Finite Group Databasebeta

← Group #73176

Character table — Group #73176

Order 384.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70
size1144446114444611444461144446228888122288881222888812228888122288881222888812
order1233664226666422666642266664441212121244412121212444121212124441212121244412121212444121212124
χ11111111111111111111111111111111111111111111111111111111111111111111111
χ211−1+i32−1−i32−1+i32−1−i32111−1+i32−1−i32−1+i32−1−i32111−1+i32−1−i32−1+i32−1−i32111−1+i32−1−i32−1+i32−1−i32111−1+i32−1−i32−1+i32−1−i32111−1+i32−1−i32−1+i32−1−i32111−1+i32−1−i32−1+i32−1−i32111−1+i32−1−i32−1+i32−1−i32111−1+i32−1−i32−1+i32−1−i32111−1+i32−1−i32−1+i32−1−i321
χ311−1−i32−1+i32−1−i32−1+i32111−1−i32−1+i32−1−i32−1+i32111−1−i32−1+i32−1−i32−1+i32111−1−i32−1+i32−1−i32−1+i32111−1−i32−1+i32−1−i32−1+i32111−1−i32−1+i32−1−i32−1+i32111−1−i32−1+i32−1−i32−1+i32111−1−i32−1+i32−1−i32−1+i32111−1−i32−1+i32−1−i32−1+i32111−1−i32−1+i32−1−i32−1+i321
χ42-2-1-11102-2-1-11102-2-1-11102-2-1-11102-2-1-11102-2-1-11102-2-1-11102-2-1-11102-2-1-11102-2-1-1110
χ52-21−i321+i32−1+i32−1−i3202-21−i321+i32−1+i32−1−i3202-21−i321+i32−1+i32−1−i3202-21−i321+i32−1+i32−1−i3202-21−i321+i32−1+i32−1−i3202-21−i321+i32−1+i32−1−i3202-21−i321+i32−1+i32−1−i3202-21−i321+i32−1+i32−1−i3202-21−i321+i32−1+i32−1−i3202-21−i321+i32−1+i32−1−i320
χ62-21+i321−i32−1−i32−1+i3202-21+i321−i32−1−i32−1+i3202-21+i321−i32−1−i32−1+i3202-21+i321−i32−1−i32−1+i3202-21+i321−i32−1−i32−1+i3202-21+i321−i32−1−i32−1+i3202-21+i321−i32−1−i32−1+i3202-21+i321−i32−1−i32−1+i3202-21+i321−i32−1−i32−1+i3202-21+i321−i32−1−i32−1+i320
χ7330000-1330000-1330000-1330000-1330000-1330000-1330000-1330000-1330000-1330000-1
χ8111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ911−1+i32−1−i32−1+i32−1−i32111−1+i32−1−i32−1+i32−1−i32111−1+i32−1−i32−1+i32−1−i32111−1+i32−1−i32−1+i32−1−i32111−1+i32−1−i32−1+i32−1−i32111−1+i32−1−i32−1+i32−1−i321-1-11−i321+i321−i321+i32-1-1-11−i321+i321−i321+i32-1-1-11−i321+i321−i321+i32-1-1-11−i321+i321−i321+i32-1
χ1011−1−i32−1+i32−1−i32−1+i32111−1−i32−1+i32−1−i32−1+i32111−1−i32−1+i32−1−i32−1+i32111−1−i32−1+i32−1−i32−1+i32111−1−i32−1+i32−1−i32−1+i32111−1−i32−1+i32−1−i32−1+i321-1-11+i321−i321+i321−i32-1-1-11+i321−i321+i321−i32-1-1-11+i321−i321+i321−i32-1-1-11+i321−i321+i321−i32-1
χ112-2-1-11102-2-1-11102-2-1-11102-2-1-11102-2-1-11102-2-1-1110-2211-1-10-2211-1-10-2211-1-10-2211-1-10
χ122-21−i321+i32−1+i32−1−i3202-21−i321+i32−1+i32−1−i3202-21−i321+i32−1+i32−1−i3202-21−i321+i32−1+i32−1−i3202-21−i321+i32−1+i32−1−i3202-21−i321+i32−1+i32−1−i320-22−1+i32−1−i321−i321+i320-22−1+i32−1−i321−i321+i320-22−1+i32−1−i321−i321+i320-22−1+i32−1−i321−i321+i320
χ132-21+i321−i32−1−i32−1+i3202-21+i321−i32−1−i32−1+i3202-21+i321−i32−1−i32−1+i3202-21+i321−i32−1−i32−1+i3202-21+i321−i32−1−i32−1+i3202-21+i321−i32−1−i32−1+i320-22−1−i32−1+i321+i321−i320-22−1−i32−1+i321+i321−i320-22−1−i32−1+i321+i321−i320-22−1−i32−1+i321+i321−i320
χ14330000-1330000-1330000-1330000-1330000-1330000-1-3-300001-3-300001-3-300001-3-300001
χ151111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ1611−1+i32−1−i32−1+i32−1−i32111−1+i32−1−i32−1+i32−1−i32111−1+i32−1−i32−1+i32−1−i32111−1+i32−1−i32−1+i32−1−i321-1-11−i321+i321−i321+i32-1-1-11−i321+i321−i321+i32-111−1+i32−1−i32−1+i32−1−i32111−1+i32−1−i32−1+i32−1−i321-1-11−i321+i321−i321+i32-1-1-11−i321+i321−i321+i32-1
χ1711−1−i32−1+i32−1−i32−1+i32111−1−i32−1+i32−1−i32−1+i32111−1−i32−1+i32−1−i32−1+i32111−1−i32−1+i32−1−i32−1+i321-1-11+i321−i321+i321−i32-1-1-11+i321−i321+i321−i32-111−1−i32−1+i32−1−i32−1+i32111−1−i32−1+i32−1−i32−1+i321-1-11+i321−i321+i321−i32-1-1-11+i321−i321+i321−i32-1
χ182-2-1-11102-2-1-11102-2-1-11102-2-1-1110-2211-1-10-2211-1-102-2-1-11102-2-1-1110-2211-1-10-2211-1-10
χ192-21−i321+i32−1+i32−1−i3202-21−i321+i32−1+i32−1−i3202-21−i321+i32−1+i32−1−i3202-21−i321+i32−1+i32−1−i320-22−1+i32−1−i321−i321+i320-22−1+i32−1−i321−i321+i3202-21−i321+i32−1+i32−1−i3202-21−i321+i32−1+i32−1−i320-22−1+i32−1−i321−i321+i320-22−1+i32−1−i321−i321+i320
χ202-21+i321−i32−1−i32−1+i3202-21+i321−i32−1−i32−1+i3202-21+i321−i32−1−i32−1+i3202-21+i321−i32−1−i32−1+i320-22−1−i32−1+i321+i321−i320-22−1−i32−1+i321+i321−i3202-21+i321−i32−1−i32−1+i3202-21+i321−i32−1−i32−1+i320-22−1−i32−1+i321+i321−i320-22−1−i32−1+i321+i321−i320
χ21330000-1330000-1330000-1330000-1-3-300001-3-300001330000-1330000-1-3-300001-3-300001
χ221111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111111111
χ2311−1+i32−1−i32−1+i32−1−i32111−1+i32−1−i32−1+i32−1−i32111−1+i32−1−i32−1+i32−1−i32111−1+i32−1−i32−1+i32−1−i321-1-11−i321+i321−i321+i32-1-1-11−i321+i321−i321+i32-1-1-11−i321+i321−i321+i32-1-1-11−i321+i321−i321+i32-111−1+i32−1−i32−1+i32−1−i32111−1+i32−1−i32−1+i32−1−i321
χ2411−1−i32−1+i32−1−i32−1+i32111−1−i32−1+i32−1−i32−1+i32111−1−i32−1+i32−1−i32−1+i32111−1−i32−1+i32−1−i32−1+i321-1-11+i321−i321+i321−i32-1-1-11+i321−i321+i321−i32-1-1-11+i321−i321+i321−i32-1-1-11+i321−i321+i321−i32-111−1−i32−1+i32−1−i32−1+i32111−1−i32−1+i32−1−i32−1+i321
χ252-2-1-11102-2-1-11102-2-1-11102-2-1-1110-2211-1-10-2211-1-10-2211-1-10-2211-1-102-2-1-11102-2-1-1110
χ262-21−i321+i32−1+i32−1−i3202-21−i321+i32−1+i32−1−i3202-21−i321+i32−1+i32−1−i3202-21−i321+i32−1+i32−1−i320-22−1+i32−1−i321−i321+i320-22−1+i32−1−i321−i321+i320-22−1+i32−1−i321−i321+i320-22−1+i32−1−i321−i321+i3202-21−i321+i32−1+i32−1−i3202-21−i321+i32−1+i32−1−i320
χ272-21+i321−i32−1−i32−1+i3202-21+i321−i32−1−i32−1+i3202-21+i321−i32−1−i32−1+i3202-21+i321−i32−1−i32−1+i320-22−1−i32−1+i321+i321−i320-22−1−i32−1+i321+i321−i320-22−1−i32−1+i321+i321−i320-22−1−i32−1+i321+i321−i3202-21+i321−i32−1−i32−1+i3202-21+i321−i32−1−i32−1+i320
χ28330000-1330000-1330000-1330000-1-3-300001-3-300001-3-300001-3-300001330000-1330000-1
χ291111111-1-1-1-1-1-1-11111111-1-1-1-1-1-1-11111111-1-1-1-1-1-1-1iiiiiii−i−i−i−i−i−i−iiiiiiii−i−i−i−i−i−i−i
χ3011−1+i32−1−i32−1+i32−1−i321-1-11−i321+i321−i321+i32-111−1+i32−1−i32−1+i32−1−i321-1-11−i321+i321−i321+i32-111−1+i32−1−i32−1+i32−1−i321-1-11−i321+i321−i321+i32-1iiζ7ζ11ζ7ζ11i−i−i−ζ7−ζ11−ζ7−ζ11−iiiζ7ζ11ζ7ζ11i−i−i−ζ7−ζ11−ζ7−ζ11−i
χ3111−1−i32−1+i32−1−i32−1+i321-1-11+i321−i321+i321−i32-111−1−i32−1+i32−1−i32−1+i321-1-11+i321−i321+i321−i32-111−1−i32−1+i32−1−i32−1+i321-1-11+i321−i321+i321−i32-1iiζ11ζ7ζ11ζ7i−i−i−ζ11−ζ7−ζ11−ζ7−iiiζ11ζ7ζ11ζ7i−i−i−ζ11−ζ7−ζ11−ζ7−i
χ322-2-1-1110-2211-1-102-2-1-1110-2211-1-102-2-1-1110-2211-1-102i−2i−i−iii0−2i2iii−i−i02i−2i−i−iii0−2i2iii−i−i0
χ332-21−i321+i32−1+i32−1−i320-22−1+i32−1−i321−i321+i3202-21−i321+i32−1+i32−1−i320-22−1+i32−1−i321−i321+i3202-21−i321+i32−1+i32−1−i320-22−1+i32−1−i321−i321+i3202i−2i−ζ7−ζ11ζ7ζ110−2i2iζ7ζ11−ζ7−ζ1102i−2i−ζ7−ζ11ζ7ζ110−2i2iζ7ζ11−ζ7−ζ110
χ342-21+i321−i32−1−i32−1+i320-22−1−i32−1+i321+i321−i3202-21+i321−i32−1−i32−1+i320-22−1−i32−1+i321+i321−i3202-21+i321−i32−1−i32−1+i320-22−1−i32−1+i321+i321−i3202i−2i−ζ11−ζ7ζ11ζ70−2i2iζ11ζ7−ζ11−ζ702i−2i−ζ11−ζ7ζ11ζ70−2i2iζ11ζ7−ζ11−ζ70
χ35330000-1-3-300001330000-1-3-300001330000-1-3-3000013i3i0000−i−3i−3i0000i3i3i0000−i−3i−3i0000i
χ361111111-1-1-1-1-1-1-11111111-1-1-1-1-1-1-11111111-1-1-1-1-1-1-1−i−i−i−i−i−i−iiiiiiii−i−i−i−i−i−i−iiiiiiii
χ3711−1+i32−1−i32−1+i32−1−i321-1-11−i321+i321−i321+i32-111−1+i32−1−i32−1+i32−1−i321-1-11−i321+i321−i321+i32-111−1+i32−1−i32−1+i32−1−i321-1-11−i321+i321−i321+i32-1−i−i−ζ7−ζ11−ζ7−ζ11−iiiζ7ζ11ζ7ζ11i−i−i−ζ7−ζ11−ζ7−ζ11−iiiζ7ζ11ζ7ζ11i
χ3811−1−i32−1+i32−1−i32−1+i321-1-11+i321−i321+i321−i32-111−1−i32−1+i32−1−i32−1+i321-1-11+i321−i321+i321−i32-111−1−i32−1+i32−1−i32−1+i321-1-11+i321−i321+i321−i32-1−i−i−ζ11−ζ7−ζ11−ζ7−iiiζ11ζ7ζ11ζ7i−i−i−ζ11−ζ7−ζ11−ζ7−iiiζ11ζ7ζ11ζ7i
χ392-2-1-1110-2211-1-102-2-1-1110-2211-1-102-2-1-1110-2211-1-10−2i2iii−i−i02i−2i−i−iii0−2i2iii−i−i02i−2i−i−iii0
χ402-21−i321+i32−1+i32−1−i320-22−1+i32−1−i321−i321+i3202-21−i321+i32−1+i32−1−i320-22−1+i32−1−i321−i321+i3202-21−i321+i32−1+i32−1−i320-22−1+i32−1−i321−i321+i320−2i2iζ7ζ11−ζ7−ζ1102i−2i−ζ7−ζ11ζ7ζ110−2i2iζ7ζ11−ζ7−ζ1102i−2i−ζ7−ζ11ζ7ζ110
χ412-21+i321−i32−1−i32−1+i320-22−1−i32−1+i321+i321−i3202-21+i321−i32−1−i32−1+i320-22−1−i32−1+i321+i321−i3202-21+i321−i32−1−i32−1+i320-22−1−i32−1+i321+i321−i320−2i2iζ11ζ7−ζ11−ζ702i−2i−ζ11−ζ7ζ11ζ70−2i2iζ11ζ7−ζ11−ζ702i−2i−ζ11−ζ7ζ11ζ70
χ42330000-1-3-300001330000-1-3-300001330000-1-3-300001−3i−3i0000i3i3i0000−i−3i−3i0000i3i3i0000−i
χ431111111-1-1-1-1-1-1-11111111-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111iiiiiii−i−i−i−i−i−i−i−i−i−i−i−i−i−iiiiiiii
χ4411−1+i32−1−i32−1+i32−1−i321-1-11−i321+i321−i321+i32-111−1+i32−1−i32−1+i32−1−i321-1-11−i321+i321−i321+i32-1-1-11−i321+i321−i321+i32-111−1+i32−1−i32−1+i32−1−i321iiζ7ζ11ζ7ζ11i−i−i−ζ7−ζ11−ζ7−ζ11−i−i−i−ζ7−ζ11−ζ7−ζ11−iiiζ7ζ11ζ7ζ11i
χ4511−1−i32−1+i32−1−i32−1+i321-1-11+i321−i321+i321−i32-111−1−i32−1+i32−1−i32−1+i321-1-11+i321−i321+i321−i32-1-1-11+i321−i321+i321−i32-111−1−i32−1+i32−1−i32−1+i321iiζ11ζ7ζ11ζ7i−i−i−ζ11−ζ7−ζ11−ζ7−i−i−i−ζ11−ζ7−ζ11−ζ7−iiiζ11ζ7ζ11ζ7i
χ462-2-1-1110-2211-1-102-2-1-1110-2211-1-10-2211-1-102-2-1-11102i−2i−i−iii0−2i2iii−i−i0−2i2iii−i−i02i−2i−i−iii0
χ472-21−i321+i32−1+i32−1−i320-22−1+i32−1−i321−i321+i3202-21−i321+i32−1+i32−1−i320-22−1+i32−1−i321−i321+i320-22−1+i32−1−i321−i321+i3202-21−i321+i32−1+i32−1−i3202i−2i−ζ7−ζ11ζ7ζ110−2i2iζ7ζ11−ζ7−ζ110−2i2iζ7ζ11−ζ7−ζ1102i−2i−ζ7−ζ11ζ7ζ110
χ482-21+i321−i32−1−i32−1+i320-22−1−i32−1+i321+i321−i3202-21+i321−i32−1−i32−1+i320-22−1−i32−1+i321+i321−i320-22−1−i32−1+i321+i321−i3202-21+i321−i32−1−i32−1+i3202i−2i−ζ11−ζ7ζ11ζ70−2i2iζ11ζ7−ζ11−ζ70−2i2iζ11ζ7−ζ11−ζ702i−2i−ζ11−ζ7ζ11ζ70
χ49330000-1-3-300001330000-1-3-300001-3-300001330000-13i3i0000−i−3i−3i0000i−3i−3i0000i3i3i0000−i
χ501111111-1-1-1-1-1-1-11111111-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111−i−i−i−i−i−i−iiiiiiiiiiiiiii−i−i−i−i−i−i−i
χ5111−1+i32−1−i32−1+i32−1−i321-1-11−i321+i321−i321+i32-111−1+i32−1−i32−1+i32−1−i321-1-11−i321+i321−i321+i32-1-1-11−i321+i321−i321+i32-111−1+i32−1−i32−1+i32−1−i321−i−i−ζ7−ζ11−ζ7−ζ11−iiiζ7ζ11ζ7ζ11iiiζ7ζ11ζ7ζ11i−i−i−ζ7−ζ11−ζ7−ζ11−i
χ5211−1−i32−1+i32−1−i32−1+i321-1-11+i321−i321+i321−i32-111−1−i32−1+i32−1−i32−1+i321-1-11+i321−i321+i321−i32-1-1-11+i321−i321+i321−i32-111−1−i32−1+i32−1−i32−1+i321−i−i−ζ11−ζ7−ζ11−ζ7−iiiζ11ζ7ζ11ζ7iiiζ11ζ7ζ11ζ7i−i−i−ζ11−ζ7−ζ11−ζ7−i
χ532-2-1-1110-2211-1-102-2-1-1110-2211-1-10-2211-1-102-2-1-1110−2i2iii−i−i02i−2i−i−iii02i−2i−i−iii0−2i2iii−i−i0
χ542-21−i321+i32−1+i32−1−i320-22−1+i32−1−i321−i321+i3202-21−i321+i32−1+i32−1−i320-22−1+i32−1−i321−i321+i320-22−1+i32−1−i321−i321+i3202-21−i321+i32−1+i32−1−i320−2i2iζ7ζ11−ζ7−ζ1102i−2i−ζ7−ζ11ζ7ζ1102i−2i−ζ7−ζ11ζ7ζ110−2i2iζ7ζ11−ζ7−ζ110
χ552-21+i321−i32−1−i32−1+i320-22−1−i32−1+i321+i321−i3202-21+i321−i32−1−i32−1+i320-22−1−i32−1+i321+i321−i320-22−1−i32−1+i321+i321−i3202-21+i321−i32−1−i32−1+i320−2i2iζ11ζ7−ζ11−ζ702i−2i−ζ11−ζ7ζ11ζ702i−2i−ζ11−ζ7ζ11ζ70−2i2iζ11ζ7−ζ11−ζ70
χ56330000-1-3-300001330000-1-3-300001-3-300001330000-1−3i−3i0000i3i3i0000−i3i3i0000−i−3i−3i0000i
χ5722222222222222-2-2-2-2-2-2-2-2-2-2-2-2-2-2000000000000000000000000000000000000000000
χ5822−1+i3−1−i3−1+i3−1−i3222−1+i3−1−i3−1+i3−1−i32-2-21−i31+i31−i31+i3-2-2-21−i31+i31−i31+i3-2000000000000000000000000000000000000000000
χ5922−1−i3−1+i3−1−i3−1+i3222−1−i3−1+i3−1−i3−1+i32-2-21+i31−i31+i31−i3-2-2-21+i31−i31+i31−i3-2000000000000000000000000000000000000000000
χ604-4-2-22204-4-2-2220-4422-2-20-4422-2-20000000000000000000000000000000000000000000
χ614-41−i31+i3−1+i3−1−i304-41−i31+i3−1+i3−1−i30-44−1+i3−1−i31−i31+i30-44−1+i3−1−i31−i31+i30000000000000000000000000000000000000000000
χ624-41+i31−i3−1−i3−1+i304-41+i31−i3−1−i3−1+i30-44−1−i3−1+i31+i31−i30-44−1−i3−1+i31+i31−i30000000000000000000000000000000000000000000
χ63660000-2660000-2-6-600002-6-600002000000000000000000000000000000000000000000
χ642222222-2-2-2-2-2-2-2-2-2-2-2-2-2-22222222000000000000000000000000000000000000000000
χ6522−1+i3−1−i3−1+i3−1−i32-2-21−i31+i31−i31+i3-2-2-21−i31+i31−i31+i3-222−1+i3−1−i3−1+i3−1−i32000000000000000000000000000000000000000000
χ6622−1−i3−1+i3−1−i3−1+i32-2-21+i31−i31+i31−i3-2-2-21+i31−i31+i31−i3-222−1−i3−1+i3−1−i3−1+i32000000000000000000000000000000000000000000
χ674-4-2-2220-4422-2-20-4422-2-204-4-2-2220000000000000000000000000000000000000000000
χ684-41−i31+i3−1+i3−1−i30-44−1+i3−1−i31−i31+i30-44−1+i3−1−i31−i31+i304-41−i31+i3−1+i3−1−i30000000000000000000000000000000000000000000
χ694-41+i31−i3−1−i3−1+i30-44−1−i3−1+i31+i31−i30-44−1−i3−1+i31+i31−i304-41+i31−i3−1−i3−1+i30000000000000000000000000000000000000000000
χ70660000-2-6-600002-6-600002660000-2000000000000000000000000000000000000000000

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