Finite Group Databasebeta

← Group #17976113

Character table — Group #17976113

Order 4352.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96C97C98C99C100C101C102C103C104C105C106C107C108C109C110C111C112C113C114C115C116
size1122244444444444488888888888888888161616161616161616161616161616161616161616161616161616161616161617173232323232323232323232323434346868686868686868686868686868686868686868136136136136136136136136136136136136136
order12244224417171717343434344448834343434686868686868686834343434343434346868686868686868686868686868686868686868686868684468686868136136136136136136136136224224444444444888888882244444888888
χ111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111-1-1-1-111-1-1-1-1
χ3111111111111111111111111111111111111111111111111111111111111111111-1-1111111111111-1-1-1-1-1-1-1iiii−i−i−i−iiiii−i−i−i−i-1-1-1ii−i−i-1-1ii−i−i
χ4111111111111111111111111111111111111111111111111111111111111111111-1-1111111111111-1-1-1-1-1-1-1−i−i−i−iiiii−i−i−i−iiiii-1-1-1−i−iii-1-1−i−iii
χ5111111111111111111-1-1-1-1111111111111111111111111111111111111-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1111111111-1-111-1-111-1-111-1-11-1-11-11-1-1-11-11-1
χ6111111111111111111-1-1-1-1111111111111111111111111111111111111-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-11111111-1-111-1-111-1-111-1-1111-1-1-11-11-1-1-11-11
χ7111111111111111111-1-1-1-1111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1ii−i−i−i−iiiii−i−i−i−iii-111i−i−ii11i−i−ii
χ8111111111111111111-1-1-1-1111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1−i−iiiii−i−i−i−iiiii−i−i-111−iii−i11−iii−i
χ9111111-11-111111111-11-11-11111111111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111-1-1-1-11111-11-111-1-111-1-111111111-11-1-1-1-1-11-1-11-11
χ10111111-11-111111111-11-11-11111111111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111-1-1-1-11111-11-1-1-111-1-111-1-1-1-1-1-1-1-1-11-111111-11-11-1
χ11111111-11-111111111-11-11-11111111111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-11-11ii−i−i−i−iiiiiii−i−i−i−i1-11−i−iii-11−iii−i
χ12111111-11-111111111-11-11-11111111111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-11-11−i−iiiii−i−i−i−i−i−iiiii1-11ii−i−i-11i−i−ii
χ13111111-11-111111111-1-11-111111111111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-111111111-11-11111111111-1-111-1-1-1-11-11-11-11-1-1-1-1
χ14111111-11-111111111-1-11-111111111111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-111111111-11-1-1-1-1-1-1-1-1-1-1-111-1-111-1-111-11-1-111111
χ15111111-11-111111111-1-11-111111111111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-11111-1-1-1-11-11iiii−i−i−i−iii−i−i−i−iii11-1−iii−i1-1−i−iii
χ16111111-11-111111111-1-11-111111111111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-11111-1-1-1-11-11−i−i−i−iiiii−i−iiiii−i−i11-1i−i−ii1-1ii−i−i
χ1711111-11-1111111111-11-1-11111111111111-1-1-1-11111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-1-11111111-11-1111-1-111-1-1-1-1-1-1-1-1-1-1-11-11111-11-11-11
χ1811111-11-1111111111-11-1-11111111111111-1-1-1-11111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-1-11111111-11-11-1-111-1-11111111111-11-1-1-1-1-1-111-11-1
χ1911111-11-1111111111-11-1-11111111111111-1-1-1-11111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1-11-11-1ii−i−i−i−iii−i−i−i−iiiii1-11ii−i−i1-1−iii−i
χ2011111-11-1111111111-11-1-11111111111111-1-1-1-11111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1-11-11-1−i−iiiii−i−iiiii−i−i−i−i1-11−i−iii1-1i−i−ii
χ2111111-11-1111111111-1-111-1111111111111-1-1-1-11111-1-1-1-11111-1-1-1-1-1-1-1-11111111111-1-1-1-11111-1-1-1-1111-11-1111111111-1-111-1-111-1-111-11-11-1-1-1-1-1
χ2211111-11-1111111111-1-111-1111111111111-1-1-1-11111-1-1-1-11111-1-1-1-1-1-1-1-11111111111-1-1-1-11111-1-1-1-1111-11-11-1-1-1-1-1-1-1-111-1-111-1-1-1-11-11-111-11111
χ2311111-11-1111111111-1-111-1111111111111-1-1-1-11111-1-1-1-11111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-11111-1-1-1-1-1-1-11-11-1iiii−i−i−i−i−i−iiiii−i−i11-1i−i−ii-11−i−iii
χ2411111-11-1111111111-1-111-1111111111111-1-1-1-11111-1-1-1-11111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-11111-1-1-1-1-1-1-11-11-1−i−i−i−iiiiiii−i−i−i−iii11-1−iii−i-11ii−i−i
χ2511111-1-1-1-111111111111-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111111111111111-1-1-1-1-1-1-1-1111-1-1-1-111111111-1-1-1-1-1-1-1-1111-1-1-1-1-1-11111
χ2611111-1-1-1-111111111111-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111111111111111-1-1-1-1-1-1-1-1111-1-1-1-1-1-1-1-1-1-1-1-1111111111111111-1-1-1-1-1-1
χ2711111-1-1-1-111111111111-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111111111-1-11111-1-1-1-1-1-1-1-1-1-1-11111iiii−i−i−i−i−i−i−i−iiiii-1-1-1−i−iii11ii−i−i
χ2811111-1-1-1-111111111111-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111111111-1-11111-1-1-1-1-1-1-1-1-1-1-11111−i−i−i−iiiiiiiii−i−i−i−i-1-1-1ii−i−i11−i−iii
χ2911111-1-1-1-1111111111-1-111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-111-1-1-1-111111111111-1-1-1-111-1-111-1-1-1-111-1-1111-1-1-11-11111-11-1
χ3011111-1-1-1-1111111111-1-111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-111-1-1-1-111111111111-1-1-1-1-1-111-1-11111-1-111-1-11-1-11-11-111-11-11
χ3111111-1-1-1-1111111111-1-111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-11111ii−i−i−i−iii−i−iiiii−i−i-111−iii−i-1-1i−i−ii
χ3211111-1-1-1-1111111111-1-111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-11111−i−iiiii−i−iii−i−i−i−iii-111i−i−ii-1-1−iii−i
χ3322-22-2020-22222222200000-2-2-2-22222-2-2-2-2000022220000-2-2-2-20000000000000000220000000000002-2-20-202002-2002-2002-2002-20000000000000
χ3422-22-2020-22222222200000-2-2-2-22222-2-2-2-2000022220000-2-2-2-20000000000000000220000000000002-2-20-20200-2200-2200-2200-220000000000000
χ3522-22-2020-22222222200000-2-2-2-22222-2-2-2-2000022220000-2-2-2-20000000000000000-2-2000000000000-222020-2002i−2i00−2i2i002i−2i00−2i2i0000000000000
χ3622-22-2020-22222222200000-2-2-2-22222-2-2-2-2000022220000-2-2-2-20000000000000000-2-2000000000000-222020-200−2i2i002i−2i00−2i2i002i−2i0000000000000
χ3722-22-20-2022222222200000-2-2-2-22222-2-2-2-20000-2-2-2-2000022220000000000000000220000000000002-2-2020-2002-2002-200-2200-220000000000000
χ3822-22-20-2022222222200000-2-2-2-22222-2-2-2-20000-2-2-2-2000022220000000000000000220000000000002-2-2020-200-2200-22002-2002-20000000000000
χ3922-22-20-2022222222200000-2-2-2-22222-2-2-2-20000-2-2-2-2000022220000000000000000-2-2000000000000-2220-202002i−2i00−2i2i00−2i2i002i−2i0000000000000
χ4022-22-20-2022222222200000-2-2-2-22222-2-2-2-20000-2-2-2-2000022220000000000000000-2-2000000000000-2220-20200−2i2i002i−2i002i−2i00−2i2i0000000000000
χ4122-2-2220-202222222200000-2-2-2-2-2-2-2-2222222220000-2-2-2-20000000000000000000022000000000000-22-2-20202-2002-2002-2002-2000000000000000
χ4222-2-2220-202222222200000-2-2-2-2-2-2-2-2222222220000-2-2-2-20000000000000000000022000000000000-22-2-2020-2200-2200-2200-22000000000000000
χ4322-2-2220-202222222200000-2-2-2-2-2-2-2-2222222220000-2-2-2-200000000000000000000-2-20000000000002-2220-202i−2i00−2i2i002i−2i00−2i2i000000000000000
χ4422-2-2220-202222222200000-2-2-2-2-2-2-2-2222222220000-2-2-2-200000000000000000000-2-20000000000002-2220-20−2i2i002i−2i00−2i2i002i−2i000000000000000
χ4522-2-22-20202222222200000-2-2-2-2-2-2-2-22222-2-2-2-2000022220000000000000000000022000000000000-22-220-202-2002-200-2200-22000000000000000
χ4622-2-22-20202222222200000-2-2-2-2-2-2-2-22222-2-2-2-2000022220000000000000000000022000000000000-22-220-20-2200-22002-2002-2000000000000000
χ4722-2-22-20202222222200000-2-2-2-2-2-2-2-22222-2-2-2-20000222200000000000000000000-2-20000000000002-22-20202i−2i00−2i2i00−2i2i002i−2i000000000000000
χ4822-2-22-20202222222200000-2-2-2-2-2-2-2-22222-2-2-2-20000222200000000000000000000-2-20000000000002-22-2020−2i2i002i−2i002i−2i00−2i2i000000000000000
χ49444444444−ζ18−ζ30−ζ38−ζ50−ζ6−ζ10−ζ58−ζ62−ζ14−ζ22−ζ46−ζ54−ζ2−ζ26−ζ42−ζ66−ζ18−ζ30−ζ38−ζ50−ζ6−ζ10−ζ58−ζ62−ζ14−ζ22−ζ46−ζ54−ζ2−ζ26−ζ42−ζ6644444−ζ18−ζ30−ζ38−ζ50−ζ6−ζ10−ζ58−ζ62−ζ14−ζ22−ζ46−ζ54−ζ2−ζ26−ζ42−ζ66−ζ18−ζ30−ζ38−ζ50−ζ6−ζ10−ζ58−ζ62−ζ14−ζ22−ζ46−ζ54−ζ2−ζ26−ζ42−ζ66−ζ18−ζ30−ζ38−ζ50−ζ6−ζ10−ζ58−ζ62−ζ14−ζ22−ζ46−ζ54−ζ2−ζ26−ζ42−ζ66−ζ18−ζ30−ζ38−ζ50−ζ6−ζ10−ζ58−ζ62−ζ14−ζ22−ζ46−ζ54−ζ2−ζ26−ζ42−ζ66−ζ18−ζ30−ζ38−ζ50−ζ6−ζ10−ζ58−ζ62−ζ14−ζ22−ζ46−ζ54−ζ2−ζ26−ζ42−ζ66−ζ18−ζ30−ζ38−ζ50−ζ6−ζ10−ζ58−ζ62−ζ14−ζ22−ζ46−ζ54−ζ2−ζ26−ζ42−ζ66−ζ18−ζ30−ζ38−ζ50−ζ6−ζ10−ζ58−ζ62−ζ14−ζ22−ζ46−ζ54−ζ2−ζ26−ζ42−ζ66−ζ18−ζ30−ζ38−ζ50−ζ18−ζ30−ζ38−ζ50−ζ6−ζ10−ζ58−ζ62−ζ6−ζ10−ζ58−ζ62−ζ14−ζ22−ζ46−ζ54−ζ14−ζ22−ζ46−ζ54−ζ2−ζ26−ζ42−ζ66−ζ2−ζ26−ζ42−ζ66−ζ18−ζ30−ζ38−ζ50−ζ18−ζ30−ζ38−ζ50−ζ6−ζ10−ζ58−ζ62−ζ6−ζ10−ζ58−ζ62−ζ14−ζ22−ζ46−ζ54−ζ14−ζ22−ζ46−ζ54−ζ2−ζ26−ζ42−ζ66−ζ2−ζ26−ζ42−ζ6600−ζ18−ζ30−ζ38−ζ50−ζ6−ζ10−ζ58−ζ62−ζ14−ζ22−ζ46−ζ54−ζ2−ζ26−ζ42−ζ66−ζ18−ζ30−ζ38−ζ50−ζ6−ζ10−ζ58−ζ62−ζ14−ζ22−ζ46−ζ54−ζ2−ζ26−ζ42−ζ66−ζ18−ζ30−ζ38−ζ50−ζ6−ζ10−ζ58−ζ62−ζ14−ζ22−ζ46−ζ54−ζ2−ζ26−ζ42−ζ66000000000000000000000000000000000000
χ50444444444−ζ18−ζ30−ζ38−ζ50−ζ6−ζ10−ζ58−ζ62−ζ14−ζ22−ζ46−ζ54−ζ2−ζ26−ζ42−ζ66−ζ18−ζ30−ζ38−ζ50−ζ6−ζ10−ζ58−ζ62−ζ14−ζ22−ζ46−ζ54−ζ2−ζ26−ζ42−ζ664-4-4-4-4−ζ18−ζ30−ζ38−ζ50−ζ6−ζ10−ζ58−ζ62−ζ14−ζ22−ζ46−ζ54−ζ2−ζ26−ζ42−ζ66−ζ18−ζ30−ζ38−ζ50−ζ6−ζ10−ζ58−ζ62−ζ14−ζ22−ζ46−ζ54−ζ2−ζ26−ζ42−ζ66−ζ18−ζ30−ζ38−ζ50−ζ6−ζ10−ζ58−ζ62−ζ14−ζ22−ζ46−ζ54−ζ2−ζ26−ζ42−ζ66−ζ18−ζ30−ζ38−ζ50−ζ6−ζ10−ζ58−ζ62−ζ14−ζ22−ζ46−ζ54−ζ2−ζ26−ζ42−ζ66−ζ18−ζ30−ζ38−ζ50−ζ6−ζ10−ζ58−ζ62−ζ14−ζ22−ζ46−ζ54−ζ2−ζ26−ζ42−ζ66−ζ18−ζ30−ζ38−ζ50−ζ6−ζ10−ζ58−ζ62−ζ14−ζ22−ζ46−ζ54−ζ2−ζ26−ζ42−ζ66−ζ18−ζ30−ζ38−ζ50−ζ6−ζ10−ζ58−ζ62−ζ14−ζ22−ζ46−ζ54−ζ2−ζ26−ζ42−ζ66−ζ18−ζ30−ζ38−ζ50−ζ18−ζ30−ζ38−ζ50−ζ6−ζ10−ζ58−ζ62−ζ6−ζ10−ζ58−ζ62−ζ14−ζ22−ζ46−ζ54−ζ14−ζ22−ζ46−ζ54−ζ2−ζ26−ζ42−ζ66−ζ2−ζ26−ζ42−ζ66ζ18+ζ30+ζ38+ζ50ζ18+ζ30+ζ38+ζ50ζ6+ζ10+ζ58+ζ62ζ6+ζ10+ζ58+ζ62ζ14+ζ22+ζ46+ζ54ζ14+ζ22+ζ46+ζ54ζ2+ζ26+ζ42+ζ66ζ2+ζ26+ζ42+ζ6600ζ18+ζ30+ζ38+ζ50ζ6+ζ10+ζ58+ζ62ζ14+ζ22+ζ46+ζ54ζ2+ζ26+ζ42+ζ66ζ18+ζ30+ζ38+ζ50ζ6+ζ10+ζ58+ζ62ζ14+ζ22+ζ46+ζ54ζ2+ζ26+ζ42+ζ66ζ18+ζ30+ζ38+ζ50ζ6+ζ10+ζ58+ζ62ζ14+ζ22+ζ46+ζ54ζ2+ζ26+ζ42+ζ66000000000000000000000000000000000000
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χ1078-800000008888-8-8-8-800000000000000000000000000000000000000000000000008i−8i000000000000000000000000000000000000000000000000
χ1088-800000008888-8-8-8-80000000000000000000000000000000000000000000000000−8i8i000000000000000000000000000000000000000000000000
χ10916-160000000−4ζ18−4ζ30−4ζ38−4ζ50−4ζ6−4ζ10−4ζ58−4ζ62−4ζ14−4ζ22−4ζ46−4ζ54−4ζ2−4ζ26−4ζ42−4ζ664ζ18+4ζ30+4ζ38+4ζ504ζ6+4ζ10+4ζ58+4ζ624ζ14+4ζ22+4ζ46+4ζ544ζ2+4ζ26+4ζ42+4ζ66000000000000000000000000000000000000000002ζ18−2ζ30−2ζ38+2ζ50−2ζ18+2ζ30+2ζ38−2ζ502ζ6−2ζ10−2ζ58+2ζ62−2ζ6+2ζ10+2ζ58−2ζ622ζ14−2ζ22−2ζ46+2ζ54−2ζ14+2ζ22+2ζ46−2ζ542ζ2−2ζ26−2ζ42+2ζ66−2ζ2+2ζ26+2ζ42−2ζ6600000000000000000000000000000000000000000000000000
χ11016-160000000−4ζ18−4ζ30−4ζ38−4ζ50−4ζ6−4ζ10−4ζ58−4ζ62−4ζ14−4ζ22−4ζ46−4ζ54−4ζ2−4ζ26−4ζ42−4ζ664ζ18+4ζ30+4ζ38+4ζ504ζ6+4ζ10+4ζ58+4ζ624ζ14+4ζ22+4ζ46+4ζ544ζ2+4ζ26+4ζ42+4ζ6600000000000000000000000000000000000000000−2ζ18+2ζ30+2ζ38−2ζ502ζ18−2ζ30−2ζ38+2ζ50−2ζ6+2ζ10+2ζ58−2ζ622ζ6−2ζ10−2ζ58+2ζ62−2ζ14+2ζ22+2ζ46−2ζ542ζ14−2ζ22−2ζ46+2ζ54−2ζ2+2ζ26+2ζ42−2ζ662ζ2−2ζ26−2ζ42+2ζ6600000000000000000000000000000000000000000000000000
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χ11516-160000000−4ζ2−4ζ26−4ζ42−4ζ66−4ζ14−4ζ22−4ζ46−4ζ54−4ζ6−4ζ10−4ζ58−4ζ62−4ζ18−4ζ30−4ζ38−4ζ504ζ2+4ζ26+4ζ42+4ζ664ζ14+4ζ22+4ζ46+4ζ544ζ6+4ζ10+4ζ58+4ζ624ζ18+4ζ30+4ζ38+4ζ50000000000000000000000000000000000000000002ζ2−2ζ26−2ζ42+2ζ66−2ζ2+2ζ26+2ζ42−2ζ66−2ζ14+2ζ22+2ζ46−2ζ542ζ14−2ζ22−2ζ46+2ζ542ζ6−2ζ10−2ζ58+2ζ62−2ζ6+2ζ10+2ζ58−2ζ62−2ζ18+2ζ30+2ζ38−2ζ502ζ18−2ζ30−2ζ38+2ζ5000000000000000000000000000000000000000000000000000
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Here ζ is a primitive root of unity of order 68 (ζ68 = 1); i = ζ17.