Finite Group Databasebeta

← Group #13146855

Character table — Group #13146855

Order 1728.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96C97C98
size11112222222222333333336666666666666666121212121212121212121212242424242424242424242424242424242424242424242424363636363636363636363636363636363636363636363636
order124436881212242424243366121212122466881212242424242424242466612121224242424242499918181836363636363672727272727272727272727224446688881212121212122424242424242424
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+i3211−1−i32−1+i3211−1−i32−1+i32−1−i32−1−i32−1−i32−1−i32−1+i32−1+i32−1+i32−1+i321−1−i32−1+i321−1−i32−1+i3211−1−i32−1−i32−1+i32−1+i321−1−i32−1+i321−1−i32−1+i3211−1−i32−1−i32−1+i32−1+i321111−1−i32−1−i32−1−i32−1−i32−1+i32−1+i32−1+i32−1+i321111−1−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−i32−1+i32−1+i32
χ411111111111111−1−i32−1+i32−1−i32−1+i32−1−i32−1−i32−1+i32−1+i3211−1−i32−1+i3211−1−i32−1+i32−1−i32−1−i32−1−i32−1−i32−1+i32−1+i32−1+i32−1+i321−1−i32−1+i321−1−i32−1+i3211−1−i32−1−i32−1+i32−1+i321−1−i32−1+i321−1−i32−1+i3211−1−i32−1−i32−1+i32−1+i321111−1−i32−1−i32−1−i32−1−i32−1+i32−1+i32−1+i32−1+i32-1-1-1-11+i321−i32-1-1-1-11+i321−i321+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−i3211−1+i32−1−i3211−1+i32−1−i32−1+i32−1+i32−1+i32−1+i32−1−i32−1−i32−1−i32−1−i321−1+i32−1−i321−1+i32−1−i3211−1+i32−1+i32−1−i32−1−i321−1+i32−1−i321−1+i32−1−i3211−1+i32−1+i32−1−i32−1−i321111−1+i32−1+i32−1+i32−1+i32−1−i32−1−i32−1−i32−1−i321111−1+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+i32−1−i32−1−i32
χ611111111111111−1+i32−1−i32−1+i32−1−i32−1+i32−1+i32−1−i32−1−i3211−1+i32−1−i3211−1+i32−1−i32−1+i32−1+i32−1+i32−1+i32−1−i32−1−i32−1−i32−1−i321−1+i32−1−i321−1+i32−1−i3211−1+i32−1+i32−1−i32−1−i321−1+i32−1−i321−1+i32−1−i3211−1+i32−1+i32−1−i32−1−i321111−1+i32−1+i32−1+i32−1+i32−1−i32−1−i32−1−i32−1−i32-1-1-1-11−i321+i32-1-1-1-11−i321+i321−i321−i321+i321+i321−i321−i321+i321+i321−i321−i321+i321+i32
χ7111111-1-111-1-1-1-1111111111111-1-111-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-111-1-111-1-11111-1-1-1-1-1-1-1-11111
χ8111111-1-111-1-1-1-1111111111111-1-111-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-111-1-1-1-111111111-1-1-1-1
χ9111111-1-111-1-1-1-1−1−i32−1+i32−1−i32−1+i32−1−i32−1−i32−1+i32−1+i3211−1−i32−1+i32-1-1−1−i32−1+i321+i321+i321+i321+i321−i321−i321−i321−i321−1−i32−1+i321−1−i32−1+i32-1-11+i321+i321−i321−i321−1−i32−1+i321−1−i32−1+i3211−1−i32−1−i32−1+i32−1+i32-1-1-1-11+i321+i321+i321+i321−i321−i321−i321−i3211-1-1−1−i32−1+i32-1-111−1−i32−1+i321+i321+i321−i321−i321+i321+i321−i321−i32−1−i32−1−i32−1+i32−1+i32
χ10111111-1-111-1-1-1-1−1−i32−1+i32−1−i32−1+i32−1−i32−1−i32−1+i32−1+i3211−1−i32−1+i32-1-1−1−i32−1+i321+i321+i321+i321+i321−i321−i321−i321−i321−1−i32−1+i321−1−i32−1+i32-1-11+i321+i321−i321−i321−1−i32−1+i321−1−i32−1+i3211−1−i32−1−i32−1+i32−1+i32-1-1-1-11+i321+i321+i321+i321−i321−i321−i321−i32-1-1111+i321−i3211-1-11+i321−i32−1−i32−1−i32−1+i32−1+i32−1−i32−1−i32−1+i32−1+i321+i321+i321−i321−i32
χ11111111-1-111-1-1-1-1−1+i32−1−i32−1+i32−1−i32−1+i32−1+i32−1−i32−1−i3211−1+i32−1−i32-1-1−1+i32−1−i321−i321−i321−i321−i321+i321+i321+i321+i321−1+i32−1−i321−1+i32−1−i32-1-11−i321−i321+i321+i321−1+i32−1−i321−1+i32−1−i3211−1+i32−1+i32−1−i32−1−i32-1-1-1-11−i321−i321−i321−i321+i321+i321+i321+i3211-1-1−1+i32−1−i32-1-111−1+i32−1−i321−i321−i321+i321+i321−i321−i321+i321+i32−1+i32−1+i32−1−i32−1−i32
χ12111111-1-111-1-1-1-1−1+i32−1−i32−1+i32−1−i32−1+i32−1+i32−1−i32−1−i3211−1+i32−1−i32-1-1−1+i32−1−i321−i321−i321−i321−i321+i321+i321+i321+i321−1+i32−1−i321−1+i32−1−i32-1-11−i321−i321+i321+i321−1+i32−1−i321−1+i32−1−i3211−1+i32−1+i32−1−i32−1−i32-1-1-1-11−i321−i321−i321−i321+i321+i321+i321+i32-1-1111−i321+i3211-1-11−i321+i32−1+i32−1+i32−1−i32−1−i32−1+i32−1+i32−1−i32−1−i321−i321−i321+i321+i32
χ1311-1-111i−i-1-1ii−i−i1111-1-1-1-1-11-1-1i−i11ii−i−iii−i−i-1-1-1111i−ii−ii−i111111-1-1-1-1-1-1ii−i−iii−i−iii−i−i1-1i−i11i−i1-1-1-1i−ii−ii−ii−i1-11-1
χ1411-1-111i−i-1-1ii−i−i1111-1-1-1-1-11-1-1i−i11ii−i−iii−i−i-1-1-1111i−ii−ii−i111111-1-1-1-1-1-1ii−i−iii−i−iii−i−i-11−ii-1-1−ii-1111−ii−ii−ii−ii-11-11
χ1511-1-111i−i-1-1ii−i−i−1−i32−1+i32−1−i32−1+i321+i321+i321−i321−i32-111+i321−i32i−i−1−i32−1+i32ζ22ζ22−ζ22−ζ22ζ14ζ14−ζ14−ζ14-11+i321−i321−1−i32−1+i32i−iζ22−ζ22ζ14−ζ141−1−i32−1+i321−1−i32−1+i32-1-11+i321+i321−i321−i32ii−i−iζ22ζ22−ζ22−ζ22ζ14ζ14−ζ14−ζ141-1i−i−1−i32−1+i32i−i1-11+i321−i32ζ22−ζ22ζ14−ζ14ζ22−ζ22ζ14−ζ14−1−i321+i32−1+i321−i32
χ1611-1-111i−i-1-1ii−i−i−1−i32−1+i32−1−i32−1+i321+i321+i321−i321−i32-111+i321−i32i−i−1−i32−1+i32ζ22ζ22−ζ22−ζ22ζ14ζ14−ζ14−ζ14-11+i321−i321−1−i32−1+i32i−iζ22−ζ22ζ14−ζ141−1−i32−1+i321−1−i32−1+i32-1-11+i321+i321−i321−i32ii−i−iζ22ζ22−ζ22−ζ22ζ14ζ14−ζ14−ζ14-11−ii1+i321−i32−ii-11−1−i32−1+i32−ζ22ζ22−ζ14ζ14−ζ22ζ22−ζ14ζ141+i32−1−i321−i32−1+i32
χ1711-1-111i−i-1-1ii−i−i−1+i32−1−i32−1+i32−1−i321−i321−i321+i321+i32-111−i321+i32i−i−1+i32−1−i32ζ14ζ14−ζ14−ζ14ζ22ζ22−ζ22−ζ22-11−i321+i321−1+i32−1−i32i−iζ14−ζ14ζ22−ζ221−1+i32−1−i321−1+i32−1−i32-1-11−i321−i321+i321+i32ii−i−iζ14ζ14−ζ14−ζ14ζ22ζ22−ζ22−ζ221-1i−i−1+i32−1−i32i−i1-11−i321+i32ζ14−ζ14ζ22−ζ22ζ14−ζ14ζ22−ζ22−1+i321−i32−1−i321+i32
χ1811-1-111i−i-1-1ii−i−i−1+i32−1−i32−1+i32−1−i321−i321−i321+i321+i32-111−i321+i32i−i−1+i32−1−i32ζ14ζ14−ζ14−ζ14ζ22ζ22−ζ22−ζ22-11−i321+i321−1+i32−1−i32i−iζ14−ζ14ζ22−ζ221−1+i32−1−i321−1+i32−1−i32-1-11−i321−i321+i321+i32ii−i−iζ14ζ14−ζ14−ζ14ζ22ζ22−ζ22−ζ22-11−ii1−i321+i32−ii-11−1+i32−1−i32−ζ14ζ14−ζ22ζ22−ζ14ζ14−ζ22ζ221−i32−1+i321+i32−1−i32
χ1911-1-111−ii-1-1−i−iii1111-1-1-1-1-11-1-1−ii11−i−iii−i−iii-1-1-1111−ii−ii−ii111111-1-1-1-1-1-1−i−iii−i−iii−i−iii1-1−ii11−ii1-1-1-1−ii−ii−ii−ii1-11-1
χ2011-1-111−ii-1-1−i−iii1111-1-1-1-1-11-1-1−ii11−i−iii−i−iii-1-1-1111−ii−ii−ii111111-1-1-1-1-1-1−i−iii−i−iii−i−iii-11i−i-1-1i−i-1111i−ii−ii−ii−i-11-11
χ2111-1-111−ii-1-1−i−iii−1−i32−1+i32−1−i32−1+i321+i321+i321−i321−i32-111+i321−i32−ii−1−i32−1+i32−ζ22−ζ22ζ22ζ22−ζ14−ζ14ζ14ζ14-11+i321−i321−1−i32−1+i32−ii−ζ22ζ22−ζ14ζ141−1−i32−1+i321−1−i32−1+i32-1-11+i321+i321−i321−i32−i−iii−ζ22−ζ22ζ22ζ22−ζ14−ζ14ζ14ζ141-1−ii−1−i32−1+i32−ii1-11+i321−i32−ζ22ζ22−ζ14ζ14−ζ22ζ22−ζ14ζ14−1−i321+i32−1+i321−i32
χ2211-1-111−ii-1-1−i−iii−1−i32−1+i32−1−i32−1+i321+i321+i321−i321−i32-111+i321−i32−ii−1−i32−1+i32−ζ22−ζ22ζ22ζ22−ζ14−ζ14ζ14ζ14-11+i321−i321−1−i32−1+i32−ii−ζ22ζ22−ζ14ζ141−1−i32−1+i321−1−i32−1+i32-1-11+i321+i321−i321−i32−i−iii−ζ22−ζ22ζ22ζ22−ζ14−ζ14ζ14ζ14-11i−i1+i321−i32i−i-11−1−i32−1+i32ζ22−ζ22ζ14−ζ14ζ22−ζ22ζ14−ζ141+i32−1−i321−i32−1+i32
χ2311-1-111−ii-1-1−i−iii−1+i32−1−i32−1+i32−1−i321−i321−i321+i321+i32-111−i321+i32−ii−1+i32−1−i32−ζ14−ζ14ζ14ζ14−ζ22−ζ22ζ22ζ22-11−i321+i321−1+i32−1−i32−ii−ζ14ζ14−ζ22ζ221−1+i32−1−i321−1+i32−1−i32-1-11−i321−i321+i321+i32−i−iii−ζ14−ζ14ζ14ζ14−ζ22−ζ22ζ22ζ221-1−ii−1+i32−1−i32−ii1-11−i321+i32−ζ14ζ14−ζ22ζ22−ζ14ζ14−ζ22ζ22−1+i321−i32−1−i321+i32
χ2411-1-111−ii-1-1−i−iii−1+i32−1−i32−1+i32−1−i321−i321−i321+i321+i32-111−i321+i32−ii−1+i32−1−i32−ζ14−ζ14ζ14ζ14−ζ22−ζ22ζ22ζ22-11−i321+i321−1+i32−1−i32−ii−ζ14ζ14−ζ22ζ221−1+i32−1−i321−1+i32−1−i32-1-11−i321−i321+i321+i32−i−iii−ζ14−ζ14ζ14ζ14−ζ22−ζ22ζ22ζ22-11i−i1−i321+i32i−i-11−1+i32−1−i32ζ14−ζ14ζ22−ζ22ζ14−ζ14ζ22−ζ221−i32−1+i321+i32−1−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+i322−1−i3−1+i322−1−i3−1+i3−1−i3−1−i3−1−i3−1−i3−1+i3−1+i3−1+i3−1+i32−1−i3−1+i32−1−i3−1+i322−1−i3−1−i3−1+i3−1+i3-11+i321−i32-11+i321−i32-1-11+i321+i321−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−i322−1+i3−1−i322−1+i3−1−i3−1+i3−1+i3−1+i3−1+i3−1−i3−1−i3−1−i3−1−i32−1+i3−1−i32−1+i3−1−i322−1+i3−1+i3−1−i3−1−i3-11−i321+i32-11−i321+i32-1-11−i321−i321+i321+i32-1-1-1-11−i321−i321−i321−i321+i321+i321+i321+i32000000000000000000000000
χ28222222-2-222-2-2-2-2222222222222-2-222-2-2-2-2-2-2-2-2222222-2-2-2-2-2-2-1-1-1-1-1-1-1-1-1-1-1-1111111111111000000000000000000000000
χ29222222-2-222-2-2-2-2−1−i3−1+i3−1−i3−1+i3−1−i3−1−i3−1+i3−1+i322−1−i3−1+i3-2-2−1−i3−1+i31+i31+i31+i31+i31−i31−i31−i31−i32−1−i3−1+i32−1−i3−1+i3-2-21+i31+i31−i31−i3-11+i321−i32-11+i321−i32-1-11+i321+i321−i321−i321111−1−i32−1−i32−1−i32−1−i32−1+i32−1+i32−1+i32−1+i32000000000000000000000000
χ30222222-2-222-2-2-2-2−1+i3−1−i3−1+i3−1−i3−1+i3−1+i3−1−i3−1−i322−1+i3−1−i3-2-2−1+i3−1−i31−i31−i31−i31−i31+i31+i31+i31+i32−1+i3−1−i32−1+i3−1−i3-2-21−i31−i31+i31+i3-11−i321+i32-11−i321+i32-1-11−i321−i321+i321+i321111−1+i32−1+i32−1+i32−1+i32−1−i32−1−i32−1−i32−1−i32000000000000000000000000
χ3122-2-2222i−2i-2-22i2i−2i−2i2222-2-2-2-2-22-2-22i−2i222i2i−2i−2i2i2i−2i−2i-2-2-22222i−2i2i−2i2i−2i-1-1-1-1-1-1111111−i−iii−i−iii−i−iii000000000000000000000000
χ3222-2-2222i−2i-2-22i2i−2i−2i−1−i3−1+i3−1−i3−1+i31+i31+i31−i31−i3-221+i31−i32i−2i−1−i3−1+i32ζ222ζ22−2ζ22−2ζ222ζ142ζ14−2ζ14−2ζ14-21+i31−i32−1−i3−1+i32i−2i2ζ22−2ζ222ζ14−2ζ14-11+i321−i32-11+i321−i3211−1−i32−1−i32−1+i32−1+i32−i−iii−ζ22−ζ22ζ22ζ22−ζ14−ζ14ζ14ζ14000000000000000000000000
χ3322-2-2222i−2i-2-22i2i−2i−2i−1+i3−1−i3−1+i3−1−i31−i31−i31+i31+i3-221−i31+i32i−2i−1+i3−1−i32ζ142ζ14−2ζ14−2ζ142ζ222ζ22−2ζ22−2ζ22-21−i31+i32−1+i3−1−i32i−2i2ζ14−2ζ142ζ22−2ζ22-11−i321+i32-11−i321+i3211−1+i32−1+i32−1−i32−1−i32−i−iii−ζ14−ζ14ζ14ζ14−ζ22−ζ22ζ22ζ22000000000000000000000000
χ3422-2-222−2i2i-2-2−2i−2i2i2i2222-2-2-2-2-22-2-2−2i2i22−2i−2i2i2i−2i−2i2i2i-2-2-2222−2i2i−2i2i−2i2i-1-1-1-1-1-1111111ii−i−iii−i−iii−i−i000000000000000000000000
χ3522-2-222−2i2i-2-2−2i−2i2i2i−1−i3−1+i3−1−i3−1+i31+i31+i31−i31−i3-221+i31−i3−2i2i−1−i3−1+i3−2ζ22−2ζ222ζ222ζ22−2ζ14−2ζ142ζ142ζ14-21+i31−i32−1−i3−1+i3−2i2i−2ζ222ζ22−2ζ142ζ14-11+i321−i32-11+i321−i3211−1−i32−1−i32−1+i32−1+i32ii−i−iζ22ζ22−ζ22−ζ22ζ14ζ14−ζ14−ζ14000000000000000000000000
χ3622-2-222−2i2i-2-2−2i−2i2i2i−1+i3−1−i3−1+i3−1−i31−i31−i31+i31+i3-221−i31+i3−2i2i−1+i3−1−i3−2ζ14−2ζ142ζ142ζ14−2ζ22−2ζ222ζ222ζ22-21−i31+i32−1+i3−1−i3−2i2i−2ζ142ζ14−2ζ222ζ22-11−i321+i32-11−i321+i3211−1+i32−1+i32−1−i32−1−i32ii−i−iζ14ζ14−ζ14−ζ14ζ22ζ22−ζ22−ζ22000000000000000000000000
χ373333333333333333333333-1-1-1-1-1-1-1-13-13-13-13-1-1-1-1-1-1-1-1-1-1-1-1-100000000000000000000000011-1-11111-1-111-1-1-1-11111-1-1-1-1
χ383333333333333333333333-1-1-1-1-1-1-1-13-13-13-13-1-1-1-1-1-1-1-1-1-1-1-1-1000000000000000000000000-1-111-1-1-1-111-1-11111-1-1-1-11111
χ3933333333333333−3−3i32−3+3i32−3−3i32−3+3i32−3−3i32−3−3i32−3+3i32−3+3i32-1-11+i321−i32-1-11+i321−i32−3−3i321+i32−3−3i321+i32−3+3i321−i32−3+3i321−i32-11+i321−i32-11+i321−i32-1-11+i321+i321−i321−i3200000000000000000000000011-1-1−1−i32−1+i3211-1-1−1−i32−1+i321+i321+i321−i321−i32−1−i32−1−i32−1+i32−1+i321+i321+i321−i321−i32
χ4033333333333333−3−3i32−3+3i32−3−3i32−3+3i32−3−3i32−3−3i32−3+3i32−3+3i32-1-11+i321−i32-1-11+i321−i32−3−3i321+i32−3−3i321+i32−3+3i321−i32−3+3i321−i32-11+i321−i32-11+i321−i32-1-11+i321+i321−i321−i32000000000000000000000000-1-1111+i321−i32-1-1111+i321−i32−1−i32−1−i32−1+i32−1+i321+i321+i321−i321−i32−1−i32−1−i32−1+i32−1+i32
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Here ζ is a primitive root of unity of order 24 (ζ24 = 1); i = ζ6.