Finite Group Databasebeta

← Group #11923271

Character table — Group #11923271

Order 1152.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96C97C98C99C100C101C102C103C104C105
size111122222222223333444444444444446666666688888888888888888888121212121212121212121212121616161616161616161616161818242424242424242424242424242424363636
order122234444446664444336666661212121212122222444433666666121212121212121212121212224121212121212121212121212121212121212121212122266666666661212121212444
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−i32−1+i32−1+i32−1+i32−1+i321−1−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+i32−1−i32−1−i32−1−i32−1−i321−1+i32−1+i32−1−i32−1−i32111
χ411111111111111-1-1-1-111111111111111-1-1-1-1-1-1111111111111111111111111111-1-1-1-1-1-1-1-1111111111111-1-111-1-1-1-1-1-1-1-11-1-1-1-1-1-1-1
χ511111111111111-1-1-1-1−1−i32−1+i32−1−i32−1+i32−1−i32−1+i32−1−i32−1+i32111111-1-1-1-1-1-111−1−i32−1+i32−1−i32−1+i32−1−i32−1+i32−1−i32−1+i32−1−i32−1−i32−1+i32−1+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+i321−i321−i321−i321−i3211+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−i32111111-1-1-1-1-1-111−1+i32−1−i32−1+i32−1−i32−1+i32−1−i32−1+i32−1−i32−1+i32−1+i32−1−i32−1−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−i321+i321+i321+i321+i3211−i321−i321+i321+i32-1-1-1
χ71111111-1-1-1-111111111111111111-1-1-1-1-1-1-1-11111111111111111-1-1-1-1-1-1-1-1-1-1111111111111111-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-1111111-1-1
χ81111111-1-1-1-11111111−1−i32−1+i32−1−i32−1+i32−1−i32−1+i32−1−i32−1+i3211-1-1-1-1-1-1-1-11111−1−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−i32-1-1111−1−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−i3211-1-11+i321+i321+i321+i321−i321−i321−i321−i321−1−i32−1−i32−1+i32−1+i321-1-1
χ91111111-1-1-1-11111111−1+i32−1−i32−1+i32−1−i32−1+i32−1−i32−1+i32−1−i3211-1-1-1-1-1-1-1-11111−1+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+i32-1-1111−1+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+i3211-1-11−i321−i321−i321−i321+i321+i321+i321+i321−1+i32−1+i32−1−i32−1−i321-1-1
χ101111111-1-1-1-1111-1-1-1-11111111111-1-1-1-11111-1-111111111111111-1-1-1-1-1-1-1-1-1-1111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1111111111-1-1-1-1-111
χ111111111-1-1-1-1111-1-1-1-1−1−i32−1+i32−1−i32−1+i32−1−i32−1+i32−1−i32−1+i3211-1-1-1-11111-1-111−1−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−i32-1-11111+i321+i321+i321+i321−i321−i321−i321−i32−1−i32−1−i32−1+i32−1+i321+i321+i321+i321+i321−i321−i321−i321−i32-1-1-1-1−1−i32−1−i32−1−i32−1−i32−1+i32−1+i32−1+i32−1+i3211+i321+i321−i321−i32-111
χ121111111-1-1-1-1111-1-1-1-1−1+i32−1−i32−1+i32−1−i32−1+i32−1−i32−1+i32−1−i3211-1-1-1-11111-1-111−1+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+i32-1-11111−i321−i321−i321−i321+i321+i321+i321+i32−1+i32−1+i32−1−i32−1−i321−i321−i321−i321−i321+i321+i321+i321+i32-1-1-1-1−1+i32−1+i32−1+i32−1+i32−1−i32−1−i32−1−i32−1−i3211−i321−i321+i321+i32-111
χ1311111-1-111-1-1111111111111111-1-111-1-111-1-1-1-11111111111-1-1-1-111-1-111-1-11-1-11111111111-1-1-1-111-1-111-1-1111-111-1-111-1-1-1-1-1-1-1-11-1
χ1411111-1-111-1-11111111−1−i32−1+i32−1−i32−1+i32−1−i32−1+i32−1−i32−1+i32-1-111-1-111-1-1-1-111−1−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−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−i32−1−i321+i321+i32−1+i32−1+i321−i321−i32-11+i321+i321−i321−i32-11-1
χ1511111-1-111-1-11111111−1+i32−1−i32−1+i32−1−i32−1+i32−1−i32−1+i32−1−i32-1-111-1-111-1-1-1-111−1+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+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+i32−1+i321−i321−i32−1−i32−1−i321+i321+i32-11−i321−i321+i321+i32-11-1
χ1611111-1-111-1-1111-1-1-1-111111111-1-111-1-1-1-111111111111111-1-1-1-111-1-111-1-11-1-111-1-1-1-1-1-1-1-1-1-1-1-111-1-111-1-1-1-11-1-1-111-1-111-111111-11
χ1711111-1-111-1-1111-1-1-1-1−1−i32−1+i32−1−i32−1+i32−1−i32−1+i32−1−i32−1+i32-1-111-1-1-1-1111111−1−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−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−i32-1-11-11+i321+i32−1−i32−1−i321−i321−i32−1+i32−1+i32-1−1−i32−1−i32−1+i32−1+i321-11
χ1811111-1-111-1-1111-1-1-1-1−1+i32−1−i32−1+i32−1−i32−1+i32−1−i32−1+i32−1−i32-1-111-1-1-1-1111111−1+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+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+i32-1-11-11−i321−i32−1+i32−1+i321+i321+i32−1−i32−1−i32-1−1+i32−1+i32−1−i32−1−i321-11
χ1911111-1-1-1-111111111111111111-1-1-1-111-1-111-1-11111111111-1-1-1-1-1-111-1-111-11-11111111111-1-1-1-1-1-111-1-11111-11-1-111-1-111-1-1-1-1-1-1-11
χ2011111-1-1-1-1111111111−1−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+i321−i321−i321+i321+i32−1−i32−1−i321−i321−i32−1+i32−1+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+i32−1−i32−1−i321−i321−i32−1+i32−1+i32-11+i321+i321−i321−i32-1-11
χ2111111-1-1-1-1111111111−1+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−i321+i321+i321−i321−i32−1+i32−1+i321+i321+i32−1−i32−1−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−i32−1+i32−1+i321+i321+i32−1−i32−1−i32-11−i321−i321+i321+i32-1-11
χ2211111-1-1-1-111111-1-1-1-111111111-1-1-1-11111-1-1111111111111-1-1-1-1-1-111-1-111-11-111-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-111-1-1-1111-1-111-1-1-1111111-1
χ2311111-1-1-1-111111-1-1-1-1−1−i32−1+i32−1−i32−1+i32−1−i32−1+i32−1−i32−1+i32-1-1-1-11111-1-11111−1−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+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−i321+i321+i32−1+i32−1+i321−i321−i32-1−1−i32−1−i32−1+i32−1+i3211-1
χ2411111-1-1-1-111111-1-1-1-1−1+i32−1−i32−1+i32−1−i32−1+i32−1−i32−1+i32−1−i32-1-1-1-11111-1-11111−1+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−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+i321−i321−i32−1−i32−1−i321+i321+i32-1−1+i32−1+i32−1−i32−1−i3211-1
χ252222-1222222-1-1-1000022222222-1-1-1-1-1-100000022-1-1-1-1-1-1-1-1222222222222222-1-100000000-1-1-1-1-1-1-1-1-1-1-1-100-1-100000000-10000000
χ262222-1222222-1-1-10000−1−i3−1+i3−1−i3−1+i3−1−i3−1+i3−1−i3−1+i3-1-1-1-1-1-1000000221+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−i3200-1-100000000-10000000
χ272222-1222222-1-1-10000−1+i3−1−i3−1+i3−1−i3−1+i3−1−i3−1+i3−1−i3-1-1-1-1-1-1000000221−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+i3200-1-100000000-10000000
χ282222-122-2-2-2-2-1-1-1000022222222-1-1111100000022-1-1-1-1-1-1-1-12222-2-2-2-2-2-2-2-2-2-22-1-100000000-1-1-1-111111111001100000000-10000000
χ292222-122-2-2-2-2-1-1-10000−1−i3−1+i3−1−i3−1+i3−1−i3−1+i3−1−i3−1+i3-1-11111000000221+i321−i321+i321−i321+i321−i321+i321−i32−1−i3−1−i3−1+i3−1+i31+i31+i31+i31+i31−i31−i31−i31−i3-2-22-1-1000000001+i321+i321−i321−i32−1−i32−1−i32−1−i32−1−i32−1+i32−1+i32−1+i32−1+i32001100000000-10000000
χ302222-122-2-2-2-2-1-1-10000−1+i3−1−i3−1+i3−1−i3−1+i3−1−i3−1+i3−1−i3-1-11111000000221−i321+i321−i321+i321−i321+i321−i321+i32−1+i3−1+i3−1−i3−1−i31−i31−i31−i31−i31+i31+i31+i31+i3-2-22-1-1000000001−i321−i321+i321+i32−1+i32−1+i32−1+i32−1+i32−1−i32−1−i32−1−i32−1−i32001100000000-10000000
χ312222-1-2-222-2-2-1-1-100002222222211-1-11100000022-1-1-1-1-1-1-1-1-2-2-2-222-2-222-2-22-2-2-1-1000000001111-1-111-1-11100-110000000010000000
χ322222-1-2-222-2-2-1-1-10000−1−i3−1+i3−1−i3−1+i3−1−i3−1+i3−1−i3−1+i311-1-111000000221+i321−i321+i321−i321+i321−i321+i321−i321+i31+i31−i31−i3−1−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+i3200-110000000010000000
χ332222-1-2-222-2-2-1-1-10000−1+i3−1−i3−1+i3−1−i3−1+i3−1−i3−1+i3−1−i311-1-111000000221−i321+i321−i321+i321−i321+i321−i321+i321−i31−i31+i31+i3−1+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−i3200-110000000010000000
χ342222-1-2-2-2-222-1-1-10000222222221111-1-100000022-1-1-1-1-1-1-1-1-2-2-2-2-2-222-2-222-22-2-1-100000000111111-1-111-1-1001-10000000010000000
χ352222-1-2-2-2-222-1-1-10000−1−i3−1+i3−1−i3−1+i3−1−i3−1+i3−1−i3−1+i31111-1-1000000221+i321−i321+i321−i321+i321−i321+i321−i321+i31+i31−i31−i31+i31+i3−1−i3−1−i31−i31−i3−1+i3−1+i3-22-2-1-100000000−1−i32−1−i32−1+i32−1+i32−1−i32−1−i321+i321+i32−1+i32−1+i321−i321−i32001-10000000010000000
χ362222-1-2-2-2-222-1-1-10000−1+i3−1−i3−1+i3−1−i3−1+i3−1−i3−1+i3−1−i31111-1-1000000221−i321+i321−i321+i321−i321+i321−i321+i321−i31−i31+i31+i31−i31−i3−1+i3−1+i31+i31+i3−1−i3−1−i3-22-2-1-100000000−1+i32−1+i32−1−i32−1−i32−1+i32−1+i321−i321−i32−1−i32−1−i321+i321+i32001-10000000010000000
χ372-22-222-22i−2i2i−2i2-2-22i2i−2i−2i-1-1-1-111112-22i−2i2i−2i2-22-22i−2i00-1-111-1-1111-11-1i−ii−ii−ii−i00000ii−i−iii−i−i1-11-1i−ii−ii−ii−i00001-11-11-11-10i−ii−i000
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χ954-4-44-200000022-20000−2+2i3−2−2i32−2i32+2i32−2i32+2i3−2+2i3−2−2i30000000000004-41−i31+i3−1+i3−1−i3−1+i3−1−i31−i31+i3000000000000000-220000000000000000000000000000000000000000
χ966666-3666666-3-3-3000000000000-3-3-3-3-3-3000000-2-200000000000000000000-2-2-2110000000000000000000000110000000010000000
χ976666-366-6-6-6-6-3-3-3000000000000-3-33333000000-2-20000000000000000000022-2110000000000000000000000-1-10000000010000000
χ986666-3-6-666-6-6-3-3-300000000000033-3-333000000-2-200000000000000000000-2221100000000000000000000001-100000000-10000000
χ996666-3-6-6-6-666-3-3-30000000000003333-3-3000000-2-2000000000000000000002-22110000000000000000000000-1100000000-10000000
χ1006-6-666000000-6-666-66-600000000000000000000-2200000000000000000000000-2200000000000000000000-22000000000000000000
χ1016-6-666000000-6-66-66-6600000000000000000000-2200000000000000000000000-22000000000000000000002-2000000000000000000
χ10288-8-8-40000004-440000-4-444-4-444000000000000002222-2-2-2-2000000000000000000000000000000000000000000000000000000000
χ10388-8-8-40000004-4400002+2i32−2i3−2−2i3−2+2i32+2i32−2i3−2−2i3−2+2i300000000000000−1−i3−1+i3−1−i3−1+i31+i31−i31+i31−i3000000000000000000000000000000000000000000000000000000000
χ10488-8-8-40000004-4400002−2i32+2i3−2+2i3−2−2i32−2i32+2i3−2+2i3−2−2i300000000000000−1+i3−1−i3−1+i3−1−i31−i31+i31−i31+i3000000000000000000000000000000000000000000000000000000000
χ10512-12-1212-600000066-6000000000000000000000000-44000000000000000000000002-20000000000000000000000000000000000000000

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