Finite Group Databasebeta

← Group #13104226

Character table — Group #13104226

Order 1600.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70
size111122444444444444444488888888888888884040404040404040404040404040404040404040505050505050505050505050
order12224455551010101010101010101010105101010202020202020202020202020444420202020202020202020202020202020444488888888
χ11111111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-1
χ311111111111111111111111111111111111111-1-11111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1
χ411111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111
χ51111-1-111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-11-11-11111-1-1-1-11111-1-1-1-1-1-1111111-1-1-1-1
χ61111-1-111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-11-1-11-1-1-1-111111111-1-1-1-1-1-111-1-1-1-11111
χ71111-1-111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-111-11111-1-1-1-1-1-1-1-11111-1-111-1-1-1-11111
χ81111-1-111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-11-11-1-1-1-11111-1-1-1-11111-1-1111111-1-1-1-1
χ92222222222222222222222222222222222222200000000000000000000-2-2-2-200000000
χ102222-2-222222222222222222222-2-2-2-2-2-2-2-2-2-2-2-20000000000000000000022-2-200000000
χ1122-2-22-22222-2-2-2-2-2-222-2-2222-2-2222-2-222-2-222-2-2000000000000000000000000i2i2−i2−i2i2i2−i2−i2
χ1222-2-22-22222-2-2-2-2-2-222-2-2222-2-2222-2-222-2-222-2-2000000000000000000000000−i2−i2i2i2−i2−i2i2i2
χ1322-2-2-222222-2-2-2-2-2-222-2-2222-2-22-2-222-2-222-2-222000000000000000000000000i2i2−i2−i2−i2−i2i2i2
χ1422-2-2-222222-2-2-2-2-2-222-2-2222-2-22-2-222-2-222-2-222000000000000000000000000−i2−i2i2i2i2i2−i2−i2
χ152-22-20022222222-2-2-2-2-2-2-2-222-2-200000000000000000000000000000000002-200002-22-2
χ162-22-20022222222-2-2-2-2-2-2-2-222-2-200000000000000000000000000000000002-20000-22-22
χ172-22-20022222222-2-2-2-2-2-2-2-222-2-20000000000000000000000000000000000-222-22-20000
χ182-22-20022222222-2-2-2-2-2-2-2-222-2-20000000000000000000000000000000000-22-22-220000
χ192-2-22002222-2-2-2-222-2-222-2-22-22-2000000000000000000000000000000002-200i2−i2−i2i2i2−i2−i2i2
χ202-2-22002222-2-2-2-222-2-222-2-22-22-2000000000000000000000000000000002-200−i2i2i2−i2−i2i2i2−i2
χ212-2-22002222-2-2-2-222-2-222-2-22-22-200000000000000000000000000000000-2200i2−i2−i2i2−i2i2i2−i2
χ222-2-22002222-2-2-2-222-2-222-2-22-22-200000000000000000000000000000000-2200−i2i2i2−i2i2−i2−i2i2
χ23444444−1+53−523+52−1−5−1+53−523+52−1−5−1+5−1−53−523+523−523+52−1+5−1−5-1-1-1-13−523+523−523+52−1+5−1−5−1+5−1−5-1-1-1-10022−1+52−1+52−1−52−1−52−1+52−1+52−1−52−1−5200000000000000000000
χ24444444−1+53−523+52−1−5−1+53−523+52−1−5−1+5−1−53−523+523−523+52−1+5−1−5-1-1-1-13−523+523−523+52−1+5−1−5−1+5−1−5-1-1-1-100-2-21−521−521+521+521−521−521+521+5200000000000000000000
χ254444443−52−1−5−1+53+523−52−1−5−1+53+523−523+52−1−5−1+5−1−5−1+53−523+52-1-1-1-1−1−5−1+5−1−5−1+53−523+523−523+52-1-1-1-1220000000000−1+52−1+52−1−52−1−52−1+52−1+52−1−52−1−52000000000000
χ264444443−52−1−5−1+53+523−52−1−5−1+53+523−523+52−1−5−1+5−1−5−1+53−523+52-1-1-1-1−1−5−1+5−1−5−1+53−523+523−523+52-1-1-1-1-2-200000000001−521−521+521+521−521−521+521+52000000000000
χ274444443+52−1+5−1−53−523+52−1+5−1−53−523+523−52−1+5−1−5−1+5−1−53+523−52-1-1-1-1−1+5−1−5−1+5−1−53+523−523+523−52-1-1-1-1220000000000−1−52−1−52−1+52−1+52−1−52−1−52−1+52−1+52000000000000
χ284444443+52−1+5−1−53−523+52−1+5−1−53−523+523−52−1+5−1−5−1+5−1−53+523−52-1-1-1-1−1+5−1−5−1+5−1−53+523−523+523−52-1-1-1-1-2-200000000001+521+521−521−521+521+521−521−52000000000000
χ29444444−1−53+523−52−1+5−1−53+523−52−1+5−1−5−1+53+523−523+523−52−1−5−1+5-1-1-1-13+523−523+523−52−1−5−1+5−1−5−1+5-1-1-1-10022−1−52−1−52−1+52−1+52−1−52−1−52−1+52−1+5200000000000000000000
χ30444444−1−53+523−52−1+5−1−53+523−52−1+5−1−5−1+53+523−523+523−52−1−5−1+5-1-1-1-13+523−523+523−52−1−5−1+5−1−5−1+5-1-1-1-100-2-21+521+521−521−521+521+521−521−5200000000000000000000
χ314444-4-4−1+53−523+52−1−5−1+53−523+52−1−5−1+5−1−53−523+523−523+52−1+5−1−5-1-1-1-1−3+52−3−52−3+52−3−521−51+51−51+51111002-2−1+52−1+52−1−52−1−521−521−521+521+5200000000000000000000
χ324444-4-4−1+53−523+52−1−5−1+53−523+52−1−5−1+5−1−53−523+523−523+52−1+5−1−5-1-1-1-1−3+52−3−52−3+52−3−521−51+51−51+5111100-221−521−521+521+52−1+52−1+52−1−52−1−5200000000000000000000
χ334444-4-43−52−1−5−1+53+523−52−1−5−1+53+523−523+52−1−5−1+5−1−5−1+53−523+52-1-1-1-11+51−51+51−5−3+52−3−52−3+52−3−5211112-20000000000−1+52−1+52−1−52−1−521−521−521+521+52000000000000
χ344444-4-43−52−1−5−1+53+523−52−1−5−1+53+523−523+52−1−5−1+5−1−5−1+53−523+52-1-1-1-11+51−51+51−5−3+52−3−52−3+52−3−521111-2200000000001−521−521+521+52−1+52−1+52−1−52−1−52000000000000
χ354444-4-43+52−1+5−1−53−523+52−1+5−1−53−523+523−52−1+5−1−5−1+5−1−53+523−52-1-1-1-11−51+51−51+5−3−52−3+52−3−52−3+5211112-20000000000−1−52−1−52−1+52−1+521+521+521−521−52000000000000
χ364444-4-43+52−1+5−1−53−523+52−1+5−1−53−523+523−52−1+5−1−5−1+5−1−53+523−52-1-1-1-11−51+51−51+5−3−52−3+52−3−52−3+521111-2200000000001+521+521−521−52−1−52−1−52−1+52−1+52000000000000
χ374444-4-4−1−53+523−52−1+5−1−53+523−52−1+5−1−5−1+53+523−523+523−52−1−5−1+5-1-1-1-1−3−52−3+52−3−52−3+521+51−51+51−51111002-2−1−52−1−52−1+52−1+521+521+521−521−5200000000000000000000
χ384444-4-4−1−53+523−52−1+5−1−53+523−52−1+5−1−5−1+53+523−523+523−52−1−5−1+5-1-1-1-1−3−52−3+52−3−52−3+521+51−51+51−5111100-221+521+521−521−52−1−52−1−52−1+52−1+5200000000000000000000
χ3944-4-44-4−1+53−523+52−1−51−5−3+52−3−521+51−51+53−523+52−3+52−3−52−1+5−1−5-111-13−523+52−3+52−3−52−1+5−1−51−51+5-1-1110000−ζ22+ζ38ζ22−ζ38ζ6−ζ14−ζ6+ζ14−ζ22+ζ38ζ22−ζ38ζ6−ζ14−ζ6+ζ1400000000000000000000
χ4044-4-44-4−1+53−523+52−1−51−5−3+52−3−521+51−51+53−523+52−3+52−3−52−1+5−1−5-111-13−523+52−3+52−3−52−1+5−1−51−51+5-1-1110000ζ22−ζ38−ζ22+ζ38−ζ6+ζ14ζ6−ζ14ζ22−ζ38−ζ22+ζ38−ζ6+ζ14ζ6−ζ1400000000000000000000
χ4144-4-44-43−52−1−5−1+53+52−3+521+51−5−3−52−3+52−3−52−1−5−1+51+51−53−523+52-111-1−1−5−1+51+51−53−523+52−3+52−3−52-1-111000000000000ζ12−ζ28−ζ12+ζ28−ζ4+ζ36ζ4−ζ36ζ12−ζ28−ζ12+ζ28−ζ4+ζ36ζ4−ζ36000000000000
χ4244-4-44-43−52−1−5−1+53+52−3+521+51−5−3−52−3+52−3−52−1−5−1+51+51−53−523+52-111-1−1−5−1+51+51−53−523+52−3+52−3−52-1-111000000000000−ζ12+ζ28ζ12−ζ28ζ4−ζ36−ζ4+ζ36−ζ12+ζ28ζ12−ζ28ζ4−ζ36−ζ4+ζ36000000000000
χ4344-4-44-43+52−1+5−1−53−52−3−521−51+5−3+52−3−52−3+52−1+5−1−51−51+53+523−52-111-1−1+5−1−51−51+53+523−52−3−52−3+52-1-111000000000000−ζ4+ζ36ζ4−ζ36−ζ12+ζ28ζ12−ζ28−ζ4+ζ36ζ4−ζ36−ζ12+ζ28ζ12−ζ28000000000000
χ4444-4-44-43+52−1+5−1−53−52−3−521−51+5−3+52−3−52−3+52−1+5−1−51−51+53+523−52-111-1−1+5−1−51−51+53+523−52−3−52−3+52-1-111000000000000ζ4−ζ36−ζ4+ζ36ζ12−ζ28−ζ12+ζ28ζ4−ζ36−ζ4+ζ36ζ12−ζ28−ζ12+ζ28000000000000
χ4544-4-44-4−1−53+523−52−1+51+5−3−52−3+521−51+51−53+523−52−3−52−3+52−1−5−1+5-111-13+523−52−3−52−3+52−1−5−1+51+51−5-1-1110000ζ6−ζ14−ζ6+ζ14ζ22−ζ38−ζ22+ζ38ζ6−ζ14−ζ6+ζ14ζ22−ζ38−ζ22+ζ3800000000000000000000
χ4644-4-44-4−1−53+523−52−1+51+5−3−52−3+521−51+51−53+523−52−3−52−3+52−1−5−1+5-111-13+523−52−3−52−3+52−1−5−1+51+51−5-1-1110000−ζ6+ζ14ζ6−ζ14−ζ22+ζ38ζ22−ζ38−ζ6+ζ14ζ6−ζ14−ζ22+ζ38ζ22−ζ3800000000000000000000
χ4744-4-4-44−1+53−523+52−1−51−5−3+52−3−521+51−51+53−523+52−3+52−3−52−1+5−1−5-111-1−3+52−3−523−523+521−51+5−1+5−1−511-1-10000−ζ22+ζ38ζ22−ζ38ζ6−ζ14−ζ6+ζ14ζ22−ζ38−ζ22+ζ38−ζ6+ζ14ζ6−ζ1400000000000000000000
χ4844-4-4-44−1+53−523+52−1−51−5−3+52−3−521+51−51+53−523+52−3+52−3−52−1+5−1−5-111-1−3+52−3−523−523+521−51+5−1+5−1−511-1-10000ζ22−ζ38−ζ22+ζ38−ζ6+ζ14ζ6−ζ14−ζ22+ζ38ζ22−ζ38ζ6−ζ14−ζ6+ζ1400000000000000000000
χ4944-4-4-443−52−1−5−1+53+52−3+521+51−5−3−52−3+52−3−52−1−5−1+51+51−53−523+52-111-11+51−5−1−5−1+5−3+52−3−523−523+5211-1-1000000000000ζ12−ζ28−ζ12+ζ28−ζ4+ζ36ζ4−ζ36−ζ12+ζ28ζ12−ζ28ζ4−ζ36−ζ4+ζ36000000000000
χ5044-4-4-443−52−1−5−1+53+52−3+521+51−5−3−52−3+52−3−52−1−5−1+51+51−53−523+52-111-11+51−5−1−5−1+5−3+52−3−523−523+5211-1-1000000000000−ζ12+ζ28ζ12−ζ28ζ4−ζ36−ζ4+ζ36ζ12−ζ28−ζ12+ζ28−ζ4+ζ36ζ4−ζ36000000000000
χ5144-4-4-443+52−1+5−1−53−52−3−521−51+5−3+52−3−52−3+52−1+5−1−51−51+53+523−52-111-11−51+5−1+5−1−5−3−52−3+523+523−5211-1-1000000000000−ζ4+ζ36ζ4−ζ36−ζ12+ζ28ζ12−ζ28ζ4−ζ36−ζ4+ζ36ζ12−ζ28−ζ12+ζ28000000000000
χ5244-4-4-443+52−1+5−1−53−52−3−521−51+5−3+52−3−52−3+52−1+5−1−51−51+53+523−52-111-11−51+5−1+5−1−5−3−52−3+523+523−5211-1-1000000000000ζ4−ζ36−ζ4+ζ36ζ12−ζ28−ζ12+ζ28−ζ4+ζ36ζ4−ζ36−ζ12+ζ28ζ12−ζ28000000000000
χ5344-4-4-44−1−53+523−52−1+51+5−3−52−3+521−51+51−53+523−52−3−52−3+52−1−5−1+5-111-1−3−52−3+523+523−521+51−5−1−5−1+511-1-10000ζ6−ζ14−ζ6+ζ14ζ22−ζ38−ζ22+ζ38−ζ6+ζ14ζ6−ζ14−ζ22+ζ38ζ22−ζ3800000000000000000000
χ5444-4-4-44−1−53+523−52−1+51+5−3−52−3+521−51+51−53+523−52−3−52−3+52−1−5−1+5-111-1−3−52−3+523+523−521+51−5−1−5−1+511-1-10000−ζ6+ζ14ζ6−ζ14−ζ22+ζ38ζ22−ζ38ζ6−ζ14−ζ6+ζ14ζ22−ζ38−ζ22+ζ3800000000000000000000
χ55888888-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-23333-2-2-2-2-2-2-2-2333300000000000000000000000000000000
χ568888-8-8-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2333322222222-3-3-3-300000000000000000000000000000000
χ5788-8-88-8-2-2-2-2222222-2-222-2-23-3-33-2-222-2-22233-3-300000000000000000000000000000000
χ5888-8-8-88-2-2-2-2222222-2-222-2-23-3-3322-2-222-2-2-3-33300000000000000000000000000000000
χ598-88-800-2-2-2-2-2-2-2-22222222233-3-3000000005i−5i5i−5i00000000000000000000000000000000
χ608-88-800-2-2-2-2-2-2-2-22222222233-3-300000000−5i5i−5i5i00000000000000000000000000000000
χ618-88-800−2+253−53+5−2−25−2+253−53+5−2−252−252+25−3+5−3−5−3+5−3−52−252+25-2-22200000000000000000000000000000000000000000000
χ628-88-8003−5−2−25−2+253+53−5−2−25−2+253+5−3+5−3−52+252−252+252−25−3+5−3−5-2-22200000000000000000000000000000000000000000000
χ638-88-8003+5−2+25−2−253−53+5−2+25−2−253−5−3−5−3+52−252+252−252+25−3−5−3+5-2-22200000000000000000000000000000000000000000000
χ648-88-800−2−253+53−5−2+25−2−253+53−5−2+252+252−25−3−5−3+5−3−5−3+52+252−25-2-22200000000000000000000000000000000000000000000
χ658-8-8800-2-2-2-22222-2-222-2-2223-33-3000000005i−5i−5i5i00000000000000000000000000000000
χ668-8-8800-2-2-2-22222-2-222-2-2223-33-300000000−5i5i5i−5i00000000000000000000000000000000
χ678-8-8800−2+253−53+5−2−252−25−3+5−3−52+25−2+25−2−25−3+5−3−53−53+52−252+25-22-2200000000000000000000000000000000000000000000
χ688-8-88003−5−2−25−2+253+5−3+52+252−25−3−53−53+52+252−25−2−25−2+25−3+5−3−5-22-2200000000000000000000000000000000000000000000
χ698-8-88003+5−2+25−2−253−5−3−52−252+25−3+53+53−52−252+25−2+25−2−25−3−5−3+5-22-2200000000000000000000000000000000000000000000
χ708-8-8800−2−253+53−5−2+252+25−3−5−3+52−25−2−25−2+25−3−5−3+53+53−52+252−25-22-2200000000000000000000000000000000000000000000

Here ζ is a primitive root of unity of order 40 (ζ40 = 1); i = ζ10.