Finite Group Databasebeta

← Group #13161497

Character table — Group #13161497

Order 1728.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96C97C98C99C100C101C102C103C104C105C106C107C108C109C110C111C112C113C114C115C116C117C118C119C120C121C122C123C124C125C126C127C128C129C130C131C132C133C134C135C136C137C138C139C140C141C142C143C144C145C146C147C148C149C150C151C152C153C154C155C156C157C158C159C160C161C162
size111122222222222222222222222222222244444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444181818181818181818181818181818181818181818181818727272727272727272727272
order122233344444466666666612121212121212121212121233333666666666666666121212121212121212121212121212121212121212121212121212121212121212121212121212121212121212121212121212121212121212121212121212121212121212121212888888882424242424242424242424242424242444441212121212121212
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1
χ3111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-11111-1-1-1-1
χ4111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-11111
χ51111111-1-1-1-111111111111-1-1-1-1-1-1-1-11111111111111111111111111111-1-1-1-1-1-1-1-111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-111111111-1-1-1-1-1-1-1-11-11-111-1-111-1-1
χ61111111-1-1-1-111111111111-1-1-1-1-1-1-1-11111111111111111111111111111-1-1-1-1-1-1-1-111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-111111111-1-1-1-1-1-1-1-1-11-11-1-111-1-111
χ71111111-1-1-1-111111111111-1-1-1-1-1-1-1-11111111111111111111111111111-1-1-1-1-1-1-1-111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1111111111-1-1111-1-1-1-111
χ81111111-1-1-1-111111111111-1-1-1-1-1-1-1-11111111111111111111111111111-1-1-1-1-1-1-1-111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-111111111-111-1-1-11111-1-1
χ9222222222-2-2-2-22222222222222-2-2-2-2-2-2-2-222222222222222222222-2-2-2-22222-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-222222222222222222222-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2000000000000000000000000000000000000
χ102222222-2-222-2-2222222222-2-2-2-22222-2-2-2-222222222222222222222-2-2-2-2-2-2-2-22222-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-222222222222222222222000000000000000000000000000000000000
χ11222222-12222222222-122-1-12222222222222-1-1-1-1222-1-1-1-1-1-1-1-1-1-1-1-122-1-122-1-122-1-12222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-12222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-12222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-100000000000000000000000000220000-1-1-1-1
χ12222222-12222222222-122-1-12222222222222-1-1-1-1222-1-1-1-1-1-1-1-1-1-1-1-122-1-122-1-122-1-12222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-12222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-12222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-100000000000000000000000000-2-200001111
χ13222222-122-2-2-2-22222-122-1-12222-2-2-2-2-2-2-2-22-1-1-1-1222-1-1-1-1-1-1-1-1-1-1-1-1-2-21122-1-1-2-211-2-2-2-211111111111111112222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-2-2-2-2111111111111111100000000000000000000000000000000−i3i3−i3i3
χ14222222-122-2-2-2-22222-122-1-12222-2-2-2-2-2-2-2-22-1-1-1-1222-1-1-1-1-1-1-1-1-1-1-1-1-2-21122-1-1-2-211-2-2-2-211111111111111112222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-2-2-2-2111111111111111100000000000000000000000000000000i3−i3i3−i3
χ15222222-1-2-222-2-22222-122-1-1-2-2-2-22222-2-2-2-22-1-1-1-1222-1-1-1-1-1-1-1-1-1-1-1-1-2-211-2-21122-1-1-2-2-2-21111111111111111-2-2-2-211111111111111112222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-100000000000000000000000000000000−i3i3i3−i3
χ16222222-1-2-222-2-22222-122-1-1-2-2-2-22222-2-2-2-22-1-1-1-1222-1-1-1-1-1-1-1-1-1-1-1-1-2-211-2-21122-1-1-2-2-2-21111111111111111-2-2-2-211111111111111112222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-100000000000000000000000000000000i3−i3−i3i3
χ17222222-1-2-2-2-2222222-122-1-1-2-2-2-2-2-2-2-222222-1-1-1-1222-1-1-1-1-1-1-1-1-1-1-1-122-1-1-2-211-2-2112222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-2-2-2-21111111111111111-2-2-2-21111111111111111000000000000000000000000002-20000-1-111
χ18222222-1-2-2-2-2222222-122-1-1-2-2-2-2-2-2-2-222222-1-1-1-1222-1-1-1-1-1-1-1-1-1-1-1-122-1-1-2-211-2-2112222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-2-2-2-21111111111111111-2-2-2-2111111111111111100000000000000000000000000-22000011-1-1
χ1922222-12222222222-12-1-122222222222222-12-1-1-1-1-1-1222-1-1-1-1-1-1-1-1-1-1-122-1-122-1-122-1-1-1-12222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-12222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-12222-1-1-1-1-1-1-1-1-1-1-1-10000000000000000000000002200-1-1-1-10000
χ2022222-12222222222-12-1-122222222222222-12-1-1-1-1-1-1222-1-1-1-1-1-1-1-1-1-1-122-1-122-1-122-1-1-1-12222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-12222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-12222-1-1-1-1-1-1-1-1-1-1-1-1000000000000000000000000-2-20011110000
χ2122222-1222-2-2-2-2222-12-1-1222222-2-2-2-2-2-2-2-2-12-1-1-1-1-1-1222-1-1-1-1-1-1-1-1-111-2-2-1-12211-2-21111-2-2-2-2111111111111-1-1-1-12222-1-1-1-1-1-1-1-1-1-1-1-11111-2-2-2-21111111111110000000000000000000000000000−i3i3−i3i30000
χ2222222-1222-2-2-2-2222-12-1-1222222-2-2-2-2-2-2-2-2-12-1-1-1-1-1-1222-1-1-1-1-1-1-1-1-111-2-2-1-12211-2-21111-2-2-2-2111111111111-1-1-1-12222-1-1-1-1-1-1-1-1-1-1-1-11111-2-2-2-21111111111110000000000000000000000000000i3−i3i3−i30000
χ2322222-12-2-222-2-2222-12-1-122-2-2-2-22222-2-2-2-2-12-1-1-1-1-1-1222-1-1-1-1-1-1-1-1-111-2-211-2-2-1-1221111-2-2-2-21111111111111111-2-2-2-2111111111111-1-1-1-12222-1-1-1-1-1-1-1-1-1-1-1-10000000000000000000000000000−i3i3i3−i30000
χ2422222-12-2-222-2-2222-12-1-122-2-2-2-22222-2-2-2-2-12-1-1-1-1-1-1222-1-1-1-1-1-1-1-1-111-2-211-2-2-1-1221111-2-2-2-21111111111111111-2-2-2-2111111111111-1-1-1-12222-1-1-1-1-1-1-1-1-1-1-1-10000000000000000000000000000i3−i3−i3i30000
χ2522222-12-2-2-2-222222-12-1-122-2-2-2-2-2-2-2-22222-12-1-1-1-1-1-1222-1-1-1-1-1-1-1-1-1-1-12211-2-211-2-2-1-1-1-12222-1-1-1-1-1-1-1-1-1-1-1-11111-2-2-2-21111111111111111-2-2-2-21111111111110000000000000000000000002-200-1-1110000
χ2622222-12-2-2-2-222222-12-1-122-2-2-2-2-2-2-2-22222-12-1-1-1-1-1-1222-1-1-1-1-1-1-1-1-1-1-12211-2-211-2-2-1-1-1-12222-1-1-1-1-1-1-1-1-1-1-1-11111-2-2-2-21111111111111111-2-2-2-2111111111111000000000000000000000000-220011-1-10000
χ272222-122222222-1-1-1222222-1-1-1-1-1-1-1-1-1-1-1-1-1-12-1-1-1-1-1-1-1-1222-1-1-1-1-1-1222222222222-1-1-1-1-1-1-1-12222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-12222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-12222-1-1-1-1-1-1-1-122222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1000000000000
χ282222-122222222-1-1-1222222-1-1-1-1-1-1-1-1-1-1-1-1-1-12-1-1-1-1-1-1-1-1222-1-1-1-1-1-1222222222222-1-1-1-1-1-1-1-12222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-12222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-12222-1-1-1-1-1-1-1-1-2-2-2-2-2-2-2-21111111111111111000000000000
χ292222-12222-2-2-2-2-1-1-1222222-1-1-1-111111111-1-12-1-1-1-1-1-1-1-1222-1-1-1-1-1-1-2-2-2-22222-2-2-2-211111111-2-2-2-211111111-1-1-1-1-1-1-1-12222-1-1-1-1-1-1-1-111111111-2-2-2-211111111000000003333−3−3−3−33333−3−3−3−3000000000000
χ302222-12222-2-2-2-2-1-1-1222222-1-1-1-111111111-1-12-1-1-1-1-1-1-1-1222-1-1-1-1-1-1-2-2-2-22222-2-2-2-211111111-2-2-2-211111111-1-1-1-1-1-1-1-12222-1-1-1-1-1-1-1-111111111-2-2-2-21111111100000000−3−3−3−33333−3−3−3−33333000000000000
χ312222-122-2-222-2-2-1-1-12222221111-1-1-1-11111-1-12-1-1-1-1-1-1-1-1222-1-1-1-1-1-1-2-2-2-2-2-2-2-2222211111111-2-2-2-21111111111111111-2-2-2-211111111-1-1-1-1-1-1-1-12222-1-1-1-1-1-1-1-1000000003333−3−3−3−3−3−3−3−33333000000000000
χ322222-122-2-222-2-2-1-1-12222221111-1-1-1-11111-1-12-1-1-1-1-1-1-1-1222-1-1-1-1-1-1-2-2-2-2-2-2-2-2222211111111-2-2-2-21111111111111111-2-2-2-211111111-1-1-1-1-1-1-1-12222-1-1-1-1-1-1-1-100000000−3−3−3−333333333−3−3−3−3000000000000
χ332222-122-2-2-2-222-1-1-122222211111111-1-1-1-1-1-12-1-1-1-1-1-1-1-1222-1-1-1-1-1-12222-2-2-2-2-2-2-2-2-1-1-1-1-1-1-1-12222-1-1-1-1-1-1-1-111111111-2-2-2-21111111111111111-2-2-2-2111111112222-2-2-2-2-1-1-1-1-1-1-1-111111111000000000000
χ342222-122-2-2-2-222-1-1-122222211111111-1-1-1-1-1-12-1-1-1-1-1-1-1-1222-1-1-1-1-1-12222-2-2-2-2-2-2-2-2-1-1-1-1-1-1-1-12222-1-1-1-1-1-1-1-111111111-2-2-2-21111111111111111-2-2-2-211111111-2-2-2-2222211111111-1-1-1-1-1-1-1-1000000000000
χ3522-2-222200002-22-2-222-2-2-2-20000000022-2-2222222-2-22-2-22-2-222-2-2-2-22-22-20000000022-2-222-2-222-2-22222-2-2-2-20000000000000000000000000000000000000000000022-2-20000000022-2-222-2-2000000000000
χ3622-2-222200002-22-2-222-2-2-2-20000000022-2-2222222-2-22-2-22-2-222-2-2-2-22-22-20000000022-2-222-2-222-2-22222-2-2-2-200000000000000000000000000000000000000000000-2-22200000000-2-222-2-222000000000000
χ3722-2-22220000-222-2-222-2-2-2-200000000-2-222222222-2-22-2-22-2-222-2-2-2-2-22-2200000000-2-222-2-222-2-222-2-2-2-22222000000000000000000000000000000000000000022-2-2000022-2-222-2-200000000000000000000
χ3822-2-22220000-222-2-222-2-2-2-200000000-2-222222222-2-22-2-22-2-222-2-2-2-2-22-2200000000-2-222-2-222-2-222-2-2-2-222220000000000000000000000000000000000000000-2-2220000-2-222-2-22200000000000000000000
χ3922-2-2-12200002-2-11122-2-2-2-233−3−333−3−3-1-111-1-12-1-1-111-1112-2-2-1-111112-22-200000000-1-111-1-11122-2-2-1-1-1-1111133−3−333−3−300003333−3−3−3−333−3−333−3−300003333−3−3−3−3000022-2-233−3−3−3−333-1-111-1-111000000000000
χ4022-2-2-12200002-2-11122-2-2-2-233−3−333−3−3-1-111-1-12-1-1-111-1112-2-2-1-111112-22-200000000-1-111-1-11122-2-2-1-1-1-1111133−3−333−3−300003333−3−3−3−333−3−333−3−300003333−3−3−3−30000-2-222−3−33333−3−311-1-111-1-1000000000000
χ4122-2-2-12200002-2-11122-2-2-2-2−3−333−3−333-1-111-1-12-1-1-111-1112-2-2-1-111112-22-200000000-1-111-1-11122-2-2-1-1-1-11111−3−333−3−3330000−3−3−3−33333−3−333−3−3330000−3−3−3−33333000022-2-2−3−33333−3−3-1-111-1-111000000000000
χ4222-2-2-12200002-2-11122-2-2-2-2−3−333−3−333-1-111-1-12-1-1-111-1112-2-2-1-111112-22-200000000-1-111-1-11122-2-2-1-1-1-11111−3−333−3−3330000−3−3−3−33333−3−333−3−3330000−3−3−3−333330000-2-22233−3−3−3−33311-1-111-1-1000000000000
χ4322-2-2-1220000-22-11122-2-2-2-233−3−3−3−33311-1-1-1-12-1-1-111-1112-2-2-1-11111-22-220000000011-1-111-1-1-2-2221111-1-1-1-133−3−333−3−300003333−3−3−3−3−3−333−3−3330000−3−3−3−3333322-2-20000-1-111-1-111−3−33333−3−3000000000000
χ4422-2-2-1220000-22-11122-2-2-2-233−3−3−3−33311-1-1-1-12-1-1-111-1112-2-2-1-11111-22-220000000011-1-111-1-1-2-2221111-1-1-1-133−3−333−3−300003333−3−3−3−3−3−333−3−3330000−3−3−3−33333-2-222000011-1-111-1-133−3−3−3−333000000000000
χ4522-2-2-1220000-22-11122-2-2-2-2−3−33333−3−311-1-1-1-12-1-1-111-1112-2-2-1-11111-22-220000000011-1-111-1-1-2-2221111-1-1-1-1−3−333−3−3330000−3−3−3−3333333−3−333−3−300003333−3−3−3−322-2-20000-1-111-1-11133−3−3−3−333000000000000
χ4622-2-2-1220000-22-11122-2-2-2-2−3−33333−3−311-1-1-1-12-1-1-111-1112-2-2-1-11111-22-220000000011-1-111-1-1-2-2221111-1-1-1-1−3−333−3−3330000−3−3−3−3333333−3−333−3−300003333−3−3−3−3-2-222000011-1-111-1-1−3−33333−3−3000000000000
χ472-22-2222002i−2i00-22-2-2-22-22-200002i−2i2i−2i000022222-22-2-22-2-22-2-2-222-2-2000000002i−2i2i−2i00000000000000000000000000000000000000002i−2i2i−2i2i−2i2i−2i2i2i−2i−2i2i2i−2i−2i2i2i−2i−2i2−22−2−i2i2−i2i22−22−22−22−2−i2i2−i2i2−i2i2−i2i2000000000000
χ482-22-2222002i−2i00-22-2-2-22-22-200002i−2i2i−2i000022222-22-2-22-2-22-2-2-222-2-2000000002i−2i2i−2i00000000000000000000000000000000000000002i−2i2i−2i2i−2i2i−2i2i2i−2i−2i2i2i−2i−2i2i2i−2i−2i−22−22i2−i2i2−i2−22−22−22−22i2−i2i2−i2i2−i2i2−i2000000000000
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χ1624-4-44-2-2-2−4i4i000022-2222-22-22i−2i−2i2i2i3−2i3−2i32i3−232323−23111−1+3i32−1−3i32-1-11-1-11-1-111−3i321+3i321−3i321+3i32−1+3i32−1−3i3200002i−2i2i−2i00003−3−333−3−333i−3i−3i3i2ζ14+ζ22−ζ14−2ζ22−2ζ14−ζ22ζ14+2ζ22−2ζ14−ζ22ζ14+2ζ222ζ14+ζ22−ζ14−2ζ22−iii−i−iii−i−i−iii−2ζ14+ζ22ζ14−2ζ222ζ14−ζ22−ζ14+2ζ222ζ14−ζ22−ζ14+2ζ22−2ζ14+ζ22ζ14−2ζ22−i3i3i3−i3−i3i3i3−i33-3-33−3+i323+i323−i32−3−i323−i32−3−i32−3+i323+i32000000000000000000000000000000000000

Here ζ is a primitive root of unity of order 24 (ζ24 = 1); i = ζ6.