Finite Group Databasebeta

← Group #13147008

Character table — Group #13147008

Order 1728.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96C97C98
size11111111111122222266666666666666666666121212121212121212121212242424242424242424242424242424242424242424242424363636363636363636363636363636363636363636363636
order122233666666441212121234444666121212121212121212121212121212121212121212121212333666666666121212121212121212121212224466668888121212122424242424242424
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
χ3111111111111-1-1-1-1-1-11-1-111111-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-111-1-1111111-1-1-1-1-1-11111-1-1-1-1
χ4111111111111-1-1-1-1-1-11-1-111111-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-1111111-1-1-1-11111
χ51-11-111-1-111-1-1i−iii−i−i1i−i1-1-11-1ii−i−iii−i−i11-1-1111-1-1-1iii−i−i−i111111-1-1-1-1-1-1iiiiii−i−i−i−i−i−i1-1i−i11-1-11-1i−iii−i−i11-1-1ii−i−i
χ61-11-111-1-111-1-1i−iii−i−i1i−i1-1-11-1ii−i−iii−i−i11-1-1111-1-1-1iii−i−i−i111111-1-1-1-1-1-1iiiiii−i−i−i−i−i−i-11−ii-1-111-11−ii−i−iii-1-111−i−iii
χ71-11-111-1-111-1-1−ii−i−iii1−ii1-1-11-1−i−iii−i−iii11-1-1111-1-1-1−i−i−iiii111111-1-1-1-1-1-1−i−i−i−i−i−iiiiiii1-1−ii11-1-11-1−ii−i−iii11-1-1−i−iii
χ81-11-111-1-111-1-1−ii−i−iii1−ii1-1-11-1−i−iii−i−iii11-1-1111-1-1-1−i−i−iiii111111-1-1-1-1-1-1−i−i−i−i−i−iiiiiii-11i−i-1-111-11i−iii−i−i-1-111ii−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
χ10222222222222222222-12222-1-1-12222-1-1-1-12222-1-1-1-1-1-1-1-1-1-1-1-12-1-12-1-12-1-12-1-122-1-1-1-122-1-1-1-1000000000000000000000000
χ11222222222222222222-12222-1-1-12222-1-1-1-12222-1-1-1-1-1-1-1-1-1-1-1-1-12-1-12-1-12-1-12-1-1-122-1-1-1-122-1-1000000000000000000000000
χ12222222222222222222-12222-1-1-12222-1-1-1-12222-1-1-1-1-1-1-1-1-1-1-1-1-1-12-1-12-1-12-1-12-1-1-1-122-1-1-1-122000000000000000000000000
χ13222222222222-2-2-2-2-2-22-2-222222-2-2-2-2-2-2-2-22222222222-2-2-2-2-2-2-1-1-1-1-1-1-1-1-1-1-1-1111111111111000000000000000000000000
χ14222222222222-2-2-2-2-2-2-1-2-222-1-1-1-2-2-2-211112222-1-1-1-1-1-11111112-1-12-1-12-1-12-1-1-2-21111-2-21111000000000000000000000000
χ15222222222222-2-2-2-2-2-2-1-2-222-1-1-1-2-2-2-211112222-1-1-1-1-1-1111111-12-1-12-1-12-1-12-111-2-21111-2-211000000000000000000000000
χ16222222222222-2-2-2-2-2-2-1-2-222-1-1-1-2-2-2-211112222-1-1-1-1-1-1111111-1-12-1-12-1-12-1-121111-2-21111-2-2000000000000000000000000
χ172-22-222-2-222-2-22i−2i2i2i−2i−2i22i−2i2-2-22-22i2i−2i−2i2i2i−2i−2i22-2-2222-2-2-22i2i2i−2i−2i−2i-1-1-1-1-1-1111111−i−i−i−i−i−iiiiiii000000000000000000000000
χ182-22-222-2-222-2-22i−2i2i2i−2i−2i-12i−2i2-21-112i2i−2i−2i−i−iii22-2-2-1-1-1111−i−i−iiii2-1-12-1-1-211-2112i2i−i−i−i−i−2i−2iiiii000000000000000000000000
χ192-22-222-2-222-2-22i−2i2i2i−2i−2i-12i−2i2-21-112i2i−2i−2i−i−iii22-2-2-1-1-1111−i−i−iiii-12-1-12-11-211-21−i−i2i2i−i−iii−2i−2iii000000000000000000000000
χ202-22-222-2-222-2-22i−2i2i2i−2i−2i-12i−2i2-21-112i2i−2i−2i−i−iii22-2-2-1-1-1111−i−i−iiii-1-12-1-1211-211-2−i−i−i−i2i2iiiii−2i−2i000000000000000000000000
χ212-22-222-2-222-2-2−2i2i−2i−2i2i2i2−2i2i2-2-22-2−2i−2i2i2i−2i−2i2i2i22-2-2222-2-2-2−2i−2i−2i2i2i2i-1-1-1-1-1-1111111iiiiii−i−i−i−i−i−i000000000000000000000000
χ222-22-222-2-222-2-2−2i2i−2i−2i2i2i-1−2i2i2-21-11−2i−2i2i2iii−i−i22-2-2-1-1-1111iii−i−i−i2-1-12-1-1-211-211−2i−2iiiii2i2i−i−i−i−i000000000000000000000000
χ232-22-222-2-222-2-2−2i2i−2i−2i2i2i-1−2i2i2-21-11−2i−2i2i2iii−i−i22-2-2-1-1-1111iii−i−i−i-12-1-12-11-211-21ii−2i−2iii−i−i2i2i−i−i000000000000000000000000
χ242-22-222-2-222-2-2−2i2i−2i−2i2i2i-1−2i2i2-21-11−2i−2i2i2iii−i−i22-2-2-1-1-1111iii−i−i−i-1-12-1-1211-211-2iiii−2i−2i−i−i−i−i2i2i000000000000000000000000
χ253333333333333333333-1-1-1-1333-1-1-1-13333-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-100000000000000000000000011111111-1-1-1-11111-1-1-1-1-1-1-1-1
χ263333333333333333333-1-1-1-1333-1-1-1-13333-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1000000000000000000000000-1-1-1-1-1-1-1-11111-1-1-1-111111111
χ27333333333333-3-3-3-3-3-3311-1-13331111-3-3-3-3-1-1-1-1-1-1-1-1-1-111111100000000000000000000000011-1-11111-1-111-1-1-1-1-1-1-1-11111
χ28333333333333-3-3-3-3-3-3311-1-13331111-3-3-3-3-1-1-1-1-1-1-1-1-1-1111111000000000000000000000000-1-111-1-1-1-111-1-111111111-1-1-1-1
χ293333−3−3i32−3+3i32−3−3i32−3+3i32−3−3i32−3+3i32−3−3i32−3+3i3233−3−3i32−3+3i32−3−3i32−3+3i3203333000−3−3i32−3+3i32−3−3i32−3+3i320000−3−3i32−3+3i32−3−3i32−3+3i320000000000000000000000000000000000001111−1−i32−1+i32−1−i32−1+i321111−1−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+3i3203333000−3−3i32−3+3i32−3−3i32−3+3i320000−3−3i32−3+3i32−3−3i32−3+3i32000000000000000000000000000000000000-1-1-1-11+i321−i321+i321−i32-1-1-1-11+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+3i320-1-1-1-10001+i321−i321+i321−i3200001+i321−i321+i321−i322−1−i3−1+i32−1−i3−1+i32−1−i3−1+i32−1−i3−1+i30000000000000000000000001111−1−i32−1+i32−1−i32−1+i32-1-1-1-1−1−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+3i320-1-1-1-10001+i321−i321+i321−i3200001+i321−i321+i321−i322−1−i3−1+i32−1−i3−1+i32−1−i3−1+i32−1−i3−1+i3000000000000000000000000-1-1-1-11+i321−i321+i321−i3211111+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+3i323−3i32011-1-1000−1−i32−1+i32−1−i32−1+i3200001+i321−i321+i321−i322−1−i3−1+i32−1−i3−1+i3-21+i31−i3-21+i31−i300000000000000000000000011-1-1−1−i32−1+i32−1−i32−1+i32-1-1111+i321−i321+i321−i321+i321−i321+i321−i32−1−i32−1+i32−1−i32−1+i32
χ343333−3−3i32−3+3i32−3−3i32−3+3i32−3−3i32−3+3i32−3−3i32−3+3i32-3-33+3i323−3i323+3i323−3i32011-1-1000−1−i32−1+i32−1−i32−1+i3200001+i321−i321+i321−i322−1−i3−1+i32−1−i3−1+i3-21+i31−i3-21+i31−i3000000000000000000000000-1-1111+i321−i321+i321−i3211-1-1−1−i32−1+i32−1−i32−1+i32−1−i32−1+i32−1−i32−1+i321+i321−i321+i321−i32
χ353333−3−3i32−3+3i32−3−3i32−3+3i32−3−3i32−3+3i32−3−3i32−3+3i32-3-33+3i323−3i323+3i323−3i320-3-3330003+3i323−3i323+3i323−3i320000−3−3i32−3+3i32−3−3i32−3+3i3200000000000000000000000000000000000011-1-1−1−i32−1+i32−1−i32−1+i3211-1-11+i321−i321+i321−i32−1−i32−1+i32−1−i32−1+i321+i321−i321+i321−i32
χ363333−3−3i32−3+3i32−3−3i32−3+3i32−3−3i32−3+3i32−3−3i32−3+3i32-3-33+3i323−3i323+3i323−3i320-3-3330003+3i323−3i323+3i323−3i320000−3−3i32−3+3i32−3−3i32−3+3i32000000000000000000000000000000000000-1-1111+i321−i321+i321−i32-1-111−1−i32−1+i32−1−i32−1+i321+i321−i321+i321−i32−1−i32−1+i32−1−i32−1+i32
χ373333−3+3i32−3−3i32−3+3i32−3−3i32−3+3i32−3−3i32−3+3i32−3−3i3233−3+3i32−3−3i32−3+3i32−3−3i3203333000−3+3i32−3−3i32−3+3i32−3−3i320000−3+3i32−3−3i32−3+3i32−3−3i320000000000000000000000000000000000001111−1+i32−1−i32−1+i32−1−i321111−1+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+3i32−3−3i3203333000−3+3i32−3−3i32−3+3i32−3−3i320000−3+3i32−3−3i32−3+3i32−3−3i32000000000000000000000000000000000000-1-1-1-11−i321+i321−i321+i32-1-1-1-11−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+3i32−3−3i320-1-1-1-10001−i321+i321−i321+i3200001−i321+i321−i321+i322−1+i3−1−i32−1+i3−1−i32−1+i3−1−i32−1+i3−1−i30000000000000000000000001111−1+i32−1−i32−1+i32−1−i32-1-1-1-1−1+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+3i32−3−3i320-1-1-1-10001−i321+i321−i321+i3200001−i321+i321−i321+i322−1+i3−1−i32−1+i3−1−i32−1+i3−1−i32−1+i3−1−i3000000000000000000000000-1-1-1-11−i321+i321−i321+i3211111−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+3i32011-1-1000−1+i32−1−i32−1+i32−1−i3200001−i321+i321−i321+i322−1+i3−1−i32−1+i3−1−i3-21−i31+i3-21−i31+i300000000000000000000000011-1-1−1+i32−1−i32−1+i32−1−i32-1-1111−i321+i321−i321+i321−i321+i321−i321+i32−1+i32−1−i32−1+i32−1−i32
χ423333−3+3i32−3−3i32−3+3i32−3−3i32−3+3i32−3−3i32−3+3i32−3−3i32-3-33−3i323+3i323−3i323+3i32011-1-1000−1+i32−1−i32−1+i32−1−i3200001−i321+i321−i321+i322−1+i3−1−i32−1+i3−1−i3-21−i31+i3-21−i31+i3000000000000000000000000-1-1111−i321+i321−i321+i3211-1-1−1+i32−1−i32−1+i32−1−i32−1+i32−1−i32−1+i32−1−i321−i321+i321−i321+i32
χ433333−3+3i32−3−3i32−3+3i32−3−3i32−3+3i32−3−3i32−3+3i32−3−3i32-3-33−3i323+3i323−3i323+3i320-3-3330003−3i323+3i323−3i323+3i320000−3+3i32−3−3i32−3+3i32−3−3i3200000000000000000000000000000000000011-1-1−1+i32−1−i32−1+i32−1−i3211-1-11−i321+i321−i321+i32−1+i32−1−i32−1+i32−1−i321−i321+i321−i321+i32
χ443333−3+3i32−3−3i32−3+3i32−3−3i32−3+3i32−3−3i32−3+3i32−3−3i32-3-33−3i323+3i323−3i323+3i320-3-3330003−3i323+3i323−3i323+3i320000−3+3i32−3−3i32−3+3i32−3−3i32000000000000000000000000000000000000-1-1111−i321+i321−i321+i32-1-111−1+i32−1−i32−1+i32−1−i321−i321+i321−i321+i32−1+i32−1−i32−1+i32−1−i32
χ453-33-333-3-333-3-33i−3i3i3i−3i−3i3−ii-11-33-3−i−iii3i3i−3i−3i-1-111-1-1-1111−i−i−iiii0000000000000000000000001-1i−i11-1-1-11−iiii−i−i-1-111−i−iii
χ463-33-333-3-333-3-33i−3i3i3i−3i−3i3−ii-11-33-3−i−iii3i3i−3i−3i-1-111-1-1-1111−i−i−iiii000000000000000000000000-11−ii-1-1111-1i−i−i−iii11-1-1ii−i−i
χ473-33-333-3-333-3-3−3i3i−3i−3i3i3i3i−i-11-33-3ii−i−i−3i−3i3i3i-1-111-1-1-1111iii−i−i−i0000000000000000000000001-1−ii11-1-1-11i−i−i−iii-1-111ii−i−i
χ483-33-333-3-333-3-3−3i3i−3i−3i3i3i3i−i-11-33-3ii−i−i−3i−3i3i3i-1-111-1-1-1111iii−i−i−i000000000000000000000000-11i−i-1-1111-1−iiii−i−i11-1-1−i−iii
χ493-33-3−3−3i32−3+3i323+3i323−3i32−3−3i32−3+3i323+3i323−3i323i−3i3ζ113ζ7−3ζ11−3ζ703i−3i3-30003ζ113ζ7−3ζ11−3ζ70000−3−3i32−3+3i323+3i323−3i320000000000000000000000000000000000001-1i−i−1−i32−1+i321+i321−i321-1i−iζ11ζ7−ζ11−ζ7−1−i32−1+i321+i321−i32ζ11ζ7−ζ11−ζ7
χ503-33-3−3−3i32−3+3i323+3i323−3i32−3−3i32−3+3i323+3i323−3i323i−3i3ζ113ζ7−3ζ11−3ζ703i−3i3-30003ζ113ζ7−3ζ11−3ζ70000−3−3i32−3+3i323+3i323−3i32000000000000000000000000000000000000-11−ii1+i321−i32−1−i32−1+i32-11−ii−ζ11−ζ7ζ11ζ71+i321−i32−1−i32−1+i32−ζ11−ζ7ζ11ζ7
χ513-33-3−3−3i32−3+3i323+3i323−3i32−3−3i32−3+3i323+3i323−3i323i−3i3ζ113ζ7−3ζ11−3ζ70−ii-11000−ζ11−ζ7ζ11ζ700001+i321−i32−1−i32−1+i322−1−i3−1+i3-21+i31−i32i2ζ112ζ7−2i−2ζ11−2ζ70000000000000000000000001-1i−i−1−i32−1+i321+i321−i32-11−iiζ11ζ7−ζ11−ζ71+i321−i32−1−i32−1+i32−ζ11−ζ7ζ11ζ7
χ523-33-3−3−3i32−3+3i323+3i323−3i32−3−3i32−3+3i323+3i323−3i323i−3i3ζ113ζ7−3ζ11−3ζ70−ii-11000−ζ11−ζ7ζ11ζ700001+i321−i32−1−i32−1+i322−1−i3−1+i3-21+i31−i32i2ζ112ζ7−2i−2ζ11−2ζ7000000000000000000000000-11−ii1+i321−i32−1−i32−1+i321-1i−i−ζ11−ζ7ζ11ζ7−1−i32−1+i321+i321−i32ζ11ζ7−ζ11−ζ7
χ533-33-3−3−3i32−3+3i323+3i323−3i32−3−3i32−3+3i323+3i323−3i32−3i3i−3ζ11−3ζ73ζ113ζ70i−i-11000ζ11ζ7−ζ11−ζ700001+i321−i32−1−i32−1+i322−1−i3−1+i3-21+i31−i3−2i−2ζ11−2ζ72i2ζ112ζ70000000000000000000000001-1−ii−1−i32−1+i321+i321−i32-11i−i−ζ11−ζ7ζ11ζ71+i321−i32−1−i32−1+i32ζ11ζ7−ζ11−ζ7
χ543-33-3−3−3i32−3+3i323+3i323−3i32−3−3i32−3+3i323+3i323−3i32−3i3i−3ζ11−3ζ73ζ113ζ70i−i-11000ζ11ζ7−ζ11−ζ700001+i321−i32−1−i32−1+i322−1−i3−1+i3-21+i31−i3−2i−2ζ11−2ζ72i2ζ112ζ7000000000000000000000000-11i−i1+i321−i32−1−i32−1+i321-1−iiζ11ζ7−ζ11−ζ7−1−i32−1+i321+i321−i32−ζ11−ζ7ζ11ζ7
χ553-33-3−3−3i32−3+3i323+3i323−3i32−3−3i32−3+3i323+3i323−3i32−3i3i−3ζ11−3ζ73ζ113ζ70−3i3i3-3000−3ζ11−3ζ73ζ113ζ70000−3−3i32−3+3i323+3i323−3i320000000000000000000000000000000000001-1−ii−1−i32−1+i321+i321−i321-1−ii−ζ11−ζ7ζ11ζ7−1−i32−1+i321+i321−i32−ζ11−ζ7ζ11ζ7
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Here ζ is a primitive root of unity of order 12 (ζ12 = 1); i = ζ3.