Finite Group Databasebeta

← Group #13014462

Character table — Group #13014462

Order 1280.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50
size112224444448888888816161616161616161616161616162020404040404040408080808080808080
order12222445101010221010202020208810101010404040404040404044224444444448888
χ111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1
χ3111111111111111111111111111111111-1-1-1-1-1-1-1-1-1ii−i−iii−i−i
χ4111111111111111111111111111111111-1-1-1-1-1-1-1-1-1−i−iii−i−iii
χ51111111111111111111-1-11111-1-1-1-1-1-1-1-111111-1-1-1-11111-1-1-1-1
χ61111111111111111111-1-11111-1-1-1-1-1-1-1-111111-1-1-1-1-1-1-1-11111
χ71111111111111111111-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-11111ii−i−i−i−iii
χ81111111111111111111-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-11111−i−iiiii−i−i
χ911-11-11-11-1-111-11-111-1-1i−i11-1-1iiii−i−i−i−i111-1-1ii−i−ii−ii−i1-11-1
χ1011-11-11-11-1-111-11-111-1-1i−i11-1-1iiii−i−i−i−i111-1-1ii−i−i−ii−ii-11-11
χ1111-11-11-11-1-111-11-111-1-1i−i11-1-1iiii−i−i−i−i-1-1-111−i−iii1-1-11−iii−i
χ1211-11-11-11-1-111-11-111-1-1i−i11-1-1iiii−i−i−i−i-1-1-111−i−iii-111-1i−i−ii
χ1311-11-11-11-1-111-11-111-1-1−ii11-1-1−i−i−i−iiiii111-1-1−i−iiii−ii−i-11-11
χ1411-11-11-11-1-111-11-111-1-1−ii11-1-1−i−i−i−iiiii111-1-1−i−iii−ii−ii1-11-1
χ1511-11-11-11-1-111-11-111-1-1−ii11-1-1−i−i−i−iiiii-1-1-111ii−i−i1-1-11i−i−ii
χ1611-11-11-11-1-111-11-111-1-1−ii11-1-1−i−i−i−iiiii-1-1-111ii−i−i-111-1−iii−i
χ1722222222222-2-222222200-2-2-2-20000000022-2-22000000000000
χ1822222222222-2-222222200-2-2-2-200000000-2-222-2000000000000
χ1922-22-22-22-2-22-222-222-2-200-2-2220000000022-22-2000000000000
χ2022-22-22-22-2-22-222-222-2-200-2-22200000000-2-22-22000000000000
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
χ2544444-4-444440044-4-4-4-40000000000000000000000000000000
χ2644444-4-4-1-1-1-100-1-11111005−55−5−ζ3+ζ7−ζ11+ζ19ζ3−ζ7+ζ11−ζ19ζ3−ζ7−ζ11+ζ19−ζ3+ζ7+ζ11−ζ19−ζ3+ζ7−ζ11+ζ19ζ3−ζ7+ζ11−ζ19ζ3−ζ7−ζ11+ζ19−ζ3+ζ7+ζ11−ζ1900000000000000000
χ2744444-4-4-1-1-1-100-1-11111005−55−5ζ3−ζ7+ζ11−ζ19−ζ3+ζ7−ζ11+ζ19−ζ3+ζ7+ζ11−ζ19ζ3−ζ7−ζ11+ζ19ζ3−ζ7+ζ11−ζ19−ζ3+ζ7−ζ11+ζ19−ζ3+ζ7+ζ11−ζ19ζ3−ζ7−ζ11+ζ1900000000000000000
χ2844444-4-4-1-1-1-100-1-1111100−55−55ζ3−ζ7−ζ11+ζ19−ζ3+ζ7+ζ11−ζ19ζ3−ζ7+ζ11−ζ19−ζ3+ζ7−ζ11+ζ19ζ3−ζ7−ζ11+ζ19−ζ3+ζ7+ζ11−ζ19ζ3−ζ7+ζ11−ζ19−ζ3+ζ7−ζ11+ζ1900000000000000000
χ2944444-4-4-1-1-1-100-1-1111100−55−55−ζ3+ζ7+ζ11−ζ19ζ3−ζ7−ζ11+ζ19−ζ3+ζ7−ζ11+ζ19ζ3−ζ7+ζ11−ζ19−ζ3+ζ7+ζ11−ζ19ζ3−ζ7−ζ11+ζ19−ζ3+ζ7−ζ11+ζ19ζ3−ζ7+ζ11−ζ1900000000000000000
χ30444-4-4004-4-4400-44000000000000000000000002i−2i2i−2i00000000
χ31444-4-4004-4-4400-4400000000000000000000000−2i2i−2i2i00000000
χ3244-44-44-4-111-14-4-11-1-1114i−4i-1-111−i−i−i−iiiii00000000000000000
χ3344-44-44-4-111-14-4-11-1-111−4i4i-1-111iiii−i−i−i−i00000000000000000
χ3444-44-44-4-111-1-44-11-1-1110011-1-1i5i5−i5−i5−i5−i5i5i500000000000000000
χ3544-44-44-4-111-1-44-11-1-1110011-1-1−i5−i5i5i5i5i5−i5−i500000000000000000
χ3644-44-4-444-4-44004-4-4-4440000000000000000000000000000000
χ3744-44-4-44-111-100-1111-1-1005−5−55−ζ2+ζ6−ζ14+ζ18ζ2−ζ6+ζ14−ζ18ζ2+ζ6−ζ14−ζ18−ζ2−ζ6+ζ14+ζ18ζ2−ζ6+ζ14−ζ18−ζ2+ζ6−ζ14+ζ18−ζ2−ζ6+ζ14+ζ18ζ2+ζ6−ζ14−ζ1800000000000000000
χ3844-44-4-44-111-100-1111-1-1005−5−55ζ2−ζ6+ζ14−ζ18−ζ2+ζ6−ζ14+ζ18−ζ2−ζ6+ζ14+ζ18ζ2+ζ6−ζ14−ζ18−ζ2+ζ6−ζ14+ζ18ζ2−ζ6+ζ14−ζ18ζ2+ζ6−ζ14−ζ18−ζ2−ζ6+ζ14+ζ1800000000000000000
χ3944-44-4-44-111-100-1111-1-100−555−5−ζ2−ζ6+ζ14+ζ18ζ2+ζ6−ζ14−ζ18−ζ2+ζ6−ζ14+ζ18ζ2−ζ6+ζ14−ζ18ζ2+ζ6−ζ14−ζ18−ζ2−ζ6+ζ14+ζ18ζ2−ζ6+ζ14−ζ18−ζ2+ζ6−ζ14+ζ1800000000000000000
χ4044-44-4-44-111-100-1111-1-100−555−5ζ2+ζ6−ζ14−ζ18−ζ2−ζ6+ζ14+ζ18ζ2−ζ6+ζ14−ζ18−ζ2+ζ6−ζ14+ζ18−ζ2−ζ6+ζ14+ζ18ζ2+ζ6−ζ14−ζ18−ζ2+ζ6−ζ14+ζ18ζ2−ζ6+ζ14−ζ1800000000000000000
χ4144-4-4400444400-4-4000000000000000000000002-2-2200000000
χ4244-4-4400444400-4-400000000000000000000000-222-200000000
χ43888-8-800-222-2002-225−2525−250000000000000000000000000000000
χ44888-8-800-222-2002-2−2525−25250000000000000000000000000000000
χ4588-8-8800-2-2-2-2002225−25−25250000000000000000000000000000000
χ4688-8-8800-2-2-2-20022−252525−250000000000000000000000000000000
χ478-800000800-800000000000000000000004-4000000000000000
χ488-800000800-80000000000000000000000-44000000000000000
χ4916-1600000-445−454000000000000000000000000000000000000000
χ5016-1600000-4−45454000000000000000000000000000000000000000

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