−1+i321−i32−1+i321−i321−i32−1+i32−1+i32−1+i321−i321−i321−i32−1+i32−1+i32−1+i32−1+i32−1+i321−i321−i321−i321−i32ζ7−ζ7−1+i32−1+i321−i321−i32−1+i32−1+i321−i321−i32ζ7−ζ7ζ7−ζ7ζ7−ζ7−1−i321+i32−1−i321+i321+i32−1−i32−1−i32−1−i321+i321+i321+i32−1−i32−1−i32−1−i32−1−i32−1−i321+i321+i321+i321+i32ζ11−ζ11−1−i32−1−i321+i321+i32−1−i32−1−i321+i321+i32ζ11−ζ11ζ11−ζ11ζ11−ζ11
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χ10166-3-3-2-2-22-22111−231+23-1-11−231+23-1-10000000000000000−3−3i3−3−3i33+3i323+3i321+i31+i31+i3−1−i31+i3−1−i3−1−i32−1−i32−ζ2−4ζ7−2ζ11−ζ2+4ζ7+2ζ111+i321+i32−ζ2−4ζ7−2ζ11−ζ2+4ζ7+2ζ111+i321+i320000000000000000−3+3i3−3+3i33−3i323−3i321−i31−i31−i3−1+i31−i3−1+i3−1+i32−1+i322ζ7−ζ10+4ζ11−2ζ7−ζ10−4ζ111−i321−i322ζ7−ζ10+4ζ11−2ζ7−ζ10−4ζ111−i321−i320000000000000000
χ1026-66-62-22-2-222-222-2-2-2-2220000000000000000−3−3i33+3i3−3−3i33+3i3−1−i31+i3−1−i31+i31+i3−1−i3−1−i31+i3−1−i3−1−i31+i31+i31+i31+i3−1−i3−1−i30000000000000000−3+3i33−3i3−3+3i33−3i3−1+i31−i3−1+i31−i31−i3−1+i3−1+i31−i3−1+i3−1+i31−i31−i31−i31−i3−1+i3−1+i30000000000000000
χ1036-66-62-2-222-22-2-2-22222-2-20000000000000000−3−3i33+3i3−3−3i33+3i3−1−i31+i31+i3−1−i3−1−i31+i3−1−i31+i31+i31+i3−1−i3−1−i3−1−i3−1−i31+i31+i30000000000000000−3+3i33−3i3−3+3i33−3i3−1+i31−i31−i3−1+i3−1+i31−i3−1+i31−i31−i31−i3−1+i3−1+i3−1+i3−1+i31−i31−i30000000000000000
χ1046-6-332-22-2-22-11-1-11+231−2311−1−23−1+230000000000000000−3−3i33+3i33+3i32−3−3i32−1−i31+i3−1−i31+i31+i3−1−i31+i32−1−i321+i321+i32−ζ2+4ζ7+2ζ11−ζ2−4ζ7−2ζ11−1−i32−1−i32ζ2−4ζ7−2ζ11ζ2+4ζ7+2ζ110000000000000000−3+3i33−3i33−3i32−3+3i32−1+i31−i3−1+i31−i31−i3−1+i31−i32−1+i321−i321−i32−2ζ7−ζ10−4ζ112ζ7−ζ10+4ζ11−1+i32−1+i322ζ7+ζ10+4ζ11−2ζ7+ζ10−4ζ110000000000000000
χ1056-6-332-22-2-22-11-1-11−231+2311−1+23−1−230000000000000000−3−3i33+3i33+3i32−3−3i32−1−i31+i3−1−i31+i31+i3−1−i31+i32−1−i321+i321+i32−ζ2−4ζ7−2ζ11−ζ2+4ζ7+2ζ11−1−i32−1−i32ζ2+4ζ7+2ζ11ζ2−4ζ7−2ζ110000000000000000−3+3i33−3i33−3i32−3+3i32−1+i31−i3−1+i31−i31−i3−1+i31−i32−1+i321−i321−i322ζ7−ζ10+4ζ11−2ζ7−ζ10−4ζ11−1+i32−1+i32−2ζ7+ζ10−4ζ112ζ7+ζ10+4ζ110000000000000000
χ1066-6-332-2-222-2-111+231−23-1-1−1−23−1+23110000000000000000−3−3i33+3i33+3i32−3−3i32−1−i31+i31+i3−1−i3−1−i31+i31+i32−1−i32−ζ2+4ζ7+2ζ11−ζ2−4ζ7−2ζ111+i321+i32ζ2−4ζ7−2ζ11ζ2+4ζ7+2ζ11−1−i32−1−i320000000000000000−3+3i33−3i33−3i32−3+3i32−1+i31−i31−i3−1+i3−1+i31−i31−i32−1+i32−2ζ7−ζ10−4ζ112ζ7−ζ10+4ζ111−i321−i322ζ7+ζ10+4ζ11−2ζ7+ζ10−4ζ11−1+i32−1+i320000000000000000
χ1076-6-332-2-222-2-111−231+23-1-1−1+23−1−23110000000000000000−3−3i33+3i33+3i32−3−3i32−1−i31+i31+i3−1−i3−1−i31+i31+i32−1−i32−ζ2−4ζ7−2ζ11−ζ2+4ζ7+2ζ111+i321+i32ζ2+4ζ7+2ζ11ζ2−4ζ7−2ζ11−1−i32−1−i320000000000000000−3+3i33−3i33−3i32−3+3i32−1+i31−i31−i3−1+i3−1+i31−i31−i32−1+i322ζ7−ζ10+4ζ11−2ζ7−ζ10−4ζ111−i321−i32−2ζ7+ζ10−4ζ112ζ7+ζ10+4ζ11−1+i32−1+i320000000000000000
χ1086-6-33-66-2-2223-31111-1-1-1-10000000000000000−3−3i33+3i33+3i32−3−3i323+3i3−3−3i31+i31+i3−1−i3−1−i3−3−3i323+3i32−1−i32−1−i32−1−i32−1−i321+i321+i321+i321+i320000000000000000−3+3i33−3i33−3i32−3+3i323−3i3−3+3i31−i31−i3−1+i3−1+i3−3+3i323−3i32−1+i32−1+i32−1+i32−1+i321−i321−i321−i321−i320000000000000000

Here ζ is a primitive root of unity of order 12 (ζ12 = 1); i = ζ3.