Finite Group Databasebeta

← Group #13014019

Character table — Group #13014019

Order 1280.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50
size112224444448888888816161616161616161616161616162020202020204080808080808080808080
order12222225101010241010101010104410102020202020202020202044444424488888888
χ111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1
χ3111111111111111111111111111111111-1-1-1-1-1-1-1-1-1iiii−i−i−i−i
χ4111111111111111111111111111111111-1-1-1-1-1-1-1-1-1−i−i−i−iiiii
χ51111111111111111111-1-11111-1-1-1-1-1-1-1-11111111-1-111-1-111-1-1
χ61111111111111111111-1-11111-1-1-1-1-1-1-1-11111111-1-1-1-111-1-111
χ71111111111111111111-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111ii−i−i−i−iii
χ81111111111111111111-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111−i−iiiii−i−i
χ911111-1-111111-111-1-1-1-1i−i11-1-1iiii−i−i−i−i1111-1-1-1i−i1-1i−i1-1i−i
χ1011111-1-111111-111-1-1-1-1i−i11-1-1iiii−i−i−i−i1111-1-1-1i−i-11−ii-11−ii
χ1111111-1-111111-111-1-1-1-1i−i11-1-1iiii−i−i−i−i-1-1-1-1111−iii−i-11−ii1-1
χ1211111-1-111111-111-1-1-1-1i−i11-1-1iiii−i−i−i−i-1-1-1-1111−ii−ii1-1i−i-11
χ1311111-1-111111-111-1-1-1-1−ii11-1-1−i−i−i−iiiii1111-1-1-1−ii1-1−ii1-1−ii
χ1411111-1-111111-111-1-1-1-1−ii11-1-1−i−i−i−iiiii1111-1-1-1−ii-11i−i-11i−i
χ1511111-1-111111-111-1-1-1-1−ii11-1-1−i−i−i−iiiii-1-1-1-1111i−ii−i1-1−ii-11
χ1611111-1-111111-111-1-1-1-1−ii11-1-1−i−i−i−iiiii-1-1-1-1111i−i−ii-11i−i1-1
χ1722222222222-2-222222200-2-2-2-20000000022-2-222-20000000000
χ1822222222222-2-222222200-2-2-2-200000000-2-222-2-220000000000
χ1922222-2-22222-2222-2-2-2-200-2-2220000000022-2-2-2-220000000000
χ2022222-2-22222-2222-2-2-2-200-2-22200000000-2-22222-20000000000
χ214444444-1-1-1-144-1-1-1-1-1-144-1-1-1-1-1-1-1-1-1-1-1-100000000000000000
χ224444444-1-1-1-144-1-1-1-1-1-1-4-4-1-1-1-11111111100000000000000000
χ234444444-1-1-1-1-4-4-1-1-1-1-1-100111155−5−555−5−500000000000000000
χ244444444-1-1-1-1-4-4-1-1-1-1-1-1001111−5−555−5−55500000000000000000
χ2544444-4-4-1-1-1-14-4-1-111114i−4i-1-111−i−i−i−iiiii00000000000000000
χ2644444-4-4-1-1-1-14-4-1-11111−4i4i-1-111iiii−i−i−i−i00000000000000000
χ2744444-4-4-1-1-1-1-44-1-111110011-1-1i5i5−i5−i5−i5−i5i5i500000000000000000
χ2844444-4-4-1-1-1-1-44-1-111110011-1-1−i5−i5i5i5i5i5−i5−i500000000000000000
χ29444-4-400444400-4-400000000000000000000004-400000000000
χ30444-4-400444400-4-40000000000000000000000-4400000000000
χ3144-44-4004-4-44004-4000000000000000000004-40000000000000
χ3244-44-4004-4-44004-400000000000000000000-440000000000000
χ3344-4-444-44-4-4400-44-4-4440000000000000000000000000000000
χ3444-4-444-4-111-1001-111-1-1005−55−5−ζ2+ζ6−ζ14+ζ18ζ2−ζ6+ζ14−ζ18−ζ2−ζ6+ζ14+ζ18ζ2+ζ6−ζ14−ζ18−ζ2+ζ6−ζ14+ζ18ζ2−ζ6+ζ14−ζ18−ζ2−ζ6+ζ14+ζ18ζ2+ζ6−ζ14−ζ1800000000000000000
χ3544-4-444-4-111-1001-111-1-1005−55−5ζ2−ζ6+ζ14−ζ18−ζ2+ζ6−ζ14+ζ18ζ2+ζ6−ζ14−ζ18−ζ2−ζ6+ζ14+ζ18ζ2−ζ6+ζ14−ζ18−ζ2+ζ6−ζ14+ζ18ζ2+ζ6−ζ14−ζ18−ζ2−ζ6+ζ14+ζ1800000000000000000
χ3644-4-444-4-111-1001-111-1-100−55−55−ζ2−ζ6+ζ14+ζ18ζ2+ζ6−ζ14−ζ18ζ2−ζ6+ζ14−ζ18−ζ2+ζ6−ζ14+ζ18−ζ2−ζ6+ζ14+ζ18ζ2+ζ6−ζ14−ζ18ζ2−ζ6+ζ14−ζ18−ζ2+ζ6−ζ14+ζ1800000000000000000
χ3744-4-444-4-111-1001-111-1-100−55−55ζ2+ζ6−ζ14−ζ18−ζ2−ζ6+ζ14+ζ18−ζ2+ζ6−ζ14+ζ18ζ2−ζ6+ζ14−ζ18ζ2+ζ6−ζ14−ζ18−ζ2−ζ6+ζ14+ζ18−ζ2+ζ6−ζ14+ζ18ζ2−ζ6+ζ14−ζ1800000000000000000
χ3844-4-44-444-4-4400-4444-4-40000000000000000000000000000000
χ3944-4-44-44-111-1001-1-1-111005−5−55−ζ3+ζ7−ζ11+ζ19ζ3−ζ7+ζ11−ζ19−ζ3+ζ7+ζ11−ζ19ζ3−ζ7−ζ11+ζ19ζ3−ζ7+ζ11−ζ19−ζ3+ζ7−ζ11+ζ19ζ3−ζ7−ζ11+ζ19−ζ3+ζ7+ζ11−ζ1900000000000000000
χ4044-4-44-44-111-1001-1-1-111005−5−55ζ3−ζ7+ζ11−ζ19−ζ3+ζ7−ζ11+ζ19ζ3−ζ7−ζ11+ζ19−ζ3+ζ7+ζ11−ζ19−ζ3+ζ7−ζ11+ζ19ζ3−ζ7+ζ11−ζ19−ζ3+ζ7+ζ11−ζ19ζ3−ζ7−ζ11+ζ1900000000000000000
χ4144-4-44-44-111-1001-1-1-11100−555−5ζ3−ζ7−ζ11+ζ19−ζ3+ζ7+ζ11−ζ19−ζ3+ζ7−ζ11+ζ19ζ3−ζ7+ζ11−ζ19−ζ3+ζ7+ζ11−ζ19ζ3−ζ7−ζ11+ζ19ζ3−ζ7+ζ11−ζ19−ζ3+ζ7−ζ11+ζ1900000000000000000
χ4244-4-44-44-111-1001-1-1-11100−555−5−ζ3+ζ7+ζ11−ζ19ζ3−ζ7−ζ11+ζ19ζ3−ζ7+ζ11−ζ19−ζ3+ζ7−ζ11+ζ19ζ3−ζ7−ζ11+ζ19−ζ3+ζ7+ζ11−ζ19−ζ3+ζ7−ζ11+ζ19ζ3−ζ7+ζ11−ζ1900000000000000000
χ43888-8-800-2-2-2-2002225−2525−250000000000000000000000000000000
χ44888-8-800-2-2-2-20022−2525−25250000000000000000000000000000000
χ4588-88-800-222-200-2225−25−25250000000000000000000000000000000
χ4688-88-800-222-200-22−252525−250000000000000000000000000000000
χ478-800000800-800000000000000000000004i−4i000000000000000
χ488-800000800-80000000000000000000000−4i4i000000000000000
χ4916-1600000-445−454000000000000000000000000000000000000000
χ5016-1600000-4−45454000000000000000000000000000000000000000

Here ζ is a primitive root of unity of order 20 (ζ20 = 1); i = ζ5.