Finite Group Databasebeta

← Group #11751690

Character table — Group #11751690

Order 960.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51
size112224444445588888888888101010121220202020202020203030303040404040484860606060
order12346581012242444152030404060601201201201202121244688888242488882424242420202244
χ1111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111-1-1-1-111-1-1-1-1-1-1-1-11111-1-1
χ3111111111111111111111111111-1-111111111-1-1-1-11111-1-1-1-1-1-1
χ4111111111111111111111111111-1-111-1-1-1-1111111-1-1-1-1-1-1-1-111
χ511111111111-1-111111111111-1-1-111-1-1ii−i−i-1-1ii−i−iii−i−i11-1-1i−i
χ611111111111-1-111111111111-1-1-111-1-1−i−iii-1-1−i−iii−i−iii11-1-1−ii
χ711111111111-1-111111111111-1-1-1-1-1-1-1ii−i−i-1-1−i−iiiii−i−i-1-111−ii
χ811111111111-1-111111111111-1-1-1-1-1-1-1−i−iii-1-1ii−i−i−i−iii-1-111i−i
χ9111111-111-1-111111-1-111-1-1-1-11111-11-11-11-1-1-111111-11-11-11-1-1-1
χ10111111-111-1-111111-1-111-1-1-1-11111-11-1-11-11-1-1-1-1-1-1-11-111-11-111
χ11111111-111-1-111111-1-111-1-1-1-1111-111-11-11-1-1-1-1-1-1-11-11-1-11-1111
χ12111111-111-1-111111-1-111-1-1-1-1111-111-1-11-11-1-11111-11-11-11-11-1-1
χ13111111-111-1-1-1-1111-1-111-1-1-1-1-1-1-11-1-11i−i−ii11ii−i−ii−i−ii1-1-11−ii
χ14111111-111-1-1-1-1111-1-111-1-1-1-1-1-1-11-1-11−iii−i11−i−iii−iii−i1-1-11i−i
χ15111111-111-1-1-1-1111-1-111-1-1-1-1-1-1-1-11-11i−i−ii11−i−iiii−i−ii-111-1i−i
χ16111111-111-1-1-1-1111-1-111-1-1-1-1-1-1-1-11-11−iii−i11ii−i−i−iii−i-111-1−ii
χ17222-22202-200222-2200-2-20000-22200-200000002-22-20000000000
χ18222-22202-200222-2200-2-20000-22200-20000000-22-220000000000
χ19222-22202-200-2-22-2200-2-200002-2-200200000002i−2i−2i2i0000000000
χ20222-22202-200-2-22-2200-2-200002-2-20020000000−2i2i2i−2i0000000000
χ2122-12-1222-1-1-122-12-122-1-1-1-1-1-12-1-100-122222-1-10000-1-1-1-1000000
χ2222-12-1222-1-1-122-12-122-1-1-1-1-1-12-1-100-12-2-2-2-2-1-100001111000000
χ2322-12-1222-1-1-1-2-2-12-122-1-1-1-1-1-1-211001-22i2i−2i−2i110000−i−iii000000
χ2422-12-1222-1-1-1-2-2-12-122-1-1-1-1-1-1-211001-2−2i−2i2i2i110000ii−i−i000000
χ2522-12-12-22-11122-12-1-2-2-1-111112-1-100-1-22-22-2110000-11-11000000
χ2622-12-12-22-11122-12-1-2-2-1-111112-1-100-1-2-22-221100001-11-1000000
χ2722-12-12-22-111-2-2-12-1-2-2-1-11111-21100122i−2i−2i2i-1-10000−iii−i000000
χ2822-12-12-22-111-2-2-12-1-2-2-1-11111-2110012−2i2i2i−2i-1-10000i−i−ii000000
χ2944444-14-144400-1-1-1-1-1-1-1-1-1-1-1000440000000000000000-1-10000
χ3044444-14-144400-1-1-1-1-1-1-1-1-1-1-1000-4-40000000000000000110000
χ3144444-1-4-14-4-400-1-1-111-1-111110004-40000000000000000-110000
χ3244444-1-4-14-4-400-1-1-111-1-11111000-4400000000000000001-10000
χ3344-2-4-240420044-2-4-200220000-4-2-2002000000000000000000000
χ3444-2-4-2404200-4-4-2-4-20022000042200-2000000000000000000000
χ354-440-440-40004i−4i40-40000000004i−4i000000000000000000000000
χ364-440-440-4000−4i4i40-4000000000−4i4i000000000000000000000000
χ374-4-20240-406−64i−4i-202000066−6−60−2i2i00000000−i6i600000000000000
χ384-4-20240-406−6−4i4i-202000066−6−602i−2i00000000i6−i600000000000000
χ394-4-20240-40−664i−4i-2020000−6−6660−2i2i00000000i6−i600000000000000
χ404-4-20240-40−66−4i4i-2020000−6−66602i−2i00000000−i6i600000000000000
χ41888-88-20-2-80000-22-200220000000000000000000000000000000
χ4288-48-4-28-2-4-4-4001-21-2-2111111000000000000000000000000000
χ4388-48-4-2-8-2-444001-212211-1-1-1-1000000000000000000000000000
χ4488-4-8-4-20-24000012100-1-1−1515−1515000000000000000000000000000
χ4588-4-8-4-20-24000012100-1-115−1515−15000000000000000000000000000
χ468-880-8-20200000-20210−100010−10−1010000000000000000000000000000
χ478-880-8-20200000-202−101000−101010−10000000000000000000000000000
χ488-8-404-202026−260010-110−10−1515−ζ7+ζ53−ζ61+ζ71+ζ77−ζ103−ζ109+ζ119−ζ13+ζ23+ζ29−ζ31−ζ37+ζ47−ζ79+ζ101ζ7−ζ53+ζ61−ζ71−ζ77+ζ103+ζ109−ζ119ζ13−ζ23−ζ29+ζ31+ζ37−ζ47+ζ79−ζ101000000000000000000000000000
χ498-8-404-202026−260010-1−101015−15−ζ13+ζ23+ζ29−ζ31−ζ37+ζ47−ζ79+ζ101−ζ7+ζ53−ζ61+ζ71+ζ77−ζ103−ζ109+ζ119ζ13−ζ23−ζ29+ζ31+ζ37−ζ47+ζ79−ζ101ζ7−ζ53+ζ61−ζ71−ζ77+ζ103+ζ109−ζ119000000000000000000000000000
χ508-8-404-2020−26260010-110−1015−15ζ13−ζ23−ζ29+ζ31+ζ37−ζ47+ζ79−ζ101ζ7−ζ53+ζ61−ζ71−ζ77+ζ103+ζ109−ζ119−ζ13+ζ23+ζ29−ζ31−ζ37+ζ47−ζ79+ζ101−ζ7+ζ53−ζ61+ζ71+ζ77−ζ103−ζ109+ζ119000000000000000000000000000
χ518-8-404-2020−26260010-1−1010−1515ζ7−ζ53+ζ61−ζ71−ζ77+ζ103+ζ109−ζ119ζ13−ζ23−ζ29+ζ31+ζ37−ζ47+ζ79−ζ101−ζ7+ζ53−ζ61+ζ71+ζ77−ζ103−ζ109+ζ119−ζ13+ζ23+ζ29−ζ31−ζ37+ζ47−ζ79+ζ101000000000000000000000000000

Here ζ is a primitive root of unity of order 120 (ζ120 = 1); i = ζ30.