Finite Group Databasebeta

← Group #13147105

Character table — Group #13147105

Order 1728.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96C97C98C99C100C101C102C103C104
size1122666991212121212121212242424243636363654112266699121212121212121224242424363636365411226669912121212121212122424242436363636541122666991212121212121212242424243636363654
order12364918223366123636369918186666444121243636441212121212363636363636361212121242266418182266661236363618181818666644412124363644121212121236363636363636121212124
χ111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ2111111111−1+i32−1−i32−1+i32−1−i321111−1+i32−1−i32−1+i32−1−i32−1+i32−1+i32−1−i32−1−i321111111111−1+i32−1−i32−1+i32−1−i321111−1+i32−1−i32−1+i32−1−i32−1+i32−1+i32−1−i32−1−i321111111111−1+i32−1−i32−1+i32−1−i321111−1+i32−1−i32−1+i32−1−i32−1+i32−1+i32−1−i32−1−i321111111111−1+i32−1−i32−1+i32−1−i321111−1+i32−1−i32−1+i32−1−i32−1+i32−1+i32−1−i32−1−i321
χ3111111111−1−i32−1+i32−1−i32−1+i321111−1−i32−1+i32−1−i32−1+i32−1−i32−1−i32−1+i32−1+i321111111111−1−i32−1+i32−1−i32−1+i321111−1−i32−1+i32−1−i32−1+i32−1−i32−1−i32−1+i32−1+i321111111111−1−i32−1+i32−1−i32−1+i321111−1−i32−1+i32−1−i32−1+i32−1−i32−1−i32−1+i32−1+i321111111111−1−i32−1+i32−1−i32−1+i321111−1−i32−1+i32−1−i32−1+i32−1−i32−1−i32−1+i32−1+i321
χ41111111-1-1111111111111-1-1-1-1-11111111-1-1111111111111-1-1-1-1-11111111-1-1111111111111-1-1-1-1-11111111-1-1111111111111-1-1-1-1-1
χ51111111-1-1−1+i32−1−i32−1+i32−1−i321111−1+i32−1−i32−1+i32−1−i321−i321−i321+i321+i32-11111111-1-1−1+i32−1−i32−1+i32−1−i321111−1+i32−1−i32−1+i32−1−i321−i321−i321+i321+i32-11111111-1-1−1+i32−1−i32−1+i32−1−i321111−1+i32−1−i32−1+i32−1−i321−i321−i321+i321+i32-11111111-1-1−1+i32−1−i32−1+i32−1−i321111−1+i32−1−i32−1+i32−1−i321−i321−i321+i321+i32-1
χ61111111-1-1−1−i32−1+i32−1−i32−1+i321111−1−i32−1+i32−1−i32−1+i321+i321+i321−i321−i32-11111111-1-1−1−i32−1+i32−1−i32−1+i321111−1−i32−1+i32−1−i32−1+i321+i321+i321−i321−i32-11111111-1-1−1−i32−1+i32−1−i32−1+i321111−1−i32−1+i32−1−i32−1+i321+i321+i321−i321−i32-11111111-1-1−1−i32−1+i32−1−i32−1+i321111−1−i32−1+i32−1−i32−1+i321+i321+i321−i321−i32-1
χ722222-1-10022222-1-1-1-1-1-1-10000022222-1-10022222-1-1-1-1-1-1-10000022222-1-10022222-1-1-1-1-1-1-10000022222-1-10022222-1-1-1-1-1-1-100000
χ822222-1-100−1+i3−1−i3−1+i3−1−i32-1-1-11−i321+i321−i321+i320000022222-1-100−1+i3−1−i3−1+i3−1−i32-1-1-11−i321+i321−i321+i320000022222-1-100−1+i3−1−i3−1+i3−1−i32-1-1-11−i321+i321−i321+i320000022222-1-100−1+i3−1−i3−1+i3−1−i32-1-1-11−i321+i321−i321+i3200000
χ922222-1-100−1−i3−1+i3−1−i3−1+i32-1-1-11+i321−i321+i321−i320000022222-1-100−1−i3−1+i3−1−i3−1+i32-1-1-11+i321−i321+i321−i320000022222-1-100−1−i3−1+i3−1−i3−1+i32-1-1-11+i321−i321+i321−i320000022222-1-100−1−i3−1+i3−1−i3−1+i32-1-1-11+i321−i321+i321−i3200000
χ102-22-202-22-2-1-1110000-1-1111-11-102-22-202-22-2-1-1110000-1-1111-11-102-22-202-22-2-1-1110000-1-1111-11-102-22-202-22-2-1-1110000-1-1111-11-10
χ112-22-202-22-21−i321+i32−1+i32−1−i3200001−i321+i32−1+i32−1−i32−1+i321−i32−1−i321+i3202-22-202-22-21−i321+i32−1+i32−1−i3200001−i321+i32−1+i32−1−i32−1+i321−i32−1−i321+i3202-22-202-22-21−i321+i32−1+i32−1−i3200001−i321+i32−1+i32−1−i32−1+i321−i32−1−i321+i3202-22-202-22-21−i321+i32−1+i32−1−i3200001−i321+i32−1+i32−1−i32−1+i321−i32−1−i321+i320
χ122-22-202-22-21+i321−i32−1−i32−1+i3200001+i321−i32−1−i32−1+i32−1−i321+i32−1+i321−i3202-22-202-22-21+i321−i32−1−i32−1+i3200001+i321−i32−1−i32−1+i32−1−i321+i32−1+i321−i3202-22-202-22-21+i321−i32−1−i32−1+i3200001+i321−i32−1−i32−1+i32−1−i321+i32−1+i321−i3202-22-202-22-21+i321−i32−1−i32−1+i3200001+i321−i32−1−i32−1+i32−1−i321+i32−1+i321−i320
χ132-22-202-2-22-1-1110000-1-111-11-1102-22-202-2-22-1-1110000-1-111-11-1102-22-202-2-22-1-1110000-1-111-11-1102-22-202-2-22-1-1110000-1-111-11-110
χ142-22-202-2-221−i321+i32−1+i32−1−i3200001−i321+i32−1+i32−1−i321−i32−1+i321+i32−1−i3202-22-202-2-221−i321+i32−1+i32−1−i3200001−i321+i32−1+i32−1−i321−i32−1+i321+i32−1−i3202-22-202-2-221−i321+i32−1+i32−1−i3200001−i321+i32−1+i32−1−i321−i32−1+i321+i32−1−i3202-22-202-2-221−i321+i32−1+i32−1−i3200001−i321+i32−1+i32−1−i321−i32−1+i321+i32−1−i320
χ152-22-202-2-221+i321−i32−1−i32−1+i3200001+i321−i32−1−i32−1+i321+i32−1−i321−i32−1+i3202-22-202-2-221+i321−i32−1−i32−1+i3200001+i321−i32−1−i32−1+i321+i32−1−i321−i32−1+i3202-22-202-2-221+i321−i32−1−i32−1+i3200001+i321−i32−1−i32−1+i321+i32−1−i321−i32−1+i3202-22-202-2-221+i321−i32−1−i32−1+i3200001+i321−i32−1−i32−1+i321+i32−1−i321−i32−1+i320
χ163333-133330000-1-1-1-100000000-13333-133330000-1-1-1-100000000-13333-133330000-1-1-1-100000000-13333-133330000-1-1-1-100000000-1
χ173333-133-3-30000-1-1-1-10000000013333-133-3-30000-1-1-1-10000000013333-133-3-30000-1-1-1-10000000013333-133-3-30000-1-1-1-1000000001
χ184-44-40-2200-2-222000011-1-1000004-44-40-2200-2-222000011-1-1000004-44-40-2200-2-222000011-1-1000004-44-40-2200-2-222000011-1-100000
χ194-44-40-22001−i31+i3−1+i3−1−i30000−1+i32−1−i321−i321+i32000004-44-40-22001−i31+i3−1+i3−1−i30000−1+i32−1−i321−i321+i32000004-44-40-22001−i31+i3−1+i3−1−i30000−1+i32−1−i321−i321+i32000004-44-40-22001−i31+i3−1+i3−1−i30000−1+i32−1−i321−i321+i3200000
χ204-44-40-22001+i31−i3−1−i3−1+i30000−1−i32−1+i321+i321−i32000004-44-40-22001+i31−i3−1−i3−1+i30000−1−i32−1+i321+i321−i32000004-44-40-22001+i31−i3−1−i3−1+i30000−1−i32−1+i321+i321−i32000004-44-40-22001+i31−i3−1−i3−1+i30000−1−i32−1+i321+i321−i3200000
χ216666-2-3-3000000-21110000000006666-2-3-3000000-21110000000006666-2-3-3000000-21110000000006666-2-3-3000000-2111000000000
χ2266-3-3600000000-300000000000066-3-3600000000-300000000000066-3-3600000000-300000000000066-3-3600000000-3000000000000
χ2366-3-3-2000000001−2ζ14−2ζ222ζ22−2ζ26+2ζ342ζ14+2ζ26−2ζ3400000000066-3-3-2000000001−2ζ14−2ζ222ζ22−2ζ26+2ζ342ζ14+2ζ26−2ζ3400000000066-3-3-2000000001−2ζ14−2ζ222ζ22−2ζ26+2ζ342ζ14+2ζ26−2ζ3400000000066-3-3-2000000001−2ζ14−2ζ222ζ22−2ζ26+2ζ342ζ14+2ζ26−2ζ34000000000
χ2466-3-3-20000000012ζ22−2ζ26+2ζ342ζ14+2ζ26−2ζ34−2ζ14−2ζ2200000000066-3-3-20000000012ζ22−2ζ26+2ζ342ζ14+2ζ26−2ζ34−2ζ14−2ζ2200000000066-3-3-20000000012ζ22−2ζ26+2ζ342ζ14+2ζ26−2ζ34−2ζ14−2ζ2200000000066-3-3-20000000012ζ22−2ζ26+2ζ342ζ14+2ζ26−2ζ34−2ζ14−2ζ22000000000
χ2566-3-3-20000000012ζ14+2ζ26−2ζ34−2ζ14−2ζ222ζ22−2ζ26+2ζ3400000000066-3-3-20000000012ζ14+2ζ26−2ζ34−2ζ14−2ζ222ζ22−2ζ26+2ζ3400000000066-3-3-20000000012ζ14+2ζ26−2ζ34−2ζ14−2ζ222ζ22−2ζ26+2ζ3400000000066-3-3-20000000012ζ14+2ζ26−2ζ34−2ζ14−2ζ222ζ22−2ζ26+2ζ34000000000
χ2612-12-66000000000000000000000012-12-66000000000000000000000012-12-66000000000000000000000012-12-660000000000000000000000
χ2711111111111111111111111111iiiiiiiiiiiiiiiiiiiiiiiiii-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−i−i−i−i−i−i−i−i−i−i−i−i−i−i−i−i−i−i−i−i−i−i−i−i−i−i
χ28111111111−1+i32−1−i32−1+i32−1−i321111−1+i32−1−i32−1+i32−1−i32−1+i32−1+i32−1−i32−1−i321iiiiiiiii−ζ3−ζ15−ζ3−ζ15iiii−ζ3−ζ15−ζ3−ζ15−ζ3−ζ3−ζ15−ζ15i-1-1-1-1-1-1-1-1-11−i321+i321−i321+i32-1-1-1-11−i321+i321−i321+i321−i321−i321+i321+i32-1−i−i−i−i−i−i−i−i−iζ3ζ15ζ3ζ15−i−i−i−iζ3ζ15ζ3ζ15ζ3ζ3ζ15ζ15−i
χ29111111111−1−i32−1+i32−1−i32−1+i321111−1−i32−1+i32−1−i32−1+i32−1−i32−1−i32−1+i32−1+i321iiiiiiiii−ζ15−ζ3−ζ15−ζ3iiii−ζ15−ζ3−ζ15−ζ3−ζ15−ζ15−ζ3−ζ3i-1-1-1-1-1-1-1-1-11+i321−i321+i321−i32-1-1-1-11+i321−i321+i321−i321+i321+i321−i321−i32-1−i−i−i−i−i−i−i−i−iζ15ζ3ζ15ζ3−i−i−i−iζ15ζ3ζ15ζ3ζ15ζ15ζ3ζ3−i
χ301111111-1-1111111111111-1-1-1-1-1iiiiiii−i−iiiiiiiiiiiii−i−i−i−i−i-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-111111−i−i−i−i−i−i−iii−i−i−i−i−i−i−i−i−i−i−i−iiiiii
χ311111111-1-1−1+i32−1−i32−1+i32−1−i321111−1+i32−1−i32−1+i32−1−i321−i321−i321+i321+i32-1iiiiiii−i−i−ζ3−ζ15−ζ3−ζ15iiii−ζ3−ζ15−ζ3−ζ15ζ3ζ3ζ15ζ15−i-1-1-1-1-1-1-1111−i321+i321−i321+i32-1-1-1-11−i321+i321−i321+i32−1+i32−1+i32−1−i32−1−i321−i−i−i−i−i−i−iiiζ3ζ15ζ3ζ15−i−i−i−iζ3ζ15ζ3ζ15−ζ3−ζ3−ζ15−ζ15i
χ321111111-1-1−1−i32−1+i32−1−i32−1+i321111−1−i32−1+i32−1−i32−1+i321+i321+i321−i321−i32-1iiiiiii−i−i−ζ15−ζ3−ζ15−ζ3iiii−ζ15−ζ3−ζ15−ζ3ζ15ζ15ζ3ζ3−i-1-1-1-1-1-1-1111+i321−i321+i321−i32-1-1-1-11+i321−i321+i321−i32−1−i32−1−i32−1+i32−1+i321−i−i−i−i−i−i−iiiζ15ζ3ζ15ζ3−i−i−i−iζ15ζ3ζ15ζ3−ζ15−ζ15−ζ3−ζ3i
χ3322222-1-10022222-1-1-1-1-1-1-1000002i2i2i2i2i−i−i002i2i2i2i2i−i−i−i−i−i−i−i00000-2-2-2-2-21100-2-2-2-2-2111111100000−2i−2i−2i−2i−2iii00−2i−2i−2i−2i−2iiiiiiii00000
χ3422222-1-100−1+i3−1−i3−1+i3−1−i32-1-1-11−i321+i321−i321+i32000002i2i2i2i2i−i−i00−2ζ3−2ζ15−2ζ3−2ζ152i−i−i−iζ3ζ15ζ3ζ1500000-2-2-2-2-211001−i31+i31−i31+i3-2111−1+i32−1−i32−1+i32−1−i3200000−2i−2i−2i−2i−2iii002ζ32ζ152ζ32ζ15−2iiii−ζ3−ζ15−ζ3−ζ1500000
χ3522222-1-100−1−i3−1+i3−1−i3−1+i32-1-1-11+i321−i321+i321−i32000002i2i2i2i2i−i−i00−2ζ15−2ζ3−2ζ15−2ζ32i−i−i−iζ15ζ3ζ15ζ300000-2-2-2-2-211001+i31−i31+i31−i3-2111−1−i32−1+i32−1−i32−1+i3200000−2i−2i−2i−2i−2iii002ζ152ζ32ζ152ζ3−2iiii−ζ15−ζ3−ζ15−ζ300000
χ362-22-202-22-2-1-1110000-1-1111-11-102i−2i2i−2i02i−2i2i−2i−i−iii0000−i−iiii−ii−i0-22-220-22-2211-1-1000011-1-1-11-110−2i2i−2i2i0−2i2i−2i2iii−i−i0000ii−i−i−ii−ii0
χ372-22-202-22-21−i321+i32−1+i32−1−i3200001−i321+i32−1+i32−1−i32−1+i321−i32−1−i321+i3202i−2i2i−2i02i−2i2i−2iζ3ζ15−ζ3−ζ150000ζ3ζ15−ζ3−ζ15−ζ3ζ3−ζ15ζ150-22-220-22-22−1+i32−1−i321−i321+i320000−1+i32−1−i321−i321+i321−i32−1+i321+i32−1−i320−2i2i−2i2i0−2i2i−2i2i−ζ3−ζ15ζ3ζ150000−ζ3−ζ15ζ3ζ15ζ3−ζ3ζ15−ζ150
χ382-22-202-22-21+i321−i32−1−i32−1+i3200001+i321−i32−1−i32−1+i32−1−i321+i32−1+i321−i3202i−2i2i−2i02i−2i2i−2iζ15ζ3−ζ15−ζ30000ζ15ζ3−ζ15−ζ3−ζ15ζ15−ζ3ζ30-22-220-22-22−1−i32−1+i321+i321−i320000−1−i32−1+i321+i321−i321+i32−1−i321−i32−1+i320−2i2i−2i2i0−2i2i−2i2i−ζ15−ζ3ζ15ζ30000−ζ15−ζ3ζ15ζ3ζ15−ζ15ζ3−ζ30
χ392-22-202-2-22-1-1110000-1-111-11-1102i−2i2i−2i02i−2i−2i2i−i−iii0000−i−iii−ii−ii0-22-220-222-211-1-1000011-1-11-11-10−2i2i−2i2i0−2i2i2i−2iii−i−i0000ii−i−ii−ii−i0
χ402-22-202-2-221−i321+i32−1+i32−1−i3200001−i321+i32−1+i32−1−i321−i32−1+i321+i32−1−i3202i−2i2i−2i02i−2i−2i2iζ3ζ15−ζ3−ζ150000ζ3ζ15−ζ3−ζ15ζ3−ζ3ζ15−ζ150-22-220-222-2−1+i32−1−i321−i321+i320000−1+i32−1−i321−i321+i32−1+i321−i32−1−i321+i320−2i2i−2i2i0−2i2i2i−2i−ζ3−ζ15ζ3ζ150000−ζ3−ζ15ζ3ζ15−ζ3ζ3−ζ15ζ150
χ412-22-202-2-221+i321−i32−1−i32−1+i3200001+i321−i32−1−i32−1+i321+i32−1−i321−i32−1+i3202i−2i2i−2i02i−2i−2i2iζ15ζ3−ζ15−ζ30000ζ15ζ3−ζ15−ζ3ζ15−ζ15ζ3−ζ30-22-220-222-2−1−i32−1+i321+i321−i320000−1−i32−1+i321+i321−i32−1−i321+i32−1+i321−i320−2i2i−2i2i0−2i2i2i−2i−ζ15−ζ3ζ15ζ30000−ζ15−ζ3ζ15ζ3−ζ15ζ15−ζ3ζ30
χ423333-133330000-1-1-1-100000000-13i3i3i3i−i3i3i3i3i0000−i−i−i−i00000000−i-3-3-3-31-3-3-3-300001111000000001−3i−3i−3i−3ii−3i−3i−3i−3i0000iiii00000000i
χ433333-133-3-30000-1-1-1-10000000013i3i3i3i−i3i3i−3i−3i0000−i−i−i−i00000000i-3-3-3-31-3-3330000111100000000-1−3i−3i−3i−3ii−3i−3i3i3i0000iiii00000000−i
χ444-44-40-2200-2-222000011-1-1000004i−4i4i−4i0−2i2i00−2i−2i2i2i0000ii−i−i00000-44-4402-20022-2-20000-1-11100000−4i4i−4i4i02i−2i002i2i−2i−2i0000−i−iii00000
χ454-44-40-22001−i31+i3−1+i3−1−i30000−1+i32−1−i321−i321+i32000004i−4i4i−4i0−2i2i002ζ32ζ15−2ζ3−2ζ150000−ζ3−ζ15ζ3ζ1500000-44-4402-200−1+i3−1−i31−i31+i300001−i321+i32−1+i32−1−i3200000−4i4i−4i4i02i−2i00−2ζ3−2ζ152ζ32ζ150000ζ3ζ15−ζ3−ζ1500000
χ464-44-40-22001+i31−i3−1−i3−1+i30000−1−i32−1+i321+i321−i32000004i−4i4i−4i0−2i2i002ζ152ζ3−2ζ15−2ζ30000−ζ15−ζ3ζ15ζ300000-44-4402-200−1−i3−1+i31+i31−i300001+i321−i32−1−i32−1+i3200000−4i4i−4i4i02i−2i00−2ζ15−2ζ32ζ152ζ30000ζ15ζ3−ζ15−ζ300000
χ476666-2-3-3000000-21110000000006i6i6i6i−2i−3i−3i000000−2iiii000000000-6-6-6-62330000002-1-1-1000000000−6i−6i−6i−6i2i3i3i0000002i−i−i−i000000000
χ4866-3-3600000000-30000000000006i6i−3i−3i6i00000000−3i000000000000-6-633-6000000003000000000000−6i−6i3i3i−6i000000003i000000000000
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χ5066-3-3-20000000012ζ22−2ζ26+2ζ342ζ14+2ζ26−2ζ34−2ζ14−2ζ220000000006i6i−3i−3i−2i00000000i2ζ7+2ζ31−2ζ35−2ζ7+2ζ23+2ζ35−2ζ23−2ζ31000000000-6-633200000000-1−2ζ22+2ζ26−2ζ34−2ζ14−2ζ26+2ζ342ζ14+2ζ22000000000−6i−6i3i3i2i00000000−i−2ζ7−2ζ31+2ζ352ζ7−2ζ23−2ζ352ζ23+2ζ31000000000
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χ996666-2-3-3000000-2111000000000−6i−6i−6i−6i2i3i3i0000002i−i−i−i000000000-6-6-6-62330000002-1-1-10000000006i6i6i6i−2i−3i−3i000000−2iiii000000000
χ10066-3-3600000000-3000000000000−6i−6i3i3i−6i000000003i000000000000-6-633-60000000030000000000006i6i−3i−3i6i00000000−3i000000000000
χ10166-3-3-2000000001−2ζ14−2ζ222ζ22−2ζ26+2ζ342ζ14+2ζ26−2ζ34000000000−6i−6i3i3i2i00000000−i2ζ23+2ζ31−2ζ7−2ζ31+2ζ352ζ7−2ζ23−2ζ35000000000-6-633200000000-12ζ14+2ζ22−2ζ22+2ζ26−2ζ34−2ζ14−2ζ26+2ζ340000000006i6i−3i−3i−2i00000000i−2ζ23−2ζ312ζ7+2ζ31−2ζ35−2ζ7+2ζ23+2ζ35000000000
χ10266-3-3-20000000012ζ22−2ζ26+2ζ342ζ14+2ζ26−2ζ34−2ζ14−2ζ22000000000−6i−6i3i3i2i00000000−i−2ζ7−2ζ31+2ζ352ζ7−2ζ23−2ζ352ζ23+2ζ31000000000-6-633200000000-1−2ζ22+2ζ26−2ζ34−2ζ14−2ζ26+2ζ342ζ14+2ζ220000000006i6i−3i−3i−2i00000000i2ζ7+2ζ31−2ζ35−2ζ7+2ζ23+2ζ35−2ζ23−2ζ31000000000
χ10366-3-3-20000000012ζ14+2ζ26−2ζ34−2ζ14−2ζ222ζ22−2ζ26+2ζ34000000000−6i−6i3i3i2i00000000−i2ζ7−2ζ23−2ζ352ζ23+2ζ31−2ζ7−2ζ31+2ζ35000000000-6-633200000000-1−2ζ14−2ζ26+2ζ342ζ14+2ζ22−2ζ22+2ζ26−2ζ340000000006i6i−3i−3i−2i00000000i−2ζ7+2ζ23+2ζ35−2ζ23−2ζ312ζ7+2ζ31−2ζ35000000000
χ10412-12-660000000000000000000000−12i12i6i−6i0000000000000000000000-12126-6000000000000000000000012i−12i−6i6i0000000000000000000000

Here ζ is a primitive root of unity of order 36 (ζ36 = 1); i = ζ9.