Finite Group Databasebeta

← Group #13180326

Character table — Group #13180326

Order 1728.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72
size11223366888888181818183366991818242424242424545454544488121224243232323232327272727244881212242432323232323272727272
order12362266333666444422662266666666444436366666333666121212123636666633366612121212
χ1111111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111-1-1-1-111111111111111-1-1-1-111111111111111-1-1-1-111111111111111-1-1-1-1
χ31-11-11-11-1111-1-1-1i−ii−i1-11-11-11-1111-1-1-1i−ii−i1-11-11-11-1111-1-1-1i−ii−i1-11-11-11-1111-1-1-1i−ii−i
χ41-11-11-11-1111-1-1-1−ii−ii1-11-11-11-1111-1-1-1−ii−ii1-11-11-11-1111-1-1-1−ii−ii1-11-11-11-1111-1-1-1−ii−ii
χ522222222-1-1-1-1-1-1000022222222-1-1-1-1-1-1000022222222-1-1-1-1-1-1000022222222-1-1-1-1-1-10000
χ622-1-122-1-12-1-12-1-1000022-1-122-1-12-1-12-1-1000022-1-122-1-12-1-12-1-1000022-1-122-1-12-1-12-1-10000
χ722-1-122-1-1-12-1-12-1000022-1-122-1-1-12-1-12-1000022-1-122-1-1-12-1-12-1000022-1-122-1-1-12-1-12-10000
χ822-1-122-1-1-1-12-1-12000022-1-122-1-1-1-12-1-12000022-1-122-1-1-1-12-1-12000022-1-122-1-1-1-12-1-120000
χ92-22-22-22-2-1-1-111100002-22-22-22-2-1-1-111100002-22-22-22-2-1-1-111100002-22-22-22-2-1-1-11110000
χ102-2-112-2-112-1-1-21100002-2-112-2-112-1-1-21100002-2-112-2-112-1-1-21100002-2-112-2-112-1-1-2110000
χ112-2-112-2-11-12-11-2100002-2-112-2-11-12-11-2100002-2-112-2-11-12-11-2100002-2-112-2-11-12-11-210000
χ122-2-112-2-11-1-1211-200002-2-112-2-11-1-1211-200002-2-112-2-11-1-1211-200002-2-112-2-11-1-1211-20000
χ133333-1-1-1-100000011-1-13333-1-1-1-100000011-1-13333-1-1-1-100000011-1-13333-1-1-1-100000011-1-1
χ143333-1-1-1-1000000-1-1113333-1-1-1-1000000-1-1113333-1-1-1-1000000-1-1113333-1-1-1-1000000-1-111
χ153-33-3-11-11000000i−i−ii3-33-3-11-11000000i−i−ii3-33-3-11-11000000i−i−ii3-33-3-11-11000000i−i−ii
χ163-33-3-11-11000000−iii−i3-33-3-11-11000000−iii−i3-33-3-11-11000000−iii−i3-33-3-11-11000000−iii−i
χ1766-3-3-2-211000000000066-3-3-2-211000000000066-3-3-2-211000000000066-3-3-2-2110000000000
χ186-6-33-221-100000000006-6-33-221-100000000006-6-33-221-100000000006-6-33-221-10000000000
χ19111111111111111111111111111111111111−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32
χ2011111111111111-1-1-1-111111111111111-1-1-1-1−1+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+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−i321+i321+i321+i321+i32
χ211-11-11-11-1111-1-1-1i−ii−i1-11-11-11-1111-1-1-1i−ii−i−1+i321−i32−1+i321−i32−1+i321−i32−1+i321−i32−1+i32−1+i32−1+i321−i321−i321−i32ζ7−ζ7ζ7−ζ7−1−i321+i32−1−i321+i32−1−i321+i32−1−i321+i32−1−i32−1−i32−1−i321+i321+i321+i32ζ11−ζ11ζ11−ζ11
χ221-11-11-11-1111-1-1-1−ii−ii1-11-11-11-1111-1-1-1−ii−ii−1+i321−i32−1+i321−i32−1+i321−i32−1+i321−i32−1+i32−1+i32−1+i321−i321−i321−i32−ζ7ζ7−ζ7ζ7−1−i321+i32−1−i321+i32−1−i321+i32−1−i321+i32−1−i32−1−i32−1−i321+i321+i321+i32−ζ11ζ11−ζ11ζ11
χ2322222222-1-1-1-1-1-1000022222222-1-1-1-1-1-10000−1+i3−1+i3−1+i3−1+i3−1+i3−1+i3−1+i3−1+i31−i321−i321−i321−i321−i321−i320000−1−i3−1−i3−1−i3−1−i3−1−i3−1−i3−1−i3−1−i31+i321+i321+i321+i321+i321+i320000
χ2422-1-122-1-12-1-12-1-1000022-1-122-1-12-1-12-1-10000−1+i3−1+i31−i321−i32−1+i3−1+i31−i321−i32−1+i31−i321−i32−1+i31−i321−i320000−1−i3−1−i31+i321+i32−1−i3−1−i31+i321+i32−1−i31+i321+i32−1−i31+i321+i320000
χ2522-1-122-1-1-12-1-12-1000022-1-122-1-1-12-1-12-10000−1+i3−1+i31−i321−i32−1+i3−1+i31−i321−i321−i32−1+i31−i321−i32−1+i31−i320000−1−i3−1−i31+i321+i32−1−i3−1−i31+i321+i321+i32−1−i31+i321+i32−1−i31+i320000
χ2622-1-122-1-1-1-12-1-12000022-1-122-1-1-1-12-1-120000−1+i3−1+i31−i321−i32−1+i3−1+i31−i321−i321−i321−i32−1+i31−i321−i32−1+i30000−1−i3−1−i31+i321+i32−1−i3−1−i31+i321+i321+i321+i32−1−i31+i321+i32−1−i30000
χ272-22-22-22-2-1-1-111100002-22-22-22-2-1-1-11110000−1+i31−i3−1+i31−i3−1+i31−i3−1+i31−i31−i321−i321−i32−1+i32−1+i32−1+i320000−1−i31+i3−1−i31+i3−1−i31+i3−1−i31+i31+i321+i321+i32−1−i32−1−i32−1−i320000
χ282-2-112-2-112-1-1-21100002-2-112-2-112-1-1-2110000−1+i31−i31−i32−1+i32−1+i31−i31−i32−1+i32−1+i31−i321−i321−i3−1+i32−1+i320000−1−i31+i31+i32−1−i32−1−i31+i31+i32−1−i32−1−i31+i321+i321+i3−1−i32−1−i320000
χ292-2-112-2-11-12-11-2100002-2-112-2-11-12-11-210000−1+i31−i31−i32−1+i32−1+i31−i31−i32−1+i321−i32−1+i31−i32−1+i321−i3−1+i320000−1−i31+i31+i32−1−i32−1−i31+i31+i32−1−i321+i32−1−i31+i32−1−i321+i3−1−i320000
χ302-2-112-2-11-1-1211-200002-2-112-2-11-1-1211-20000−1+i31−i31−i32−1+i32−1+i31−i31−i32−1+i321−i321−i32−1+i3−1+i32−1+i321−i30000−1−i31+i31+i32−1−i32−1−i31+i31+i32−1−i321+i321+i32−1−i3−1−i32−1−i321+i30000
χ313333-1-1-1-100000011-1-13333-1-1-1-100000011-1-1−3+3i32−3+3i32−3+3i32−3+3i321−i321−i321−i321−i32000000−1+i32−1+i321−i321−i32−3−3i32−3−3i32−3−3i32−3−3i321+i321+i321+i321+i32000000−1−i32−1−i321+i321+i32
χ323333-1-1-1-1000000-1-1113333-1-1-1-1000000-1-111−3+3i32−3+3i32−3+3i32−3+3i321−i321−i321−i321−i320000001−i321−i32−1+i32−1+i32−3−3i32−3−3i32−3−3i32−3−3i321+i321+i321+i321+i320000001+i321+i32−1−i32−1−i32
χ333-33-3-11-11000000i−i−ii3-33-3-11-11000000i−i−ii−3+3i323−3i32−3+3i323−3i321−i32−1+i321−i32−1+i32000000ζ7−ζ7−ζ7ζ7−3−3i323+3i32−3−3i323+3i321+i32−1−i321+i32−1−i32000000ζ11−ζ11−ζ11ζ11
χ343-33-3-11-11000000−iii−i3-33-3-11-11000000−iii−i−3+3i323−3i32−3+3i323−3i321−i32−1+i321−i32−1+i32000000−ζ7ζ7ζ7−ζ7−3−3i323+3i32−3−3i323+3i321+i32−1−i321+i32−1−i32000000−ζ11ζ11ζ11−ζ11
χ3566-3-3-2-211000000000066-3-3-2-2110000000000−3+3i3−3+3i33−3i323−3i321−i31−i3−1+i32−1+i320000000000−3−3i3−3−3i33+3i323+3i321+i31+i3−1−i32−1−i320000000000
χ366-6-33-221-100000000006-6-33-221-10000000000−3+3i33−3i33−3i32−3+3i321−i3−1+i3−1+i321−i320000000000−3−3i33+3i33+3i32−3−3i321+i3−1−i3−1−i321+i320000000000
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
χ3811111111111111-1-1-1-111111111111111-1-1-1-1−1−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−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+i321−i321−i321−i321−i32
χ391-11-11-11-1111-1-1-1i−ii−i1-11-11-11-1111-1-1-1i−ii−i−1−i321+i32−1−i321+i32−1−i321+i32−1−i321+i32−1−i32−1−i32−1−i321+i321+i321+i32ζ11−ζ11ζ11−ζ11−1+i321−i32−1+i321−i32−1+i321−i32−1+i321−i32−1+i32−1+i32−1+i321−i321−i321−i32ζ7−ζ7ζ7−ζ7
χ401-11-11-11-1111-1-1-1−ii−ii1-11-11-11-1111-1-1-1−ii−ii−1−i321+i32−1−i321+i32−1−i321+i32−1−i321+i32−1−i32−1−i32−1−i321+i321+i321+i32−ζ11ζ11−ζ11ζ11−1+i321−i32−1+i321−i32−1+i321−i32−1+i321−i32−1+i32−1+i32−1+i321−i321−i321−i32−ζ7ζ7−ζ7ζ7
χ4122222222-1-1-1-1-1-1000022222222-1-1-1-1-1-10000−1−i3−1−i3−1−i3−1−i3−1−i3−1−i3−1−i3−1−i31+i321+i321+i321+i321+i321+i320000−1+i3−1+i3−1+i3−1+i3−1+i3−1+i3−1+i3−1+i31−i321−i321−i321−i321−i321−i320000
χ4222-1-122-1-12-1-12-1-1000022-1-122-1-12-1-12-1-10000−1−i3−1−i31+i321+i32−1−i3−1−i31+i321+i32−1−i31+i321+i32−1−i31+i321+i320000−1+i3−1+i31−i321−i32−1+i3−1+i31−i321−i32−1+i31−i321−i32−1+i31−i321−i320000
χ4322-1-122-1-1-12-1-12-1000022-1-122-1-1-12-1-12-10000−1−i3−1−i31+i321+i32−1−i3−1−i31+i321+i321+i32−1−i31+i321+i32−1−i31+i320000−1+i3−1+i31−i321−i32−1+i3−1+i31−i321−i321−i32−1+i31−i321−i32−1+i31−i320000
χ4422-1-122-1-1-1-12-1-12000022-1-122-1-1-1-12-1-120000−1−i3−1−i31+i321+i32−1−i3−1−i31+i321+i321+i321+i32−1−i31+i321+i32−1−i30000−1+i3−1+i31−i321−i32−1+i3−1+i31−i321−i321−i321−i32−1+i31−i321−i32−1+i30000
χ452-22-22-22-2-1-1-111100002-22-22-22-2-1-1-11110000−1−i31+i3−1−i31+i3−1−i31+i3−1−i31+i31+i321+i321+i32−1−i32−1−i32−1−i320000−1+i31−i3−1+i31−i3−1+i31−i3−1+i31−i31−i321−i321−i32−1+i32−1+i32−1+i320000
χ462-2-112-2-112-1-1-21100002-2-112-2-112-1-1-2110000−1−i31+i31+i32−1−i32−1−i31+i31+i32−1−i32−1−i31+i321+i321+i3−1−i32−1−i320000−1+i31−i31−i32−1+i32−1+i31−i31−i32−1+i32−1+i31−i321−i321−i3−1+i32−1+i320000
χ472-2-112-2-11-12-11-2100002-2-112-2-11-12-11-210000−1−i31+i31+i32−1−i32−1−i31+i31+i32−1−i321+i32−1−i31+i32−1−i321+i3−1−i320000−1+i31−i31−i32−1+i32−1+i31−i31−i32−1+i321−i32−1+i31−i32−1+i321−i3−1+i320000
χ482-2-112-2-11-1-1211-200002-2-112-2-11-1-1211-20000−1−i31+i31+i32−1−i32−1−i31+i31+i32−1−i321+i321+i32−1−i3−1−i32−1−i321+i30000−1+i31−i31−i32−1+i32−1+i31−i31−i32−1+i321−i321−i32−1+i3−1+i32−1+i321−i30000
χ493333-1-1-1-100000011-1-13333-1-1-1-100000011-1-1−3−3i32−3−3i32−3−3i32−3−3i321+i321+i321+i321+i32000000−1−i32−1−i321+i321+i32−3+3i32−3+3i32−3+3i32−3+3i321−i321−i321−i321−i32000000−1+i32−1+i321−i321−i32
χ503333-1-1-1-1000000-1-1113333-1-1-1-1000000-1-111−3−3i32−3−3i32−3−3i32−3−3i321+i321+i321+i321+i320000001+i321+i32−1−i32−1−i32−3+3i32−3+3i32−3+3i32−3+3i321−i321−i321−i321−i320000001−i321−i32−1+i32−1+i32
χ513-33-3-11-11000000i−i−ii3-33-3-11-11000000i−i−ii−3−3i323+3i32−3−3i323+3i321+i32−1−i321+i32−1−i32000000ζ11−ζ11−ζ11ζ11−3+3i323−3i32−3+3i323−3i321−i32−1+i321−i32−1+i32000000ζ7−ζ7−ζ7ζ7
χ523-33-3-11-11000000−iii−i3-33-3-11-11000000−iii−i−3−3i323+3i32−3−3i323+3i321+i32−1−i321+i32−1−i32000000−ζ11ζ11ζ11−ζ11−3+3i323−3i32−3+3i323−3i321−i32−1+i321−i32−1+i32000000−ζ7ζ7ζ7−ζ7
χ5366-3-3-2-211000000000066-3-3-2-2110000000000−3−3i3−3−3i33+3i323+3i321+i31+i3−1−i32−1−i320000000000−3+3i3−3+3i33−3i323−3i321−i31−i3−1+i32−1+i320000000000
χ546-6-33-221-100000000006-6-33-221-10000000000−3−3i33+3i33+3i32−3−3i321+i3−1−i3−1−i321+i320000000000−3+3i33−3i33−3i32−3+3i321−i3−1+i3−1+i321−i320000000000
χ55333333333333333333-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1000000000000000000000000000000000000
χ5633333333333333-3-3-3-3-1-1-1-1-1-1-1-1-1-1-1-1-1-11111000000000000000000000000000000000000
χ573-33-33-33-3333-3-3-33i−3i3i−3i-11-11-11-11-1-1-1111−ii−ii000000000000000000000000000000000000
χ583-33-33-33-3333-3-3-3−3i3i−3i3i-11-11-11-11-1-1-1111i−ii−i000000000000000000000000000000000000
χ5966666666-3-3-3-3-3-30000-2-2-2-2-2-2-2-21111110000000000000000000000000000000000000000
χ6066-3-366-3-36-3-36-3-30000-2-211-2-211-211-2110000000000000000000000000000000000000000
χ6166-3-366-3-3-36-3-36-30000-2-211-2-2111-211-210000000000000000000000000000000000000000
χ6266-3-366-3-3-3-36-3-360000-2-211-2-21111-211-20000000000000000000000000000000000000000
χ636-66-66-66-6-3-3-33330000-22-22-22-22111-1-1-10000000000000000000000000000000000000000
χ646-6-336-6-336-3-3-6330000-221-1-221-1-2112-1-10000000000000000000000000000000000000000
χ656-6-336-6-33-36-33-630000-221-1-221-11-21-12-10000000000000000000000000000000000000000
χ666-6-336-6-33-3-3633-60000-221-1-221-111-2-1-120000000000000000000000000000000000000000
χ679999-3-3-3-300000033-3-3-3-3-3-31111000000-1-111000000000000000000000000000000000000
χ689999-3-3-3-3000000-3-333-3-3-3-3111100000011-1-1000000000000000000000000000000000000
χ699-99-9-33-330000003i−3i−3i3i-33-331-11-1000000−iii−i000000000000000000000000000000000000
χ709-99-9-33-33000000−3i3i3i−3i-33-331-11-1000000i−i−ii000000000000000000000000000000000000
χ711818-9-9-6-6330000000000-6-63322-1-10000000000000000000000000000000000000000000000
χ7218-18-99-663-30000000000-663-32-2-110000000000000000000000000000000000000000000000

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