Finite Group Databasebeta

← Group #11923236

Character table — Group #11923236

Order 1152.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96C97C98C99C100C101C102C103C104C105
size111122222222223333444444444444446666666688888888888888888888121212121212121212121212121616161616161616161616161818242424242424242424242424242424363636
order12222234444666444433666666661212121244444444336666666666121212121212121224412121212121212121212666612121212121212124461212121212121212121212121212244
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111−1−i32−1+i3211−1−i32−1−i32−1+i32−1+i32−1−i32−1+i32111111111111−1−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−i32−1+i32−1+i32−1+i32−1+i3211111−1−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−i32−1+i32−1+i32−1+i32−1+i3211111−1−i32−1−i32−1−i32−1−i32−1+i32−1+i32−1+i32−1+i32−1−i32−1−i32−1+i32−1+i32111
χ3111111111111111111−1+i32−1−i3211−1+i32−1+i32−1−i32−1−i32−1+i32−1−i32111111111111−1+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+i32−1−i32−1−i32−1−i32−1−i3211111−1+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+i32−1−i32−1−i32−1−i32−1−i3211111−1+i32−1+i32−1+i32−1+i32−1−i32−1−i32−1−i32−1−i32−1+i32−1+i32−1−i32−1−i32111
χ411111111111111-1-1-1-11111111111111111-1-1-1-1-1-11111111111111111111111111-1-1-1-1-1-1-1-1111111111111-1-1111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ511111111111111-1-1-1-1−1−i32−1+i3211−1−i32−1−i32−1+i32−1+i32−1−i32−1+i32111111-1-1-1-1-1-1−1−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−i32−1+i32−1+i32−1+i32−1+i32111111+i321+i321+i321+i321−i321−i321−i321−i32−1−i32−1−i32−1+i32−1+i32−1−i32−1−i32−1−i32−1−i32−1+i32−1+i32−1+i32−1+i32-1-11111+i321+i321+i321+i321−i321−i321−i321−i321+i321+i321−i321−i32-1-1-1
χ611111111111111-1-1-1-1−1+i32−1−i3211−1+i32−1+i32−1−i32−1−i32−1+i32−1−i32111111-1-1-1-1-1-1−1+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+i32−1−i32−1−i32−1−i32−1−i32111111−i321−i321−i321−i321+i321+i321+i321+i32−1+i32−1+i32−1−i32−1−i32−1+i32−1+i32−1+i32−1+i32−1−i32−1−i32−1−i32−1−i32-1-11111−i321−i321−i321−i321+i321+i321+i321+i321−i321−i321+i321+i32-1-1-1
χ71111111-1-1-1-111111111111111111-1-1-1-111-1-111-1-1111111111111-1-1-1-1-1-1-1-1-11-111111111111111-1-1-1-1-1-1-1-111-1-11-1-1-1-1-1-1-1-11111-1-11
χ81111111-1-1-1-11111111−1−i32−1+i3211−1−i32−1−i32−1+i32−1+i32−1−i32−1+i32-1-1-1-111-1-111-1-1−1−i32−1+i32−1−i32−1−i32−1+i32−1+i32−1−i32−1+i32−1−i32−1−i32−1+i32−1+i321+i321+i321+i321+i321−i321−i321−i321−i32-11-111−1−i32−1−i32−1−i32−1−i32−1+i32−1+i32−1+i32−1+i32−1−i32−1−i32−1+i32−1+i321+i321+i321+i321+i321−i321−i321−i321−i3211-1-111+i321+i321+i321+i321−i321−i321−i321−i32−1−i32−1−i32−1+i32−1+i32-1-11
χ91111111-1-1-1-11111111−1+i32−1−i3211−1+i32−1+i32−1−i32−1−i32−1+i32−1−i32-1-1-1-111-1-111-1-1−1+i32−1−i32−1+i32−1+i32−1−i32−1−i32−1+i32−1−i32−1+i32−1+i32−1−i32−1−i321−i321−i321−i321−i321+i321+i321+i321+i32-11-111−1+i32−1+i32−1+i32−1+i32−1−i32−1−i32−1−i32−1−i32−1+i32−1+i32−1−i32−1−i321−i321−i321−i321−i321+i321+i321+i321+i3211-1-111−i321−i321−i321−i321+i321+i321+i321+i32−1+i32−1+i32−1−i32−1−i32-1-11
χ101111111-1-1-1-1111-1-1-1-11111111111-1-1-1-11111-1-111111111111111-1-1-1-1-1-1-1-1-11-111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1111111111-1-1-1-111-1
χ111111111-1-1-1-1111-1-1-1-1−1−i32−1+i3211−1−i32−1−i32−1+i32−1+i32−1−i32−1+i32-1-1-1-11111-1-111−1−i32−1+i32−1−i32−1−i32−1+i32−1+i32−1−i32−1+i32−1−i32−1−i32−1+i32−1+i321+i321+i321+i321+i321−i321−i321−i321−i32-11-1111+i321+i321+i321+i321−i321−i321−i321−i32−1−i32−1−i32−1+i32−1+i321+i321+i321+i321+i321−i321−i321−i321−i32-1-1-1-11−1−i32−1−i32−1−i32−1−i32−1+i32−1+i32−1+i32−1+i321+i321+i321−i321−i3211-1
χ121111111-1-1-1-1111-1-1-1-1−1+i32−1−i3211−1+i32−1+i32−1−i32−1−i32−1+i32−1−i32-1-1-1-11111-1-111−1+i32−1−i32−1+i32−1+i32−1−i32−1−i32−1+i32−1−i32−1+i32−1+i32−1−i32−1−i321−i321−i321−i321−i321+i321+i321+i321+i32-11-1111−i321−i321−i321−i321+i321+i321+i321+i32−1+i32−1+i32−1−i32−1−i321−i321−i321−i321−i321+i321+i321+i321+i32-1-1-1-11−1+i32−1+i32−1+i32−1+i32−1−i32−1−i32−1−i32−1−i321−i321−i321+i321+i3211-1
χ131111-1-1111-1-1111111111-1-1111111-1-11111-1-1-1-11111-1-1-1-111111111-1-111-1-11-1-11111111111-1-1-1-111-1-111-1-1111-1-111-1-111-1-1-1-1-1-1-11-1
χ141111-1-1111-1-11111111−1−i32−1+i32-1-1−1−i32−1−i32−1+i32−1+i32−1−i32−1+i32-1-11111-1-1-1-111−1−i32−1+i321+i321+i321−i321−i32−1−i32−1+i32−1−i32−1−i32−1+i32−1+i32−1−i32−1−i321+i321+i32−1+i32−1+i321−i321−i321-1-111−1−i32−1−i32−1−i32−1−i32−1+i32−1+i32−1+i32−1+i321+i321+i321−i321−i32−1−i32−1−i321+i321+i32−1+i32−1+i321−i321−i32111-1-1−1−i32−1−i321+i321+i32−1+i32−1+i321−i321−i321+i321+i321−i321−i32-11-1
χ151111-1-1111-1-11111111−1+i32−1−i32-1-1−1+i32−1+i32−1−i32−1−i32−1+i32−1−i32-1-11111-1-1-1-111−1+i32−1−i321−i321−i321+i321+i32−1+i32−1−i32−1+i32−1+i32−1−i32−1−i32−1+i32−1+i321−i321−i32−1−i32−1−i321+i321+i321-1-111−1+i32−1+i32−1+i32−1+i32−1−i32−1−i32−1−i32−1−i321−i321−i321+i321+i32−1+i32−1+i321−i321−i32−1−i32−1−i321+i321+i32111-1-1−1+i32−1+i321−i321−i32−1−i32−1−i321+i321+i321−i321−i321+i321+i32-11-1
χ161111-1-1111-1-1111-1-1-1-111-1-1111111-1-111111111-1-111-1-1-1-111111111-1-111-1-11-1-111-1-1-1-1-1-1-1-1-1-1-1-111-1-111-1-1-1-11-1-1-1-111-1-11111111-11
χ171111-1-1111-1-1111-1-1-1-1−1−i32−1+i32-1-1−1−i32−1−i32−1+i32−1+i32−1−i32−1+i32-1-111111111-1-1−1−i32−1+i321+i321+i321−i321−i32−1−i32−1+i32−1−i32−1−i32−1+i32−1+i32−1−i32−1−i321+i321+i32−1+i32−1+i321−i321−i321-1-1111+i321+i321+i321+i321−i321−i321−i321−i321+i321+i321−i321−i32−1−i32−1−i321+i321+i32−1+i32−1+i321−i321−i32-1-11-1-11+i321+i32−1−i32−1−i321−i321−i32−1+i32−1+i32−1−i32−1−i32−1+i32−1+i321-11
χ181111-1-1111-1-1111-1-1-1-1−1+i32−1−i32-1-1−1+i32−1+i32−1−i32−1−i32−1+i32−1−i32-1-111111111-1-1−1+i32−1−i321−i321−i321+i321+i32−1+i32−1−i32−1+i32−1+i32−1−i32−1−i32−1+i32−1+i321−i321−i32−1−i32−1−i321+i321+i321-1-1111−i321−i321−i321−i321+i321+i321+i321+i321−i321−i321+i321+i32−1+i32−1+i321−i321−i32−1−i32−1−i321+i321+i32-1-11-1-11−i321−i32−1+i32−1+i321+i321+i32−1−i32−1−i32−1+i32−1+i32−1−i32−1−i321-11
χ191111-1-11-1-111111111111-1-111111111-1-11111-1-1-1-111-1-1-1-1111111-1-111-1-111-1-111111111111-1-1-1-1-1-111-1-11111-11-1-1-111-1-111-1-1-1-11-1-1
χ201111-1-11-1-1111111111−1−i32−1+i32-1-1−1−i32−1−i32−1+i32−1+i32−1−i32−1+i3211-1-11111-1-1-1-1−1−i32−1+i321+i321+i321−i321−i32−1−i32−1+i32−1−i32−1−i32−1+i32−1+i321+i321+i32−1−i32−1−i321−i321−i32−1+i32−1+i32-1-1111−1−i32−1−i32−1−i32−1−i32−1+i32−1+i32−1+i32−1+i321+i321+i321−i321−i321+i321+i32−1−i32−1−i321−i321−i32−1+i32−1+i3211-11-11+i321+i32−1−i32−1−i321−i321−i32−1+i32−1+i321+i321+i321−i321−i321-1-1
χ211111-1-11-1-1111111111−1+i32−1−i32-1-1−1+i32−1+i32−1−i32−1−i32−1+i32−1−i3211-1-11111-1-1-1-1−1+i32−1−i321−i321−i321+i321+i32−1+i32−1−i32−1+i32−1+i32−1−i32−1−i321−i321−i32−1+i32−1+i321+i321+i32−1−i32−1−i32-1-1111−1+i32−1+i32−1+i32−1+i32−1−i32−1−i32−1−i32−1−i321−i321−i321+i321+i321−i321−i32−1+i32−1+i321+i321+i32−1−i32−1−i3211-11-11−i321−i32−1+i32−1+i321+i321+i32−1−i32−1−i321−i321−i321+i321+i321-1-1
χ221111-1-11-1-111111-1-1-1-111-1-111111111-1-111-1-1111111-1-1-1-1111111-1-111-1-111-1-1111-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-111-1-1-11-111-1-111-1-11111-111
χ231111-1-11-1-111111-1-1-1-1−1−i32−1+i32-1-1−1−i32−1−i32−1+i32−1+i32−1−i32−1+i3211-1-111-1-11111−1−i32−1+i321+i321+i321−i321−i32−1−i32−1+i32−1−i32−1−i32−1+i32−1+i321+i321+i32−1−i32−1−i321−i321−i32−1+i32−1+i32-1-11111+i321+i321+i321+i321−i321−i321−i321−i321+i321+i321−i321−i321+i321+i32−1−i32−1−i321−i321−i32−1+i32−1+i32-1-1-11-1−1−i32−1−i321+i321+i32−1+i32−1+i321−i321−i32−1−i32−1−i32−1+i32−1+i32-111
χ241111-1-11-1-111111-1-1-1-1−1+i32−1−i32-1-1−1+i32−1+i32−1−i32−1−i32−1+i32−1−i3211-1-111-1-11111−1+i32−1−i321−i321−i321+i321+i32−1+i32−1−i32−1+i32−1+i32−1−i32−1−i321−i321−i32−1+i32−1+i321+i321+i32−1−i32−1−i32-1-11111−i321−i321−i321−i321+i321+i321+i321+i321−i321−i321+i321+i321−i321−i32−1+i32−1+i321+i321+i32−1−i32−1−i32-1-1-11-1−1+i32−1+i321−i321−i32−1−i32−1−i321+i321+i32−1+i32−1+i32−1−i32−1−i32-111
χ25222222-12222-1-1-1000022-1-1222222-1-1-1-122000000-1-12222-1-1-1-1-1-122222222222-1-100000000-1-1-1-1-1-1-1-1-1-1-1-100-1-1-1000000000000000
χ26222222-12222-1-1-10000−1−i3−1+i3-1-1−1−i3−1−i3−1+i3−1+i3−1−i3−1+i3-1-1-1-1220000001+i321−i32−1−i3−1−i3−1+i3−1+i31+i321−i321+i321+i321−i321−i32−1−i3−1−i3−1−i3−1−i3−1+i3−1+i3−1+i3−1+i3222-1-1000000001+i321+i321−i321−i321+i321+i321+i321+i321−i321−i321−i321−i3200-1-1-1000000000000000
χ27222222-12222-1-1-10000−1+i3−1−i3-1-1−1+i3−1+i3−1−i3−1−i3−1+i3−1−i3-1-1-1-1220000001−i321+i32−1+i3−1+i3−1−i3−1−i31−i321+i321−i321−i321+i321+i32−1+i3−1+i3−1+i3−1+i3−1−i3−1−i3−1−i3−1−i3222-1-1000000001−i321−i321+i321+i321−i321−i321−i321−i321+i321+i321+i321+i3200-1-1-1000000000000000
χ28222222-1-2-2-2-2-1-1-1000022-1-1222222111122000000-1-12222-1-1-1-1-1-1-2-2-2-2-2-2-2-2-22-2-1-100000000-1-1-1-1111111110011-1000000000000000
χ29222222-1-2-2-2-2-1-1-10000−1−i3−1+i3-1-1−1−i3−1−i3−1+i3−1+i3−1−i3−1+i31111220000001+i321−i32−1−i3−1−i3−1+i3−1+i31+i321−i321+i321+i321−i321−i321+i31+i31+i31+i31−i31−i31−i31−i3-22-2-1-1000000001+i321+i321−i321−i32−1−i32−1−i32−1−i32−1−i32−1+i32−1+i32−1+i32−1+i320011-1000000000000000
χ30222222-1-2-2-2-2-1-1-10000−1+i3−1−i3-1-1−1+i3−1+i3−1−i3−1−i3−1+i3−1−i31111220000001−i321+i32−1+i3−1+i3−1−i3−1−i31−i321+i321−i321−i321+i321+i321−i31−i31−i31−i31+i31+i31+i31+i3-22-2-1-1000000001−i321−i321+i321+i32−1+i32−1+i32−1+i32−1+i32−1−i32−1−i32−1−i32−1−i320011-1000000000000000
χ312222-2-2-122-2-2-1-1-10000221122222211-1-122000000-1-1-2-2-2-2-1-1-1-1-1-122-2-222-2-22-2-2-1-1000000001111-1-111-1-11100-111000000000000000
χ322222-2-2-122-2-2-1-1-10000−1−i3−1+i311−1−i3−1−i3−1+i3−1+i3−1−i3−1+i311-1-1220000001+i321−i321+i31+i31−i31−i31+i321−i321+i321+i321−i321−i32−1−i3−1−i31+i31+i3−1+i3−1+i31−i31−i32-2-2-1-100000000−1−i32−1−i32−1+i32−1+i321+i321+i32−1−i32−1−i321−i321−i32−1+i32−1+i3200-111000000000000000
χ332222-2-2-122-2-2-1-1-10000−1+i3−1−i311−1+i3−1+i3−1−i3−1−i3−1+i3−1−i311-1-1220000001−i321+i321−i31−i31+i31+i31−i321+i321−i321−i321+i321+i32−1+i3−1+i31−i31−i3−1−i3−1−i31+i31+i32-2-2-1-100000000−1+i32−1+i32−1−i32−1−i321−i321−i32−1+i32−1+i321+i321+i32−1−i32−1−i3200-111000000000000000
χ342222-2-2-1-2-222-1-1-100002211222222-1-11122000000-1-1-2-2-2-2-1-1-1-1-1-1-2-222-2-222-2-22-1-100000000111111-1-111-1-1001-11000000000000000
χ352222-2-2-1-2-222-1-1-10000−1−i3−1+i311−1−i3−1−i3−1+i3−1+i3−1−i3−1+i3-1-111220000001+i321−i321+i31+i31−i31−i31+i321−i321+i321+i321−i321−i321+i31+i3−1−i3−1−i31−i31−i3−1+i3−1+i3-2-22-1-100000000−1−i32−1−i32−1+i32−1+i32−1−i32−1−i321+i321+i32−1+i32−1+i321−i321−i32001-11000000000000000
χ362222-2-2-1-2-222-1-1-10000−1+i3−1−i311−1+i3−1+i3−1−i3−1−i3−1+i3−1−i3-1-111220000001−i321+i321−i31−i31+i31+i31−i321+i321−i321−i321+i321+i321−i31−i3−1+i3−1+i31+i31+i3−1−i3−1−i3-2-22-1-100000000−1+i32−1+i32−1−i32−1−i32−1+i32−1+i321−i321−i32−1−i32−1−i321+i321+i32001-11000000000000000
χ3722-2-20020000-2-222i2i−2i−2i22002-22-2-2-200002-2000000220000-2-22-22-2000000000002-22i2i−2i−2i2i2i−2i−2i0000000000002i−2i000000000000000000
χ3822-2-20020000-2-222i2i−2i−2i−1−i3−1+i300−1−i31+i3−1+i31−i31+i31−i300002-2000000−1−i3−1+i300001+i31−i3−1−i31+i3−1+i31−i3000000000002-22ζ112ζ11−2ζ11−2ζ112ζ72ζ7−2ζ7−2ζ70000000000002i−2i000000000000000000
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χ904-4-4400400004-4-44i−4i−4i4i-2-2002-22-222000000000000-2-20000222-22-200000000000002i−2i−2i2i2i−2i−2i2i00000000000000000000000000000000
χ914-4-4400400004-4-44i−4i−4i4i1+i31−i300−1−i31+i3−1+i31−i3−1−i3−1+i30000000000001+i31−i30000−1−i3−1+i3−1−i31+i3−1+i31−i300000000000002ζ11−2ζ11−2ζ112ζ112ζ7−2ζ7−2ζ72ζ700000000000000000000000000000000
χ924-4-4400400004-4-44i−4i−4i4i1−i31+i300−1+i31−i3−1−i31+i3−1+i3−1−i30000000000001−i31+i30000−1+i3−1−i3−1+i31−i3−1−i31+i300000000000002ζ7−2ζ7−2ζ72ζ72ζ11−2ζ11−2ζ112ζ1100000000000000000000000000000000
χ934-4-4400400004-4-4−4i4i4i−4i-2-2002-22-222000000000000-2-20000222-22-20000000000000−2i2i2i−2i−2i2i2i−2i00000000000000000000000000000000
χ944-4-4400400004-4-4−4i4i4i−4i1+i31−i300−1−i31+i3−1+i31−i3−1−i3−1+i30000000000001+i31−i30000−1−i3−1+i3−1−i31+i3−1+i31−i30000000000000−2ζ112ζ112ζ11−2ζ11−2ζ72ζ72ζ7−2ζ700000000000000000000000000000000
χ954-4-4400400004-4-4−4i4i4i−4i1−i31+i300−1+i31−i3−1−i31+i3−1+i3−1−i30000000000001−i31+i30000−1+i3−1−i3−1+i31−i3−1−i31+i30000000000000−2ζ72ζ72ζ7−2ζ7−2ζ112ζ112ζ11−2ζ1100000000000000000000000000000000
χ96666666-36666-3-3-3000000-3-3000000-3-3-3-3-2-200000000000000000000000000-2-2-2110000000000000000000000111000000000000000
χ97666666-3-6-6-6-6-3-3-3000000-3-30000003333-2-2000000000000000000000000002-22110000000000000000000000-1-11000000000000000
χ986666-6-6-366-6-6-3-3-30000003300000033-3-3-2-200000000000000000000000000-2221100000000000000000000001-1-1000000000000000
χ996666-6-6-3-6-666-3-3-300000033000000-3-333-2-20000000000000000000000000022-2110000000000000000000000-11-1000000000000000
χ10066-6-60060000-6-666i6i−6i−6i00000000000000-2200000000000000000000000000000-2200000000000000000000−2i2i000000000000000000
χ10166-6-60060000-6-66−6i−6i6i6i00000000000000-2200000000000000000000000000000-22000000000000000000002i−2i000000000000000000
χ1028-8-8800-40000-4440000-4-4004-44-444000000000000220000-2-2-22-2200000000000000000000000000000000000000000000000000000
χ1038-8-8800-40000-44400002+2i32−2i300−2−2i32+2i3−2+2i32−2i3−2−2i3−2+2i3000000000000−1−i3−1+i300001+i31−i31+i3−1−i31−i3−1+i300000000000000000000000000000000000000000000000000000
χ1048-8-8800-40000-44400002−2i32+2i300−2+2i32−2i3−2−2i32+2i3−2+2i3−2−2i3000000000000−1+i3−1−i300001−i31+i31−i3−1+i31+i3−1−i300000000000000000000000000000000000000000000000000000
χ1051212-12-1200-6000066-6000000000000000000-44000000000000000000000000000002-20000000000000000000000000000000000000000

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