Finite Group Databasebeta

← Group #72259626

Character table — Group #72259626

Order 5184.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96C97C98C99C100C101C102C103C104C105C106C107C108C109C110C111C112C113C114C115C116C117C118C119C120
size18912122424363654216182424484872721083242736367272108108162189121224243636542161824244848727210832427363672721081081621891212242436365421618242448487272108324273636727210810816218912122424363654216182424484872721083242736367272108108162
order13233336643363333661226266666644124121212121212412121212121212121212412412121212121242626666664666666666122626666664412412121212121241212121212121212121241241212121212124
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ2111−1+i32−1−i32−1+i32−1−i32−1+i32−1−i321111−1+i32−1−i32−1+i32−1−i32−1+i32−1−i321111−1+i32−1−i32−1+i32−1−i32−1+i32−1−i321111−1+i32−1−i32−1+i32−1−i32−1+i32−1−i321111−1+i32−1−i32−1+i32−1−i32−1+i32−1−i321111−1+i32−1−i32−1+i32−1−i32−1+i32−1−i321111−1+i32−1−i32−1+i32−1−i32−1+i32−1−i321111−1+i32−1−i32−1+i32−1−i32−1+i32−1−i321111−1+i32−1−i32−1+i32−1−i32−1+i32−1−i321111−1+i32−1−i32−1+i32−1−i32−1+i32−1−i321111−1+i32−1−i32−1+i32−1−i32−1+i32−1−i321111−1+i32−1−i32−1+i32−1−i32−1+i32−1−i321
χ3111−1−i32−1+i32−1−i32−1+i32−1−i32−1+i321111−1−i32−1+i32−1−i32−1+i32−1−i32−1+i321111−1−i32−1+i32−1−i32−1+i32−1−i32−1+i321111−1−i32−1+i32−1−i32−1+i32−1−i32−1+i321111−1−i32−1+i32−1−i32−1+i32−1−i32−1+i321111−1−i32−1+i32−1−i32−1+i32−1−i32−1+i321111−1−i32−1+i32−1−i32−1+i32−1−i32−1+i321111−1−i32−1+i32−1−i32−1+i32−1−i32−1+i321111−1−i32−1+i32−1−i32−1+i32−1−i32−1+i321111−1−i32−1+i32−1−i32−1+i32−1−i32−1+i321111−1−i32−1+i32−1−i32−1+i32−1−i32−1+i321111−1−i32−1+i32−1−i32−1+i32−1−i32−1+i321
χ422-2-1-1-1-111022-2-1-1-1-111022-2-1-1-1-111022-2-1-1-1-111022-2-1-1-1-111022-2-1-1-1-111022-2-1-1-1-111022-2-1-1-1-111022-2-1-1-1-111022-2-1-1-1-111022-2-1-1-1-111022-2-1-1-1-1110
χ522-21−i321+i321−i321+i32−1+i32−1−i32022-21−i321+i321−i321+i32−1+i32−1−i32022-21−i321+i321−i321+i32−1+i32−1−i32022-21−i321+i321−i321+i32−1+i32−1−i32022-21−i321+i321−i321+i32−1+i32−1−i32022-21−i321+i321−i321+i32−1+i32−1−i32022-21−i321+i321−i321+i32−1+i32−1−i32022-21−i321+i321−i321+i32−1+i32−1−i32022-21−i321+i321−i321+i32−1+i32−1−i32022-21−i321+i321−i321+i32−1+i32−1−i32022-21−i321+i321−i321+i32−1+i32−1−i32022-21−i321+i321−i321+i32−1+i32−1−i320
χ622-21+i321−i321+i321−i32−1−i32−1+i32022-21+i321−i321+i321−i32−1−i32−1+i32022-21+i321−i321+i321−i32−1−i32−1+i32022-21+i321−i321+i321−i32−1−i32−1+i32022-21+i321−i321+i321−i32−1−i32−1+i32022-21+i321−i321+i321−i32−1−i32−1+i32022-21+i321−i321+i321−i32−1−i32−1+i32022-21+i321−i321+i321−i32−1−i32−1+i32022-21+i321−i321+i321−i32−1−i32−1+i32022-21+i321−i321+i321−i32−1−i32−1+i32022-21+i321−i321+i321−i32−1−i32−1+i32022-21+i321−i321+i321−i32−1−i32−1+i320
χ7333000000-1333000000-1333000000-1333000000-1333000000-1333000000-1333000000-1333000000-1333000000-1333000000-1333000000-1333000000-1
χ88-1022-1-10008-1022-1-10008-1022-1-10008-1022-1-10008-1022-1-10008-1022-1-10008-1022-1-10008-1022-1-10008-1022-1-10008-1022-1-10008-1022-1-10008-1022-1-1000
χ98-10−1+i3−1−i31−i321+i320008-10−1+i3−1−i31−i321+i320008-10−1+i3−1−i31−i321+i320008-10−1+i3−1−i31−i321+i320008-10−1+i3−1−i31−i321+i320008-10−1+i3−1−i31−i321+i320008-10−1+i3−1−i31−i321+i320008-10−1+i3−1−i31−i321+i320008-10−1+i3−1−i31−i321+i320008-10−1+i3−1−i31−i321+i320008-10−1+i3−1−i31−i321+i320008-10−1+i3−1−i31−i321+i32000
χ108-10−1−i3−1+i31+i321−i320008-10−1−i3−1+i31+i321−i320008-10−1−i3−1+i31+i321−i320008-10−1−i3−1+i31+i321−i320008-10−1−i3−1+i31+i321−i320008-10−1−i3−1+i31+i321−i320008-10−1−i3−1+i31+i321−i320008-10−1−i3−1+i31+i321−i320008-10−1−i3−1+i31+i321−i320008-10−1−i3−1+i31+i321−i320008-10−1−i3−1+i31+i321−i320008-10−1−i3−1+i31+i321−i32000
χ1111111111111111111111-1-1-1-1-1-1-1-1-1-111111111111111111111-1-1-1-1-1-1-1-1-1-111111111111111111111-1-1-1-1-1-1-1-1-1-111111111111111111111-1-1-1-1-1-1-1-1-1-1
χ12111−1+i32−1−i32−1+i32−1−i32−1+i32−1−i321111−1+i32−1−i32−1+i32−1−i32−1+i32−1−i321-1-1-11−i321+i321−i321+i321−i321+i32-1111−1+i32−1−i32−1+i32−1−i32−1+i32−1−i321111−1+i32−1−i32−1+i32−1−i32−1+i32−1−i321-1-1-11−i321+i321−i321+i321−i321+i32-1111−1+i32−1−i32−1+i32−1−i32−1+i32−1−i321111−1+i32−1−i32−1+i32−1−i32−1+i32−1−i321-1-1-11−i321+i321−i321+i321−i321+i32-1111−1+i32−1−i32−1+i32−1−i32−1+i32−1−i321111−1+i32−1−i32−1+i32−1−i32−1+i32−1−i321-1-1-11−i321+i321−i321+i321−i321+i32-1
χ13111−1−i32−1+i32−1−i32−1+i32−1−i32−1+i321111−1−i32−1+i32−1−i32−1+i32−1−i32−1+i321-1-1-11+i321−i321+i321−i321+i321−i32-1111−1−i32−1+i32−1−i32−1+i32−1−i32−1+i321111−1−i32−1+i32−1−i32−1+i32−1−i32−1+i321-1-1-11+i321−i321+i321−i321+i321−i32-1111−1−i32−1+i32−1−i32−1+i32−1−i32−1+i321111−1−i32−1+i32−1−i32−1+i32−1−i32−1+i321-1-1-11+i321−i321+i321−i321+i321−i32-1111−1−i32−1+i32−1−i32−1+i32−1−i32−1+i321111−1−i32−1+i32−1−i32−1+i32−1−i32−1+i321-1-1-11+i321−i321+i321−i321+i321−i32-1
χ1422-2-1-1-1-111022-2-1-1-1-1110-2-221111-1-1022-2-1-1-1-111022-2-1-1-1-1110-2-221111-1-1022-2-1-1-1-111022-2-1-1-1-1110-2-221111-1-1022-2-1-1-1-111022-2-1-1-1-1110-2-221111-1-10
χ1522-21−i321+i321−i321+i32−1+i32−1−i32022-21−i321+i321−i321+i32−1+i32−1−i320-2-22−1+i32−1−i32−1+i32−1−i321−i321+i32022-21−i321+i321−i321+i32−1+i32−1−i32022-21−i321+i321−i321+i32−1+i32−1−i320-2-22−1+i32−1−i32−1+i32−1−i321−i321+i32022-21−i321+i321−i321+i32−1+i32−1−i32022-21−i321+i321−i321+i32−1+i32−1−i320-2-22−1+i32−1−i32−1+i32−1−i321−i321+i32022-21−i321+i321−i321+i32−1+i32−1−i32022-21−i321+i321−i321+i32−1+i32−1−i320-2-22−1+i32−1−i32−1+i32−1−i321−i321+i320
χ1622-21+i321−i321+i321−i32−1−i32−1+i32022-21+i321−i321+i321−i32−1−i32−1+i320-2-22−1−i32−1+i32−1−i32−1+i321+i321−i32022-21+i321−i321+i321−i32−1−i32−1+i32022-21+i321−i321+i321−i32−1−i32−1+i320-2-22−1−i32−1+i32−1−i32−1+i321+i321−i32022-21+i321−i321+i321−i32−1−i32−1+i32022-21+i321−i321+i321−i32−1−i32−1+i320-2-22−1−i32−1+i32−1−i32−1+i321+i321−i32022-21+i321−i321+i321−i32−1−i32−1+i32022-21+i321−i321+i321−i32−1−i32−1+i320-2-22−1−i32−1+i32−1−i32−1+i321+i321−i320
χ17333000000-1333000000-1-3-3-30000001333000000-1333000000-1-3-3-30000001333000000-1333000000-1-3-3-30000001333000000-1333000000-1-3-3-30000001
χ188-1022-1-10008-1022-1-1000-810-2-2110008-1022-1-10008-1022-1-1000-810-2-2110008-1022-1-10008-1022-1-1000-810-2-2110008-1022-1-10008-1022-1-1000-810-2-211000
χ198-10−1+i3−1−i31−i321+i320008-10−1+i3−1−i31−i321+i32000-8101−i31+i3−1+i32−1−i320008-10−1+i3−1−i31−i321+i320008-10−1+i3−1−i31−i321+i32000-8101−i31+i3−1+i32−1−i320008-10−1+i3−1−i31−i321+i320008-10−1+i3−1−i31−i321+i32000-8101−i31+i3−1+i32−1−i320008-10−1+i3−1−i31−i321+i320008-10−1+i3−1−i31−i321+i32000-8101−i31+i3−1+i32−1−i32000
χ208-10−1−i3−1+i31+i321−i320008-10−1−i3−1+i31+i321−i32000-8101+i31−i3−1−i32−1+i320008-10−1−i3−1+i31+i321−i320008-10−1−i3−1+i31+i321−i32000-8101+i31−i3−1−i32−1+i320008-10−1−i3−1+i31+i321−i320008-10−1−i3−1+i31+i321−i32000-8101+i31−i3−1−i32−1+i320008-10−1−i3−1+i31+i321−i320008-10−1−i3−1+i31+i321−i32000-8101+i31−i3−1−i32−1+i32000
χ212222222222-1-1-1-1-1-1-1-1-1-100000000002222222222-1-1-1-1-1-1-1-1-1-100000000002222222222-1-1-1-1-1-1-1-1-1-100000000002222222222-1-1-1-1-1-1-1-1-1-10000000000
χ22222−1+i3−1−i3−1+i3−1−i3−1+i3−1−i32-1-1-11−i321+i321−i321+i321−i321+i32-10000000000222−1+i3−1−i3−1+i3−1−i3−1+i3−1−i32-1-1-11−i321+i321−i321+i321−i321+i32-10000000000222−1+i3−1−i3−1+i3−1−i3−1+i3−1−i32-1-1-11−i321+i321−i321+i321−i321+i32-10000000000222−1+i3−1−i3−1+i3−1−i3−1+i3−1−i32-1-1-11−i321+i321−i321+i321−i321+i32-10000000000
χ23222−1−i3−1+i3−1−i3−1+i3−1−i3−1+i32-1-1-11+i321−i321+i321−i321+i321−i32-10000000000222−1−i3−1+i3−1−i3−1+i3−1−i3−1+i32-1-1-11+i321−i321+i321−i321+i321−i32-10000000000222−1−i3−1+i3−1−i3−1+i3−1−i3−1+i32-1-1-11+i321−i321+i321−i321+i321−i32-10000000000222−1−i3−1+i3−1−i3−1+i3−1−i3−1+i32-1-1-11+i321−i321+i321−i321+i321−i32-10000000000
χ2444-4-2-2-2-2220-2-221111-1-10000000000044-4-2-2-2-2220-2-221111-1-10000000000044-4-2-2-2-2220-2-221111-1-10000000000044-4-2-2-2-2220-2-221111-1-100000000000
χ2544-41−i31+i31−i31+i3−1+i3−1−i30-2-22−1+i32−1−i32−1+i32−1−i321−i321+i320000000000044-41−i31+i31−i31+i3−1+i3−1−i30-2-22−1+i32−1−i32−1+i32−1−i321−i321+i320000000000044-41−i31+i31−i31+i3−1+i3−1−i30-2-22−1+i32−1−i32−1+i32−1−i321−i321+i320000000000044-41−i31+i31−i31+i3−1+i3−1−i30-2-22−1+i32−1−i32−1+i32−1−i321−i321+i3200000000000
χ2644-41+i31−i31+i31−i3−1−i3−1+i30-2-22−1−i32−1+i32−1−i32−1+i321+i321−i320000000000044-41+i31−i31+i31−i3−1−i3−1+i30-2-22−1−i32−1+i32−1−i32−1+i321+i321−i320000000000044-41+i31−i31+i31−i3−1−i3−1+i30-2-22−1−i32−1+i32−1−i32−1+i321+i321−i320000000000044-41+i31−i31+i31−i3−1−i3−1+i30-2-22−1−i32−1+i32−1−i32−1+i321+i321−i3200000000000
χ27666000000-2-3-3-300000010000000000666000000-2-3-3-300000010000000000666000000-2-3-3-300000010000000000666000000-2-3-3-300000010000000000
χ2816-2044-2-2000-810-2-211000000000000016-2044-2-2000-810-2-211000000000000016-2044-2-2000-810-2-211000000000000016-2044-2-2000-810-2-2110000000000000
χ2916-20−2+2i3−2−2i31−i31+i3000-8101−i31+i3−1+i32−1−i32000000000000016-20−2+2i3−2−2i31−i31+i3000-8101−i31+i3−1+i32−1−i32000000000000016-20−2+2i3−2−2i31−i31+i3000-8101−i31+i3−1+i32−1−i32000000000000016-20−2+2i3−2−2i31−i31+i3000-8101−i31+i3−1+i32−1−i320000000000000
χ3016-20−2−2i3−2+2i31+i31−i3000-8101+i31−i3−1−i32−1+i32000000000000016-20−2−2i3−2+2i31+i31−i3000-8101+i31−i3−1−i32−1+i32000000000000016-20−2−2i3−2+2i31+i31−i3000-8101+i31−i3−1−i32−1+i32000000000000016-20−2−2i3−2+2i31+i31−i3000-8101+i31−i3−1−i32−1+i320000000000000
χ31111111111111111111111111111111iiiiiiiiiiiiiiiiiiiiiiiiiiiiii-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−i−i−i−i−i−i−i−i−i−i−i−i−i−i−i−i−i−i−i−i−i−i−i−i−i−i−i−i−i−i
χ32111−1+i32−1−i32−1+i32−1−i32−1+i32−1−i321111−1+i32−1−i32−1+i32−1−i32−1+i32−1−i321111−1+i32−1−i32−1+i32−1−i32−1+i32−1−i321iiiζ7ζ11ζ7ζ11ζ7ζ11iiiiζ7ζ11ζ7ζ11ζ7ζ11iiiiζ7ζ11ζ7ζ11ζ7ζ11i-1-1-11−i321+i321−i321+i321−i321+i32-1-1-1-11−i321+i321−i321+i321−i321+i32-1-1-1-11−i321+i321−i321+i321−i321+i32-1−i−i−i−ζ7−ζ11−ζ7−ζ11−ζ7−ζ11−i−i−i−i−ζ7−ζ11−ζ7−ζ11−ζ7−ζ11−i−i−i−i−ζ7−ζ11−ζ7−ζ11−ζ7−ζ11−i
χ33111−1−i32−1+i32−1−i32−1+i32−1−i32−1+i321111−1−i32−1+i32−1−i32−1+i32−1−i32−1+i321111−1−i32−1+i32−1−i32−1+i32−1−i32−1+i321iiiζ11ζ7ζ11ζ7ζ11ζ7iiiiζ11ζ7ζ11ζ7ζ11ζ7iiiiζ11ζ7ζ11ζ7ζ11ζ7i-1-1-11+i321−i321+i321−i321+i321−i32-1-1-1-11+i321−i321+i321−i321+i321−i32-1-1-1-11+i321−i321+i321−i321+i321−i32-1−i−i−i−ζ11−ζ7−ζ11−ζ7−ζ11−ζ7−i−i−i−i−ζ11−ζ7−ζ11−ζ7−ζ11−ζ7−i−i−i−i−ζ11−ζ7−ζ11−ζ7−ζ11−ζ7−i
χ3422-2-1-1-1-111022-2-1-1-1-111022-2-1-1-1-11102i2i−2i−i−i−i−iii02i2i−2i−i−i−i−iii02i2i−2i−i−i−i−iii0-2-221111-1-10-2-221111-1-10-2-221111-1-10−2i−2i2iiiii−i−i0−2i−2i2iiiii−i−i0−2i−2i2iiiii−i−i0
χ3522-21−i321+i321−i321+i32−1+i32−1−i32022-21−i321+i321−i321+i32−1+i32−1−i32022-21−i321+i321−i321+i32−1+i32−1−i3202i2i−2i−ζ7−ζ11−ζ7−ζ11ζ7ζ1102i2i−2i−ζ7−ζ11−ζ7−ζ11ζ7ζ1102i2i−2i−ζ7−ζ11−ζ7−ζ11ζ7ζ110-2-22−1+i32−1−i32−1+i32−1−i321−i321+i320-2-22−1+i32−1−i32−1+i32−1−i321−i321+i320-2-22−1+i32−1−i32−1+i32−1−i321−i321+i320−2i−2i2iζ7ζ11ζ7ζ11−ζ7−ζ110−2i−2i2iζ7ζ11ζ7ζ11−ζ7−ζ110−2i−2i2iζ7ζ11ζ7ζ11−ζ7−ζ110
χ3622-21+i321−i321+i321−i32−1−i32−1+i32022-21+i321−i321+i321−i32−1−i32−1+i32022-21+i321−i321+i321−i32−1−i32−1+i3202i2i−2i−ζ11−ζ7−ζ11−ζ7ζ11ζ702i2i−2i−ζ11−ζ7−ζ11−ζ7ζ11ζ702i2i−2i−ζ11−ζ7−ζ11−ζ7ζ11ζ70-2-22−1−i32−1+i32−1−i32−1+i321+i321−i320-2-22−1−i32−1+i32−1−i32−1+i321+i321−i320-2-22−1−i32−1+i32−1−i32−1+i321+i321−i320−2i−2i2iζ11ζ7ζ11ζ7−ζ11−ζ70−2i−2i2iζ11ζ7ζ11ζ7−ζ11−ζ70−2i−2i2iζ11ζ7ζ11ζ7−ζ11−ζ70
χ37333000000-1333000000-1333000000-13i3i3i000000−i3i3i3i000000−i3i3i3i000000−i-3-3-30000001-3-3-30000001-3-3-30000001−3i−3i−3i000000i−3i−3i−3i000000i−3i−3i−3i000000i
χ388-1022-1-10008-1022-1-10008-1022-1-10008i−i02i2i−i−i0008i−i02i2i−i−i0008i−i02i2i−i−i000-810-2-211000-810-2-211000-810-2-211000−8ii0−2i−2iii000−8ii0−2i−2iii000−8ii0−2i−2iii000
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χ113222−1−i3−1+i3−1−i3−1+i3−1−i3−1+i32-1-1-11+i321−i321+i321−i321+i321−i32-10000000000−2i−2i−2i−2ζ11−2ζ7−2ζ11−2ζ7−2ζ11−2ζ7−2iiiiζ11ζ7ζ11ζ7ζ11ζ7i0000000000-2-2-21+i31−i31+i31−i31+i31−i3-2111−1−i32−1+i32−1−i32−1+i32−1−i32−1+i32100000000002i2i2i2ζ112ζ72ζ112ζ72ζ112ζ72i−i−i−i−ζ11−ζ7−ζ11−ζ7−ζ11−ζ7−i0000000000
χ11444-4-2-2-2-2220-2-221111-1-100000000000−4i−4i4i2i2i2i2i−2i−2i02i2i−2i−i−i−i−iii00000000000-4-442222-2-2022-2-1-1-1-111000000000004i4i−4i−2i−2i−2i−2i2i2i0−2i−2i2iiiii−i−i00000000000
χ11544-41−i31+i31−i31+i3−1+i3−1−i30-2-22−1+i32−1−i32−1+i32−1−i321−i321+i3200000000000−4i−4i4i2ζ72ζ112ζ72ζ11−2ζ7−2ζ1102i2i−2i−ζ7−ζ11−ζ7−ζ11ζ7ζ1100000000000-4-44−1+i3−1−i3−1+i3−1−i31−i31+i3022-21−i321+i321−i321+i32−1+i32−1−i32000000000004i4i−4i−2ζ7−2ζ11−2ζ7−2ζ112ζ72ζ110−2i−2i2iζ7ζ11ζ7ζ11−ζ7−ζ1100000000000
χ11644-41+i31−i31+i31−i3−1−i3−1+i30-2-22−1−i32−1+i32−1−i32−1+i321+i321−i3200000000000−4i−4i4i2ζ112ζ72ζ112ζ7−2ζ11−2ζ702i2i−2i−ζ11−ζ7−ζ11−ζ7ζ11ζ700000000000-4-44−1−i3−1+i3−1−i3−1+i31+i31−i3022-21+i321−i321+i321−i32−1−i32−1+i32000000000004i4i−4i−2ζ11−2ζ7−2ζ11−2ζ72ζ112ζ70−2i−2i2iζ11ζ7ζ11ζ7−ζ11−ζ700000000000
χ117666000000-2-3-3-300000010000000000−6i−6i−6i0000002i3i3i3i000000−i0000000000-6-6-60000002333000000-100000000006i6i6i000000−2i−3i−3i−3i000000i0000000000
χ11816-2044-2-2000-810-2-2110000000000000−16i2i0−4i−4i2i2i0008i−i02i2i−i−i0000000000000-1620-4-4220008-1022-1-1000000000000016i−2i04i4i−2i−2i000−8ii0−2i−2iii0000000000000
χ11916-20−2+2i3−2−2i31−i31+i3000-8101−i31+i3−1+i32−1−i320000000000000−16i2i0−4ζ7−4ζ112ζ72ζ110008i−i02ζ72ζ11−ζ7−ζ110000000000000-16202−2i32+2i3−1+i3−1−i30008-10−1+i3−1−i31−i321+i32000000000000016i−2i04ζ74ζ11−2ζ7−2ζ11000−8ii0−2ζ7−2ζ11ζ7ζ110000000000000
χ12016-20−2−2i3−2+2i31+i31−i3000-8101+i31−i3−1−i32−1+i320000000000000−16i2i0−4ζ11−4ζ72ζ112ζ70008i−i02ζ112ζ7−ζ11−ζ70000000000000-16202+2i32−2i3−1−i3−1+i30008-10−1−i3−1+i31+i321−i32000000000000016i−2i04ζ114ζ7−2ζ11−2ζ7000−8ii0−2ζ11−2ζ7ζ11ζ70000000000000

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