Finite Group Databasebeta

← Group #13104231

Character table — Group #13104231

Order 1600.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70
size111122444444444444444488888888888888884040404040404040404040404040404040404040505050505050505050505050
order12224455551010101010101010101010105101010202020202020202020202020444420202020202020202020202020202020444488888888
χ11111111111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111111111-11-11111-1-1-1-11111-1-1-1-11111-1-1-1-1-1-1-1-1
χ311111111111111111111111111111111111111-11-11-1-1-1-11111-1-1-1-111111111-1-1-1-1-1-1-1-1
χ411111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111
χ51111-1-111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-111111111-1-1111111-1-1-1-1
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
χ81111-1-111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-1111111-1-1-1-1
χ92222222222222222222222222222222222222200000000000000000000-2-2-2-200000000
χ102222-2-222222222222222222222-2-2-2-2-2-2-2-2-2-2-2-20000000000000000000022-2-200000000
χ1122-2-2002222-2-2-2-2-2-2-2-222222-2-22000000000000000000000000000000002i−2i0022−2−2i2i2−i2−i2
χ1222-2-2002222-2-2-2-2-2-2-2-222222-2-22000000000000000000000000000000002i−2i00−2−222−i2−i2i2i2
χ1322-2-2002222-2-2-2-2-2-2-2-222222-2-2200000000000000000000000000000000−2i2i0022−2−2−i2−i2i2i2
χ1422-2-2002222-2-2-2-2-2-2-2-222222-2-2200000000000000000000000000000000−2i2i00−2−222i2i2−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
χ192-2-222i−2i2222-2-2-2-22222-2-2-2-22-22-22i2i2i2i−2i−2i−2i−2i2i2i−2i−2i0000000000000000000000002−2−22i2−i2−i2i2
χ202-2-222i−2i2222-2-2-2-22222-2-2-2-22-22-22i2i2i2i−2i−2i−2i−2i2i2i−2i−2i000000000000000000000000−222−2−i2i2i2−i2
χ212-2-22−2i2i2222-2-2-2-22222-2-2-2-22-22-2−2i−2i−2i−2i2i2i2i2i−2i−2i2i2i0000000000000000000000002−2−22−i2i2i2−i2
χ222-2-22−2i2i2222-2-2-2-22222-2-2-2-22-22-2−2i−2i−2i−2i2i2i2i2i−2i−2i2i2i000000000000000000000000−222−2i2−i2−i2i2
χ23444444−1+53−523+52−1−5−1+53−523+52−1−5−1+53−523+52−1−5−1+53−523+52−1−5-1-1-1-1−1+53−523+52−1−5−1+53−523+52−1−5-1-1-1-102020000−1+52−1+52−1−52−1−520000−1+52−1+52−1−52−1−52000000000000
χ24444444−1+53−523+52−1−5−1+53−523+52−1−5−1+53−523+52−1−5−1+53−523+52−1−5-1-1-1-1−1+53−523+52−1−5−1+53−523+52−1−5-1-1-1-10-20-200001−521−521+521+5200001−521−521+521+52000000000000
χ254444443−52−1−5−1+53+523−52−1−5−1+53+523−52−1−5−1+53+523−52−1−5−1+53+52-1-1-1-13−52−1−5−1+53+523−52−1−5−1+53+52-1-1-1-12020−1+52−1+52−1−52−1−520000−1+52−1+52−1−52−1−520000000000000000
χ264444443−52−1−5−1+53+523−52−1−5−1+53+523−52−1−5−1+53+523−52−1−5−1+53+52-1-1-1-13−52−1−5−1+53+523−52−1−5−1+53+52-1-1-1-1-20-201−521−521+521+5200001−521−521+521+520000000000000000
χ274444443+52−1+5−1−53−523+52−1+5−1−53−523+52−1+5−1−53−523+52−1+5−1−53−52-1-1-1-13+52−1+5−1−53−523+52−1+5−1−53−52-1-1-1-12020−1−52−1−52−1+52−1+520000−1−52−1−52−1+52−1+520000000000000000
χ284444443+52−1+5−1−53−523+52−1+5−1−53−523+52−1+5−1−53−523+52−1+5−1−53−52-1-1-1-13+52−1+5−1−53−523+52−1+5−1−53−52-1-1-1-1-20-201+521+521−521−5200001+521+521−521−520000000000000000
χ29444444−1−53+523−52−1+5−1−53+523−52−1+5−1−53+523−52−1+5−1−53+523−52−1+5-1-1-1-1−1−53+523−52−1+5−1−53+523−52−1+5-1-1-1-102020000−1−52−1−52−1+52−1+520000−1−52−1−52−1+52−1+52000000000000
χ30444444−1−53+523−52−1+5−1−53+523−52−1+5−1−53+523−52−1+5−1−53+523−52−1+5-1-1-1-1−1−53+523−52−1+5−1−53+523−52−1+5-1-1-1-10-20-200001+521+521−521−5200001+521+521−521−52000000000000
χ314444-4-4−1+53−523+52−1−5−1+53−523+52−1−5−1+53−523+52−1−5−1+53−523+52−1−5-1-1-1-11−5−3+52−3−521+51−5−3+52−3−521+51111020-200001−521−521+521+520000−1+52−1+52−1−52−1−52000000000000
χ324444-4-4−1+53−523+52−1−5−1+53−523+52−1−5−1+53−523+52−1−5−1+53−523+52−1−5-1-1-1-11−5−3+52−3−521+51−5−3+52−3−521+511110-2020000−1+52−1+52−1−52−1−5200001−521−521+521+52000000000000
χ334444-4-43−52−1−5−1+53+523−52−1−5−1+53+523−52−1−5−1+53+523−52−1−5−1+53+52-1-1-1-1−3+521+51−5−3−52−3+521+51−5−3−52111120-201−521−521+521+520000−1+52−1+52−1−52−1−520000000000000000
χ344444-4-43−52−1−5−1+53+523−52−1−5−1+53+523−52−1−5−1+53+523−52−1−5−1+53+52-1-1-1-1−3+521+51−5−3−52−3+521+51−5−3−521111-2020−1+52−1+52−1−52−1−5200001−521−521+521+520000000000000000
χ354444-4-43+52−1+5−1−53−523+52−1+5−1−53−523+52−1+5−1−53−523+52−1+5−1−53−52-1-1-1-1−3−521−51+5−3+52−3−521−51+5−3+52111120-201+521+521−521−520000−1−52−1−52−1+52−1+520000000000000000
χ364444-4-43+52−1+5−1−53−523+52−1+5−1−53−523+52−1+5−1−53−523+52−1+5−1−53−52-1-1-1-1−3−521−51+5−3+52−3−521−51+5−3+521111-2020−1−52−1−52−1+52−1+5200001+521+521−521−520000000000000000
χ374444-4-4−1−53+523−52−1+5−1−53+523−52−1+5−1−53+523−52−1+5−1−53+523−52−1+5-1-1-1-11+5−3−52−3+521−51+5−3−52−3+521−51111020-200001+521+521−521−520000−1−52−1−52−1+52−1+52000000000000
χ384444-4-4−1−53+523−52−1+5−1−53+523−52−1+5−1−53+523−52−1+5−1−53+523−52−1+5-1-1-1-11+5−3−52−3+521−51+5−3−52−3+521−511110-2020000−1−52−1−52−1+52−1+5200001+521+521−521−52000000000000
χ394-4-444i−4i−1+53−523+52−1−51−5−3+52−3−521+5−1+53−523+52−1−51−5−3+52−3−521+5-11-11−2ζ22−2ζ38ζ6+ζ14+2ζ22+2ζ382ζ6+2ζ14+ζ22+ζ38−2ζ6−2ζ142ζ22+2ζ38−ζ6−ζ14−2ζ22−2ζ38−2ζ6−2ζ14−ζ22−ζ382ζ6+2ζ14−i−iii00000000ζ12−ζ28−ζ12+ζ28−ζ4+ζ36ζ4−ζ360000−ζ22+ζ38ζ22−ζ38ζ6−ζ14−ζ6+ζ14000000000000
χ404-4-444i−4i−1+53−523+52−1−51−5−3+52−3−521+5−1+53−523+52−1−51−5−3+52−3−521+5-11-11−2ζ22−2ζ38ζ6+ζ14+2ζ22+2ζ382ζ6+2ζ14+ζ22+ζ38−2ζ6−2ζ142ζ22+2ζ38−ζ6−ζ14−2ζ22−2ζ38−2ζ6−2ζ14−ζ22−ζ382ζ6+2ζ14−i−iii00000000−ζ12+ζ28ζ12−ζ28ζ4−ζ36−ζ4+ζ360000ζ22−ζ38−ζ22+ζ38−ζ6+ζ14ζ6−ζ14000000000000
χ414-4-444i−4i3−52−1−5−1+53+52−3+521+51−5−3−523−52−1−5−1+53+52−3+521+51−5−3−52-11-11ζ6+ζ14+2ζ22+2ζ38−2ζ6−2ζ14−2ζ22−2ζ382ζ6+2ζ14+ζ22+ζ38−ζ6−ζ14−2ζ22−2ζ382ζ6+2ζ142ζ22+2ζ38−2ζ6−2ζ14−ζ22−ζ38−i−iii0000ζ12−ζ28−ζ12+ζ28−ζ4+ζ36ζ4−ζ360000−ζ22+ζ38ζ22−ζ38ζ6−ζ14−ζ6+ζ140000000000000000
χ424-4-444i−4i3−52−1−5−1+53+52−3+521+51−5−3−523−52−1−5−1+53+52−3+521+51−5−3−52-11-11ζ6+ζ14+2ζ22+2ζ38−2ζ6−2ζ14−2ζ22−2ζ382ζ6+2ζ14+ζ22+ζ38−ζ6−ζ14−2ζ22−2ζ382ζ6+2ζ142ζ22+2ζ38−2ζ6−2ζ14−ζ22−ζ38−i−iii0000−ζ12+ζ28ζ12−ζ28ζ4−ζ36−ζ4+ζ360000ζ22−ζ38−ζ22+ζ38−ζ6+ζ14ζ6−ζ140000000000000000
χ434-4-444i−4i3+52−1+5−1−53−52−3−521−51+5−3+523+52−1+5−1−53−52−3−521−51+5−3+52-11-112ζ6+2ζ14+ζ22+ζ38−2ζ22−2ζ38−2ζ6−2ζ14ζ6+ζ14+2ζ22+2ζ38−2ζ6−2ζ14−ζ22−ζ382ζ22+2ζ382ζ6+2ζ14−ζ6−ζ14−2ζ22−2ζ38−i−iii0000−ζ4+ζ36ζ4−ζ36−ζ12+ζ28ζ12−ζ280000−ζ6+ζ14ζ6−ζ14−ζ22+ζ38ζ22−ζ380000000000000000
χ444-4-444i−4i3+52−1+5−1−53−52−3−521−51+5−3+523+52−1+5−1−53−52−3−521−51+5−3+52-11-112ζ6+2ζ14+ζ22+ζ38−2ζ22−2ζ38−2ζ6−2ζ14ζ6+ζ14+2ζ22+2ζ38−2ζ6−2ζ14−ζ22−ζ382ζ22+2ζ382ζ6+2ζ14−ζ6−ζ14−2ζ22−2ζ38−i−iii0000ζ4−ζ36−ζ4+ζ36ζ12−ζ28−ζ12+ζ280000ζ6−ζ14−ζ6+ζ14ζ22−ζ38−ζ22+ζ380000000000000000
χ454-4-444i−4i−1−53+523−52−1+51+5−3−52−3+521−5−1−53+523−52−1+51+5−3−52−3+521−5-11-11−2ζ6−2ζ142ζ6+2ζ14+ζ22+ζ38ζ6+ζ14+2ζ22+2ζ38−2ζ22−2ζ382ζ6+2ζ14−2ζ6−2ζ14−ζ22−ζ38−ζ6−ζ14−2ζ22−2ζ382ζ22+2ζ38−i−iii00000000−ζ4+ζ36ζ4−ζ36−ζ12+ζ28ζ12−ζ280000−ζ6+ζ14ζ6−ζ14−ζ22+ζ38ζ22−ζ38000000000000
χ464-4-444i−4i−1−53+523−52−1+51+5−3−52−3+521−5−1−53+523−52−1+51+5−3−52−3+521−5-11-11−2ζ6−2ζ142ζ6+2ζ14+ζ22+ζ38ζ6+ζ14+2ζ22+2ζ38−2ζ22−2ζ382ζ6+2ζ14−2ζ6−2ζ14−ζ22−ζ38−ζ6−ζ14−2ζ22−2ζ382ζ22+2ζ38−i−iii00000000ζ4−ζ36−ζ4+ζ36ζ12−ζ28−ζ12+ζ280000ζ6−ζ14−ζ6+ζ14ζ22−ζ38−ζ22+ζ38000000000000
χ474-4-44−4i4i−1+53−523+52−1−51−5−3+52−3−521+5−1+53−523+52−1−51−5−3+52−3−521+5-11-112ζ22+2ζ38−ζ6−ζ14−2ζ22−2ζ38−2ζ6−2ζ14−ζ22−ζ382ζ6+2ζ14−2ζ22−2ζ38ζ6+ζ14+2ζ22+2ζ382ζ6+2ζ14+ζ22+ζ38−2ζ6−2ζ14ii−i−i00000000ζ12−ζ28−ζ12+ζ28−ζ4+ζ36ζ4−ζ360000ζ22−ζ38−ζ22+ζ38−ζ6+ζ14ζ6−ζ14000000000000
χ484-4-44−4i4i−1+53−523+52−1−51−5−3+52−3−521+5−1+53−523+52−1−51−5−3+52−3−521+5-11-112ζ22+2ζ38−ζ6−ζ14−2ζ22−2ζ38−2ζ6−2ζ14−ζ22−ζ382ζ6+2ζ14−2ζ22−2ζ38ζ6+ζ14+2ζ22+2ζ382ζ6+2ζ14+ζ22+ζ38−2ζ6−2ζ14ii−i−i00000000−ζ12+ζ28ζ12−ζ28ζ4−ζ36−ζ4+ζ360000−ζ22+ζ38ζ22−ζ38ζ6−ζ14−ζ6+ζ14000000000000
χ494-4-44−4i4i3−52−1−5−1+53+52−3+521+51−5−3−523−52−1−5−1+53+52−3+521+51−5−3−52-11-11−ζ6−ζ14−2ζ22−2ζ382ζ6+2ζ142ζ22+2ζ38−2ζ6−2ζ14−ζ22−ζ38ζ6+ζ14+2ζ22+2ζ38−2ζ6−2ζ14−2ζ22−2ζ382ζ6+2ζ14+ζ22+ζ38ii−i−i0000ζ12−ζ28−ζ12+ζ28−ζ4+ζ36ζ4−ζ360000ζ22−ζ38−ζ22+ζ38−ζ6+ζ14ζ6−ζ140000000000000000
χ504-4-44−4i4i3−52−1−5−1+53+52−3+521+51−5−3−523−52−1−5−1+53+52−3+521+51−5−3−52-11-11−ζ6−ζ14−2ζ22−2ζ382ζ6+2ζ142ζ22+2ζ38−2ζ6−2ζ14−ζ22−ζ38ζ6+ζ14+2ζ22+2ζ38−2ζ6−2ζ14−2ζ22−2ζ382ζ6+2ζ14+ζ22+ζ38ii−i−i0000−ζ12+ζ28ζ12−ζ28ζ4−ζ36−ζ4+ζ360000−ζ22+ζ38ζ22−ζ38ζ6−ζ14−ζ6+ζ140000000000000000
χ514-4-44−4i4i3+52−1+5−1−53−52−3−521−51+5−3+523+52−1+5−1−53−52−3−521−51+5−3+52-11-11−2ζ6−2ζ14−ζ22−ζ382ζ22+2ζ382ζ6+2ζ14−ζ6−ζ14−2ζ22−2ζ382ζ6+2ζ14+ζ22+ζ38−2ζ22−2ζ38−2ζ6−2ζ14ζ6+ζ14+2ζ22+2ζ38ii−i−i0000−ζ4+ζ36ζ4−ζ36−ζ12+ζ28ζ12−ζ280000ζ6−ζ14−ζ6+ζ14ζ22−ζ38−ζ22+ζ380000000000000000
χ524-4-44−4i4i3+52−1+5−1−53−52−3−521−51+5−3+523+52−1+5−1−53−52−3−521−51+5−3+52-11-11−2ζ6−2ζ14−ζ22−ζ382ζ22+2ζ382ζ6+2ζ14−ζ6−ζ14−2ζ22−2ζ382ζ6+2ζ14+ζ22+ζ38−2ζ22−2ζ38−2ζ6−2ζ14ζ6+ζ14+2ζ22+2ζ38ii−i−i0000ζ4−ζ36−ζ4+ζ36ζ12−ζ28−ζ12+ζ280000−ζ6+ζ14ζ6−ζ14−ζ22+ζ38ζ22−ζ380000000000000000
χ534-4-44−4i4i−1−53+523−52−1+51+5−3−52−3+521−5−1−53+523−52−1+51+5−3−52−3+521−5-11-112ζ6+2ζ14−2ζ6−2ζ14−ζ22−ζ38−ζ6−ζ14−2ζ22−2ζ382ζ22+2ζ38−2ζ6−2ζ142ζ6+2ζ14+ζ22+ζ38ζ6+ζ14+2ζ22+2ζ38−2ζ22−2ζ38ii−i−i00000000−ζ4+ζ36ζ4−ζ36−ζ12+ζ28ζ12−ζ280000ζ6−ζ14−ζ6+ζ14ζ22−ζ38−ζ22+ζ38000000000000
χ544-4-44−4i4i−1−53+523−52−1+51+5−3−52−3+521−5−1−53+523−52−1+51+5−3−52−3+521−5-11-112ζ6+2ζ14−2ζ6−2ζ14−ζ22−ζ38−ζ6−ζ14−2ζ22−2ζ382ζ22+2ζ38−2ζ6−2ζ142ζ6+2ζ14+ζ22+ζ38ζ6+ζ14+2ζ22+2ζ38−2ζ22−2ζ38ii−i−i00000000ζ4−ζ36−ζ4+ζ36ζ12−ζ28−ζ12+ζ280000−ζ6+ζ14ζ6−ζ14−ζ22+ζ38ζ22−ζ38000000000000
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
χ5788-8-800-2-2-2-222222222-2-2-2-23-3-33000000005-55-500000000000000000000000000000000
χ5888-8-800-2-2-2-222222222-2-2-2-23-3-3300000000-55-5500000000000000000000000000000000
χ5988-8-800−2+253−53+5−2−252−25−3+5−3−52+252−25−3+5−3−52+25−2+253−53+5−2−25-222-200000000000000000000000000000000000000000000
χ6088-8-8003−5−2−25−2+253+5−3+52+252−25−3−5−3+52+252−25−3−53−5−2−25−2+253+5-222-200000000000000000000000000000000000000000000
χ6188-8-8003+5−2+25−2−253−5−3−52−252+25−3+5−3−52−252+25−3+53+5−2+25−2−253−5-222-200000000000000000000000000000000000000000000
χ6288-8-800−2−253+53−5−2+252+25−3−5−3+52−252+25−3−5−3+52−25−2−253+53−5−2+25-222-200000000000000000000000000000000000000000000
χ638-88-800-2-2-2-2-2-2-2-22222222233-3-3000000005i−5i−5i5i00000000000000000000000000000000
χ648-88-800-2-2-2-2-2-2-2-22222222233-3-300000000−5i5i5i−5i00000000000000000000000000000000
χ658-88-800−2+253−53+5−2−25−2+253−53+5−2−252−25−3+5−3−52+252−25−3+5−3−52+25-2-22200000000000000000000000000000000000000000000
χ668-88-8003−5−2−25−2+253+53−5−2−25−2+253+5−3+52+252−25−3−5−3+52+252−25−3−5-2-22200000000000000000000000000000000000000000000
χ678-88-8003+5−2+25−2−253−53+5−2+25−2−253−5−3−52−252+25−3+5−3−52−252+25−3+5-2-22200000000000000000000000000000000000000000000
χ688-88-800−2−253+53−5−2+25−2−253+53−5−2+252+25−3−5−3+52−252+25−3−5−3+52−25-2-22200000000000000000000000000000000000000000000
χ698-8-888i−8i-2-2-2-22222-2-2-2-222223-33-3−2i−2i−2i−2i2i2i2i2i3i3i−3i−3i00000000000000000000000000000000
χ708-8-88−8i8i-2-2-2-22222-2-2-2-222223-33-32i2i2i2i−2i−2i−2i−2i−3i−3i3i3i00000000000000000000000000000000

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