Finite Group Databasebeta

← Group #14418084

Character table — Group #14418084

Order 1920.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90
size1122244444444555555668888810101010101010101012121216161616161620202020202020202020202020202020202024243030303030303232404040404040484848606060606060606060
order123462458101224244488882461215203028812122424242422810204060120120244468888812121212242424241020248888306061224242424101040444488888
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111-1-111111111111111-1-1-1111111111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1
χ3111111111111111-1-1-1-111111111-1-111-1-1-1-111111111111-1-111-1-1-1-1-1-1-1-111-1-11111-1-1-1-11111-1-1-1-111111-1-11-1-1-1-1
χ4111111111111111-1-1-1-1-1-1111111-1-111-1-1-1-1-1-1-111111111-1-111-1-1-1-1-1-1-1-111-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-111-11111
χ51111111111111-1-1ii−i−i1111111-1i−i-1-1ii−i−i111111111-1-1i−i-1-1ii−i−iii−i−i-1-1i−i11-1-1ii−i−i11-1-1ii−i−i111-1-1i−i-1ii−i−i
χ61111111111111-1-1ii−i−i-1-111111-1i−i-1-1ii−i−i-1-1-1111111-1-1i−i-1-1ii−i−iii−i−i-1-1i−i-1-111−i−iii11-1-1ii−i−i-1-1-111−ii1−i−iii
χ71111111111111-1-1−i−iii1111111-1−ii-1-1−i−iii111111111-1-1−ii-1-1−i−iii−i−iii-1-1−ii11-1-1−i−iii11-1-1−i−iii111-1-1−ii-1−i−iii
χ81111111111111-1-1−i−iii-1-111111-1−ii-1-1−i−iii-1-1-1111111-1-1−ii-1-1−i−iii−i−iii-1-1−ii-1-111ii−i−i11-1-1−i−iii-1-1-111i−i1ii−i−i
χ9111111-11-111-1-1111111111-11111111111111-1-11-1-11-1-1-11-1-11-11-11-1-1-1-1-1-1-111111111111-1-111-11-11-1-11-1-1-1-11-11-1
χ10111111-11-111-1-1111111-1-11-1111111111111-1111-1-11-1-1-11-1-11-11-11-1-1-1-1-1-1-111-1-1-1-1-1-1-1-11-1-111-11-1-111-11111-11-11
χ11111111-11-111-1-111-1-1-1-1111-11111-1-111-1-1-1-11-1-11-1-11-1-1-11111-1-11-111111-1-1-1-11111-1-1-1-11-1-11-11-111-1-11-111-1-11-11
χ12111111-11-111-1-111-1-1-1-1-1-11-11111-1-111-1-1-1-1-1111-1-11-1-1-11111-1-11-111111-1-1-1-1-1-1-1-111111-1-11-11-11-111-11-1-111-11-1
χ13111111-11-111-1-1-1-1ii−i−i111-1111-1i−i-1-1ii−i−i1-1-11-1-11-1-11-1−ii-11i−i−ii−i−iii11i−i11-1-1ii−i−i1-11-1i−i−ii1-1-1-11−ii1i−i−ii
χ14111111-11-111-1-1-1-1ii−i−i-1-11-1111-1i−i-1-1ii−i−i-1111-1-11-1-11-1−ii-11i−i−ii−i−iii11i−i-1-111−i−iii1-11-1i−i−ii-1111-1i−i-1−iii−i
χ15111111-11-111-1-1-1-1−i−iii111-1111-1−ii-1-1−i−iii1-1-11-1-11-1-11-1i−i-11−iii−iii−i−i11−ii11-1-1−i−iii1-11-1−iii−i1-1-1-11i−i1−iii−i
χ16111111-11-111-1-1-1-1−i−iii-1-11-1111-1−ii-1-1−i−iii-1111-1-11-1-11-1i−i-11−iii−iii−i−i11−ii-1-111ii−i−i1-11-1−iii−i-1111-1−ii-1i−i−ii
χ1711111-111-111-1-111111111-11111111111111-11-1-11-11-1-11-1-1-11-1-11-11-1-1-1-1-1-11111111111-111-1-11-11-11-1-11-1-1-1-11-11
χ1811111-111-111-1-1111111-1-1-111111111111111-11-11-11-1-11-1-1-11-1-11-11-1-1-1-1-1-111-1-1-1-1-1-1-1-1-111-1-11-111-111-11111-11-1
χ1911111-111-111-1-111-1-1-1-111-111111-1-111-1-1-1-1-11-1-11-11-1-11-1111-11-11-11111-1-1-1-11111-1-1-1-1-111-11-11-1-11-1-1111-11-11-1
χ2011111-111-111-1-111-1-1-1-1-1-1-111111-1-111-1-1-1-11-11-11-11-1-11-1111-11-11-11111-1-1-1-1-1-1-1-11111-111-11-11-11-111-1-1-11-11-11
χ2111111-111-111-1-1-1-1ii−i−i11-11111-1i−i-1-1ii−i−i-11-1-11-11-1-1-11−ii-11−iii−i−i−iii11i−i11-1-1ii−i−i-11-11−iii−i-11-11-1−ii1−iii−i
χ2211111-111-111-1-1-1-1ii−i−i-1-1-11111-1i−i-1-1ii−i−i1-11-11-11-1-1-11−ii-11−iii−i−i−iii11i−i-1-111−i−iii-11-11−iii−i1-11-11i−i-1i−i−ii
χ2311111-111-111-1-1-1-1−i−iii11-11111-1−ii-1-1−i−iii-11-1-11-11-1-1-11i−i-11i−i−iiii−i−i11−ii11-1-1−i−iii-11-11i−i−ii-11-11-1i−i1i−i−ii
χ2411111-111-111-1-1-1-1−i−iii-1-1-11111-1−ii-1-1−i−iii1-11-11-11-1-1-11i−i-11i−i−iiii−i−i11−ii-1-111ii−i−i-11-11i−i−ii1-11-11−ii-1−iii−i
χ2511111-1-111111111111111-1-1111111111111-1-11-1-11111-1-11111-1-1-1-11111111111111111-1-1-1-1-1-1-1-1-1-11-1-1111-1-1-1-1
χ2611111-1-1111111111111-1-1-1-111111111111111-1-1-11111-1-11111-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-111-1-1-11111
χ2711111-1-111111111-1-1-1-111-1-11111-1-111-1-1-1-1-1-11-1-11111-1-1-1-1111111-1-1-1-111-1-11111-1-1-1-1-1-1-1-11111-1-11-1-1-1-111111
χ2811111-1-111111111-1-1-1-1-1-1-1-11111-1-111-1-1-1-111-1-1-11111-1-1-1-1111111-1-1-1-111-1-1-1-1-1-11111-1-1-1-1111111-11111-1-1-1-1-1
χ2911111-1-1111111-1-1ii−i−i11-1-1111-1i−i-1-1ii−i−i-1-11-1-1111111i−i-1-1−i−iiiii−i−i-1-1i−i11-1-1ii−i−i-1-111−i−iii-1-1111i−i-1−i−iii
χ3011111-1-1111111-1-1ii−i−i-1-1-1-1111-1i−i-1-1ii−i−i11-1-1-1111111i−i-1-1−i−iiiii−i−i-1-1i−i-1-111−i−iii-1-111−i−iii11-1-1-1−ii1ii−i−i
χ3111111-1-1111111-1-1−i−iii11-1-1111-1−ii-1-1−i−iii-1-11-1-1111111−ii-1-1ii−i−i−i−iii-1-1−ii11-1-1−i−iii-1-111ii−i−i-1-1111−ii-1ii−i−i
χ3211111-1-1111111-1-1−i−iii-1-1-1-1111-1−ii-1-1−i−iii11-1-1-1111111−ii-1-1ii−i−i−i−iii-1-1−ii-1-111ii−i−i-1-111ii−i−i11-1-1-1i−i1−i−iii
χ33222-2200202-2002222222-2002-22-2-2-2222222000000-2000000-200000000000-2-22-2-222-22-200000000000000000000
χ34222-2200202-200222222-22002-22-2-2-2222222000000-2000000-200000000000-2-2-222-2-22-2200000000000000000000
χ35222-2200202-20022-2-2-2-22-2002-22-22222-2-2-2-2000000-2000000-200000000000222-2-22-22-2200000000000000000000
χ36222-2200202-20022-2-2-2-2-22002-22-22222-2-2-2-2000000-2000000-20000000000022-222-22-22-200000000000000000000
χ37222-2200202-200-2-22i2i−2i−2i2-2002-222−2i2i-2-22i2i−2i−2i000000-2000000200000000000−2i2i2-22-22i−2i−2i2i00000000000000000000
χ38222-2200202-200-2-22i2i−2i−2i-22002-222−2i2i-2-22i2i−2i−2i000000-2000000200000000000−2i2i-22-22−2i2i2i−2i00000000000000000000
χ39222-2200202-200-2-2−2i−2i2i2i2-2002-2222i−2i-2-2−2i−2i2i2i000000-20000002000000000002i−2i2-22-2−2i2i2i−2i00000000000000000000
χ40222-2200202-200-2-2−2i−2i2i2i-22002-2222i−2i-2-2−2i−2i2i2i000000-20000002000000000002i−2i-22-222i−2i−2i2i00000000000000000000
χ4122-12-122222-1-1-122222200-1-1-12-1222-1-1-1-1-1-1000222-1-1-12222-122222-1-1-1-1-1-1-1-100000000-1-1-1-1-1-1-1-1000000000000
χ4222-12-122222-1-1-122-2-2-2-200-1-1-12-12-2-2-1-11111000222-1-1-122-2-2-12-2-2-2-21111-1-11100000000-1-1-1-11111000000000000
χ4322-12-122222-1-1-1-2-22i2i−2i−2i00-1-1-12-1-22i−2i11−i−iii000222-1-1-1-2-22i−2i1-22i2i−2i−2i−i−iii11−ii00000000-1-111−i−iii000000000000
χ4422-12-122222-1-1-1-2-2−2i−2i2i2i00-1-1-12-1-2−2i2i11ii−i−i000222-1-1-1-2-2−2i2i1-2−2i−2i2i2iii−i−i11i−i00000000-1-111ii−i−i000000000000
χ4522-12-12-22-22-11122222200-11-12-1222-1-1-1-1-1-10002-2-2-111-22-2-2-1-22-22-2111111-1-100000000-111-1-11-11000000000000
χ4622-12-12-22-22-11122-2-2-2-200-11-12-12-2-2-1-111110002-2-2-111-2222-1-2-22-22-1-1-1-1111100000000-111-11-11-1000000000000
χ4722-12-12-22-22-111-2-22i2i−2i−2i00-11-12-1-22i−2i11−i−iii0002-2-2-1112-2−2i2i122i−2i−2i2iii−i−i-1-1−ii00000000-11-11−iii−i000000000000
χ4822-12-12-22-22-111-2-2−2i−2i2i2i00-11-12-1-2−2i2i11ii−i−i0002-2-2-1112-22i−2i12−2i2i2i−2i−i−iii-1-1i−i00000000-11-11i−i−ii000000000000
χ4922-12-1-222-22-111222222001-1-12-1222-1-1-1-1-1-1000-22-2-1112-2-2-2-1-2-22-22111111-1-1000000001-1-111-11-1000000000000
χ5022-12-1-222-22-11122-2-2-2-2001-1-12-12-2-2-1-11111000-22-2-1112-222-1-22-22-2-1-1-1-11111000000001-1-11-11-11000000000000
χ5122-12-1-222-22-111-2-22i2i−2i−2i001-1-12-1-22i−2i11−i−iii000-22-2-111-22−2i2i12−2i2i2i−2iii−i−i-1-1−ii000000001-11-1i−i−ii000000000000
χ5222-12-1-222-22-111-2-2−2i−2i2i2i001-1-12-1-2−2i2i11ii−i−i000-22-2-111-222i−2i122i−2i−2i2i−i−iii-1-1i−i000000001-11-1−iii−i000000000000
χ5322-12-1-2-2222-1-1-12222220011-12-1222-1-1-1-1-1-1000-2-22-1-1-1-2-222-12-2-2-2-2-1-1-1-1-1-1-1-10000000011111111000000000000
χ5422-12-1-2-2222-1-1-122-2-2-2-20011-12-12-2-2-1-11111000-2-22-1-1-1-2-2-2-2-1222221111-1-111000000001111-1-1-1-1000000000000
χ5522-12-1-2-2222-1-1-1-2-22i2i−2i−2i0011-12-1-22i−2i11−i−iii000-2-22-1-1-1222i−2i1-2−2i−2i2i2i−i−iii11−ii0000000011-1-1ii−i−i000000000000
χ5622-12-1-2-2222-1-1-1-2-2−2i−2i2i2i0011-12-1-2−2i2i11ii−i−i000-2-22-1-1-122−2i2i1-22i2i−2i−2iii−i−i11i−i0000000011-1-1−i−iii000000000000
χ574444444-14-14440000004444-1-1-1000000000444-1-1-1-1-1-1000000000000000000-1-1000000-1-1000000-1-1-1000000000
χ584444444-14-1444000000-4-444-1-1-1000000000-4-4-4-1-1-1-1-1-100000000000000000011000000-1-1000000111000000000
χ59444444-4-1-4-14-4-4000000444-4-1-1-10000000004-4-4-111-111000000000000000000-1-1000000-11000000-111000000000
χ60444444-4-1-4-14-4-4000000-4-44-4-1-1-1000000000-444-111-11100000000000000000011000000-110000001-1-1000000000
χ6144444-44-1-4-14-4-400000044-44-1-1-1000000000-44-41-11-111000000000000000000-1-10000001-10000001-11000000000
χ6244444-44-1-4-14-4-4000000-4-4-44-1-1-10000000004-441-11-111000000000000000000110000001-1000000-11-1000000000
χ6344444-4-4-14-144400000044-4-4-1-1-1000000000-4-4411-1-1-1-1000000000000000000-1-10000001100000011-1000000000
χ6444444-4-4-14-1444000000-4-4-4-4-1-1-100000000044-411-1-1-1-10000000000000000001100000011000000-1-11000000000
χ6544-2-4-2004042004444440000-2-4-2-4-4-4-2-2-2-2-2-20000002000000200000000000220000000000000000000000000000
χ6644-2-4-20040420044-4-4-4-40000-2-4-2-444-2-222220000002000000200000000000-2-20000000000000000000000000000
χ6744-2-4-200404200-4-44i4i−4i−4i0000-2-4-24−4i4i22−2i−2i2i2i0000002000000-2000000000002i−2i0000000000000000000000000000
χ6844-2-4-200404200-4-4−4i−4i4i4i0000-2-4-244i−4i222i2i−2i−2i0000002000000-200000000000−2i2i0000000000000000000000000000
χ694-440-40040-40004i−4i4ζ7+4ζ23−4ζ7−4ζ23−4ζ5−4ζ134ζ5+4ζ13000040-40004i−4i4ζ7+4ζ23−4ζ7−4ζ23−4ζ5−4ζ134ζ5+4ζ130000000000000000000000000000000000000000000000000000000
χ704-440-40040-40004i−4i−4ζ7−4ζ234ζ7+4ζ234ζ5+4ζ13−4ζ5−4ζ13000040-40004i−4i−4ζ7−4ζ234ζ7+4ζ234ζ5+4ζ13−4ζ5−4ζ130000000000000000000000000000000000000000000000000000000
χ714-440-40040-4000−4i4i−4ζ5−4ζ134ζ5+4ζ134ζ7+4ζ23−4ζ7−4ζ23000040-4000−4i4i−4ζ5−4ζ134ζ5+4ζ134ζ7+4ζ23−4ζ7−4ζ230000000000000000000000000000000000000000000000000000000
χ724-440-40040-4000−4i4i4ζ5+4ζ13−4ζ5−4ζ13−4ζ7−4ζ234ζ7+4ζ23000040-4000−4i4i4ζ5+4ζ13−4ζ5−4ζ13−4ζ7−4ζ234ζ7+4ζ230000000000000000000000000000000000000000000000000000000
χ734-4-2020040-406−64i−4i4ζ7+4ζ23−4ζ7−4ζ23−4ζ5−4ζ134ζ5+4ζ130000-202000−2i2i−2ζ7−2ζ232ζ7+2ζ232ζ5+2ζ13−2ζ5−2ζ1300000006−60000000000−ζ4+ζ14+ζ20−ζ22ζ4−ζ14−ζ20+ζ22−ζ4−ζ14+ζ20+ζ22ζ4+ζ14−ζ20−ζ22i6−i6000000000000000000000000000000
χ744-4-2020040-406−64i−4i−4ζ7−4ζ234ζ7+4ζ234ζ5+4ζ13−4ζ5−4ζ130000-202000−2i2i2ζ7+2ζ23−2ζ7−2ζ23−2ζ5−2ζ132ζ5+2ζ1300000006−60000000000ζ4−ζ14−ζ20+ζ22−ζ4+ζ14+ζ20−ζ22ζ4+ζ14−ζ20−ζ22−ζ4−ζ14+ζ20+ζ22i6−i6000000000000000000000000000000
χ754-4-2020040-406−6−4i4i−4ζ5−4ζ134ζ5+4ζ134ζ7+4ζ23−4ζ7−4ζ230000-2020002i−2i2ζ5+2ζ13−2ζ5−2ζ13−2ζ7−2ζ232ζ7+2ζ2300000006−60000000000ζ4+ζ14−ζ20−ζ22−ζ4−ζ14+ζ20+ζ22ζ4−ζ14−ζ20+ζ22−ζ4+ζ14+ζ20−ζ22−i6i6000000000000000000000000000000
χ764-4-2020040-406−6−4i4i4ζ5+4ζ13−4ζ5−4ζ13−4ζ7−4ζ234ζ7+4ζ230000-2020002i−2i−2ζ5−2ζ132ζ5+2ζ132ζ7+2ζ23−2ζ7−2ζ2300000006−60000000000−ζ4−ζ14+ζ20+ζ22ζ4+ζ14−ζ20−ζ22−ζ4+ζ14+ζ20−ζ22ζ4−ζ14−ζ20+ζ22−i6i6000000000000000000000000000000
χ774-4-2020040-40−664i−4i4ζ7+4ζ23−4ζ7−4ζ23−4ζ5−4ζ134ζ5+4ζ130000-202000−2i2i−2ζ7−2ζ232ζ7+2ζ232ζ5+2ζ13−2ζ5−2ζ130000000−660000000000ζ4−ζ14−ζ20+ζ22−ζ4+ζ14+ζ20−ζ22ζ4+ζ14−ζ20−ζ22−ζ4−ζ14+ζ20+ζ22−i6i6000000000000000000000000000000
χ784-4-2020040-40−664i−4i−4ζ7−4ζ234ζ7+4ζ234ζ5+4ζ13−4ζ5−4ζ130000-202000−2i2i2ζ7+2ζ23−2ζ7−2ζ23−2ζ5−2ζ132ζ5+2ζ130000000−660000000000−ζ4+ζ14+ζ20−ζ22ζ4−ζ14−ζ20+ζ22−ζ4−ζ14+ζ20+ζ22ζ4+ζ14−ζ20−ζ22−i6i6000000000000000000000000000000
χ794-4-2020040-40−66−4i4i−4ζ5−4ζ134ζ5+4ζ134ζ7+4ζ23−4ζ7−4ζ230000-2020002i−2i2ζ5+2ζ13−2ζ5−2ζ13−2ζ7−2ζ232ζ7+2ζ230000000−660000000000−ζ4−ζ14+ζ20+ζ22ζ4+ζ14−ζ20−ζ22−ζ4+ζ14+ζ20−ζ22ζ4−ζ14−ζ20+ζ22i6−i6000000000000000000000000000000
χ804-4-2020040-40−66−4i4i4ζ5+4ζ13−4ζ5−4ζ13−4ζ7−4ζ234ζ7+4ζ230000-2020002i−2i−2ζ5−2ζ132ζ5+2ζ132ζ7+2ζ23−2ζ7−2ζ230000000−660000000000ζ4+ζ14−ζ20−ζ22−ζ4−ζ14+ζ20+ζ22ζ4−ζ14−ζ20+ζ22−ζ4+ζ14+ζ20−ζ22i6−i6000000000000000000000000000000
χ81888-8800-20-2-8000000008-800-22-2000000000000000200000000000000000000-2200000000000000000000000000
χ82888-8800-20-2-800000000-8800-22-20000000000000002000000000000000000002-200000000000000000000000000
χ8388-48-488-28-2-4-4-400000000-4-41-21000000000000-2-2-21110000000000000000000000000011000000000000000000
χ8488-48-48-8-2-8-2-44400000000-441-21000000000000-2221-1-1000000000000000000000000001-1000000000000000000
χ8588-48-4-88-2-8-2-444000000004-41-210000000000002-221-1-100000000000000000000000000-11000000000000000000
χ8688-48-4-8-8-28-2-4-4-400000000441-2100000000000022-211100000000000000000000000000-1-1000000000000000000
χ871616-8-16-800-40-48000000000000242000000000000000-2000000000000000000000000000000000000000000000000
χ8816-16160-1600-4040000000000000-4040000000000000000000000000000000000000000000000000000000000000000
χ8916-16-80800-404046−46000000000020-20000000000000000−660000000000000000000000000000000000000000000000
χ9016-16-80800-4040−4646000000000020-200000000000000006−60000000000000000000000000000000000000000000000

Here ζ is a primitive root of unity of order 24 (ζ24 = 1); i = ζ6.