Finite Group Databasebeta

← Group #11923270

Character table — Group #11923270

Order 1152.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96C97C98C99C100C101C102C103C104C105
size111122222222223333444444444444446666666688888888888888888888121212121212121212121212121616161616161616161616161818242424242424242424242424242424363636
order1222344444466644443366666612121212121222444444336666661212121212121212121212122241212121212121212121212121212121212121212121244666666121212121212121212444
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111−1−i32−1+i32−1−i32−1+i32−1−i32−1+i32−1−i32−1+i3211111111111111−1−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+i321111−1−i32−1−i32−1+i32−1+i321−1−i32−1−i32−1−i32−1−i32−1+i32−1+i32−1+i32−1+i32111
χ3111111111111111111−1+i32−1−i32−1+i32−1−i32−1+i32−1−i32−1+i32−1−i3211111111111111−1+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−i321111−1+i32−1+i32−1−i32−1−i321−1+i32−1+i32−1+i32−1+i32−1−i32−1−i32−1−i32−1−i32111
χ411111111111111-1-1-1-111111111111111-1-111-1-1-1-11111111111111111111111111-1-1-1-1-1-1-1-1111111111111-1-111-1-1-1-11-1-1-1-1-1-1-1-1-1-1-1
χ511111111111111-1-1-1-1−1−i32−1+i32−1−i32−1+i32−1−i32−1+i32−1−i32−1+i32111111-1-111-1-1-1-1−1−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+i32-1-1111+i321+i321−i321−i3211+i321+i321+i321+i321−i321−i321−i321−i32-1-1-1
χ611111111111111-1-1-1-1−1+i32−1−i32−1+i32−1−i32−1+i32−1−i32−1+i32−1−i32111111-1-111-1-1-1-1−1+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−i32-1-1111−i321−i321+i321+i3211−i321−i321−i321−i321+i321+i321+i321+i32-1-1-1
χ71111111-1-1-1-1111111111111111-1-111-1-1-1-11111-1-11111111111-1-111-1-1-1-1-1-11-1-11111111111-1-1-1-111-1-111-1-1111-1-1-1-1-1-111-1-111-1-1-11-1
χ81111111-1-1-1-11111111−1−i32−1+i32−1−i32−1+i32−1−i32−1+i32−1−i32−1+i32-1-111-1-1-1-11111-1-1−1−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−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−i32111-11+i321+i321−i321−i32-1−1−i32−1−i321+i321+i32−1+i32−1+i321−i321−i32-11-1
χ91111111-1-1-1-11111111−1+i32−1−i32−1+i32−1−i32−1+i32−1−i32−1+i32−1−i32-1-111-1-1-1-11111-1-1−1+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+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+i32111-11−i321−i321+i321+i32-1−1+i32−1+i321−i321−i32−1−i32−1−i321+i321+i32-11-1
χ101111111-1-1-1-1111-1-1-1-111111111-1-111-1-11111-1-1111111111111-1-111-1-1-1-1-1-11-1-111-1-1-1-1-1-1-1-1-1-1-1-111-1-111-1-1-1-11-11111-1-1-111-1-1111-11
χ111111111-1-1-1-1111-1-1-1-1−1−i32−1+i32−1−i32−1+i32−1−i32−1+i32−1−i32−1+i32-1-111-1-11111-1-111−1−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−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−i32-1-11-1−1−i32−1−i32−1+i32−1+i32-11+i321+i32−1−i32−1−i321−i321−i32−1+i32−1+i321-11
χ121111111-1-1-1-1111-1-1-1-1−1+i32−1−i32−1+i32−1−i32−1+i32−1−i32−1+i32−1−i32-1-111-1-11111-1-111−1+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+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+i32-1-11-1−1+i32−1+i32−1−i32−1−i32-11−i321−i32−1+i32−1+i321+i321+i32−1−i32−1−i321-11
χ1311111-1-111-1-1111111111111111-1-1-1-111-1-111-1-11111111111-1-111-1-111-1-1-1-1-11-11111111111-1-1-1-1-1-111-1-11111-11-1-1-1-1-1-1-111-1-111-1-11
χ1411111-1-111-1-11111111−1−i32−1+i32−1−i32−1+i32−1−i32−1+i32−1−i32−1+i32-1-1-1-111-1-111-1-111−1−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−i32-11-111−1−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+i3211-111+i321+i321−i321−i32-11+i321+i32−1−i32−1−i321−i321−i32−1+i32−1+i32-1-11
χ1511111-1-111-1-11111111−1+i32−1−i32−1+i32−1−i32−1+i32−1−i32−1+i32−1−i32-1-1-1-111-1-111-1-111−1+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+i32-11-111−1+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−i3211-111−i321−i321+i321+i32-11−i321−i32−1+i32−1+i321+i321+i32−1−i32−1−i32-1-11
χ1611111-1-111-1-1111-1-1-1-111111111-1-1-1-111111111-1-111111111-1-111-1-111-1-1-1-1-11-111-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-111-1-1-111111-111-1-111-1-111-1
χ1711111-1-111-1-1111-1-1-1-1−1−i32−1+i32−1−i32−1+i32−1−i32−1+i32−1−i32−1+i32-1-1-1-111111111-1-1−1−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−i32-11-1111+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−i32−1−i32−1+i32−1+i32-1−1−i32−1−i321+i321+i32−1+i32−1+i321−i321−i3211-1
χ1811111-1-111-1-1111-1-1-1-1−1+i32−1−i32−1+i32−1−i32−1+i32−1−i32−1+i32−1−i32-1-1-1-111111111-1-1−1+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+i32-11-1111−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+i32−1+i32−1−i32−1−i32-1−1+i32−1+i321−i321−i32−1−i32−1−i321+i321+i3211-1
χ1911111-1-1-1-11111111111111111111-1-1-1-11111-1-1-1-111111111-1-1-1-1-1-1-1-11111-1-1111111111111111-1-1-1-1-1-1-1-111-1-111111-1-1-1-1-1-1-1-11-1-1
χ2011111-1-1-1-1111111111−1−i32−1+i32−1−i32−1+i32−1−i32−1+i32−1−i32−1+i3211-1-1-1-11111-1-1-1-1−1−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+i32-1-1111−1−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−i3211-1-1−1−i32−1−i32−1+i32−1+i3211+i321+i321+i321+i321−i321−i321−i321−i321-1-1
χ2111111-1-1-1-1111111111−1+i32−1−i32−1+i32−1−i32−1+i32−1−i32−1+i32−1−i3211-1-1-1-11111-1-1-1-1−1+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−i32-1-1111−1+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+i3211-1-1−1+i32−1+i32−1−i32−1−i3211−i321−i321−i321−i321+i321+i321+i321+i321-1-1
χ2211111-1-1-1-111111-1-1-1-11111111111-1-1-1-1-1-111111111111111-1-1-1-1-1-1-1-11111-1-1111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111-111
χ2311111-1-1-1-111111-1-1-1-1−1−i32−1+i32−1−i32−1+i32−1−i32−1+i32−1−i32−1+i3211-1-1-1-1-1-1111111−1−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+i32-1-11111+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+i321+i321−i321−i321−1−i32−1−i32−1−i32−1−i32−1+i32−1+i32−1+i32−1+i32-111
χ2411111-1-1-1-111111-1-1-1-1−1+i32−1−i32−1+i32−1−i32−1+i32−1−i32−1+i32−1−i3211-1-1-1-1-1-1111111−1+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−i32-1-11111−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−i321−i321+i321+i321−1+i32−1+i32−1+i32−1+i32−1−i32−1−i32−1−i32−1−i32-111
χ252222-1222222-1-1-1000022222222-1-1-1-1-1-100220000-1-1-1-1-1-1-1-1222222222222222-1-100000000-1-1-1-1-1-1-1-1-1-1-1-100-1-10000-100000000000
χ262222-1222222-1-1-10000−1−i3−1+i3−1−i3−1+i3−1−i3−1+i3−1−i3−1+i3-1-1-1-1-1-1002200001+i321−i321+i321−i321+i321−i321+i321−i32−1−i3−1−i3−1−i3−1−i3−1+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−i3200-1-10000-100000000000
χ272222-1222222-1-1-10000−1+i3−1−i3−1+i3−1−i3−1+i3−1−i3−1+i3−1−i3-1-1-1-1-1-1002200001−i321+i321−i321+i321−i321+i321−i321+i32−1+i3−1+i3−1+i3−1+i3−1−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+i3200-1-10000-100000000000
χ282222-122-2-2-2-2-1-1-100002222222211-1-11100220000-1-1-1-1-1-1-1-122-2-222-2-2-2-2-2-22-2-2-1-1000000001111-1-111-1-11100-110000100000000000
χ292222-122-2-2-2-2-1-1-10000−1−i3−1+i3−1−i3−1+i3−1−i3−1+i3−1−i3−1+i311-1-111002200001+i321−i321+i321−i321+i321−i321+i321−i32−1−i3−1−i31+i31+i3−1+i3−1+i31−i31−i31+i31+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+i3200-110000100000000000
χ302222-122-2-2-2-2-1-1-10000−1+i3−1−i3−1+i3−1−i3−1+i3−1−i3−1+i3−1−i311-1-111002200001−i321+i321−i321+i321−i321+i321−i321+i32−1+i3−1+i31−i31−i3−1−i3−1−i31+i31+i31−i31−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−i3200-110000100000000000
χ312222-1-2-222-2-2-1-1-10000222222221111-1-100220000-1-1-1-1-1-1-1-1-2-222-2-222-2-2-2-2-22-2-1-100000000111111-1-111-1-1001-10000100000000000
χ322222-1-2-222-2-2-1-1-10000−1−i3−1+i3−1−i3−1+i3−1−i3−1+i3−1−i3−1+i31111-1-1002200001+i321−i321+i321−i321+i321−i321+i321−i321+i31+i3−1−i3−1−i31−i31−i3−1+i3−1+i31+i31+i31−i31−i3-22-2-1-100000000−1−i32−1−i32−1+i32−1+i32−1−i32−1−i321+i321+i32−1+i32−1+i321−i321−i32001-10000100000000000
χ332222-1-2-222-2-2-1-1-10000−1+i3−1−i3−1+i3−1−i3−1+i3−1−i3−1+i3−1−i31111-1-1002200001−i321+i321−i321+i321−i321+i321−i321+i321−i31−i3−1+i3−1+i31+i31+i3−1−i3−1−i31−i31−i31+i31+i3-22-2-1-100000000−1+i32−1+i32−1−i32−1−i32−1+i32−1+i321−i321−i32−1−i32−1−i321+i321+i32001-10000100000000000
χ342222-1-2-2-2-222-1-1-1000022222222-1-1111100220000-1-1-1-1-1-1-1-1-2-2-2-2-2-2-2-22222-2-22-1-100000000-1-1-1-11111111100110000-100000000000
χ352222-1-2-2-2-222-1-1-10000−1−i3−1+i3−1−i3−1+i3−1−i3−1+i3−1−i3−1+i3-1-11111002200001+i321−i321+i321−i321+i321−i321+i321−i321+i31+i31+i31+i31−i31−i31−i31−i3−1−i3−1−i3−1+i3−1+i3-2-22-1-1000000001+i321+i321−i321−i32−1−i32−1−i32−1−i32−1−i32−1+i32−1+i32−1+i32−1+i3200110000-100000000000
χ362222-1-2-2-2-222-1-1-10000−1+i3−1−i3−1+i3−1−i3−1+i3−1−i3−1+i3−1−i3-1-11111002200001−i321+i321−i321+i321−i321+i321−i321+i321−i31−i31−i31−i31+i31+i31+i31+i3−1+i3−1+i3−1−i3−1−i3-2-22-1-1000000001−i321−i321+i321+i32−1+i32−1+i32−1+i32−1+i32−1−i32−1−i32−1−i32−1−i3200110000-100000000000
χ3722-2-22000000-2-222i2i−2i−2i2222-2-2-2-2000000002-2000022-2-2-2-2220000000000000002-22i2i−2i−2i2i2i−2i−2i0000000000002i−2i000000000000000000
χ3822-2-22000000-2-222i2i−2i−2i−1−i3−1+i3−1−i3−1+i31+i31−i31+i31−i3000000002-20000−1−i3−1+i31+i31−i31+i31−i3−1−i3−1+i30000000000000002-22ζ112ζ11−2ζ11−2ζ112ζ72ζ7−2ζ7−2ζ70000000000002i−2i000000000000000000
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χ914-4-44-2−4i4i4i−4i-44-22200001+i31−i3−1−i3−1+i31+i31−i3−1−i3−1+i32-22i−2i−2i2i00000000−1−i32−1+i321+i321−i32−1−i32−1+i321+i321−i32−2ζ112ζ112ζ11−2ζ11−2ζ72ζ72ζ7−2ζ71+i3−1−i31−i3−1+i30000000000000−1−i321+i32−1+i321−i32ζ11−ζ11−ζ11ζ11ζ7−ζ7−ζ7ζ700000000000000000000
χ924-4-44-2−4i4i4i−4i-44-22200001−i31+i3−1+i3−1−i31−i31+i3−1+i3−1−i32-22i−2i−2i2i00000000−1+i32−1−i321−i321+i32−1+i32−1−i321−i321+i32−2ζ72ζ72ζ7−2ζ7−2ζ112ζ112ζ11−2ζ111−i3−1+i31+i3−1−i30000000000000−1+i321−i32−1−i321+i32ζ7−ζ7−ζ7ζ7ζ11−ζ11−ζ11ζ1100000000000000000000
χ934-4-44-2−4i4i−4i4i4-4-2220000-2-222-2-222-222i−2i2i−2i0000000011-1-111-1-1−2i2i−2i2i−2i2i−2i2i2-22-20000000000000-11-11i−ii−ii−ii−i00000000000000000000
χ944-4-44-2−4i4i−4i4i4-4-22200001+i31−i3−1−i3−1+i31+i31−i3−1−i3−1+i3-222i−2i2i−2i00000000−1−i32−1+i321+i321−i32−1−i32−1+i321+i321−i32−2ζ112ζ11−2ζ112ζ11−2ζ72ζ7−2ζ72ζ7−1−i31+i3−1+i31−i300000000000001+i32−1−i321−i32−1+i32ζ11−ζ11ζ11−ζ11ζ7−ζ7ζ7−ζ700000000000000000000
χ954-4-44-2−4i4i−4i4i4-4-22200001−i31+i3−1+i3−1−i31−i31+i3−1+i3−1−i3-222i−2i2i−2i00000000−1+i32−1−i321−i321+i32−1+i32−1−i321−i321+i32−2ζ72ζ7−2ζ72ζ7−2ζ112ζ11−2ζ112ζ11−1+i31−i3−1−i31+i300000000000001−i32−1+i321+i32−1−i32ζ7−ζ7ζ7−ζ7ζ11−ζ11ζ11−ζ1100000000000000000000
χ966666-3666666-3-3-3000000000000-3-3-3-3-3-300-2-2000000000000000000000000-2-2-2110000000000000000000000110000100000000000
χ976666-366-6-6-6-6-3-3-300000000000033-3-33300-2-2000000000000000000000000-2221100000000000000000000001-10000-100000000000
χ986666-3-6-666-6-6-3-3-30000000000003333-3-300-2-20000000000000000000000002-22110000000000000000000000-110000-100000000000
χ996666-3-6-6-6-666-3-3-3000000000000-3-3333300-2-200000000000000000000000022-2110000000000000000000000-1-10000100000000000
χ10066-6-66000000-6-666i6i−6i−6i0000000000000000-22000000000000000000000000000-2200000000000000000000−2i2i000000000000000000
χ10166-6-66000000-6-66−6i−6i6i6i0000000000000000-22000000000000000000000000000-22000000000000000000002i−2i000000000000000000
χ1028-88-8-40000004-440000-4-44444-4-4000000000000002222-2-2-2-2000000000000000000000000000000000000000000000000000000000
χ1038-88-8-40000004-4400002+2i32−2i3−2−2i3−2+2i3−2−2i3−2+2i32+2i32−2i300000000000000−1−i3−1+i3−1−i3−1+i31+i31−i31+i31−i3000000000000000000000000000000000000000000000000000000000
χ1048-88-8-40000004-4400002−2i32+2i3−2+2i3−2−2i3−2+2i3−2−2i32−2i32+2i300000000000000−1+i3−1−i3−1+i3−1−i31−i31+i31−i31+i3000000000000000000000000000000000000000000000000000000000
χ1051212-12-12-600000066-600000000000000000000-440000000000000000000000000002-20000000000000000000000000000000000000000

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