Finite Group Databasebeta

← Group #13164430

Character table — Group #13164430

Order 1728.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96C97C98
size11112222222222333333336666666666666666121212121212121212121212242424242424242424242424242424242424242424242424363636363636363636363636363636363636363636363636
order1244234666121212123366121212122244666666121212121212666666121212121212333666666666121212121212121212121212224466668888121212122424242424242424
χ111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ311111111111111−1−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−i32−1+i32−1+i32−1−i32−1+i3211−1−i32−1−i32−1+i32−1+i3211−1−i32−1−i32−1+i32−1+i321−1−i32−1+i3211−1−i32−1−i32−1+i32−1+i321−1−i32−1+i321111−1−i32−1−i32−1−i32−1−i32−1+i32−1+i32−1+i32−1+i321111−1−i32−1−i32−1+i32−1+i321111−1−i32−1−i32−1+i32−1+i32−1−i32−1−i32−1−i32−1−i32−1+i32−1+i32−1+i32−1+i32
χ411111111111111−1−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−i32−1+i32−1+i32−1−i32−1+i3211−1−i32−1−i32−1+i32−1+i3211−1−i32−1−i32−1+i32−1+i321−1−i32−1+i3211−1−i32−1−i32−1+i32−1+i321−1−i32−1+i321111−1−i32−1−i32−1−i32−1−i32−1+i32−1+i32−1+i32−1+i32-1-1-1-11+i321+i321−i321−i32-1-1-1-11+i321+i321−i321−i321+i321+i321+i321+i321−i321−i321−i321−i32
χ511111111111111−1+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+i32−1−i32−1−i32−1+i32−1−i3211−1+i32−1+i32−1−i32−1−i3211−1+i32−1+i32−1−i32−1−i321−1+i32−1−i3211−1+i32−1+i32−1−i32−1−i321−1+i32−1−i321111−1+i32−1+i32−1+i32−1+i32−1−i32−1−i32−1−i32−1−i321111−1+i32−1+i32−1−i32−1−i321111−1+i32−1+i32−1−i32−1−i32−1+i32−1+i32−1+i32−1+i32−1−i32−1−i32−1−i32−1−i32
χ611111111111111−1+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+i32−1−i32−1−i32−1+i32−1−i3211−1+i32−1+i32−1−i32−1−i3211−1+i32−1+i32−1−i32−1−i321−1+i32−1−i3211−1+i32−1+i32−1−i32−1−i321−1+i32−1−i321111−1+i32−1+i32−1+i32−1+i32−1−i32−1−i32−1−i32−1−i32-1-1-1-11−i321−i321+i321+i32-1-1-1-11−i321−i321+i321+i321−i321−i321−i321−i321+i321+i321+i321+i32
χ71111-11-1-1-1111-1-1111111111-1-111-1-11-1-1-1-1-1-1111-11-11-11-11-11-1111-1-1-1-1-1-111111-1-111-1-111-1-11-11-11-11-111-1-11-11-111-1-111-1-1
χ81111-11-1-1-1111-1-1111111111-1-111-1-11-1-1-1-1-1-1111-11-11-11-11-11-1111-1-1-1-1-1-111111-1-111-1-111-1-1-11-11-11-11-1-111-11-11-1-111-1-111
χ91111-11-1-1-1111-1-1−1−i32−1+i32−1−i32−1+i32−1−i32−1−i32−1+i32−1+i321-1-11−1−i321+i321+i32−1+i321−i321−i321+i321+i321−i321−i32−1−i32−1+i321-1−1−i321+i32−1+i321−i321-1−1−i321+i32−1+i321−i321−1−i32−1+i32-1-11+i321+i321−i321−i321−1−i32−1+i3211-1-1−1−i32−1−i321+i321+i32−1+i32−1+i321−i321−i321-11-1−1−i321+i32−1+i321−i3211-1-1−1−i321+i32−1+i321−i32−1−i32−1−i321+i321+i32−1+i32−1+i321−i321−i32
χ101111-11-1-1-1111-1-1−1−i32−1+i32−1−i32−1+i32−1−i32−1−i32−1+i32−1+i321-1-11−1−i321+i321+i32−1+i321−i321−i321+i321+i321−i321−i32−1−i32−1+i321-1−1−i321+i32−1+i321−i321-1−1−i321+i32−1+i321−i321−1−i32−1+i32-1-11+i321+i321−i321−i321−1−i32−1+i3211-1-1−1−i32−1−i321+i321+i32−1+i32−1+i321−i321−i32-11-111+i32−1−i321−i32−1+i32-1-1111+i32−1−i321−i32−1+i321+i321+i32−1−i32−1−i321−i321−i32−1+i32−1+i32
χ111111-11-1-1-1111-1-1−1+i32−1−i32−1+i32−1−i32−1+i32−1+i32−1−i32−1−i321-1-11−1+i321−i321−i32−1−i321+i321+i321−i321−i321+i321+i32−1+i32−1−i321-1−1+i321−i32−1−i321+i321-1−1+i321−i32−1−i321+i321−1+i32−1−i32-1-11−i321−i321+i321+i321−1+i32−1−i3211-1-1−1+i32−1+i321−i321−i32−1−i32−1−i321+i321+i321-11-1−1+i321−i32−1−i321+i3211-1-1−1+i321−i32−1−i321+i32−1+i32−1+i321−i321−i32−1−i32−1−i321+i321+i32
χ121111-11-1-1-1111-1-1−1+i32−1−i32−1+i32−1−i32−1+i32−1+i32−1−i32−1−i321-1-11−1+i321−i321−i32−1−i321+i321+i321−i321−i321+i321+i32−1+i32−1−i321-1−1+i321−i32−1−i321+i321-1−1+i321−i32−1−i321+i321−1+i32−1−i32-1-11−i321−i321+i321+i321−1+i32−1−i3211-1-1−1+i32−1+i321−i321−i32−1−i32−1−i321+i321+i32-11-111−i32−1+i321+i32−1−i32-1-1111−i32−1+i321+i32−1−i321−i321−i32−1+i32−1+i321+i321+i32−1−i32−1−i32
χ1311-1-111-1111-1-1-1-11111-1-1-1-1-1-111-11-1-11-11-11-111-1-1-1-1-1-1111111111111111111-1-1-1-1-1-1-1-1-1-1-1-11-1-111-11-11-11-1-11-111-11-11-11-1
χ1411-1-111-1111-1-1-1-11111-1-1-1-1-1-111-11-1-11-11-11-111-1-1-1-1-1-1111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-111-1-11-11-11-111-11-1-11-11-11-11
χ1511-1-111-1111-1-1-1-1−1−i32−1+i32−1−i32−1+i321+i321+i321−i321−i32-1-1111+i32−1−i321+i321−i32−1+i321−i32−1−i321+i32−1+i321−i32−1−i32−1+i32-1-11+i321+i321−i321−i3211−1−i32−1−i32−1+i32−1+i321−1−i32−1+i3211−1−i32−1−i32−1+i32−1+i321−1−i32−1+i32-1-1-1-11+i321+i321+i321+i321−i321−i321−i321−i321-1-11−1−i321+i32−1+i321−i321-11-11+i32−1−i321−i32−1+i32−1−i321+i32−1−i321+i32−1+i321−i32−1+i321−i32
χ1611-1-111-1111-1-1-1-1−1−i32−1+i32−1−i32−1+i321+i321+i321−i321−i32-1-1111+i32−1−i321+i321−i32−1+i321−i32−1−i321+i32−1+i321−i32−1−i32−1+i32-1-11+i321+i321−i321−i3211−1−i32−1−i32−1+i32−1+i321−1−i32−1+i3211−1−i32−1−i32−1+i32−1+i321−1−i32−1+i32-1-1-1-11+i321+i321+i321+i321−i321−i321−i321−i32-111-11+i32−1−i321−i32−1+i32-11-11−1−i321+i32−1+i321−i321+i32−1−i321+i32−1−i321−i32−1+i321−i32−1+i32
χ1711-1-111-1111-1-1-1-1−1+i32−1−i32−1+i32−1−i321−i321−i321+i321+i32-1-1111−i32−1+i321−i321+i32−1−i321+i32−1+i321−i32−1−i321+i32−1+i32−1−i32-1-11−i321−i321+i321+i3211−1+i32−1+i32−1−i32−1−i321−1+i32−1−i3211−1+i32−1+i32−1−i32−1−i321−1+i32−1−i32-1-1-1-11−i321−i321−i321−i321+i321+i321+i321+i321-1-11−1+i321−i32−1−i321+i321-11-11−i32−1+i321+i32−1−i32−1+i321−i32−1+i321−i32−1−i321+i32−1−i321+i32
χ1811-1-111-1111-1-1-1-1−1+i32−1−i32−1+i32−1−i321−i321−i321+i321+i32-1-1111−i32−1+i321−i321+i32−1−i321+i32−1+i321−i32−1−i321+i32−1+i32−1−i32-1-11−i321−i321+i321+i3211−1+i32−1+i32−1−i32−1−i321−1+i32−1−i3211−1+i32−1+i32−1−i32−1−i321−1+i32−1−i32-1-1-1-11−i321−i321−i321−i321+i321+i321+i321+i32-111-11−i32−1+i321+i32−1−i32-11-11−1+i321−i32−1−i321+i321−i32−1+i321−i32−1+i321+i32−1−i321+i32−1−i32
χ1911-1-1-111-1-11-1-1111111-1-1-1-1-11-11-1-11-1-11-11-1111-11-11-111-11-11-1111-1-1-1-1-1-1111-1-111-1-111-1-11111-1-111111-1-11-1-1-1-11-1-111-1-11
χ2011-1-1-111-1-11-1-1111111-1-1-1-1-11-11-1-11-1-11-11-1111-11-11-111-11-11-1111-1-1-1-1-1-1111-1-111-1-111-1-111-1-111-1-1-1-1-111-11111-111-1-111-1
χ2111-1-1-111-1-11-1-111−1−i32−1+i32−1−i32−1+i321+i321+i321−i321−i32-11-111+i321+i32−1−i321−i321−i32−1+i321+i32−1−i321−i32−1+i32−1−i32−1+i32-111+i32−1−i321−i32−1+i321-1−1−i321+i32−1+i321−i321−1−i32−1+i32-1-11+i321+i321−i321−i321−1−i32−1+i32-1-1111+i321+i32−1−i32−1−i321−i321−i32−1+i32−1+i3211-1-1−1−i32−1−i32−1+i32−1+i321-1-111+i321+i321−i321−i32−1−i321+i321+i32−1−i32−1+i321−i321−i32−1+i32
χ2211-1-1-111-1-11-1-111−1−i32−1+i32−1−i32−1+i321+i321+i321−i321−i32-11-111+i321+i32−1−i321−i321−i32−1+i321+i32−1−i321−i32−1+i32−1−i32−1+i32-111+i32−1−i321−i32−1+i321-1−1−i321+i32−1+i321−i321−1−i32−1+i32-1-11+i321+i321−i321−i321−1−i32−1+i32-1-1111+i321+i32−1−i32−1−i321−i321−i32−1+i32−1+i32-1-1111+i321+i321−i321−i32-111-1−1−i32−1−i32−1+i32−1+i321+i32−1−i32−1−i321+i321−i32−1+i32−1+i321−i32
χ2311-1-1-111-1-11-1-111−1+i32−1−i32−1+i32−1−i321−i321−i321+i321+i32-11-111−i321−i32−1+i321+i321+i32−1−i321−i32−1+i321+i32−1−i32−1+i32−1−i32-111−i32−1+i321+i32−1−i321-1−1+i321−i32−1−i321+i321−1+i32−1−i32-1-11−i321−i321+i321+i321−1+i32−1−i32-1-1111−i321−i32−1+i32−1+i321+i321+i32−1−i32−1−i3211-1-1−1+i32−1+i32−1−i32−1−i321-1-111−i321−i321+i321+i32−1+i321−i321−i32−1+i32−1−i321+i321+i32−1−i32
χ2411-1-1-111-1-11-1-111−1+i32−1−i32−1+i32−1−i321−i321−i321+i321+i32-11-111−i321−i32−1+i321+i321+i32−1−i321−i32−1+i321+i32−1−i32−1+i32−1−i32-111−i32−1+i321+i32−1−i321-1−1+i321−i32−1−i321+i321−1+i32−1−i32-1-11−i321−i321+i321+i321−1+i32−1−i32-1-1111−i321−i32−1+i32−1+i321+i321+i32−1−i32−1−i32-1-1111−i321−i321+i321+i32-111-1−1+i32−1+i32−1−i32−1−i321−i32−1+i32−1+i321−i321+i32−1−i32−1−i321+i32
χ2522222222222222222222222222222222222222222222222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1000000000000000000000000
χ2622222222222222−1−i3−1+i3−1−i3−1+i3−1−i3−1−i3−1+i3−1+i32222−1−i3−1−i3−1−i3−1+i3−1+i3−1+i3−1−i3−1−i3−1+i3−1+i3−1−i3−1+i322−1−i3−1−i3−1+i3−1+i322−1−i3−1−i3−1+i3−1+i3-11+i321−i32-1-11+i321+i321−i321−i32-11+i321−i32-1-1-1-11+i321+i321+i321+i321−i321−i321−i321−i32000000000000000000000000
χ2722222222222222−1+i3−1−i3−1+i3−1−i3−1+i3−1+i3−1−i3−1−i32222−1+i3−1+i3−1+i3−1−i3−1−i3−1−i3−1+i3−1+i3−1−i3−1−i3−1+i3−1−i322−1+i3−1+i3−1−i3−1−i322−1+i3−1+i3−1−i3−1−i3-11−i321+i32-1-11−i321−i321+i321+i32-11−i321+i32-1-1-1-11−i321−i321−i321−i321+i321+i321+i321+i32000000000000000000000000
χ282222-22-2-2-2222-2-2222222222-2-222-2-22-2-2-2-2-2-2222-22-22-22-22-22-2-1-1-1111111-1-1-1-1-111-1-111-1-111000000000000000000000000
χ292222-22-2-2-2222-2-2−1−i3−1+i3−1−i3−1+i3−1−i3−1−i3−1+i3−1+i32-2-22−1−i31+i31+i3−1+i31−i31−i31+i31+i31−i31−i3−1−i3−1+i32-2−1−i31+i3−1+i31−i32-2−1−i31+i3−1+i31−i3-11+i321−i3211−1−i32−1−i32−1+i32−1+i32-11+i321−i32-1-1111+i321+i32−1−i32−1−i321−i321−i32−1+i32−1+i32000000000000000000000000
χ302222-22-2-2-2222-2-2−1+i3−1−i3−1+i3−1−i3−1+i3−1+i3−1−i3−1−i32-2-22−1+i31−i31−i3−1−i31+i31+i31−i31−i31+i31+i3−1+i3−1−i32-2−1+i31−i3−1−i31+i32-2−1+i31−i3−1−i31+i3-11−i321+i3211−1+i32−1+i32−1−i32−1−i32-11−i321+i32-1-1111−i321−i32−1+i32−1+i321+i321+i32−1−i32−1−i32000000000000000000000000
χ3122-2-222-2222-2-2-2-22222-2-2-2-2-2-222-22-2-22-22-22-222-2-2-2-2-2-2222222-1-1-1-1-1-1-1-1-1-1-1-1111111111111000000000000000000000000
χ3222-2-222-2222-2-2-2-2−1−i3−1+i3−1−i3−1+i31+i31+i31−i31−i3-2-2221+i3−1−i31+i31−i3−1+i31−i3−1−i31+i3−1+i31−i3−1−i3−1+i3-2-21+i31+i31−i31−i322−1−i3−1−i3−1+i3−1+i3-11+i321−i32-1-11+i321+i321−i321−i32-11+i321−i321111−1−i32−1−i32−1−i32−1−i32−1+i32−1+i32−1+i32−1+i32000000000000000000000000
χ3322-2-222-2222-2-2-2-2−1+i3−1−i3−1+i3−1−i31−i31−i31+i31+i3-2-2221−i3−1+i31−i31+i3−1−i31+i3−1+i31−i3−1−i31+i3−1+i3−1−i3-2-21−i31−i31+i31+i322−1+i3−1+i3−1−i3−1−i3-11−i321+i32-1-11−i321−i321+i321+i32-11−i321+i321111−1+i32−1+i32−1+i32−1+i32−1−i32−1−i32−1−i32−1−i32000000000000000000000000
χ3422-2-2-222-2-22-2-2222222-2-2-2-2-22-22-2-22-2-22-22-2222-22-22-222-22-22-2-1-1-1111111-1-1-111-1-111-1-111-1-1000000000000000000000000
χ3522-2-2-222-2-22-2-222−1−i3−1+i3−1−i3−1+i31+i31+i31−i31−i3-22-221+i31+i3−1−i31−i31−i3−1+i31+i3−1−i31−i3−1+i3−1−i3−1+i3-221+i3−1−i31−i3−1+i32-2−1−i31+i3−1+i31−i3-11+i321−i3211−1−i32−1−i32−1+i32−1+i32-11+i321−i3211-1-1−1−i32−1−i321+i321+i32−1+i32−1+i321−i321−i32000000000000000000000000
χ3622-2-2-222-2-22-2-222−1+i3−1−i3−1+i3−1−i31−i31−i31+i31+i3-22-221−i31−i3−1+i31+i31+i3−1−i31−i3−1+i31+i3−1−i3−1+i3−1−i3-221−i3−1+i31+i3−1−i32-2−1+i31−i3−1−i31+i3-11−i321+i3211−1+i32−1+i32−1−i32−1−i32-11−i321+i3211-1-1−1+i32−1+i321−i321−i32−1−i32−1−i321+i321+i32000000000000000000000000
χ373333333333333333333333-1-1-1-1-13-1-13-1-13-13-1-1-1-1-1-1-1-1-1-1-1-1-1-100000000000000000000000011111111-1-1-1-11111-1-1-1-1-1-1-1-1
χ383333333333333333333333-1-1-1-1-13-1-13-1-13-13-1-1-1-1-1-1-1-1-1-1-1-1-1-1000000000000000000000000-1-1-1-1-1-1-1-11111-1-1-1-111111111
χ3933333333333333−3−3i32−3+3i32−3−3i32−3+3i32−3−3i32−3−3i32−3+3i32−3+3i32-1-1-1-11+i32−3−3i321+i321−i32−3+3i321−i321+i32−3−3i321−i32−3+3i321+i321−i32-1-11+i321+i321−i321−i32-1-11+i321+i321−i321−i320000000000000000000000001111−1−i32−1−i32−1+i32−1+i32-1-1-1-1−1−i32−1−i32−1+i32−1+i321+i321+i321+i321+i321−i321−i321−i321−i32
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Here ζ is a primitive root of unity of order 12 (ζ12 = 1); i = ζ3.