Finite Group Databasebeta

← Group #13147061

Character table — Group #13147061

Order 1728.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96C97C98
size11111111111122222266666666666666666666121212121212121212121212242424242424242424242424242424242424242424242424363636363636363636363636363636363636363636363636
order12223366666622666634444666666612121212121212121212121212121212121212123336666666666666666666664444888812121212121212122424242424242424
χ111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ3111111111111-1-1-1-1-1-111-1-1111-1-1-1-1111-1-1-1-111111111-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-111-1-111-1-11111-1-1-1-11111-1-1-1-1
χ4111111111111-1-1-1-1-1-111-1-1111-1-1-1-1111-1-1-1-111111111-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-111-1-1-1-11111-1-1-1-11111
χ511-1-11111-1-1-1-11-111-1-1111-1-1-1-111-1-111111-1-1-1-1111-1-1-1111-1-1-1111111-1-1-1-1-1-1111111-1-1-1-1-1-1i−ii−ii−ii−iii−i−iii−i−iii−i−iii−i−i
χ611-1-11111-1-1-1-11-111-1-1111-1-1-1-111-1-111111-1-1-1-1111-1-1-1111-1-1-1111111-1-1-1-1-1-1111111-1-1-1-1-1-1−ii−ii−ii−ii−i−iii−i−iii−i−iii−i−iii
χ711-1-11111-1-1-1-1-11-1-11111-11-1-1-1-1-111111-1-111-1-1111-1-1-1-1-1-1111111111-1-1-1-1-1-1-1-1-1-1-1-1111111i−i−iii−i−iiii−i−i−i−iiiii−i−i−i−iii
χ811-1-11111-1-1-1-1-11-1-11111-11-1-1-1-1-111111-1-111-1-1111-1-1-1-1-1-1111111111-1-1-1-1-1-1-1-1-1-1-1-1111111−iii−i−iii−i−i−iiiii−i−i−i−iiiii−i−i
χ922222222222222222222222222222222222222222222222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1000000000000000000000000
χ10222222222222222222-12222-1-1-1-1-1-1-122222222-1-1-1-1-1-1-1-1-1-1-1-12-1-12-1-122-1-1-1-122-1-1-1-122-1-1-1-1000000000000000000000000
χ11222222222222222222-12222-1-1-1-1-1-1-122222222-1-1-1-1-1-1-1-1-1-1-1-1-12-1-12-1-1-122-1-1-1-122-1-1-1-122-1-1000000000000000000000000
χ12222222222222222222-12222-1-1-1-1-1-1-122222222-1-1-1-1-1-1-1-1-1-1-1-1-1-12-1-12-1-1-1-122-1-1-1-122-1-1-1-122000000000000000000000000
χ13222222222222-2-2-2-2-2-222-2-2222-2-2-2-2222-2-2-2-222222222-2-2-2-2-2-2-1-1-1-1-1-1-1-1-1-1-1-1111111111111000000000000000000000000
χ14222222222222-2-2-2-2-2-2-12-2-22-1-11111-122-2-2-2-222-1-1-1-1-1-11111112-1-12-1-122-1-1-1-1-2-21111-2-21111000000000000000000000000
χ15222222222222-2-2-2-2-2-2-12-2-22-1-11111-122-2-2-2-222-1-1-1-1-1-1111111-12-1-12-1-1-122-1-111-2-21111-2-211000000000000000000000000
χ16222222222222-2-2-2-2-2-2-12-2-22-1-11111-122-2-2-2-222-1-1-1-1-1-1111111-1-12-1-12-1-1-1-1221111-2-21111-2-2000000000000000000000000
χ1722-2-22222-2-2-2-22-222-2-2222-2-2-2-222-2-222222-2-2-2-2222-2-2-2222-2-2-2-1-1-1-1-1-1111111-1-1-1-1-1-1111111000000000000000000000000
χ1822-2-22222-2-2-2-22-222-2-2-122-2-211-1-111-12222-2-2-2-2-1-1-1111-1-1-11112-1-12-1-1-2-2111122-1-1-1-1-2-21111000000000000000000000000
χ1922-2-22222-2-2-2-22-222-2-2-122-2-211-1-111-12222-2-2-2-2-1-1-1111-1-1-1111-12-1-12-111-2-211-1-122-1-111-2-211000000000000000000000000
χ2022-2-22222-2-2-2-22-222-2-2-122-2-211-1-111-12222-2-2-2-2-1-1-1111-1-1-1111-1-12-1-121111-2-2-1-1-1-1221111-2-2000000000000000000000000
χ2122-2-22222-2-2-2-2-22-2-22222-22-2-2-2-2-222222-2-222-2-2222-2-2-2-2-2-2222-1-1-1-1-1-1111111111111-1-1-1-1-1-1000000000000000000000000
χ2222-2-22222-2-2-2-2-22-2-222-12-22-21111-1-1-122-2-222-2-2-1-1-1111111-1-1-12-1-12-1-1-2-21111-2-2111122-1-1-1-1000000000000000000000000
χ2322-2-22222-2-2-2-2-22-2-222-12-22-21111-1-1-122-2-222-2-2-1-1-1111111-1-1-1-12-1-12-111-2-21111-2-211-1-122-1-1000000000000000000000000
χ2422-2-22222-2-2-2-2-22-2-222-12-22-21111-1-1-122-2-222-2-2-1-1-1111111-1-1-1-1-12-1-121111-2-21111-2-2-1-1-1-122000000000000000000000000
χ253333333333333333333-1-1-1-13333333-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-10000000000000000000000001111-1-1-1-111111111-1-1-1-1-1-1-1-1
χ263333333333333333333-1-1-1-13333333-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1000000000000000000000000-1-1-1-11111-1-1-1-1-1-1-1-111111111
χ27333333333333-3-3-3-3-3-33-111-133-3-3-3-33-1-11111-1-1-1-1-1-1-1-111111100000000000000000000000011-1-1-1-1111111-1-1-1-1-1-1-1-11111
χ28333333333333-3-3-3-3-3-33-111-133-3-3-3-33-1-11111-1-1-1-1-1-1-1-1111111000000000000000000000000-1-11111-1-1-1-1-1-111111111-1-1-1-1
χ293333−3−3i32−3+3i32−3−3i32−3+3i32−3−3i32−3−3i32−3+3i32−3+3i3233−3−3i32−3+3i32−3−3i32−3+3i32033330000000−3−3i32−3+3i32−3−3i32−3+3i32−3−3i32−3+3i32−3−3i32−3+3i3200000000000000000000000000000000000011111111−1−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
χ303333−3−3i32−3+3i32−3−3i32−3+3i32−3−3i32−3−3i32−3+3i32−3+3i3233−3−3i32−3+3i32−3−3i32−3+3i32033330000000−3−3i32−3+3i32−3−3i32−3+3i32−3−3i32−3+3i32−3−3i32−3+3i32000000000000000000000000000000000000-1-1-1-1-1-1-1-11+i321−i321+i321−i321+i321−i321+i321−i321+i321−i321+i321−i321+i321−i321+i321−i32
χ313333−3−3i32−3+3i32−3−3i32−3+3i32−3−3i32−3−3i32−3+3i32−3+3i3233−3−3i32−3+3i32−3−3i32−3+3i320-1-1-1-100000001+i321−i321+i321−i321+i321−i321+i321−i322−1−i3−1+i32−1−i3−1+i32−1−i3−1+i32−1−i3−1+i30000000000000000000000001111-1-1-1-1−1−i32−1+i32−1−i32−1+i32−1−i32−1+i32−1−i32−1+i321+i321−i321+i321−i321+i321−i321+i321−i32
χ323333−3−3i32−3+3i32−3−3i32−3+3i32−3−3i32−3−3i32−3+3i32−3+3i3233−3−3i32−3+3i32−3−3i32−3+3i320-1-1-1-100000001+i321−i321+i321−i321+i321−i321+i321−i322−1−i3−1+i32−1−i3−1+i32−1−i3−1+i32−1−i3−1+i3000000000000000000000000-1-1-1-111111+i321−i321+i321−i321+i321−i321+i321−i32−1−i32−1+i32−1−i32−1+i32−1−i32−1+i32−1−i32−1+i32
χ333333−3−3i32−3+3i32−3−3i32−3+3i32−3−3i32−3−3i32−3+3i32−3+3i32-3-33+3i323−3i323+3i323−3i3203-3-330000000−3−3i32−3+3i323+3i323−3i323+3i323−3i32−3−3i32−3+3i3200000000000000000000000000000000000011-1-111-1-1−1−i32−1+i32−1−i32−1+i321+i321−i321+i321−i32−1−i32−1+i32−1−i32−1+i321+i321−i321+i321−i32
χ343333−3−3i32−3+3i32−3−3i32−3+3i32−3−3i32−3−3i32−3+3i32−3+3i32-3-33+3i323−3i323+3i323−3i3203-3-330000000−3−3i32−3+3i323+3i323−3i323+3i323−3i32−3−3i32−3+3i32000000000000000000000000000000000000-1-111-1-1111+i321−i321+i321−i32−1−i32−1+i32−1−i32−1+i321+i321−i321+i321−i32−1−i32−1+i32−1−i32−1+i32
χ353333−3−3i32−3+3i32−3−3i32−3+3i32−3−3i32−3−3i32−3+3i32−3+3i32-3-33+3i323−3i323+3i323−3i320-111-100000001+i321−i32−1−i32−1+i32−1−i32−1+i321+i321−i322−1−i3−1+i32−1−i3−1+i3-21+i31−i3-21+i31−i300000000000000000000000011-1-1-1-111−1−i32−1+i32−1−i32−1+i321+i321−i321+i321−i321+i321−i321+i321−i32−1−i32−1+i32−1−i32−1+i32
χ363333−3−3i32−3+3i32−3−3i32−3+3i32−3−3i32−3−3i32−3+3i32−3+3i32-3-33+3i323−3i323+3i323−3i320-111-100000001+i321−i32−1−i32−1+i32−1−i32−1+i321+i321−i322−1−i3−1+i32−1−i3−1+i3-21+i31−i3-21+i31−i3000000000000000000000000-1-11111-1-11+i321−i321+i321−i32−1−i32−1+i32−1−i32−1+i32−1−i32−1+i32−1−i32−1+i321+i321−i321+i321−i32
χ373333−3+3i32−3−3i32−3+3i32−3−3i32−3+3i32−3+3i32−3−3i32−3−3i3233−3+3i32−3−3i32−3+3i32−3−3i32033330000000−3+3i32−3−3i32−3+3i32−3−3i32−3+3i32−3−3i32−3+3i32−3−3i3200000000000000000000000000000000000011111111−1+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
χ383333−3+3i32−3−3i32−3+3i32−3−3i32−3+3i32−3+3i32−3−3i32−3−3i3233−3+3i32−3−3i32−3+3i32−3−3i32033330000000−3+3i32−3−3i32−3+3i32−3−3i32−3+3i32−3−3i32−3+3i32−3−3i32000000000000000000000000000000000000-1-1-1-1-1-1-1-11−i321+i321−i321+i321−i321+i321−i321+i321−i321+i321−i321+i321−i321+i321−i321+i32
χ393333−3+3i32−3−3i32−3+3i32−3−3i32−3+3i32−3+3i32−3−3i32−3−3i3233−3+3i32−3−3i32−3+3i32−3−3i320-1-1-1-100000001−i321+i321−i321+i321−i321+i321−i321+i322−1+i3−1−i32−1+i3−1−i32−1+i3−1−i32−1+i3−1−i30000000000000000000000001111-1-1-1-1−1+i32−1−i32−1+i32−1−i32−1+i32−1−i32−1+i32−1−i321−i321+i321−i321+i321−i321+i321−i321+i32
χ403333−3+3i32−3−3i32−3+3i32−3−3i32−3+3i32−3+3i32−3−3i32−3−3i3233−3+3i32−3−3i32−3+3i32−3−3i320-1-1-1-100000001−i321+i321−i321+i321−i321+i321−i321+i322−1+i3−1−i32−1+i3−1−i32−1+i3−1−i32−1+i3−1−i3000000000000000000000000-1-1-1-111111−i321+i321−i321+i321−i321+i321−i321+i32−1+i32−1−i32−1+i32−1−i32−1+i32−1−i32−1+i32−1−i32
χ413333−3+3i32−3−3i32−3+3i32−3−3i32−3+3i32−3+3i32−3−3i32−3−3i32-3-33−3i323+3i323−3i323+3i3203-3-330000000−3+3i32−3−3i323−3i323+3i323−3i323+3i32−3+3i32−3−3i3200000000000000000000000000000000000011-1-111-1-1−1+i32−1−i32−1+i32−1−i321−i321+i321−i321+i32−1+i32−1−i32−1+i32−1−i321−i321+i321−i321+i32
χ423333−3+3i32−3−3i32−3+3i32−3−3i32−3+3i32−3+3i32−3−3i32−3−3i32-3-33−3i323+3i323−3i323+3i3203-3-330000000−3+3i32−3−3i323−3i323+3i323−3i323+3i32−3+3i32−3−3i32000000000000000000000000000000000000-1-111-1-1111−i321+i321−i321+i32−1+i32−1−i32−1+i32−1−i321−i321+i321−i321+i32−1+i32−1−i32−1+i32−1−i32
χ433333−3+3i32−3−3i32−3+3i32−3−3i32−3+3i32−3+3i32−3−3i32−3−3i32-3-33−3i323+3i323−3i323+3i320-111-100000001−i321+i32−1+i32−1−i32−1+i32−1−i321−i321+i322−1+i3−1−i32−1+i3−1−i3-21−i31+i3-21−i31+i300000000000000000000000011-1-1-1-111−1+i32−1−i32−1+i32−1−i321−i321+i321−i321+i321−i321+i321−i321+i32−1+i32−1−i32−1+i32−1−i32
χ443333−3+3i32−3−3i32−3+3i32−3−3i32−3+3i32−3+3i32−3−3i32−3−3i32-3-33−3i323+3i323−3i323+3i320-111-100000001−i321+i32−1+i32−1−i32−1+i32−1−i321−i321+i322−1+i3−1−i32−1+i3−1−i3-21−i31+i3-21−i31+i3000000000000000000000000-1-11111-1-11−i321+i321−i321+i32−1+i32−1−i32−1+i32−1−i32−1+i32−1−i32−1+i32−1−i321−i321+i321−i321+i32
χ4533-3-33333-3-3-3-33-333-3-33-1-111-3-333-3-33-1-1-1-11111-1-1-1111-1-1-1111000000000000000000000000i−ii−i−ii−iiii−i−iii−i−i−i−iii−i−iii
χ4633-3-33333-3-3-3-33-333-3-33-1-111-3-333-3-33-1-1-1-11111-1-1-1111-1-1-1111000000000000000000000000−ii−iii−ii−i−i−iii−i−iiiii−i−iii−i−i
χ4733-3-33333-3-3-3-3-33-3-3333-11-11-3-3-3-3333-1-111-1-111-1-1-1111111-1-1-1000000000000000000000000i−i−ii−iii−iii−i−i−i−iii−i−iiiii−i−i
χ4833-3-33333-3-3-3-3-33-3-3333-11-11-3-3-3-3333-1-111-1-111-1-1-1111111-1-1-1000000000000000000000000−iii−ii−i−ii−i−iiiii−i−iii−i−i−i−iii
χ4933-3-3−3−3i32−3+3i32−3−3i32−3+3i323+3i323+3i323−3i323−3i323-3−3−3i32−3+3i323+3i323−3i32033-3-30000000−3−3i32−3+3i32−3−3i32−3+3i323+3i323−3i323+3i323−3i32000000000000000000000000000000000000i−ii−ii−ii−iζ11ζ7−ζ11−ζ7ζ11ζ7−ζ11−ζ7ζ11ζ7−ζ11−ζ7ζ11ζ7−ζ11−ζ7
χ5033-3-3−3−3i32−3+3i32−3−3i32−3+3i323+3i323+3i323−3i323−3i323-3−3−3i32−3+3i323+3i323−3i32033-3-30000000−3−3i32−3+3i32−3−3i32−3+3i323+3i323−3i323+3i323−3i32000000000000000000000000000000000000−ii−ii−ii−ii−ζ11−ζ7ζ11ζ7−ζ11−ζ7ζ11ζ7−ζ11−ζ7ζ11ζ7−ζ11−ζ7ζ11ζ7
χ5133-3-3−3−3i32−3+3i32−3−3i32−3+3i323+3i323+3i323−3i323−3i323-3−3−3i32−3+3i323+3i323−3i320-1-11100000001+i321−i321+i321−i32−1−i32−1+i32−1−i32−1+i322−1−i3−1+i3-21+i31−i32−1−i3−1+i3-21+i31−i3000000000000000000000000i−ii−i−ii−iiζ11ζ7−ζ11−ζ7ζ11ζ7−ζ11−ζ7−ζ11−ζ7ζ11ζ7−ζ11−ζ7ζ11ζ7
χ5233-3-3−3−3i32−3+3i32−3−3i32−3+3i323+3i323+3i323−3i323−3i323-3−3−3i32−3+3i323+3i323−3i320-1-11100000001+i321−i321+i321−i32−1−i32−1+i32−1−i32−1+i322−1−i3−1+i3-21+i31−i32−1−i3−1+i3-21+i31−i3000000000000000000000000−ii−iii−ii−i−ζ11−ζ7ζ11ζ7−ζ11−ζ7ζ11ζ7ζ11ζ7−ζ11−ζ7ζ11ζ7−ζ11−ζ7
χ5333-3-3−3−3i32−3+3i32−3−3i32−3+3i323+3i323+3i323−3i323−3i32-333+3i323−3i32−3−3i32−3+3i3203-33-30000000−3−3i32−3+3i323+3i323−3i32−3−3i32−3+3i323+3i323−3i32000000000000000000000000000000000000i−i−iii−i−iiζ11ζ7−ζ11−ζ7−ζ11−ζ7ζ11ζ7ζ11ζ7−ζ11−ζ7−ζ11−ζ7ζ11ζ7
χ5433-3-3−3−3i32−3+3i32−3−3i32−3+3i323+3i323+3i323−3i323−3i32-333+3i323−3i32−3−3i32−3+3i3203-33-30000000−3−3i32−3+3i323+3i323−3i32−3−3i32−3+3i323+3i323−3i32000000000000000000000000000000000000−iii−i−iii−i−ζ11−ζ7ζ11ζ7ζ11ζ7−ζ11−ζ7−ζ11−ζ7ζ11ζ7ζ11ζ7−ζ11−ζ7
χ5533-3-3−3−3i32−3+3i32−3−3i32−3+3i323+3i323+3i323−3i323−3i32-333+3i323−3i32−3−3i32−3+3i320-11-1100000001+i321−i32−1−i32−1+i321+i321−i32−1−i32−1+i322−1−i3−1+i3-21+i31−i3-21+i31−i32−1−i3−1+i3000000000000000000000000i−i−ii−iii−iζ11ζ7−ζ11−ζ7−ζ11−ζ7ζ11ζ7−ζ11−ζ7ζ11ζ7ζ11ζ7−ζ11−ζ7
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Here ζ is a primitive root of unity of order 12 (ζ12 = 1); i = ζ3.