Finite Group Databasebeta

← Group #88751

Character table — Group #88751

Order 432.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80
size11111166666666999999111111666666669999991111116666666699999911111166666666999999
order123366333366664412121212226666666666664412121212226666666666664412121212226666666666664412121212
χ111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111-1-1-1-1-1-111111111111111-1-1-1-1-1-111111111111111-1-1-1-1-1-111111111111111-1-1-1-1-1-1
χ31-111-1-11111-1-1-1-1i−iii−i−i1-111-1-11111-1-1-1-1i−iii−i−i1-111-1-11111-1-1-1-1i−iii−i−i1-111-1-11111-1-1-1-1i−iii−i−i
χ41-111-1-11111-1-1-1-1−ii−i−iii1-111-1-11111-1-1-1-1−ii−i−iii1-111-1-11111-1-1-1-1−ii−i−iii1-111-1-11111-1-1-1-1−ii−i−iii
χ52222222-1-1-12-1-1-10000002222222-1-1-12-1-1-10000002222222-1-1-12-1-1-10000002222222-1-1-12-1-1-1000000
χ6222222-12-1-1-12-1-1000000222222-12-1-1-12-1-1000000222222-12-1-1-12-1-1000000222222-12-1-1-12-1-1000000
χ7222222-1-12-1-1-12-1000000222222-1-12-1-1-12-1000000222222-1-12-1-1-12-1000000222222-1-12-1-1-12-1000000
χ8222222-1-1-12-1-1-12000000222222-1-1-12-1-1-12000000222222-1-1-12-1-1-12000000222222-1-1-12-1-1-12000000
χ92-222-2-22-1-1-1-21110000002-222-2-22-1-1-1-21110000002-222-2-22-1-1-1-21110000002-222-2-22-1-1-1-2111000000
χ102-222-2-2-12-1-11-2110000002-222-2-2-12-1-11-2110000002-222-2-2-12-1-11-2110000002-222-2-2-12-1-11-211000000
χ112-222-2-2-1-12-111-210000002-222-2-2-1-12-111-210000002-222-2-2-1-12-111-210000002-222-2-2-1-12-111-21000000
χ122-222-2-2-1-1-12111-20000002-222-2-2-1-1-12111-20000002-222-2-2-1-1-12111-20000002-222-2-2-1-1-12111-2000000
χ1333−3−3i32−3+3i32−3−3i32−3+3i320000000011−1−i32−1+i32−1−i32−1+i3233−3−3i32−3+3i32−3−3i32−3+3i320000000011−1−i32−1+i32−1−i32−1+i3233−3−3i32−3+3i32−3−3i32−3+3i320000000011−1−i32−1+i32−1−i32−1+i3233−3−3i32−3+3i32−3−3i32−3+3i320000000011−1−i32−1+i32−1−i32−1+i32
χ1433−3−3i32−3+3i32−3−3i32−3+3i3200000000-1-11+i321−i321+i321−i3233−3−3i32−3+3i32−3−3i32−3+3i3200000000-1-11+i321−i321+i321−i3233−3−3i32−3+3i32−3−3i32−3+3i3200000000-1-11+i321−i321+i321−i3233−3−3i32−3+3i32−3−3i32−3+3i3200000000-1-11+i321−i321+i321−i32
χ1533−3+3i32−3−3i32−3+3i32−3−3i320000000011−1+i32−1−i32−1+i32−1−i3233−3+3i32−3−3i32−3+3i32−3−3i320000000011−1+i32−1−i32−1+i32−1−i3233−3+3i32−3−3i32−3+3i32−3−3i320000000011−1+i32−1−i32−1+i32−1−i3233−3+3i32−3−3i32−3+3i32−3−3i320000000011−1+i32−1−i32−1+i32−1−i32
χ1633−3+3i32−3−3i32−3+3i32−3−3i3200000000-1-11−i321+i321−i321+i3233−3+3i32−3−3i32−3+3i32−3−3i3200000000-1-11−i321+i321−i321+i3233−3+3i32−3−3i32−3+3i32−3−3i3200000000-1-11−i321+i321−i321+i3233−3+3i32−3−3i32−3+3i32−3−3i3200000000-1-11−i321+i321−i321+i32
χ173-3−3−3i32−3+3i323+3i323−3i3200000000i−iζ11ζ7−ζ11−ζ73-3−3−3i32−3+3i323+3i323−3i3200000000i−iζ11ζ7−ζ11−ζ73-3−3−3i32−3+3i323+3i323−3i3200000000i−iζ11ζ7−ζ11−ζ73-3−3−3i32−3+3i323+3i323−3i3200000000i−iζ11ζ7−ζ11−ζ7
χ183-3−3−3i32−3+3i323+3i323−3i3200000000−ii−ζ11−ζ7ζ11ζ73-3−3−3i32−3+3i323+3i323−3i3200000000−ii−ζ11−ζ7ζ11ζ73-3−3−3i32−3+3i323+3i323−3i3200000000−ii−ζ11−ζ7ζ11ζ73-3−3−3i32−3+3i323+3i323−3i3200000000−ii−ζ11−ζ7ζ11ζ7
χ193-3−3+3i32−3−3i323−3i323+3i3200000000i−iζ7ζ11−ζ7−ζ113-3−3+3i32−3−3i323−3i323+3i3200000000i−iζ7ζ11−ζ7−ζ113-3−3+3i32−3−3i323−3i323+3i3200000000i−iζ7ζ11−ζ7−ζ113-3−3+3i32−3−3i323−3i323+3i3200000000i−iζ7ζ11−ζ7−ζ11
χ203-3−3+3i32−3−3i323−3i323+3i3200000000−ii−ζ7−ζ11ζ7ζ113-3−3+3i32−3−3i323−3i323+3i3200000000−ii−ζ7−ζ11ζ7ζ113-3−3+3i32−3−3i323−3i323+3i3200000000−ii−ζ7−ζ11ζ7ζ113-3−3+3i32−3−3i323−3i323+3i3200000000−ii−ζ7−ζ11ζ7ζ11
χ2111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ2211111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111
χ231-111-1-11111-1-1-1-1i−iii−i−i-11-1-111-1-1-1-11111−ii−i−iii1-111-1-11111-1-1-1-1i−iii−i−i-11-1-111-1-1-1-11111−ii−i−iii
χ241-111-1-11111-1-1-1-1−ii−i−iii-11-1-111-1-1-1-11111i−iii−i−i1-111-1-11111-1-1-1-1−ii−i−iii-11-1-111-1-1-1-11111i−iii−i−i
χ252222222-1-1-12-1-1-1000000-2-2-2-2-2-2-2111-21110000002222222-1-1-12-1-1-1000000-2-2-2-2-2-2-2111-2111000000
χ26222222-12-1-1-12-1-1000000-2-2-2-2-2-21-2111-211000000222222-12-1-1-12-1-1000000-2-2-2-2-2-21-2111-211000000
χ27222222-1-12-1-1-12-1000000-2-2-2-2-2-211-2111-21000000222222-1-12-1-1-12-1000000-2-2-2-2-2-211-2111-21000000
χ28222222-1-1-12-1-1-12000000-2-2-2-2-2-2111-2111-2000000222222-1-1-12-1-1-12000000-2-2-2-2-2-2111-2111-2000000
χ292-222-2-22-1-1-1-2111000000-22-2-222-21112-1-1-10000002-222-2-22-1-1-1-2111000000-22-2-222-21112-1-1-1000000
χ302-222-2-2-12-1-11-211000000-22-2-2221-211-12-1-10000002-222-2-2-12-1-11-211000000-22-2-2221-211-12-1-1000000
χ312-222-2-2-1-12-111-21000000-22-2-22211-21-1-12-10000002-222-2-2-1-12-111-21000000-22-2-22211-21-1-12-1000000
χ322-222-2-2-1-1-12111-2000000-22-2-222111-2-1-1-120000002-222-2-2-1-1-12111-2000000-22-2-222111-2-1-1-12000000
χ3333−3−3i32−3+3i32−3−3i32−3+3i320000000011−1−i32−1+i32−1−i32−1+i32-3-33+3i323−3i323+3i323−3i3200000000-1-11+i321−i321+i321−i3233−3−3i32−3+3i32−3−3i32−3+3i320000000011−1−i32−1+i32−1−i32−1+i32-3-33+3i323−3i323+3i323−3i3200000000-1-11+i321−i321+i321−i32
χ3433−3−3i32−3+3i32−3−3i32−3+3i3200000000-1-11+i321−i321+i321−i32-3-33+3i323−3i323+3i323−3i320000000011−1−i32−1+i32−1−i32−1+i3233−3−3i32−3+3i32−3−3i32−3+3i3200000000-1-11+i321−i321+i321−i32-3-33+3i323−3i323+3i323−3i320000000011−1−i32−1+i32−1−i32−1+i32
χ3533−3+3i32−3−3i32−3+3i32−3−3i320000000011−1+i32−1−i32−1+i32−1−i32-3-33−3i323+3i323−3i323+3i3200000000-1-11−i321+i321−i321+i3233−3+3i32−3−3i32−3+3i32−3−3i320000000011−1+i32−1−i32−1+i32−1−i32-3-33−3i323+3i323−3i323+3i3200000000-1-11−i321+i321−i321+i32
χ3633−3+3i32−3−3i32−3+3i32−3−3i3200000000-1-11−i321+i321−i321+i32-3-33−3i323+3i323−3i323+3i320000000011−1+i32−1−i32−1+i32−1−i3233−3+3i32−3−3i32−3+3i32−3−3i3200000000-1-11−i321+i321−i321+i32-3-33−3i323+3i323−3i323+3i320000000011−1+i32−1−i32−1+i32−1−i32
χ373-3−3−3i32−3+3i323+3i323−3i3200000000i−iζ11ζ7−ζ11−ζ7-333+3i323−3i32−3−3i32−3+3i3200000000−ii−ζ11−ζ7ζ11ζ73-3−3−3i32−3+3i323+3i323−3i3200000000i−iζ11ζ7−ζ11−ζ7-333+3i323−3i32−3−3i32−3+3i3200000000−ii−ζ11−ζ7ζ11ζ7
χ383-3−3−3i32−3+3i323+3i323−3i3200000000−ii−ζ11−ζ7ζ11ζ7-333+3i323−3i32−3−3i32−3+3i3200000000i−iζ11ζ7−ζ11−ζ73-3−3−3i32−3+3i323+3i323−3i3200000000−ii−ζ11−ζ7ζ11ζ7-333+3i323−3i32−3−3i32−3+3i3200000000i−iζ11ζ7−ζ11−ζ7
χ393-3−3+3i32−3−3i323−3i323+3i3200000000i−iζ7ζ11−ζ7−ζ11-333−3i323+3i32−3+3i32−3−3i3200000000−ii−ζ7−ζ11ζ7ζ113-3−3+3i32−3−3i323−3i323+3i3200000000i−iζ7ζ11−ζ7−ζ11-333−3i323+3i32−3+3i32−3−3i3200000000−ii−ζ7−ζ11ζ7ζ11
χ403-3−3+3i32−3−3i323−3i323+3i3200000000−ii−ζ7−ζ11ζ7ζ11-333−3i323+3i32−3+3i32−3−3i3200000000i−iζ7ζ11−ζ7−ζ113-3−3+3i32−3−3i323−3i323+3i3200000000−ii−ζ7−ζ11ζ7ζ11-333−3i323+3i32−3+3i32−3−3i3200000000i−iζ7ζ11−ζ7−ζ11
χ411111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ4211111111111111-1-1-1-1-1-111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111
χ431-111-1-11111-1-1-1-1i−iii−i−i1-111-1-11111-1-1-1-1i−iii−i−i-11-1-111-1-1-1-11111−ii−i−iii-11-1-111-1-1-1-11111−ii−i−iii
χ441-111-1-11111-1-1-1-1−ii−i−iii1-111-1-11111-1-1-1-1−ii−i−iii-11-1-111-1-1-1-11111i−iii−i−i-11-1-111-1-1-1-11111i−iii−i−i
χ452222222-1-1-12-1-1-10000002222222-1-1-12-1-1-1000000-2-2-2-2-2-2-2111-2111000000-2-2-2-2-2-2-2111-2111000000
χ46222222-12-1-1-12-1-1000000222222-12-1-1-12-1-1000000-2-2-2-2-2-21-2111-211000000-2-2-2-2-2-21-2111-211000000
χ47222222-1-12-1-1-12-1000000222222-1-12-1-1-12-1000000-2-2-2-2-2-211-2111-21000000-2-2-2-2-2-211-2111-21000000
χ48222222-1-1-12-1-1-12000000222222-1-1-12-1-1-12000000-2-2-2-2-2-2111-2111-2000000-2-2-2-2-2-2111-2111-2000000
χ492-222-2-22-1-1-1-21110000002-222-2-22-1-1-1-2111000000-22-2-222-21112-1-1-1000000-22-2-222-21112-1-1-1000000
χ502-222-2-2-12-1-11-2110000002-222-2-2-12-1-11-211000000-22-2-2221-211-12-1-1000000-22-2-2221-211-12-1-1000000
χ512-222-2-2-1-12-111-210000002-222-2-2-1-12-111-21000000-22-2-22211-21-1-12-1000000-22-2-22211-21-1-12-1000000
χ522-222-2-2-1-1-12111-20000002-222-2-2-1-1-12111-2000000-22-2-222111-2-1-1-12000000-22-2-222111-2-1-1-12000000
χ5333−3−3i32−3+3i32−3−3i32−3+3i320000000011−1−i32−1+i32−1−i32−1+i3233−3−3i32−3+3i32−3−3i32−3+3i320000000011−1−i32−1+i32−1−i32−1+i32-3-33+3i323−3i323+3i323−3i3200000000-1-11+i321−i321+i321−i32-3-33+3i323−3i323+3i323−3i3200000000-1-11+i321−i321+i321−i32
χ5433−3−3i32−3+3i32−3−3i32−3+3i3200000000-1-11+i321−i321+i321−i3233−3−3i32−3+3i32−3−3i32−3+3i3200000000-1-11+i321−i321+i321−i32-3-33+3i323−3i323+3i323−3i320000000011−1−i32−1+i32−1−i32−1+i32-3-33+3i323−3i323+3i323−3i320000000011−1−i32−1+i32−1−i32−1+i32
χ5533−3+3i32−3−3i32−3+3i32−3−3i320000000011−1+i32−1−i32−1+i32−1−i3233−3+3i32−3−3i32−3+3i32−3−3i320000000011−1+i32−1−i32−1+i32−1−i32-3-33−3i323+3i323−3i323+3i3200000000-1-11−i321+i321−i321+i32-3-33−3i323+3i323−3i323+3i3200000000-1-11−i321+i321−i321+i32
χ5633−3+3i32−3−3i32−3+3i32−3−3i3200000000-1-11−i321+i321−i321+i3233−3+3i32−3−3i32−3+3i32−3−3i3200000000-1-11−i321+i321−i321+i32-3-33−3i323+3i323−3i323+3i320000000011−1+i32−1−i32−1+i32−1−i32-3-33−3i323+3i323−3i323+3i320000000011−1+i32−1−i32−1+i32−1−i32
χ573-3−3−3i32−3+3i323+3i323−3i3200000000i−iζ11ζ7−ζ11−ζ73-3−3−3i32−3+3i323+3i323−3i3200000000i−iζ11ζ7−ζ11−ζ7-333+3i323−3i32−3−3i32−3+3i3200000000−ii−ζ11−ζ7ζ11ζ7-333+3i323−3i32−3−3i32−3+3i3200000000−ii−ζ11−ζ7ζ11ζ7
χ583-3−3−3i32−3+3i323+3i323−3i3200000000−ii−ζ11−ζ7ζ11ζ73-3−3−3i32−3+3i323+3i323−3i3200000000−ii−ζ11−ζ7ζ11ζ7-333+3i323−3i32−3−3i32−3+3i3200000000i−iζ11ζ7−ζ11−ζ7-333+3i323−3i32−3−3i32−3+3i3200000000i−iζ11ζ7−ζ11−ζ7
χ593-3−3+3i32−3−3i323−3i323+3i3200000000i−iζ7ζ11−ζ7−ζ113-3−3+3i32−3−3i323−3i323+3i3200000000i−iζ7ζ11−ζ7−ζ11-333−3i323+3i32−3+3i32−3−3i3200000000−ii−ζ7−ζ11ζ7ζ11-333−3i323+3i32−3+3i32−3−3i3200000000−ii−ζ7−ζ11ζ7ζ11
χ603-3−3+3i32−3−3i323−3i323+3i3200000000−ii−ζ7−ζ11ζ7ζ113-3−3+3i32−3−3i323−3i323+3i3200000000−ii−ζ7−ζ11ζ7ζ11-333−3i323+3i32−3+3i32−3−3i3200000000i−iζ7ζ11−ζ7−ζ11-333−3i323+3i32−3+3i32−3−3i3200000000i−iζ7ζ11−ζ7−ζ11
χ6111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111111111111111
χ6211111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111111111111111-1-1-1-1-1-1
χ631-111-1-11111-1-1-1-1i−iii−i−i-11-1-111-1-1-1-11111−ii−i−iii-11-1-111-1-1-1-11111−ii−i−iii1-111-1-11111-1-1-1-1i−iii−i−i
χ641-111-1-11111-1-1-1-1−ii−i−iii-11-1-111-1-1-1-11111i−iii−i−i-11-1-111-1-1-1-11111i−iii−i−i1-111-1-11111-1-1-1-1−ii−i−iii
χ652222222-1-1-12-1-1-1000000-2-2-2-2-2-2-2111-2111000000-2-2-2-2-2-2-2111-21110000002222222-1-1-12-1-1-1000000
χ66222222-12-1-1-12-1-1000000-2-2-2-2-2-21-2111-211000000-2-2-2-2-2-21-2111-211000000222222-12-1-1-12-1-1000000
χ67222222-1-12-1-1-12-1000000-2-2-2-2-2-211-2111-21000000-2-2-2-2-2-211-2111-21000000222222-1-12-1-1-12-1000000
χ68222222-1-1-12-1-1-12000000-2-2-2-2-2-2111-2111-2000000-2-2-2-2-2-2111-2111-2000000222222-1-1-12-1-1-12000000
χ692-222-2-22-1-1-1-2111000000-22-2-222-21112-1-1-1000000-22-2-222-21112-1-1-10000002-222-2-22-1-1-1-2111000000
χ702-222-2-2-12-1-11-211000000-22-2-2221-211-12-1-1000000-22-2-2221-211-12-1-10000002-222-2-2-12-1-11-211000000
χ712-222-2-2-1-12-111-21000000-22-2-22211-21-1-12-1000000-22-2-22211-21-1-12-10000002-222-2-2-1-12-111-21000000
χ722-222-2-2-1-1-12111-2000000-22-2-222111-2-1-1-12000000-22-2-222111-2-1-1-120000002-222-2-2-1-1-12111-2000000
χ7333−3−3i32−3+3i32−3−3i32−3+3i320000000011−1−i32−1+i32−1−i32−1+i32-3-33+3i323−3i323+3i323−3i3200000000-1-11+i321−i321+i321−i32-3-33+3i323−3i323+3i323−3i3200000000-1-11+i321−i321+i321−i3233−3−3i32−3+3i32−3−3i32−3+3i320000000011−1−i32−1+i32−1−i32−1+i32
χ7433−3−3i32−3+3i32−3−3i32−3+3i3200000000-1-11+i321−i321+i321−i32-3-33+3i323−3i323+3i323−3i320000000011−1−i32−1+i32−1−i32−1+i32-3-33+3i323−3i323+3i323−3i320000000011−1−i32−1+i32−1−i32−1+i3233−3−3i32−3+3i32−3−3i32−3+3i3200000000-1-11+i321−i321+i321−i32
χ7533−3+3i32−3−3i32−3+3i32−3−3i320000000011−1+i32−1−i32−1+i32−1−i32-3-33−3i323+3i323−3i323+3i3200000000-1-11−i321+i321−i321+i32-3-33−3i323+3i323−3i323+3i3200000000-1-11−i321+i321−i321+i3233−3+3i32−3−3i32−3+3i32−3−3i320000000011−1+i32−1−i32−1+i32−1−i32
χ7633−3+3i32−3−3i32−3+3i32−3−3i3200000000-1-11−i321+i321−i321+i32-3-33−3i323+3i323−3i323+3i320000000011−1+i32−1−i32−1+i32−1−i32-3-33−3i323+3i323−3i323+3i320000000011−1+i32−1−i32−1+i32−1−i3233−3+3i32−3−3i32−3+3i32−3−3i3200000000-1-11−i321+i321−i321+i32
χ773-3−3−3i32−3+3i323+3i323−3i3200000000i−iζ11ζ7−ζ11−ζ7-333+3i323−3i32−3−3i32−3+3i3200000000−ii−ζ11−ζ7ζ11ζ7-333+3i323−3i32−3−3i32−3+3i3200000000−ii−ζ11−ζ7ζ11ζ73-3−3−3i32−3+3i323+3i323−3i3200000000i−iζ11ζ7−ζ11−ζ7
χ783-3−3−3i32−3+3i323+3i323−3i3200000000−ii−ζ11−ζ7ζ11ζ7-333+3i323−3i32−3−3i32−3+3i3200000000i−iζ11ζ7−ζ11−ζ7-333+3i323−3i32−3−3i32−3+3i3200000000i−iζ11ζ7−ζ11−ζ73-3−3−3i32−3+3i323+3i323−3i3200000000−ii−ζ11−ζ7ζ11ζ7
χ793-3−3+3i32−3−3i323−3i323+3i3200000000i−iζ7ζ11−ζ7−ζ11-333−3i323+3i32−3+3i32−3−3i3200000000−ii−ζ7−ζ11ζ7ζ11-333−3i323+3i32−3+3i32−3−3i3200000000−ii−ζ7−ζ11ζ7ζ113-3−3+3i32−3−3i323−3i323+3i3200000000i−iζ7ζ11−ζ7−ζ11
χ803-3−3+3i32−3−3i323−3i323+3i3200000000−ii−ζ7−ζ11ζ7ζ11-333−3i323+3i32−3+3i32−3−3i3200000000i−iζ7ζ11−ζ7−ζ11-333−3i323+3i32−3+3i32−3−3i3200000000i−iζ7ζ11−ζ7−ζ113-3−3+3i32−3−3i323−3i323+3i3200000000−ii−ζ7−ζ11ζ7ζ11

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