Finite Group Databasebeta

← Group #13013774

Character table — Group #13013774

Order 1280.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62
size1111224444444488888881010101016161616161616161616161616162020202020202020202020204040404040808080808080
order12442424588102020810101020202088888840404040404040404040404022441616161616161616816161616888888
χ111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111111-1-1-1-1-1-1-1-11-1-1-1-111-1-1-1-1
χ31111111111111111111111111-1-11111-1-1-1-1-1-1-1-111111111111111111-1-1-1-1-1-1
χ41111111111111111111111111-1-11111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-11-1-1-1-1-1-11111
χ5111111111111111111111-1-1-1-111111111111111-1-1-1-1iiii−i−i−i−i-1ii−i−i-1-1ii−i−i
χ6111111111111111111111-1-1-1-111111111111111-1-1-1-1−i−i−i−iiiii-1−i−iii-1-1−i−iii
χ7111111111111111111111-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1iiii−i−i−i−i-1ii−i−i11−i−iii
χ8111111111111111111111-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1−i−i−i−iiiii-1−i−iii11ii−i−i
χ9111111-1-1111111-11-1-11-1-11111i−i11-1-1iiii−i−i−i−i1-11-111111111-1-1-1-1-1i−ii−ii−i
χ10111111-1-1111111-11-1-11-1-11111i−i11-1-1iiii−i−i−i−i1-11-1-1-1-1-1-1-1-1-1-11111i−i−ii−ii
χ11111111-1-1111111-11-1-11-1-11111−ii11-1-1−i−i−i−iiiii1-11-111111111-1-1-1-1-1−ii−ii−ii
χ12111111-1-1111111-11-1-11-1-11111−ii11-1-1−i−i−i−iiiii1-11-1-1-1-1-1-1-1-1-1-11111−iii−ii−i
χ13111111-1-1111111-11-1-11-1-1-1-1-1-1i−i11-1-1iiii−i−i−i−i-11-11iiii−i−i−i−i1−i−iii−ii-111-1
χ14111111-1-1111111-11-1-11-1-1-1-1-1-1i−i11-1-1iiii−i−i−i−i-11-11−i−i−i−iiiii1ii−i−i−ii1-1-11
χ15111111-1-1111111-11-1-11-1-1-1-1-1-1−ii11-1-1−i−i−i−iiiii-11-11iiii−i−i−i−i1−i−iiii−i1-1-11
χ16111111-1-1111111-11-1-11-1-1-1-1-1-1−ii11-1-1−i−i−i−iiiii-11-11−i−i−i−iiiii1ii−i−ii−i-111-1
χ17222222222-2-2222-2222222222200-2-2-2-200000000-2-2-2-20000000020000000000
χ18222222222-2-2222-2222222-2-2-2-200-2-2-2-200000000222200000000-20000000000
χ19222222-2-22-2-222222-2-22-2-2222200-2-22200000000-22-2200000000-20000000000
χ20222222-2-22-2-222222-2-22-2-2-2-2-2-200-2-222000000002-22-20000000020000000000
χ2122-2-22-22-22002-2-20222-2-2-20000000000000000002-2-22i2i2−i2−i2i2i2−i2−i20i2−i2i2−i2000000
χ2222-2-22-22-22002-2-20222-2-2-20000000000000000002-2-22−i2−i2i2i2−i2−i2i2i20−i2i2−i2i2000000
χ2322-2-22-22-22002-2-20222-2-2-2000000000000000000-222-222−2−2−2−22202−2−22000000
χ2422-2-22-22-22002-2-20222-2-2-2000000000000000000-222-2−2−22222−2−20−222−2000000
χ2522-2-22-2-222002-2-202-2-2-22200000000000000000022-2-2i2i2−i2−i2i2i2−i2−i20−i2i2−i2i2000000
χ2622-2-22-2-222002-2-202-2-2-22200000000000000000022-2-2−i2−i2i2i2−i2−i2i2i20i2−i2i2−i2000000
χ2722-2-22-2-222002-2-202-2-2-222000000000000000000-2-22222−2−2−2−2220−222−2000000
χ2822-2-22-2-222002-2-202-2-2-222000000000000000000-2-222−2−22222−2−202−2−22000000
χ2944444444-144-1-1-14-1-1-1-1-1-1000044-1-1-1-1-1-1-1-1-1-1-1-100000000000000000000000
χ3044444444-144-1-1-14-1-1-1-1-1-10000-4-4-1-1-1-11111111100000000000000000000000
χ3144444444-1-4-4-1-1-1-4-1-1-1-1-1-1000000111155−5−555−5−500000000000000000000000
χ3244444444-1-4-4-1-1-1-4-1-1-1-1-1-10000001111−5−555−5−55500000000000000000000000
χ33444444-4-4-144-1-1-1-4-111-11100004i−4i-1-111−i−i−i−iiiii00000000000000000000000
χ34444444-4-4-144-1-1-1-4-111-1110000−4i4i-1-111iiii−i−i−i−i00000000000000000000000
χ35444444-4-4-1-4-4-1-1-14-111-11100000011-1-1i5i5−i5−i5−i5−i5i5i500000000000000000000000
χ36444444-4-4-1-4-4-1-1-14-111-11100000011-1-1−i5−i5i5i5i5i5−i5−i500000000000000000000000
χ374444-4-40044i−4i4440-400-4000000004i−4i000000000000000000000000000000000
χ384444-4-4004−4i4i4440-400-400000000−4i4i000000000000000000000000000000000
χ394444-4-400-14i−4i-1-1-1015−515−5000000−iii5−i5ζ12+ζ24−ζ28−ζ56−ζ12−ζ24+ζ28+ζ56−ζ8−ζ44+ζ72+ζ76ζ8+ζ44−ζ72−ζ76ζ12−ζ24−ζ28+ζ56−ζ12+ζ24+ζ28−ζ56−ζ8+ζ44+ζ72−ζ76ζ8−ζ44−ζ72+ζ7600000000000000000000000
χ404444-4-400-14i−4i-1-1-1015−515−5000000−iii5−i5−ζ12−ζ24+ζ28+ζ56ζ12+ζ24−ζ28−ζ56ζ8+ζ44−ζ72−ζ76−ζ8−ζ44+ζ72+ζ76−ζ12+ζ24+ζ28−ζ56ζ12−ζ24−ζ28+ζ56ζ8−ζ44−ζ72+ζ76−ζ8+ζ44+ζ72−ζ7600000000000000000000000
χ414444-4-400-14i−4i-1-1-101−551−55000000−ii−i5i5−ζ8−ζ44+ζ72+ζ76ζ8+ζ44−ζ72−ζ76−ζ12−ζ24+ζ28+ζ56ζ12+ζ24−ζ28−ζ56ζ8−ζ44−ζ72+ζ76−ζ8+ζ44+ζ72−ζ76ζ12−ζ24−ζ28+ζ56−ζ12+ζ24+ζ28−ζ5600000000000000000000000
χ424444-4-400-14i−4i-1-1-101−551−55000000−ii−i5i5ζ8+ζ44−ζ72−ζ76−ζ8−ζ44+ζ72+ζ76ζ12+ζ24−ζ28−ζ56−ζ12−ζ24+ζ28+ζ56−ζ8+ζ44+ζ72−ζ76ζ8−ζ44−ζ72+ζ76−ζ12+ζ24+ζ28−ζ56ζ12−ζ24−ζ28+ζ5600000000000000000000000
χ434444-4-400-1−4i4i-1-1-1015−515−5000000i−i−i5i5ζ12−ζ24−ζ28+ζ56−ζ12+ζ24+ζ28−ζ56ζ8−ζ44−ζ72+ζ76−ζ8+ζ44+ζ72−ζ76ζ12+ζ24−ζ28−ζ56−ζ12−ζ24+ζ28+ζ56ζ8+ζ44−ζ72−ζ76−ζ8−ζ44+ζ72+ζ7600000000000000000000000
χ444444-4-400-1−4i4i-1-1-1015−515−5000000i−i−i5i5−ζ12+ζ24+ζ28−ζ56ζ12−ζ24−ζ28+ζ56−ζ8+ζ44+ζ72−ζ76ζ8−ζ44−ζ72+ζ76−ζ12−ζ24+ζ28+ζ56ζ12+ζ24−ζ28−ζ56−ζ8−ζ44+ζ72+ζ76ζ8+ζ44−ζ72−ζ7600000000000000000000000
χ454444-4-400-1−4i4i-1-1-101−551−55000000i−ii5−i5−ζ8+ζ44+ζ72−ζ76ζ8−ζ44−ζ72+ζ76ζ12−ζ24−ζ28+ζ56−ζ12+ζ24+ζ28−ζ56ζ8+ζ44−ζ72−ζ76−ζ8−ζ44+ζ72+ζ76−ζ12−ζ24+ζ28+ζ56ζ12+ζ24−ζ28−ζ5600000000000000000000000
χ464444-4-400-1−4i4i-1-1-101−551−55000000i−ii5−i5ζ8−ζ44−ζ72+ζ76−ζ8+ζ44+ζ72−ζ76−ζ12+ζ24+ζ28−ζ56ζ12−ζ24−ζ28+ζ56−ζ8−ζ44+ζ72+ζ76ζ8+ζ44−ζ72−ζ76ζ12+ζ24−ζ28−ζ56−ζ12−ζ24+ζ28+ζ5600000000000000000000000
χ4744-4-4-44004004-4-40-40040044-4-40000000000000000000000000000000000000
χ4844-4-4-44004004-4-40-400400-4-4440000000000000000000000000000000000000
χ494-44i−4i0000400-44i−4i00000002i2−2i222−220000000000000000002ζ13+2ζ29+2ζ61+2ζ77−2ζ13−2ζ29−2ζ61−2ζ77−2ζ9−2ζ41−2ζ57−2ζ732ζ9+2ζ41+2ζ57+2ζ73−2ζ31−2ζ47−2ζ63−2ζ792ζ31+2ζ47+2ζ63+2ζ79−2ζ11−2ζ27−2ζ43−2ζ592ζ11+2ζ27+2ζ43+2ζ5900000000000
χ504-44i−4i0000400-44i−4i00000002i2−2i222−22000000000000000000−2ζ13−2ζ29−2ζ61−2ζ772ζ13+2ζ29+2ζ61+2ζ772ζ9+2ζ41+2ζ57+2ζ73−2ζ9−2ζ41−2ζ57−2ζ732ζ31+2ζ47+2ζ63+2ζ79−2ζ31−2ζ47−2ζ63−2ζ792ζ11+2ζ27+2ζ43+2ζ59−2ζ11−2ζ27−2ζ43−2ζ5900000000000
χ514-44i−4i0000400-44i−4i0000000−2i22i2−2222000000000000000000−2ζ9−2ζ41−2ζ57−2ζ732ζ9+2ζ41+2ζ57+2ζ73−2ζ13−2ζ29−2ζ61−2ζ772ζ13+2ζ29+2ζ61+2ζ77−2ζ11−2ζ27−2ζ43−2ζ592ζ11+2ζ27+2ζ43+2ζ592ζ31+2ζ47+2ζ63+2ζ79−2ζ31−2ζ47−2ζ63−2ζ7900000000000
χ524-44i−4i0000400-44i−4i0000000−2i22i2−22220000000000000000002ζ9+2ζ41+2ζ57+2ζ73−2ζ9−2ζ41−2ζ57−2ζ732ζ13+2ζ29+2ζ61+2ζ77−2ζ13−2ζ29−2ζ61−2ζ772ζ11+2ζ27+2ζ43+2ζ59−2ζ11−2ζ27−2ζ43−2ζ59−2ζ31−2ζ47−2ζ63−2ζ792ζ31+2ζ47+2ζ63+2ζ7900000000000
χ534-4−4i4i0000400-4−4i4i00000002i2−2i2−2222000000000000000000−2ζ31−2ζ47−2ζ63−2ζ792ζ31+2ζ47+2ζ63+2ζ79−2ζ11−2ζ27−2ζ43−2ζ592ζ11+2ζ27+2ζ43+2ζ59−2ζ13−2ζ29−2ζ61−2ζ772ζ13+2ζ29+2ζ61+2ζ772ζ9+2ζ41+2ζ57+2ζ73−2ζ9−2ζ41−2ζ57−2ζ7300000000000
χ544-4−4i4i0000400-4−4i4i00000002i2−2i2−22220000000000000000002ζ31+2ζ47+2ζ63+2ζ79−2ζ31−2ζ47−2ζ63−2ζ792ζ11+2ζ27+2ζ43+2ζ59−2ζ11−2ζ27−2ζ43−2ζ592ζ13+2ζ29+2ζ61+2ζ77−2ζ13−2ζ29−2ζ61−2ζ77−2ζ9−2ζ41−2ζ57−2ζ732ζ9+2ζ41+2ζ57+2ζ7300000000000
χ554-4−4i4i0000400-4−4i4i0000000−2i22i222−22000000000000000000−2ζ11−2ζ27−2ζ43−2ζ592ζ11+2ζ27+2ζ43+2ζ592ζ31+2ζ47+2ζ63+2ζ79−2ζ31−2ζ47−2ζ63−2ζ792ζ9+2ζ41+2ζ57+2ζ73−2ζ9−2ζ41−2ζ57−2ζ732ζ13+2ζ29+2ζ61+2ζ77−2ζ13−2ζ29−2ζ61−2ζ7700000000000
χ564-4−4i4i0000400-4−4i4i0000000−2i22i222−220000000000000000002ζ11+2ζ27+2ζ43+2ζ59−2ζ11−2ζ27−2ζ43−2ζ59−2ζ31−2ζ47−2ζ63−2ζ792ζ31+2ζ47+2ζ63+2ζ79−2ζ9−2ζ41−2ζ57−2ζ732ζ9+2ζ41+2ζ57+2ζ73−2ζ13−2ζ29−2ζ61−2ζ772ζ13+2ζ29+2ζ61+2ζ7700000000000
χ5788-8-88-88-8-200-2220-2-2-222200000000000000000000000000000000000000000
χ5888-8-88-8-88-200-2220-2222-2-200000000000000000000000000000000000000000
χ5988-8-8-8800-200-2220225−25-2−252500000000000000000000000000000000000000000
χ6088-8-8-8800-200-22202−2525-225−2500000000000000000000000000000000000000000
χ6116-1616i−16i0000-4004−4i4i000000000000000000000000000000000000000000000000
χ6216-16−16i16i0000-40044i−4i000000000000000000000000000000000000000000000000

Here ζ is a primitive root of unity of order 80 (ζ80 = 1); i = ζ20.