Finite Group Databasebeta

← Group #11923255

Character table — Group #11923255

Order 1152.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96C97C98C99C100C101C102C103C104C105
size111122222222223333444444444444446666666688888888888888888888121212121212121212121212121616161616161616161616161818242424242424242424242424242424363636
order12222222344666444433666666666612124444444433666666666666661212121244412121212121212121212666666661212121244121212121212121212121212121212244
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111−1−i32−1+i321111−1−i32−1+i32−1−i32−1+i32−1−i32−1+i321111111111−1−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−i321111−1+i32−1−i32−1+i32−1−i32−1+i32−1−i321111111111−1+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+i321111−1−i32−1+i32−1−i32−1+i32−1−i32−1+i321111-1-1-1-1-1-1−1−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−i321111−1+i32−1−i32−1+i32−1−i32−1+i32−1−i321111-1-1-1-1-1-1−1+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
χ7111111-1-11-1-111111111111-1-1111111-1-11111-1-1-1-11111-1-111-1-1111111-1-1-1-11-1-1111111111111-1-111-1-1-1-1-1-111-11-1-1-1-1-111-1-111-1-1-11-1
χ8111111-1-11-1-11111111−1−i32−1+i3211-1-1−1−i32−1+i32−1−i32−1+i32−1−i32−1+i32-1-11111-1-1-1-1−1−i32−1+i32−1−i32−1−i321+i321+i32−1+i32−1+i321−i321−i32−1−i32−1−i32−1+i32−1+i32−1−i32−1+i321+i321+i321−i321−i321-1-111−1−i32−1−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+i321+i321−i321−i3211-11-11+i321+i321−i321−i32−1−i32−1−i321+i321+i32−1+i32−1+i321−i321−i32-11-1
χ9111111-1-11-1-11111111−1+i32−1−i3211-1-1−1+i32−1−i32−1+i32−1−i32−1+i32−1−i32-1-11111-1-1-1-1−1+i32−1−i32−1+i32−1+i321−i321−i32−1−i32−1−i321+i321+i32−1+i32−1+i32−1−i32−1−i32−1+i32−1−i321−i321−i321+i321+i321-1-111−1+i32−1+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−i321−i321+i321+i3211-11-11−i321−i321+i321+i32−1+i32−1+i321−i321−i32−1−i32−1−i321+i321+i32-11-1
χ10111111-1-11-1-1111-1-1-1-11111-1-1111111-1-111-1-111111111-1-111-1-1111111-1-1-1-11-1-111-1-1-1-1-1-1-1-111-1-111-1-1-1-1-1-1-1-1-11-11111-1-111-1-1111-11
χ11111111-1-11-1-1111-1-1-1-1−1−i32−1+i3211-1-1−1−i32−1+i32−1−i32−1+i32−1−i32−1+i32-1-111-1-11111−1−i32−1+i32−1−i32−1−i321+i321+i32−1+i32−1+i321−i321−i32−1−i32−1−i32−1+i32−1+i32−1−i32−1+i321+i321+i321−i321−i321-1-1111+i321+i321+i321+i321−i321−i321−i321−i32−1−i32−1−i321+i321+i32−1+i32−1+i321−i321−i321+i321+i321−i321−i32-1-1-11-1−1−i32−1−i32−1+i32−1+i321+i321+i32−1−i32−1−i321−i321−i32−1+i32−1+i321-11
χ12111111-1-11-1-1111-1-1-1-1−1+i32−1−i3211-1-1−1+i32−1−i32−1+i32−1−i32−1+i32−1−i32-1-111-1-11111−1+i32−1−i32−1+i32−1+i321−i321−i32−1−i32−1−i321+i321+i32−1+i32−1+i32−1−i32−1−i32−1+i32−1−i321−i321−i321+i321+i321-1-1111−i321−i321−i321−i321+i321+i321+i321+i32−1+i32−1+i321−i321−i32−1−i32−1−i321+i321+i321−i321−i321+i321+i32-1-1-11-1−1+i32−1+i32−1−i32−1−i321−i321−i32−1+i32−1+i321+i321+i32−1−i32−1−i321-11
χ131111-1-1111-1-1111111111-1-111111111-1-111-1-111-1-111-1-111-1-111111111-1-1-1-1-11-11111111111-1-111-1-111-1-1-1-111-1-11-1-1-1-1-1-111-1-111-1-11
χ141111-1-1111-1-11111111−1−i32−1+i32-1-111−1−i32−1+i32−1−i32−1+i32−1−i32−1+i32-1-111-1-111-1-1−1−i32−1+i321+i321+i32−1−i32−1−i321−i321−i32−1+i32−1+i32−1−i32−1−i32−1+i32−1+i32−1−i32−1+i321+i321+i321−i321−i32-11-111−1−i32−1−i32−1−i32−1−i32−1+i32−1+i32−1+i32−1+i321+i321+i32−1−i32−1−i321−i321−i32−1+i32−1+i321+i321+i321−i321−i3211-1-111+i321+i321−i321−i321+i321+i32−1−i32−1−i321−i321−i32−1+i32−1+i32-1-11
χ151111-1-1111-1-11111111−1+i32−1−i32-1-111−1+i32−1−i32−1+i32−1−i32−1+i32−1−i32-1-111-1-111-1-1−1+i32−1−i321−i321−i32−1+i32−1+i321+i321+i32−1−i32−1−i32−1+i32−1+i32−1−i32−1−i32−1+i32−1−i321−i321−i321+i321+i32-11-111−1+i32−1+i32−1+i32−1+i32−1−i32−1−i32−1−i32−1−i321−i321−i32−1+i32−1+i321+i321+i32−1−i32−1−i321−i321−i321+i321+i3211-1-111−i321−i321+i321+i321−i321−i32−1+i32−1+i321+i321+i32−1−i32−1−i32-1-11
χ161111-1-1111-1-1111-1-1-1-111-1-111111111-1-11111-1-11111-1-111-1-111111111-1-1-1-1-11-111-1-1-1-1-1-1-1-1-1-111-1-111-1-1-1-1-1-1-1-11111111-1-111-1-111-1
χ171111-1-1111-1-1111-1-1-1-1−1−i32−1+i32-1-111−1−i32−1+i32−1−i32−1+i32−1−i32−1+i32-1-11111-1-111−1−i32−1+i321+i321+i32−1−i32−1−i321−i321−i32−1+i32−1+i32−1−i32−1−i32−1+i32−1+i32−1−i32−1+i321+i321+i321−i321−i32-11-1111+i321+i321+i321+i321−i321−i321−i321−i321+i321+i32−1−i32−1−i321−i321−i32−1+i32−1+i321+i321+i321−i321−i32-1-1-1-11−1−i32−1−i32−1+i32−1+i32−1−i32−1−i321+i321+i32−1+i32−1+i321−i321−i3211-1
χ181111-1-1111-1-1111-1-1-1-1−1+i32−1−i32-1-111−1+i32−1−i32−1+i32−1−i32−1+i32−1−i32-1-11111-1-111−1+i32−1−i321−i321−i32−1+i32−1+i321+i321+i32−1−i32−1−i32−1+i32−1+i32−1−i32−1−i32−1+i32−1−i321−i321−i321+i321+i32-11-1111−i321−i321−i321−i321+i321+i321+i321+i321−i321−i32−1+i32−1+i321+i321+i32−1−i32−1−i321−i321−i321+i321+i32-1-1-1-11−1+i32−1+i32−1−i32−1−i32−1+i32−1+i321−i321−i32−1−i32−1−i321+i321+i3211-1
χ191111-1-1-1-1111111111111-1-1-1-11111111111-1-1-1-11111-1-1-1-1-1-1-1-11111111111-1-111111111111-1-1-1-1-1-1-1-11111111-1-11111-1-1-1-1-1-1-1-11-1-1
χ201111-1-1-1-11111111111−1−i32−1+i32-1-1-1-1−1−i32−1+i32−1−i32−1+i32−1−i32−1+i321111-1-1-1-111−1−i32−1+i321+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+i32-1-1111−1−i32−1−i32−1−i32−1−i32−1+i32−1+i32−1+i32−1+i321+i321+i321+i321+i321−i321−i321−i321−i32−1−i32−1−i32−1+i32−1+i32111-1-1−1−i32−1−i32−1+i32−1+i321+i321+i321+i321+i321−i321−i321−i321−i321-1-1
χ211111-1-1-1-11111111111−1+i32−1−i32-1-1-1-1−1+i32−1−i32−1+i32−1−i32−1+i32−1−i321111-1-1-1-111−1+i32−1−i321−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−i32-1-1111−1+i32−1+i32−1+i32−1+i32−1−i32−1−i32−1−i32−1−i321−i321−i321−i321−i321+i321+i321+i321+i32−1+i32−1+i32−1−i32−1−i32111-1-1−1+i32−1+i32−1−i32−1−i321−i321−i321−i321−i321+i321+i321+i321+i321-1-1
χ221111-1-1-1-1111111-1-1-1-111-1-1-1-111111111111111-1-111-1-1-1-1-1-1-1-11111111111-1-1111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-11-1-1-1-1-1-111111111-111
χ231111-1-1-1-1111111-1-1-1-1−1−i32−1+i32-1-1-1-1−1−i32−1+i32−1−i32−1+i32−1−i32−1+i3211111111-1-1−1−i32−1+i321+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+i32-1-11111+i321+i321+i321+i321−i321−i321−i321−i321+i321+i321+i321+i321−i321−i321−i321−i32−1−i32−1−i32−1+i32−1+i32-1-11-1-11+i321+i321−i321−i32−1−i32−1−i32−1−i32−1−i32−1+i32−1+i32−1+i32−1+i32-111
χ241111-1-1-1-1111111-1-1-1-1−1+i32−1−i32-1-1-1-1−1+i32−1−i32−1+i32−1−i32−1+i32−1−i3211111111-1-1−1+i32−1−i321−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−i32-1-11111−i321−i321−i321−i321+i321+i321+i321+i321−i321−i321−i321−i321+i321+i321+i321+i32−1+i32−1+i32−1−i32−1−i32-1-11-1-11−i321−i321+i321+i32−1+i32−1+i32−1+i32−1+i32−1−i32−1−i32−1−i32−1−i32-111
χ2522222222-122-1-1-1000022-1-1-1-1222222-1-122000000-1-122222222-1-1-1-1-1-12222222-1-100000000-1-1-1-1-1-1-1-1-1-1-1-100-1-1-1000000000000000
χ2622222222-122-1-1-10000−1−i3−1+i3-1-1-1-1−1−i3−1+i3−1−i3−1+i3−1−i3−1+i3-1-1220000001+i321−i32−1−i3−1−i3−1−i3−1−i3−1+i3−1+i3−1+i3−1+i31+i321+i321−i321−i321+i321−i32−1−i3−1−i3−1+i3−1+i3222-1-1000000001+i321+i321+i321+i321−i321−i321−i321−i321+i321+i321−i321−i3200-1-1-1000000000000000
χ2722222222-122-1-1-10000−1+i3−1−i3-1-1-1-1−1+i3−1−i3−1+i3−1−i3−1+i3−1−i3-1-1220000001−i321+i32−1+i3−1+i3−1+i3−1+i3−1−i3−1−i3−1−i3−1−i31−i321−i321+i321+i321−i321+i32−1+i3−1+i3−1−i3−1−i3222-1-1000000001−i321−i321−i321−i321+i321+i321+i321+i321−i321−i321+i321+i3200-1-1-1000000000000000
χ28222222-2-2-1-2-2-1-1-1000022-1-1112222221122000000-1-122-2-222-2-2-1-1-1-1-1-1-2-2-2-22-2-2-1-100000000-1-111-1-1111111001-11000000000000000
χ29222222-2-2-1-2-2-1-1-10000−1−i3−1+i3-1-111−1−i3−1+i3−1−i3−1+i3−1−i3−1+i311220000001+i321−i32−1−i3−1−i31+i31+i3−1+i3−1+i31−i31−i31+i321+i321−i321−i321+i321−i321+i31+i31−i31−i32-2-2-1-1000000001+i321+i32−1−i32−1−i321−i321−i32−1+i32−1+i32−1−i32−1−i32−1+i32−1+i32001-11000000000000000
χ30222222-2-2-1-2-2-1-1-10000−1+i3−1−i3-1-111−1+i3−1−i3−1+i3−1−i3−1+i3−1−i311220000001−i321+i32−1+i3−1+i31−i31−i3−1−i3−1−i31+i31+i31−i321−i321+i321+i321−i321+i321−i31−i31+i31+i32-2-2-1-1000000001−i321−i32−1+i32−1+i321+i321+i32−1−i32−1−i32−1+i32−1+i32−1−i32−1−i32001-11000000000000000
χ312222-2-222-1-2-2-1-1-100002211-1-12222221122000000-1-1-2-222-2-222-1-1-1-1-1-1-2-2-2-2-22-2-1-10000000011-1-111-1-111110011-1000000000000000
χ322222-2-222-1-2-2-1-1-10000−1−i3−1+i311-1-1−1−i3−1+i3−1−i3−1+i3−1−i3−1+i311220000001+i321−i321+i31+i3−1−i3−1−i31−i31−i3−1+i3−1+i31+i321+i321−i321−i321+i321−i321+i31+i31−i31−i3-22-2-1-100000000−1−i32−1−i321+i321+i32−1+i32−1+i321−i321−i32−1−i32−1−i32−1+i32−1+i320011-1000000000000000
χ332222-2-222-1-2-2-1-1-10000−1+i3−1−i311-1-1−1+i3−1−i3−1+i3−1−i3−1+i3−1−i311220000001−i321+i321−i31−i3−1+i3−1+i31+i31+i3−1−i3−1−i31−i321−i321+i321+i321−i321+i321−i31−i31+i31+i3-22-2-1-100000000−1+i32−1+i321−i321−i32−1−i32−1−i321+i321+i32−1+i32−1+i32−1−i32−1−i320011-1000000000000000
χ342222-2-2-2-2-122-1-1-10000221111222222-1-122000000-1-1-2-2-2-2-2-2-2-2-1-1-1-1-1-12222-2-22-1-10000000011111111-1-1-1-100-111000000000000000
χ352222-2-2-2-2-122-1-1-10000−1−i3−1+i31111−1−i3−1+i3−1−i3−1+i3−1−i3−1+i3-1-1220000001+i321−i321+i31+i31+i31+i31−i31−i31−i31−i31+i321+i321−i321−i321+i321−i32−1−i3−1−i3−1+i3−1+i3-2-22-1-100000000−1−i32−1−i32−1−i32−1−i32−1+i32−1+i32−1+i32−1+i321+i321+i321−i321−i3200-111000000000000000
χ362222-2-2-2-2-122-1-1-10000−1+i3−1−i31111−1+i3−1−i3−1+i3−1−i3−1+i3−1−i3-1-1220000001−i321+i321−i31−i31−i31−i31+i31+i31+i31+i31−i321−i321+i321+i321−i321+i32−1+i3−1+i3−1−i3−1−i3-2-22-1-100000000−1+i32−1+i32−1+i32−1+i32−1−i32−1−i32−1−i32−1−i321−i321−i321+i321+i3200-111000000000000000
χ3722-2-20000200-2-222i2i−2i−2i220000-2-222-2-2002-200000022000000002-22-2-2-200000002-22i2i−2i−2i2i2i−2i−2i0000000000002i−2i000000000000000000
χ3822-2-20000200-2-222i2i−2i−2i−1−i3−1+i300001+i31−i3−1−i3−1+i31+i31−i3002-2000000−1−i3−1+i300000000−1−i31+i3−1+i31−i31+i31−i300000002-22ζ112ζ11−2ζ11−2ζ112ζ72ζ7−2ζ7−2ζ70000000000002i−2i000000000000000000
χ3922-2-20000200-2-222i2i−2i−2i−1+i3−1−i300001−i31+i3−1+i3−1−i31−i31+i3002-2000000−1+i3−1−i300000000−1+i31−i3−1−i31+i31−i31+i300000002-22ζ72ζ7−2ζ7−2ζ72ζ112ζ11−2ζ11−2ζ110000000000002i−2i000000000000000000
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χ97666666-6-6-3-6-6-3-3-3000000-3-33300000033-2-200000000000000000000000000-222110000000000000000000000-11-1000000000000000
χ986666-6-666-3-6-6-3-3-300000033-3-300000033-2-2000000000000000000000000002-22110000000000000000000000-1-11000000000000000
χ996666-6-6-6-6-366-3-3-30000003333000000-3-3-2-20000000000000000000000000022-21100000000000000000000001-1-1000000000000000
χ10066-6-60000600-6-666i6i−6i−6i00000000000000-2200000000000000000000000000000-2200000000000000000000−2i2i000000000000000000
χ10166-6-60000600-6-66−6i−6i6i6i00000000000000-2200000000000000000000000000000-22000000000000000000002i−2i000000000000000000
χ1028-88-80000-4004-440000-4-400004444-4-400000000002200000000-22-22-2-20000000000000000000000000000000000000000000000000
χ1038-88-80000-4004-4400002+2i32−2i30000−2−2i3−2+2i3−2−2i3−2+2i32+2i32−2i30000000000−1−i3−1+i3000000001+i3−1−i31−i3−1+i31+i31−i30000000000000000000000000000000000000000000000000
χ1048-88-80000-4004-4400002−2i32+2i30000−2+2i3−2−2i3−2+2i3−2−2i32−2i32+2i30000000000−1+i3−1−i3000000001−i3−1+i31+i3−1−i31−i31+i30000000000000000000000000000000000000000000000000
χ1051212-12-120000-60066-6000000000000000000-44000000000000000000000000000002-20000000000000000000000000000000000000000

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