Finite Group Databasebeta

← Group #13104246

Character table — Group #13104246

Order 1600.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70
size112444444448888888840404040404040404040505050505050112444444448888888840404040404040404040505050505050
order1245555101010105102020202020202210101010101010108816161616224101010101010101010102020202020202210101010101010108816161616
χ11111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111-11111-1-1-1-111-1-1-1-111111111111111111111-11111-1-1-1-111-1-1-1-1
χ31111111111111111111-11-1-1-1-1111111-1-1-1-11111111111111111111-11-1-1-1-1111111-1-1-1-1
χ41111111111111111111-1-1-1-1-1-1-1-1-1-11111111111111111111111111-1-1-1-1-1-1-1-1-1-1111111
χ522222222222222222220000000000-2-2000022222222222222222220000000000-2-20000
χ622-22222222222-2-2-2-2-2-200000000000022−2−222-22222222222-2-2-2-2-2-200000000000022−2−2
χ722-22222222222-2-2-2-2-2-2000000000000−2−22222-22222222222-2-2-2-2-2-2000000000000−2−222
χ82-202222-2-2-2-22-200000000000000002−2ζ9−ζ31+ζ41−ζ47+ζ57−ζ63+ζ73−ζ79−ζ9+ζ31−ζ41+ζ47−ζ57+ζ63−ζ73+ζ79−ζ11+ζ13−ζ27+ζ29−ζ43−ζ59+ζ61+ζ77ζ11−ζ13+ζ27−ζ29+ζ43+ζ59−ζ61−ζ772-202222-2-2-2-22-200000000000000002−2ζ9−ζ31+ζ41−ζ47+ζ57−ζ63+ζ73−ζ79−ζ9+ζ31−ζ41+ζ47−ζ57+ζ63−ζ73+ζ79−ζ11+ζ13−ζ27+ζ29−ζ43−ζ59+ζ61+ζ77ζ11−ζ13+ζ27−ζ29+ζ43+ζ59−ζ61−ζ77
χ92-202222-2-2-2-22-200000000000000002−2−ζ9+ζ31−ζ41+ζ47−ζ57+ζ63−ζ73+ζ79ζ9−ζ31+ζ41−ζ47+ζ57−ζ63+ζ73−ζ79ζ11−ζ13+ζ27−ζ29+ζ43+ζ59−ζ61−ζ77−ζ11+ζ13−ζ27+ζ29−ζ43−ζ59+ζ61+ζ772-202222-2-2-2-22-200000000000000002−2−ζ9+ζ31−ζ41+ζ47−ζ57+ζ63−ζ73+ζ79ζ9−ζ31+ζ41−ζ47+ζ57−ζ63+ζ73−ζ79ζ11−ζ13+ζ27−ζ29+ζ43+ζ59−ζ61−ζ77−ζ11+ζ13−ζ27+ζ29−ζ43−ζ59+ζ61+ζ77
χ102-202222-2-2-2-22-20000000000000000−22−ζ11+ζ13−ζ27+ζ29−ζ43−ζ59+ζ61+ζ77ζ11−ζ13+ζ27−ζ29+ζ43+ζ59−ζ61−ζ77−ζ9+ζ31−ζ41+ζ47−ζ57+ζ63−ζ73+ζ79ζ9−ζ31+ζ41−ζ47+ζ57−ζ63+ζ73−ζ792-202222-2-2-2-22-20000000000000000−22−ζ11+ζ13−ζ27+ζ29−ζ43−ζ59+ζ61+ζ77ζ11−ζ13+ζ27−ζ29+ζ43+ζ59−ζ61−ζ77−ζ9+ζ31−ζ41+ζ47−ζ57+ζ63−ζ73+ζ79ζ9−ζ31+ζ41−ζ47+ζ57−ζ63+ζ73−ζ79
χ112-202222-2-2-2-22-20000000000000000−22ζ11−ζ13+ζ27−ζ29+ζ43+ζ59−ζ61−ζ77−ζ11+ζ13−ζ27+ζ29−ζ43−ζ59+ζ61+ζ77ζ9−ζ31+ζ41−ζ47+ζ57−ζ63+ζ73−ζ79−ζ9+ζ31−ζ41+ζ47−ζ57+ζ63−ζ73+ζ792-202222-2-2-2-22-20000000000000000−22ζ11−ζ13+ζ27−ζ29+ζ43+ζ59−ζ61−ζ77−ζ11+ζ13−ζ27+ζ29−ζ43−ζ59+ζ61+ζ77ζ9−ζ31+ζ41−ζ47+ζ57−ζ63+ζ73−ζ79−ζ9+ζ31−ζ41+ζ47−ζ57+ζ63−ζ73+ζ79
χ12444−1+53−523+52−1−5−1+53−523+52−1−5-1-1−1+53−523+52−1−5-1-1020000−1+52−1+52−1−52−1−52000000444−1+53−523+52−1−5−1+53−523+52−1−5-1-1−1+53−523+52−1−5-1-1020000−1+52−1+52−1−52−1−52000000
χ13444−1+53−523+52−1−5−1+53−523+52−1−5-1-1−1+53−523+52−1−5-1-10-200001−521−521+521+52000000444−1+53−523+52−1−5−1+53−523+52−1−5-1-1−1+53−523+52−1−5-1-10-200001−521−521+521+52000000
χ144443−52−1−5−1+53+523−52−1−5−1+53+52-1-13−52−1−5−1+53+52-1-120−1+52−1+52−1−52−1−5200000000004443−52−1−5−1+53+523−52−1−5−1+53+52-1-13−52−1−5−1+53+52-1-120−1+52−1+52−1−52−1−520000000000
χ154443−52−1−5−1+53+523−52−1−5−1+53+52-1-13−52−1−5−1+53+52-1-1-201−521−521+521+5200000000004443−52−1−5−1+53+523−52−1−5−1+53+52-1-13−52−1−5−1+53+52-1-1-201−521−521+521+520000000000
χ164443+52−1+5−1−53−523+52−1+5−1−53−52-1-13+52−1+5−1−53−52-1-120−1−52−1−52−1+52−1+5200000000004443+52−1+5−1−53−523+52−1+5−1−53−52-1-13+52−1+5−1−53−52-1-120−1−52−1−52−1+52−1+520000000000
χ174443+52−1+5−1−53−523+52−1+5−1−53−52-1-13+52−1+5−1−53−52-1-1-201+521+521−521−5200000000004443+52−1+5−1−53−523+52−1+5−1−53−52-1-13+52−1+5−1−53−52-1-1-201+521+521−521−520000000000
χ18444−1−53+523−52−1+5−1−53+523−52−1+5-1-1−1−53+523−52−1+5-1-1020000−1−52−1−52−1+52−1+52000000444−1−53+523−52−1+5−1−53+523−52−1+5-1-1−1−53+523−52−1+5-1-1020000−1−52−1−52−1+52−1+52000000
χ19444−1−53+523−52−1+5−1−53+523−52−1+5-1-1−1−53+523−52−1+5-1-10-200001+521+521−521−52000000444−1−53+523−52−1+5−1−53+523−52−1+5-1-1−1−53+523−52−1+5-1-10-200001+521+521−521−52000000
χ2044-4−1+53−523+52−1−5−1+53−523+52−1−5-1-11−5−3+52−3−521+511000000ζ24−ζ56−ζ24+ζ56−ζ8+ζ72ζ8−ζ7200000044-4−1+53−523+52−1−5−1+53−523+52−1−5-1-11−5−3+52−3−521+511000000ζ24−ζ56−ζ24+ζ56−ζ8+ζ72ζ8−ζ72000000
χ2144-4−1+53−523+52−1−5−1+53−523+52−1−5-1-11−5−3+52−3−521+511000000−ζ24+ζ56ζ24−ζ56ζ8−ζ72−ζ8+ζ7200000044-4−1+53−523+52−1−5−1+53−523+52−1−5-1-11−5−3+52−3−521+511000000−ζ24+ζ56ζ24−ζ56ζ8−ζ72−ζ8+ζ72000000
χ2244-43−52−1−5−1+53+523−52−1−5−1+53+52-1-1−3+521+51−5−3−521100ζ24−ζ56−ζ24+ζ56−ζ8+ζ72ζ8−ζ72000000000044-43−52−1−5−1+53+523−52−1−5−1+53+52-1-1−3+521+51−5−3−521100ζ24−ζ56−ζ24+ζ56−ζ8+ζ72ζ8−ζ720000000000
χ2344-43−52−1−5−1+53+523−52−1−5−1+53+52-1-1−3+521+51−5−3−521100−ζ24+ζ56ζ24−ζ56ζ8−ζ72−ζ8+ζ72000000000044-43−52−1−5−1+53+523−52−1−5−1+53+52-1-1−3+521+51−5−3−521100−ζ24+ζ56ζ24−ζ56ζ8−ζ72−ζ8+ζ720000000000
χ2444-43+52−1+5−1−53−523+52−1+5−1−53−52-1-1−3−521−51+5−3+521100−ζ8+ζ72ζ8−ζ72−ζ24+ζ56ζ24−ζ56000000000044-43+52−1+5−1−53−523+52−1+5−1−53−52-1-1−3−521−51+5−3+521100−ζ8+ζ72ζ8−ζ72−ζ24+ζ56ζ24−ζ560000000000
χ2544-43+52−1+5−1−53−523+52−1+5−1−53−52-1-1−3−521−51+5−3+521100ζ8−ζ72−ζ8+ζ72ζ24−ζ56−ζ24+ζ56000000000044-43+52−1+5−1−53−523+52−1+5−1−53−52-1-1−3−521−51+5−3+521100ζ8−ζ72−ζ8+ζ72ζ24−ζ56−ζ24+ζ560000000000
χ2644-4−1−53+523−52−1+5−1−53+523−52−1+5-1-11+5−3−52−3+521−511000000−ζ8+ζ72ζ8−ζ72−ζ24+ζ56ζ24−ζ5600000044-4−1−53+523−52−1+5−1−53+523−52−1+5-1-11+5−3−52−3+521−511000000−ζ8+ζ72ζ8−ζ72−ζ24+ζ56ζ24−ζ56000000
χ2744-4−1−53+523−52−1+5−1−53+523−52−1+5-1-11+5−3−52−3+521−511000000ζ8−ζ72−ζ8+ζ72ζ24−ζ56−ζ24+ζ5600000044-4−1−53+523−52−1+5−1−53+523−52−1+5-1-11+5−3−52−3+521−511000000ζ8−ζ72−ζ8+ζ72ζ24−ζ56−ζ24+ζ56000000
χ28888-2-2-2-2-2-2-2-233-2-2-2-2330000000000000000888-2-2-2-2-2-2-2-233-2-2-2-2330000000000000000
χ2988-8-2-2-2-2-2-2-2-2332222-3-3000000000000000088-8-2-2-2-2-2-2-2-2332222-3-30000000000000000
χ308-80-2-2-2-222223-300005i−5i00000000000000008-80-2-2-2-222223-300005i−5i0000000000000000
χ318-80-2-2-2-222223-30000−5i5i00000000000000008-80-2-2-2-222223-30000−5i5i0000000000000000
χ328-80−2+253−53+5−2−252−25−3+5−3−52+25-2200000000000000000000008-80−2+253−53+5−2−252−25−3+5−3−52+25-220000000000000000000000
χ338-803−5−2−25−2+253+5−3+52+252−25−3−5-2200000000000000000000008-803−5−2−25−2+253+5−3+52+252−25−3−5-220000000000000000000000
χ348-803+5−2+25−2−253−5−3−52−252+25−3+5-2200000000000000000000008-803+5−2+25−2−253−5−3−52−252+25−3+5-220000000000000000000000
χ358-80−2−253+53−5−2+252+25−3−5−3+52−25-2200000000000000000000008-80−2−253+53−5−2+252+25−3−5−3+52−25-220000000000000000000000
χ3611111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ3711111111111111111111-11111-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11-1-1-1-11111-1-11111
χ381111111111111111111-11-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11-11111-1-1-1-1-1-11111
χ391111111111111111111-1-1-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-1
χ4022222222222222222220000000000-2-20000-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-20000000000220000
χ4122-22222222222-2-2-2-2-2-200000000000022−2−2-2-22-2-2-2-2-2-2-2-2-2-2222222000000000000−2−222
χ4222-22222222222-2-2-2-2-2-2000000000000−2−222-2-22-2-2-2-2-2-2-2-2-2-222222200000000000022−2−2
χ432-202222-2-2-2-22-200000000000000002−2ζ9−ζ31+ζ41−ζ47+ζ57−ζ63+ζ73−ζ79−ζ9+ζ31−ζ41+ζ47−ζ57+ζ63−ζ73+ζ79−ζ11+ζ13−ζ27+ζ29−ζ43−ζ59+ζ61+ζ77ζ11−ζ13+ζ27−ζ29+ζ43+ζ59−ζ61−ζ77-220-2-2-2-22222-220000000000000000−22−ζ9+ζ31−ζ41+ζ47−ζ57+ζ63−ζ73+ζ79ζ9−ζ31+ζ41−ζ47+ζ57−ζ63+ζ73−ζ79ζ11−ζ13+ζ27−ζ29+ζ43+ζ59−ζ61−ζ77−ζ11+ζ13−ζ27+ζ29−ζ43−ζ59+ζ61+ζ77
χ442-202222-2-2-2-22-200000000000000002−2−ζ9+ζ31−ζ41+ζ47−ζ57+ζ63−ζ73+ζ79ζ9−ζ31+ζ41−ζ47+ζ57−ζ63+ζ73−ζ79ζ11−ζ13+ζ27−ζ29+ζ43+ζ59−ζ61−ζ77−ζ11+ζ13−ζ27+ζ29−ζ43−ζ59+ζ61+ζ77-220-2-2-2-22222-220000000000000000−22ζ9−ζ31+ζ41−ζ47+ζ57−ζ63+ζ73−ζ79−ζ9+ζ31−ζ41+ζ47−ζ57+ζ63−ζ73+ζ79−ζ11+ζ13−ζ27+ζ29−ζ43−ζ59+ζ61+ζ77ζ11−ζ13+ζ27−ζ29+ζ43+ζ59−ζ61−ζ77
χ452-202222-2-2-2-22-20000000000000000−22−ζ11+ζ13−ζ27+ζ29−ζ43−ζ59+ζ61+ζ77ζ11−ζ13+ζ27−ζ29+ζ43+ζ59−ζ61−ζ77−ζ9+ζ31−ζ41+ζ47−ζ57+ζ63−ζ73+ζ79ζ9−ζ31+ζ41−ζ47+ζ57−ζ63+ζ73−ζ79-220-2-2-2-22222-2200000000000000002−2ζ11−ζ13+ζ27−ζ29+ζ43+ζ59−ζ61−ζ77−ζ11+ζ13−ζ27+ζ29−ζ43−ζ59+ζ61+ζ77ζ9−ζ31+ζ41−ζ47+ζ57−ζ63+ζ73−ζ79−ζ9+ζ31−ζ41+ζ47−ζ57+ζ63−ζ73+ζ79
χ462-202222-2-2-2-22-20000000000000000−22ζ11−ζ13+ζ27−ζ29+ζ43+ζ59−ζ61−ζ77−ζ11+ζ13−ζ27+ζ29−ζ43−ζ59+ζ61+ζ77ζ9−ζ31+ζ41−ζ47+ζ57−ζ63+ζ73−ζ79−ζ9+ζ31−ζ41+ζ47−ζ57+ζ63−ζ73+ζ79-220-2-2-2-22222-2200000000000000002−2−ζ11+ζ13−ζ27+ζ29−ζ43−ζ59+ζ61+ζ77ζ11−ζ13+ζ27−ζ29+ζ43+ζ59−ζ61−ζ77−ζ9+ζ31−ζ41+ζ47−ζ57+ζ63−ζ73+ζ79ζ9−ζ31+ζ41−ζ47+ζ57−ζ63+ζ73−ζ79
χ47444−1+53−523+52−1−5−1+53−523+52−1−5-1-1−1+53−523+52−1−5-1-1020000−1+52−1+52−1−52−1−52000000-4-4-41−5−3+52−3−521+51−5−3+52−3−521+5111−5−3+52−3−521+5110-200001−521−521+521+52000000
χ48444−1+53−523+52−1−5−1+53−523+52−1−5-1-1−1+53−523+52−1−5-1-10-200001−521−521+521+52000000-4-4-41−5−3+52−3−521+51−5−3+52−3−521+5111−5−3+52−3−521+511020000−1+52−1+52−1−52−1−52000000
χ494443−52−1−5−1+53+523−52−1−5−1+53+52-1-13−52−1−5−1+53+52-1-120−1+52−1+52−1−52−1−520000000000-4-4-4−3+521+51−5−3−52−3+521+51−5−3−5211−3+521+51−5−3−5211-201−521−521+521+520000000000
χ504443−52−1−5−1+53+523−52−1−5−1+53+52-1-13−52−1−5−1+53+52-1-1-201−521−521+521+520000000000-4-4-4−3+521+51−5−3−52−3+521+51−5−3−5211−3+521+51−5−3−521120−1+52−1+52−1−52−1−520000000000
χ514443+52−1+5−1−53−523+52−1+5−1−53−52-1-13+52−1+5−1−53−52-1-120−1−52−1−52−1+52−1+520000000000-4-4-4−3−521−51+5−3+52−3−521−51+5−3+5211−3−521−51+5−3+5211-201+521+521−521−520000000000
χ524443+52−1+5−1−53−523+52−1+5−1−53−52-1-13+52−1+5−1−53−52-1-1-201+521+521−521−520000000000-4-4-4−3−521−51+5−3+52−3−521−51+5−3+5211−3−521−51+5−3+521120−1−52−1−52−1+52−1+520000000000
χ53444−1−53+523−52−1+5−1−53+523−52−1+5-1-1−1−53+523−52−1+5-1-1020000−1−52−1−52−1+52−1+52000000-4-4-41+5−3−52−3+521−51+5−3−52−3+521−5111+5−3−52−3+521−5110-200001+521+521−521−52000000
χ54444−1−53+523−52−1+5−1−53+523−52−1+5-1-1−1−53+523−52−1+5-1-10-200001+521+521−521−52000000-4-4-41+5−3−52−3+521−51+5−3−52−3+521−5111+5−3−52−3+521−511020000−1−52−1−52−1+52−1+52000000
χ5544-4−1+53−523+52−1−5−1+53−523+52−1−5-1-11−5−3+52−3−521+511000000ζ24−ζ56−ζ24+ζ56−ζ8+ζ72ζ8−ζ72000000-4-441−5−3+52−3−521+51−5−3+52−3−521+511−1+53−523+52−1−5-1-1000000−ζ24+ζ56ζ24−ζ56ζ8−ζ72−ζ8+ζ72000000
χ5644-4−1+53−523+52−1−5−1+53−523+52−1−5-1-11−5−3+52−3−521+511000000−ζ24+ζ56ζ24−ζ56ζ8−ζ72−ζ8+ζ72000000-4-441−5−3+52−3−521+51−5−3+52−3−521+511−1+53−523+52−1−5-1-1000000ζ24−ζ56−ζ24+ζ56−ζ8+ζ72ζ8−ζ72000000
χ5744-43−52−1−5−1+53+523−52−1−5−1+53+52-1-1−3+521+51−5−3−521100ζ24−ζ56−ζ24+ζ56−ζ8+ζ72ζ8−ζ720000000000-4-44−3+521+51−5−3−52−3+521+51−5−3−52113−52−1−5−1+53+52-1-100−ζ24+ζ56ζ24−ζ56ζ8−ζ72−ζ8+ζ720000000000
χ5844-43−52−1−5−1+53+523−52−1−5−1+53+52-1-1−3+521+51−5−3−521100−ζ24+ζ56ζ24−ζ56ζ8−ζ72−ζ8+ζ720000000000-4-44−3+521+51−5−3−52−3+521+51−5−3−52113−52−1−5−1+53+52-1-100ζ24−ζ56−ζ24+ζ56−ζ8+ζ72ζ8−ζ720000000000
χ5944-43+52−1+5−1−53−523+52−1+5−1−53−52-1-1−3−521−51+5−3+521100−ζ8+ζ72ζ8−ζ72−ζ24+ζ56ζ24−ζ560000000000-4-44−3−521−51+5−3+52−3−521−51+5−3+52113+52−1+5−1−53−52-1-100ζ8−ζ72−ζ8+ζ72ζ24−ζ56−ζ24+ζ560000000000
χ6044-43+52−1+5−1−53−523+52−1+5−1−53−52-1-1−3−521−51+5−3+521100ζ8−ζ72−ζ8+ζ72ζ24−ζ56−ζ24+ζ560000000000-4-44−3−521−51+5−3+52−3−521−51+5−3+52113+52−1+5−1−53−52-1-100−ζ8+ζ72ζ8−ζ72−ζ24+ζ56ζ24−ζ560000000000
χ6144-4−1−53+523−52−1+5−1−53+523−52−1+5-1-11+5−3−52−3+521−511000000−ζ8+ζ72ζ8−ζ72−ζ24+ζ56ζ24−ζ56000000-4-441+5−3−52−3+521−51+5−3−52−3+521−511−1−53+523−52−1+5-1-1000000ζ8−ζ72−ζ8+ζ72ζ24−ζ56−ζ24+ζ56000000
χ6244-4−1−53+523−52−1+5−1−53+523−52−1+5-1-11+5−3−52−3+521−511000000ζ8−ζ72−ζ8+ζ72ζ24−ζ56−ζ24+ζ56000000-4-441+5−3−52−3+521−51+5−3−52−3+521−511−1−53+523−52−1+5-1-1000000−ζ8+ζ72ζ8−ζ72−ζ24+ζ56ζ24−ζ56000000
χ63888-2-2-2-2-2-2-2-233-2-2-2-2330000000000000000-8-8-822222222-3-32222-3-30000000000000000
χ6488-8-2-2-2-2-2-2-2-2332222-3-30000000000000000-8-8822222222-3-3-2-2-2-2330000000000000000
χ658-80-2-2-2-222223-300005i−5i0000000000000000-8802222-2-2-2-2-330000−5i5i0000000000000000
χ668-80-2-2-2-222223-30000−5i5i0000000000000000-8802222-2-2-2-2-3300005i−5i0000000000000000
χ678-80−2+253−53+5−2−252−25−3+5−3−52+25-220000000000000000000000-8802−25−3+5−3−52+25−2+253−53+5−2−252-20000000000000000000000
χ688-803−5−2−25−2+253+5−3+52+252−25−3−5-220000000000000000000000-880−3+52+252−25−3−53−5−2−25−2+253+52-20000000000000000000000
χ698-803+5−2+25−2−253−5−3−52−252+25−3+5-220000000000000000000000-880−3−52−252+25−3+53+5−2+25−2−253−52-20000000000000000000000
χ708-80−2−253+53−5−2+252+25−3−5−3+52−25-220000000000000000000000-8802+25−3−5−3+52−25−2−253+53−5−2+252-20000000000000000000000

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