Finite Group Databasebeta

← Group #73164

Character table — Group #73164

Order 384.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96C97C98C99C100C101C102C103C104C105C106C107C108C109C110C111C112
size1144446114444611444461144446114444611444461144446114444611444461144446114444611444461144446114444611444461144446
order1233664441212121242266664441212121244412121212444121212124441212121244412121212422666644412121212422666644412121212444121212124441212121244412121212444121212124
χ11111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
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−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+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
χ42-2-1-11102-2-1-11102-2-1-11102-2-1-11102-2-1-11102-2-1-11102-2-1-11102-2-1-11102-2-1-11102-2-1-11102-2-1-11102-2-1-11102-2-1-11102-2-1-11102-2-1-11102-2-1-1110
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−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+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
χ7330000-1330000-1330000-1330000-1330000-1330000-1330000-1330000-1330000-1330000-1330000-1330000-1330000-1330000-1330000-1330000-1
χ81111111iiiiiii-1-1-1-1-1-1-1−i−i−i−i−i−i−i1111111iiiiiii-1-1-1-1-1-1-1−i−i−i−i−i−i−i1111111iiiiiii-1-1-1-1-1-1-1−i−i−i−i−i−i−i1111111iiiiiii-1-1-1-1-1-1-1−i−i−i−i−i−i−i
χ911−1+i32−1−i32−1+i32−1−i321iiζ7ζ11ζ7ζ11i-1-11−i321+i321−i321+i32-1−i−i−ζ7−ζ11−ζ7−ζ11−i11−1+i32−1−i32−1+i32−1−i321iiζ7ζ11ζ7ζ11i-1-11−i321+i321−i321+i32-1−i−i−ζ7−ζ11−ζ7−ζ11−i11−1+i32−1−i32−1+i32−1−i321iiζ7ζ11ζ7ζ11i-1-11−i321+i321−i321+i32-1−i−i−ζ7−ζ11−ζ7−ζ11−i11−1+i32−1−i32−1+i32−1−i321iiζ7ζ11ζ7ζ11i-1-11−i321+i321−i321+i32-1−i−i−ζ7−ζ11−ζ7−ζ11−i
χ1011−1−i32−1+i32−1−i32−1+i321iiζ11ζ7ζ11ζ7i-1-11+i321−i321+i321−i32-1−i−i−ζ11−ζ7−ζ11−ζ7−i11−1−i32−1+i32−1−i32−1+i321iiζ11ζ7ζ11ζ7i-1-11+i321−i321+i321−i32-1−i−i−ζ11−ζ7−ζ11−ζ7−i11−1−i32−1+i32−1−i32−1+i321iiζ11ζ7ζ11ζ7i-1-11+i321−i321+i321−i32-1−i−i−ζ11−ζ7−ζ11−ζ7−i11−1−i32−1+i32−1−i32−1+i321iiζ11ζ7ζ11ζ7i-1-11+i321−i321+i321−i32-1−i−i−ζ11−ζ7−ζ11−ζ7−i
χ112-2-1-11102i−2i−i−iii0-2211-1-10−2i2iii−i−i02-2-1-11102i−2i−i−iii0-2211-1-10−2i2iii−i−i02-2-1-11102i−2i−i−iii0-2211-1-10−2i2iii−i−i02-2-1-11102i−2i−i−iii0-2211-1-10−2i2iii−i−i0
χ122-21−i321+i32−1+i32−1−i3202i−2i−ζ7−ζ11ζ7ζ110-22−1+i32−1−i321−i321+i320−2i2iζ7ζ11−ζ7−ζ1102-21−i321+i32−1+i32−1−i3202i−2i−ζ7−ζ11ζ7ζ110-22−1+i32−1−i321−i321+i320−2i2iζ7ζ11−ζ7−ζ1102-21−i321+i32−1+i32−1−i3202i−2i−ζ7−ζ11ζ7ζ110-22−1+i32−1−i321−i321+i320−2i2iζ7ζ11−ζ7−ζ1102-21−i321+i32−1+i32−1−i3202i−2i−ζ7−ζ11ζ7ζ110-22−1+i32−1−i321−i321+i320−2i2iζ7ζ11−ζ7−ζ110
χ132-21+i321−i32−1−i32−1+i3202i−2i−ζ11−ζ7ζ11ζ70-22−1−i32−1+i321+i321−i320−2i2iζ11ζ7−ζ11−ζ702-21+i321−i32−1−i32−1+i3202i−2i−ζ11−ζ7ζ11ζ70-22−1−i32−1+i321+i321−i320−2i2iζ11ζ7−ζ11−ζ702-21+i321−i32−1−i32−1+i3202i−2i−ζ11−ζ7ζ11ζ70-22−1−i32−1+i321+i321−i320−2i2iζ11ζ7−ζ11−ζ702-21+i321−i32−1−i32−1+i3202i−2i−ζ11−ζ7ζ11ζ70-22−1−i32−1+i321+i321−i320−2i2iζ11ζ7−ζ11−ζ70
χ14330000-13i3i0000−i-3-300001−3i−3i0000i330000-13i3i0000−i-3-300001−3i−3i0000i330000-13i3i0000−i-3-300001−3i−3i0000i330000-13i3i0000−i-3-300001−3i−3i0000i
χ151111111-1-1-1-1-1-1-11111111-1-1-1-1-1-1-11111111-1-1-1-1-1-1-11111111-1-1-1-1-1-1-11111111-1-1-1-1-1-1-11111111-1-1-1-1-1-1-11111111-1-1-1-1-1-1-11111111-1-1-1-1-1-1-1
χ1611−1+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+i32-111−1+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+i32-111−1+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+i32-111−1+i32−1−i32−1+i32−1−i321-1-11−i321+i321−i321+i32-1
χ1711−1−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−i32-111−1−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−i32-111−1−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−i32-111−1−i32−1+i32−1−i32−1+i321-1-11+i321−i321+i321−i32-1
χ182-2-1-1110-2211-1-102-2-1-1110-2211-1-102-2-1-1110-2211-1-102-2-1-1110-2211-1-102-2-1-1110-2211-1-102-2-1-1110-2211-1-102-2-1-1110-2211-1-102-2-1-1110-2211-1-10
χ192-21−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+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+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+i3202-21−i321+i32−1+i32−1−i320-22−1+i32−1−i321−i321+i320
χ202-21+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−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−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−i3202-21+i321−i32−1−i32−1+i320-22−1−i32−1+i321+i321−i320
χ21330000-1-3-300001330000-1-3-300001330000-1-3-300001330000-1-3-300001330000-1-3-300001330000-1-3-300001330000-1-3-300001330000-1-3-300001
χ221111111−i−i−i−i−i−i−i-1-1-1-1-1-1-1iiiiiii1111111−i−i−i−i−i−i−i-1-1-1-1-1-1-1iiiiiii1111111−i−i−i−i−i−i−i-1-1-1-1-1-1-1iiiiiii1111111−i−i−i−i−i−i−i-1-1-1-1-1-1-1iiiiiii
χ2311−1+i32−1−i32−1+i32−1−i321−i−i−ζ7−ζ11−ζ7−ζ11−i-1-11−i321+i321−i321+i32-1iiζ7ζ11ζ7ζ11i11−1+i32−1−i32−1+i32−1−i321−i−i−ζ7−ζ11−ζ7−ζ11−i-1-11−i321+i321−i321+i32-1iiζ7ζ11ζ7ζ11i11−1+i32−1−i32−1+i32−1−i321−i−i−ζ7−ζ11−ζ7−ζ11−i-1-11−i321+i321−i321+i32-1iiζ7ζ11ζ7ζ11i11−1+i32−1−i32−1+i32−1−i321−i−i−ζ7−ζ11−ζ7−ζ11−i-1-11−i321+i321−i321+i32-1iiζ7ζ11ζ7ζ11i
χ2411−1−i32−1+i32−1−i32−1+i321−i−i−ζ11−ζ7−ζ11−ζ7−i-1-11+i321−i321+i321−i32-1iiζ11ζ7ζ11ζ7i11−1−i32−1+i32−1−i32−1+i321−i−i−ζ11−ζ7−ζ11−ζ7−i-1-11+i321−i321+i321−i32-1iiζ11ζ7ζ11ζ7i11−1−i32−1+i32−1−i32−1+i321−i−i−ζ11−ζ7−ζ11−ζ7−i-1-11+i321−i321+i321−i32-1iiζ11ζ7ζ11ζ7i11−1−i32−1+i32−1−i32−1+i321−i−i−ζ11−ζ7−ζ11−ζ7−i-1-11+i321−i321+i321−i32-1iiζ11ζ7ζ11ζ7i
χ252-2-1-1110−2i2iii−i−i0-2211-1-102i−2i−i−iii02-2-1-1110−2i2iii−i−i0-2211-1-102i−2i−i−iii02-2-1-1110−2i2iii−i−i0-2211-1-102i−2i−i−iii02-2-1-1110−2i2iii−i−i0-2211-1-102i−2i−i−iii0
χ262-21−i321+i32−1+i32−1−i320−2i2iζ7ζ11−ζ7−ζ110-22−1+i32−1−i321−i321+i3202i−2i−ζ7−ζ11ζ7ζ1102-21−i321+i32−1+i32−1−i320−2i2iζ7ζ11−ζ7−ζ110-22−1+i32−1−i321−i321+i3202i−2i−ζ7−ζ11ζ7ζ1102-21−i321+i32−1+i32−1−i320−2i2iζ7ζ11−ζ7−ζ110-22−1+i32−1−i321−i321+i3202i−2i−ζ7−ζ11ζ7ζ1102-21−i321+i32−1+i32−1−i320−2i2iζ7ζ11−ζ7−ζ110-22−1+i32−1−i321−i321+i3202i−2i−ζ7−ζ11ζ7ζ110
χ272-21+i321−i32−1−i32−1+i320−2i2iζ11ζ7−ζ11−ζ70-22−1−i32−1+i321+i321−i3202i−2i−ζ11−ζ7ζ11ζ702-21+i321−i32−1−i32−1+i320−2i2iζ11ζ7−ζ11−ζ70-22−1−i32−1+i321+i321−i3202i−2i−ζ11−ζ7ζ11ζ702-21+i321−i32−1−i32−1+i320−2i2iζ11ζ7−ζ11−ζ70-22−1−i32−1+i321+i321−i3202i−2i−ζ11−ζ7ζ11ζ702-21+i321−i32−1−i32−1+i320−2i2iζ11ζ7−ζ11−ζ70-22−1−i32−1+i321+i321−i3202i−2i−ζ11−ζ7ζ11ζ70
χ28330000-1−3i−3i0000i-3-3000013i3i0000−i330000-1−3i−3i0000i-3-3000013i3i0000−i330000-1−3i−3i0000i-3-3000013i3i0000−i330000-1−3i−3i0000i-3-3000013i3i0000−i
χ291111111111111111111111111111iiiiiiiiiiiiiiiiiiiiiiiiiiii-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−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−i−i
χ3011−1+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−i321iiζ7ζ11ζ7ζ11iiiζ7ζ11ζ7ζ11iiiζ7ζ11ζ7ζ11iiiζ7ζ11ζ7ζ11i-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−i−i−ζ7−ζ11−ζ7−ζ11−i−i−i−ζ7−ζ11−ζ7−ζ11−i−i−i−ζ7−ζ11−ζ7−ζ11−i−i−i−ζ7−ζ11−ζ7−ζ11−i
χ3111−1−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+i321iiζ11ζ7ζ11ζ7iiiζ11ζ7ζ11ζ7iiiζ11ζ7ζ11ζ7iiiζ11ζ7ζ11ζ7i-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−i−i−ζ11−ζ7−ζ11−ζ7−i−i−i−ζ11−ζ7−ζ11−ζ7−i−i−i−ζ11−ζ7−ζ11−ζ7−i−i−i−ζ11−ζ7−ζ11−ζ7−i
χ322-2-1-11102-2-1-11102-2-1-11102-2-1-11102i−2i−i−iii02i−2i−i−iii02i−2i−i−iii02i−2i−i−iii0-2211-1-10-2211-1-10-2211-1-10-2211-1-10−2i2iii−i−i0−2i2iii−i−i0−2i2iii−i−i0−2i2iii−i−i0
χ332-21−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−i3202i−2i−ζ7−ζ11ζ7ζ1102i−2i−ζ7−ζ11ζ7ζ1102i−2i−ζ7−ζ11ζ7ζ1102i−2i−ζ7−ζ11ζ7ζ110-22−1+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+i320−2i2iζ7ζ11−ζ7−ζ110−2i2iζ7ζ11−ζ7−ζ110−2i2iζ7ζ11−ζ7−ζ110−2i2iζ7ζ11−ζ7−ζ110
χ342-21+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+i3202i−2i−ζ11−ζ7ζ11ζ702i−2i−ζ11−ζ7ζ11ζ702i−2i−ζ11−ζ7ζ11ζ702i−2i−ζ11−ζ7ζ11ζ70-22−1−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−i320−2i2iζ11ζ7−ζ11−ζ70−2i2iζ11ζ7−ζ11−ζ70−2i2iζ11ζ7−ζ11−ζ70−2i2iζ11ζ7−ζ11−ζ70
χ35330000-1330000-1330000-1330000-13i3i0000−i3i3i0000−i3i3i0000−i3i3i0000−i-3-300001-3-300001-3-300001-3-300001−3i−3i0000i−3i−3i0000i−3i−3i0000i−3i−3i0000i
χ361111111iiiiiii-1-1-1-1-1-1-1−i−i−i−i−i−i−iiiiiiii-1-1-1-1-1-1-1−i−i−i−i−i−i−i1111111-1-1-1-1-1-1-1−i−i−i−i−i−i−i1111111iiiiiii−i−i−i−i−i−i−i1111111iiiiiii-1-1-1-1-1-1-1
χ3711−1+i32−1−i32−1+i32−1−i321iiζ7ζ11ζ7ζ11i-1-11−i321+i321−i321+i32-1−i−i−ζ7−ζ11−ζ7−ζ11−iiiζ7ζ11ζ7ζ11i-1-11−i321+i321−i321+i32-1−i−i−ζ7−ζ11−ζ7−ζ11−i11−1+i32−1−i32−1+i32−1−i321-1-11−i321+i321−i321+i32-1−i−i−ζ7−ζ11−ζ7−ζ11−i11−1+i32−1−i32−1+i32−1−i321iiζ7ζ11ζ7ζ11i−i−i−ζ7−ζ11−ζ7−ζ11−i11−1+i32−1−i32−1+i32−1−i321iiζ7ζ11ζ7ζ11i-1-11−i321+i321−i321+i32-1
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χ1092-2-1-1110−2i2iii−i−i0-2211-1-102i−2i−i−iii0−2i2iii−i−i0-2211-1-102i−2i−i−iii02-2-1-1110-2211-1-102i−2i−i−iii02-2-1-1110−2i2iii−i−i02i−2i−i−iii02-2-1-1110−2i2iii−i−i0-2211-1-10
χ1102-21−i321+i32−1+i32−1−i320−2i2iζ7ζ11−ζ7−ζ110-22−1+i32−1−i321−i321+i3202i−2i−ζ7−ζ11ζ7ζ110−2i2iζ7ζ11−ζ7−ζ110-22−1+i32−1−i321−i321+i3202i−2i−ζ7−ζ11ζ7ζ1102-21−i321+i32−1+i32−1−i320-22−1+i32−1−i321−i321+i3202i−2i−ζ7−ζ11ζ7ζ1102-21−i321+i32−1+i32−1−i320−2i2iζ7ζ11−ζ7−ζ1102i−2i−ζ7−ζ11ζ7ζ1102-21−i321+i32−1+i32−1−i320−2i2iζ7ζ11−ζ7−ζ110-22−1+i32−1−i321−i321+i320
χ1112-21+i321−i32−1−i32−1+i320−2i2iζ11ζ7−ζ11−ζ70-22−1−i32−1+i321+i321−i3202i−2i−ζ11−ζ7ζ11ζ70−2i2iζ11ζ7−ζ11−ζ70-22−1−i32−1+i321+i321−i3202i−2i−ζ11−ζ7ζ11ζ702-21+i321−i32−1−i32−1+i320-22−1−i32−1+i321+i321−i3202i−2i−ζ11−ζ7ζ11ζ702-21+i321−i32−1−i32−1+i320−2i2iζ11ζ7−ζ11−ζ702i−2i−ζ11−ζ7ζ11ζ702-21+i321−i32−1−i32−1+i320−2i2iζ11ζ7−ζ11−ζ70-22−1−i32−1+i321+i321−i320
χ112330000-1−3i−3i0000i-3-3000013i3i0000−i−3i−3i0000i-3-3000013i3i0000−i330000-1-3-3000013i3i0000−i330000-1−3i−3i0000i3i3i0000−i330000-1−3i−3i0000i-3-300001

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