Finite Group Databasebeta

← Group #11721521

Character table — Group #11721521

Order 864.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96C97C98C99C100
size1233666999123366699912336669991233666999246612121218181824661212121818182466121212181818246612121218181824661212121818182466121212181818
order133333326626666662664121212121212412124121212121212412122666666266412121212121241212824242424242482424824242424242482424824242424242482424824242424242482424
χ11111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ21111111-1-1-11111111-1-1-11111111-1-1-11111111-1-1-11111111-1-1-11111111-1-1-11111111-1-1-11111111-1-1-11111111-1-1-11111111-1-1-1
χ311−1+i32−1−i321−1+i32−1−i321−1+i32−1−i3211−1+i32−1−i321−1+i32−1−i321−1+i32−1−i3211−1+i32−1−i321−1+i32−1−i321−1+i32−1−i3211−1+i32−1−i321−1+i32−1−i321−1+i32−1−i3211−1+i32−1−i321−1+i32−1−i321−1+i32−1−i3211−1+i32−1−i321−1+i32−1−i321−1+i32−1−i3211−1+i32−1−i321−1+i32−1−i321−1+i32−1−i3211−1+i32−1−i321−1+i32−1−i321−1+i32−1−i3211−1+i32−1−i321−1+i32−1−i321−1+i32−1−i3211−1+i32−1−i321−1+i32−1−i321−1+i32−1−i32
χ411−1+i32−1−i321−1+i32−1−i32-11−i321+i3211−1+i32−1−i321−1+i32−1−i32-11−i321+i3211−1+i32−1−i321−1+i32−1−i32-11−i321+i3211−1+i32−1−i321−1+i32−1−i32-11−i321+i3211−1+i32−1−i321−1+i32−1−i32-11−i321+i3211−1+i32−1−i321−1+i32−1−i32-11−i321+i3211−1+i32−1−i321−1+i32−1−i32-11−i321+i3211−1+i32−1−i321−1+i32−1−i32-11−i321+i3211−1+i32−1−i321−1+i32−1−i32-11−i321+i3211−1+i32−1−i321−1+i32−1−i32-11−i321+i32
χ511−1−i32−1+i321−1−i32−1+i321−1−i32−1+i3211−1−i32−1+i321−1−i32−1+i321−1−i32−1+i3211−1−i32−1+i321−1−i32−1+i321−1−i32−1+i3211−1−i32−1+i321−1−i32−1+i321−1−i32−1+i3211−1−i32−1+i321−1−i32−1+i321−1−i32−1+i3211−1−i32−1+i321−1−i32−1+i321−1−i32−1+i3211−1−i32−1+i321−1−i32−1+i321−1−i32−1+i3211−1−i32−1+i321−1−i32−1+i321−1−i32−1+i3211−1−i32−1+i321−1−i32−1+i321−1−i32−1+i3211−1−i32−1+i321−1−i32−1+i321−1−i32−1+i32
χ611−1−i32−1+i321−1−i32−1+i32-11+i321−i3211−1−i32−1+i321−1−i32−1+i32-11+i321−i3211−1−i32−1+i321−1−i32−1+i32-11+i321−i3211−1−i32−1+i321−1−i32−1+i32-11+i321−i3211−1−i32−1+i321−1−i32−1+i32-11+i321−i3211−1−i32−1+i321−1−i32−1+i32-11+i321−i3211−1−i32−1+i321−1−i32−1+i32-11+i321−i3211−1−i32−1+i321−1−i32−1+i32-11+i321−i3211−1−i32−1+i321−1−i32−1+i32-11+i321−i3211−1−i32−1+i321−1−i32−1+i32-11+i321−i32
χ72222-1-1-10002222-1-1-10002222-1-1-10002222-1-1-10002222-1-1-10002222-1-1-10002222-1-1-10002222-1-1-10002222-1-1-10002222-1-1-1000
χ822−1+i3−1−i3-11−i321+i3200022−1+i3−1−i3-11−i321+i3200022−1+i3−1−i3-11−i321+i3200022−1+i3−1−i3-11−i321+i3200022−1+i3−1−i3-11−i321+i3200022−1+i3−1−i3-11−i321+i3200022−1+i3−1−i3-11−i321+i3200022−1+i3−1−i3-11−i321+i3200022−1+i3−1−i3-11−i321+i3200022−1+i3−1−i3-11−i321+i32000
χ922−1−i3−1+i3-11+i321−i3200022−1−i3−1+i3-11+i321−i3200022−1−i3−1+i3-11+i321−i3200022−1−i3−1+i3-11+i321−i3200022−1−i3−1+i3-11+i321−i3200022−1−i3−1+i3-11+i321−i3200022−1−i3−1+i3-11+i321−i3200022−1−i3−1+i3-11+i321−i3200022−1−i3−1+i3-11+i321−i3200022−1−i3−1+i3-11+i321−i32000
χ106-3000000006-3000000006-3000000006-3000000006-3000000006-3000000006-3000000006-3000000006-3000000006-300000000
χ11111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ121111111-1-1-11111111-1-1-11111111-1-1-11111111-1-1-11111111-1-1-11111111-1-1-1-1-1-1-1-1-1-1111-1-1-1-1-1-1-1111-1-1-1-1-1-1-1111-1-1-1-1-1-1-1111
χ1311−1+i32−1−i321−1+i32−1−i321−1+i32−1−i3211−1+i32−1−i321−1+i32−1−i321−1+i32−1−i3211−1+i32−1−i321−1+i32−1−i321−1+i32−1−i3211−1+i32−1−i321−1+i32−1−i321−1+i32−1−i3211−1+i32−1−i321−1+i32−1−i321−1+i32−1−i3211−1+i32−1−i321−1+i32−1−i321−1+i32−1−i32-1-11−i321+i32-11−i321+i32-11−i321+i32-1-11−i321+i32-11−i321+i32-11−i321+i32-1-11−i321+i32-11−i321+i32-11−i321+i32-1-11−i321+i32-11−i321+i32-11−i321+i32
χ1411−1+i32−1−i321−1+i32−1−i32-11−i321+i3211−1+i32−1−i321−1+i32−1−i32-11−i321+i3211−1+i32−1−i321−1+i32−1−i32-11−i321+i3211−1+i32−1−i321−1+i32−1−i32-11−i321+i3211−1+i32−1−i321−1+i32−1−i32-11−i321+i3211−1+i32−1−i321−1+i32−1−i32-11−i321+i32-1-11−i321+i32-11−i321+i321−1+i32−1−i32-1-11−i321+i32-11−i321+i321−1+i32−1−i32-1-11−i321+i32-11−i321+i321−1+i32−1−i32-1-11−i321+i32-11−i321+i321−1+i32−1−i32
χ1511−1−i32−1+i321−1−i32−1+i321−1−i32−1+i3211−1−i32−1+i321−1−i32−1+i321−1−i32−1+i3211−1−i32−1+i321−1−i32−1+i321−1−i32−1+i3211−1−i32−1+i321−1−i32−1+i321−1−i32−1+i3211−1−i32−1+i321−1−i32−1+i321−1−i32−1+i3211−1−i32−1+i321−1−i32−1+i321−1−i32−1+i32-1-11+i321−i32-11+i321−i32-11+i321−i32-1-11+i321−i32-11+i321−i32-11+i321−i32-1-11+i321−i32-11+i321−i32-11+i321−i32-1-11+i321−i32-11+i321−i32-11+i321−i32
χ1611−1−i32−1+i321−1−i32−1+i32-11+i321−i3211−1−i32−1+i321−1−i32−1+i32-11+i321−i3211−1−i32−1+i321−1−i32−1+i32-11+i321−i3211−1−i32−1+i321−1−i32−1+i32-11+i321−i3211−1−i32−1+i321−1−i32−1+i32-11+i321−i3211−1−i32−1+i321−1−i32−1+i32-11+i321−i32-1-11+i321−i32-11+i321−i321−1−i32−1+i32-1-11+i321−i32-11+i321−i321−1−i32−1+i32-1-11+i321−i32-11+i321−i321−1−i32−1+i32-1-11+i321−i32-11+i321−i321−1−i32−1+i32
χ172222-1-1-10002222-1-1-10002222-1-1-10002222-1-1-10002222-1-1-10002222-1-1-1000-2-2-2-2111000-2-2-2-2111000-2-2-2-2111000-2-2-2-2111000
χ1822−1+i3−1−i3-11−i321+i3200022−1+i3−1−i3-11−i321+i3200022−1+i3−1−i3-11−i321+i3200022−1+i3−1−i3-11−i321+i3200022−1+i3−1−i3-11−i321+i3200022−1+i3−1−i3-11−i321+i32000-2-21−i31+i31−1+i32−1−i32000-2-21−i31+i31−1+i32−1−i32000-2-21−i31+i31−1+i32−1−i32000-2-21−i31+i31−1+i32−1−i32000
χ1922−1−i3−1+i3-11+i321−i3200022−1−i3−1+i3-11+i321−i3200022−1−i3−1+i3-11+i321−i3200022−1−i3−1+i3-11+i321−i3200022−1−i3−1+i3-11+i321−i3200022−1−i3−1+i3-11+i321−i32000-2-21+i31−i31−1−i32−1+i32000-2-21+i31−i31−1−i32−1+i32000-2-21+i31−i31−1−i32−1+i32000-2-21+i31−i31−1−i32−1+i32000
χ206-3000000006-3000000006-3000000006-3000000006-3000000006-300000000-6300000000-6300000000-6300000000-6300000000
χ211111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ221111111-1-1-11111111-1-1-11111111-1-1-11111111-1-1-1-1-1-1-1-1-1-1111-1-1-1-1-1-1-11111111111-1-1-11111111-1-1-1-1-1-1-1-1-1-1111-1-1-1-1-1-1-1111
χ2311−1+i32−1−i321−1+i32−1−i321−1+i32−1−i3211−1+i32−1−i321−1+i32−1−i321−1+i32−1−i3211−1+i32−1−i321−1+i32−1−i321−1+i32−1−i3211−1+i32−1−i321−1+i32−1−i321−1+i32−1−i32-1-11−i321+i32-11−i321+i32-11−i321+i32-1-11−i321+i32-11−i321+i32-11−i321+i3211−1+i32−1−i321−1+i32−1−i321−1+i32−1−i3211−1+i32−1−i321−1+i32−1−i321−1+i32−1−i32-1-11−i321+i32-11−i321+i32-11−i321+i32-1-11−i321+i32-11−i321+i32-11−i321+i32
χ2411−1+i32−1−i321−1+i32−1−i32-11−i321+i3211−1+i32−1−i321−1+i32−1−i32-11−i321+i3211−1+i32−1−i321−1+i32−1−i32-11−i321+i3211−1+i32−1−i321−1+i32−1−i32-11−i321+i32-1-11−i321+i32-11−i321+i321−1+i32−1−i32-1-11−i321+i32-11−i321+i321−1+i32−1−i3211−1+i32−1−i321−1+i32−1−i32-11−i321+i3211−1+i32−1−i321−1+i32−1−i32-11−i321+i32-1-11−i321+i32-11−i321+i321−1+i32−1−i32-1-11−i321+i32-11−i321+i321−1+i32−1−i32
χ2511−1−i32−1+i321−1−i32−1+i321−1−i32−1+i3211−1−i32−1+i321−1−i32−1+i321−1−i32−1+i3211−1−i32−1+i321−1−i32−1+i321−1−i32−1+i3211−1−i32−1+i321−1−i32−1+i321−1−i32−1+i32-1-11+i321−i32-11+i321−i32-11+i321−i32-1-11+i321−i32-11+i321−i32-11+i321−i3211−1−i32−1+i321−1−i32−1+i321−1−i32−1+i3211−1−i32−1+i321−1−i32−1+i321−1−i32−1+i32-1-11+i321−i32-11+i321−i32-11+i321−i32-1-11+i321−i32-11+i321−i32-11+i321−i32
χ2611−1−i32−1+i321−1−i32−1+i32-11+i321−i3211−1−i32−1+i321−1−i32−1+i32-11+i321−i3211−1−i32−1+i321−1−i32−1+i32-11+i321−i3211−1−i32−1+i321−1−i32−1+i32-11+i321−i32-1-11+i321−i32-11+i321−i321−1−i32−1+i32-1-11+i321−i32-11+i321−i321−1−i32−1+i3211−1−i32−1+i321−1−i32−1+i32-11+i321−i3211−1−i32−1+i321−1−i32−1+i32-11+i321−i32-1-11+i321−i32-11+i321−i321−1−i32−1+i32-1-11+i321−i32-11+i321−i321−1−i32−1+i32
χ272222-1-1-10002222-1-1-10002222-1-1-10002222-1-1-1000-2-2-2-2111000-2-2-2-21110002222-1-1-10002222-1-1-1000-2-2-2-2111000-2-2-2-2111000
χ2822−1+i3−1−i3-11−i321+i3200022−1+i3−1−i3-11−i321+i3200022−1+i3−1−i3-11−i321+i3200022−1+i3−1−i3-11−i321+i32000-2-21−i31+i31−1+i32−1−i32000-2-21−i31+i31−1+i32−1−i3200022−1+i3−1−i3-11−i321+i3200022−1+i3−1−i3-11−i321+i32000-2-21−i31+i31−1+i32−1−i32000-2-21−i31+i31−1+i32−1−i32000
χ2922−1−i3−1+i3-11+i321−i3200022−1−i3−1+i3-11+i321−i3200022−1−i3−1+i3-11+i321−i3200022−1−i3−1+i3-11+i321−i32000-2-21+i31−i31−1−i32−1+i32000-2-21+i31−i31−1−i32−1+i3200022−1−i3−1+i3-11+i321−i3200022−1−i3−1+i3-11+i321−i32000-2-21+i31−i31−1−i32−1+i32000-2-21+i31−i31−1−i32−1+i32000
χ306-3000000006-3000000006-3000000006-300000000-6300000000-63000000006-3000000006-300000000-6300000000-6300000000
χ311111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111111111111111
χ321111111-1-1-11111111-1-1-11111111-1-1-11111111-1-1-1-1-1-1-1-1-1-1111-1-1-1-1-1-1-1111-1-1-1-1-1-1-1111-1-1-1-1-1-1-11111111111-1-1-11111111-1-1-1
χ3311−1+i32−1−i321−1+i32−1−i321−1+i32−1−i3211−1+i32−1−i321−1+i32−1−i321−1+i32−1−i3211−1+i32−1−i321−1+i32−1−i321−1+i32−1−i3211−1+i32−1−i321−1+i32−1−i321−1+i32−1−i32-1-11−i321+i32-11−i321+i32-11−i321+i32-1-11−i321+i32-11−i321+i32-11−i321+i32-1-11−i321+i32-11−i321+i32-11−i321+i32-1-11−i321+i32-11−i321+i32-11−i321+i3211−1+i32−1−i321−1+i32−1−i321−1+i32−1−i3211−1+i32−1−i321−1+i32−1−i321−1+i32−1−i32
χ3411−1+i32−1−i321−1+i32−1−i32-11−i321+i3211−1+i32−1−i321−1+i32−1−i32-11−i321+i3211−1+i32−1−i321−1+i32−1−i32-11−i321+i3211−1+i32−1−i321−1+i32−1−i32-11−i321+i32-1-11−i321+i32-11−i321+i321−1+i32−1−i32-1-11−i321+i32-11−i321+i321−1+i32−1−i32-1-11−i321+i32-11−i321+i321−1+i32−1−i32-1-11−i321+i32-11−i321+i321−1+i32−1−i3211−1+i32−1−i321−1+i32−1−i32-11−i321+i3211−1+i32−1−i321−1+i32−1−i32-11−i321+i32
χ3511−1−i32−1+i321−1−i32−1+i321−1−i32−1+i3211−1−i32−1+i321−1−i32−1+i321−1−i32−1+i3211−1−i32−1+i321−1−i32−1+i321−1−i32−1+i3211−1−i32−1+i321−1−i32−1+i321−1−i32−1+i32-1-11+i321−i32-11+i321−i32-11+i321−i32-1-11+i321−i32-11+i321−i32-11+i321−i32-1-11+i321−i32-11+i321−i32-11+i321−i32-1-11+i321−i32-11+i321−i32-11+i321−i3211−1−i32−1+i321−1−i32−1+i321−1−i32−1+i3211−1−i32−1+i321−1−i32−1+i321−1−i32−1+i32
χ3611−1−i32−1+i321−1−i32−1+i32-11+i321−i3211−1−i32−1+i321−1−i32−1+i32-11+i321−i3211−1−i32−1+i321−1−i32−1+i32-11+i321−i3211−1−i32−1+i321−1−i32−1+i32-11+i321−i32-1-11+i321−i32-11+i321−i321−1−i32−1+i32-1-11+i321−i32-11+i321−i321−1−i32−1+i32-1-11+i321−i32-11+i321−i321−1−i32−1+i32-1-11+i321−i32-11+i321−i321−1−i32−1+i3211−1−i32−1+i321−1−i32−1+i32-11+i321−i3211−1−i32−1+i321−1−i32−1+i32-11+i321−i32
χ372222-1-1-10002222-1-1-10002222-1-1-10002222-1-1-1000-2-2-2-2111000-2-2-2-2111000-2-2-2-2111000-2-2-2-21110002222-1-1-10002222-1-1-1000
χ3822−1+i3−1−i3-11−i321+i3200022−1+i3−1−i3-11−i321+i3200022−1+i3−1−i3-11−i321+i3200022−1+i3−1−i3-11−i321+i32000-2-21−i31+i31−1+i32−1−i32000-2-21−i31+i31−1+i32−1−i32000-2-21−i31+i31−1+i32−1−i32000-2-21−i31+i31−1+i32−1−i3200022−1+i3−1−i3-11−i321+i3200022−1+i3−1−i3-11−i321+i32000
χ3922−1−i3−1+i3-11+i321−i3200022−1−i3−1+i3-11+i321−i3200022−1−i3−1+i3-11+i321−i3200022−1−i3−1+i3-11+i321−i32000-2-21+i31−i31−1−i32−1+i32000-2-21+i31−i31−1−i32−1+i32000-2-21+i31−i31−1−i32−1+i32000-2-21+i31−i31−1−i32−1+i3200022−1−i3−1+i3-11+i321−i3200022−1−i3−1+i3-11+i321−i32000
χ406-3000000006-3000000006-3000000006-300000000-6300000000-6300000000-6300000000-63000000006-3000000006-300000000
χ4111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-1iiiiiiiiii−i−i−i−i−i−i−i−i−i−iiiiiiiiiii−i−i−i−i−i−i−i−i−i−i
χ421111111-1-1-11111111-1-1-1-1-1-1-1-1-1-1111-1-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-1111iiiiiii−i−i−i−i−i−i−i−i−i−iiiiiiiiiii−i−i−i−i−i−i−i−i−i−iiii
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χ8944−2−2i3−2+2i3-21+i31−i3000-4-42+2i32−2i32−1−i3−1+i30004i4i4ζ114ζ7−2i−2ζ11−2ζ7000−4i−4i−4ζ11−4ζ72i2ζ112ζ7000000000000000000000000000000000000000000000000000000000000000
χ9012-600000000-1260000000012i−6i00000000−12i6i00000000000000000000000000000000000000000000000000000000000000000000
χ912222222222-2-2-2-2-2-2-2-2-2-2−2i−2i−2i−2i−2i−2i−2i−2i−2i−2i2i2i2i2i2i2i2i2i2i2i000000000000000000000000000000000000000000000000000000000000
χ922222222-2-2-2-2-2-2-2-2-2-2222−2i−2i−2i−2i−2i−2i−2i2i2i2i2i2i2i2i2i2i2i−2i−2i−2i000000000000000000000000000000000000000000000000000000000000
χ9322−1+i3−1−i32−1+i3−1−i32−1+i3−1−i3-2-21−i31+i3-21−i31+i3-21−i31+i3−2i−2i−2ζ7−2ζ11−2i−2ζ7−2ζ11−2i−2ζ7−2ζ112i2i2ζ72ζ112i2ζ72ζ112i2ζ72ζ11000000000000000000000000000000000000000000000000000000000000
χ9422−1+i3−1−i32−1+i3−1−i3-21−i31+i3-2-21−i31+i3-21−i31+i32−1+i3−1−i3−2i−2i−2ζ7−2ζ11−2i−2ζ7−2ζ112i2ζ72ζ112i2i2ζ72ζ112i2ζ72ζ11−2i−2ζ7−2ζ11000000000000000000000000000000000000000000000000000000000000
χ9522−1−i3−1+i32−1−i3−1+i32−1−i3−1+i3-2-21+i31−i3-21+i31−i3-21+i31−i3−2i−2i−2ζ11−2ζ7−2i−2ζ11−2ζ7−2i−2ζ11−2ζ72i2i2ζ112ζ72i2ζ112ζ72i2ζ112ζ7000000000000000000000000000000000000000000000000000000000000
χ9622−1−i3−1+i32−1−i3−1+i3-21+i31−i3-2-21+i31−i3-21+i31−i32−1−i3−1+i3−2i−2i−2ζ11−2ζ7−2i−2ζ11−2ζ72i2ζ112ζ72i2i2ζ112ζ72i2ζ112ζ7−2i−2ζ11−2ζ7000000000000000000000000000000000000000000000000000000000000
χ974444-2-2-2000-4-4-4-4222000−4i−4i−4i−4i2i2i2i0004i4i4i4i−2i−2i−2i000000000000000000000000000000000000000000000000000000000000000
χ9844−2+2i3−2−2i3-21−i31+i3000-4-42−2i32+2i32−1+i3−1−i3000−4i−4i−4ζ7−4ζ112i2ζ72ζ110004i4i4ζ74ζ11−2i−2ζ7−2ζ11000000000000000000000000000000000000000000000000000000000000000
χ9944−2−2i3−2+2i3-21+i31−i3000-4-42+2i32−2i32−1−i3−1+i3000−4i−4i−4ζ11−4ζ72i2ζ112ζ70004i4i4ζ114ζ7−2i−2ζ11−2ζ7000000000000000000000000000000000000000000000000000000000000000
χ10012-600000000-12600000000−12i6i0000000012i−6i00000000000000000000000000000000000000000000000000000000000000000000

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