Finite Group Databasebeta

← Group #13017438

Character table — Group #13017438

Order 1280.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92
size1111111122224444444444444444444488888888888888888888888888881010101010101010202020204040404040404040404040404040404040404040
order12222222222244445101010101010101010101010101010224410101010101010102020202020202020202020202020202044444444444444448888888888888888
χ111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ3111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1iiiiiiii−i−i−i−i−i−i−i−i
χ4111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1−i−i−i−i−i−i−i−iiiiiiiii
χ511111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1111111111111-1-1-1-11111-1-1-1-11111-1-1-1-1
χ611111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-11111-1-1-1-11111
χ711111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111iiii−i−i−i−i−i−i−i−iiiii
χ811111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111−i−i−i−iiiiiiiii−i−i−i−i
χ9111111111111-1-1-1-1111111111111111111-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-111-1-111-1-111-1-111-1-111-1-1
χ10111111111111-1-1-1-1111111111111111111-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-111-1-1-1-111-1-111-1-111-1-111
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χ13111111111111-1-1-1-11111111111111111-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111111111-1-1-1-1-1-11111-1-1-1-11111-1-1-1-111
χ14111111111111-1-1-1-11111111111111111-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111111111-1-1-1-1-1-111-1-11111-1-1-1-11111-1-1
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χ724-444-4-4-44000000−4i4i-11-1-11-15−5−55−555−5110000ζ4−ζ12+ζ28−ζ36−ζ4+ζ12−ζ28+ζ36ζ4+ζ12−ζ28−ζ36−ζ4−ζ12+ζ28+ζ36−ζ4+ζ12−ζ28+ζ36ζ4−ζ12+ζ28−ζ36−ζ4−ζ12+ζ28+ζ36ζ4+ζ12−ζ28−ζ36−i5i5−i5i5i−ii−iζ6−ζ14−ζ22+ζ38−ζ6+ζ14+ζ22−ζ38ζ6−ζ14+ζ22−ζ38−ζ6+ζ14−ζ22+ζ38−ζ6+ζ14+ζ22−ζ38ζ6−ζ14−ζ22+ζ38−ζ6+ζ14−ζ22+ζ38ζ6−ζ14+ζ22−ζ3800000000000000000000000000000000
χ734-444-4-4-44000000−4i4i-11-1-11-1−555−55−5−55110000−ζ4−ζ12+ζ28+ζ36ζ4+ζ12−ζ28−ζ36ζ4−ζ12+ζ28−ζ36−ζ4+ζ12−ζ28+ζ36ζ4+ζ12−ζ28−ζ36−ζ4−ζ12+ζ28+ζ36−ζ4+ζ12−ζ28+ζ36ζ4−ζ12+ζ28−ζ36i5−i5i5−i5i−ii−iζ6−ζ14+ζ22−ζ38−ζ6+ζ14−ζ22+ζ38−ζ6+ζ14+ζ22−ζ38ζ6−ζ14−ζ22+ζ38−ζ6+ζ14−ζ22+ζ38ζ6−ζ14+ζ22−ζ38ζ6−ζ14−ζ22+ζ38−ζ6+ζ14+ζ22−ζ3800000000000000000000000000000000
χ744-444-4-4-44000000−4i4i-11-1-11-1−555−55−5−55110000ζ4+ζ12−ζ28−ζ36−ζ4−ζ12+ζ28+ζ36−ζ4+ζ12−ζ28+ζ36ζ4−ζ12+ζ28−ζ36−ζ4−ζ12+ζ28+ζ36ζ4+ζ12−ζ28−ζ36ζ4−ζ12+ζ28−ζ36−ζ4+ζ12−ζ28+ζ36i5−i5i5−i5i−ii−i−ζ6+ζ14−ζ22+ζ38ζ6−ζ14+ζ22−ζ38ζ6−ζ14−ζ22+ζ38−ζ6+ζ14+ζ22−ζ38ζ6−ζ14+ζ22−ζ38−ζ6+ζ14−ζ22+ζ38−ζ6+ζ14+ζ22−ζ38ζ6−ζ14−ζ22+ζ3800000000000000000000000000000000
χ754-44-44-44-4000000004-44-44-400000000-440000000000000000000000000000000000004i−4i0000000000000000000000
χ764-44-44-44-4000000004-44-44-400000000-44000000000000000000000000000000000000−4i4i0000000000000000000000
χ774-4-4-4-44444-4-440000-11111-1-1-11111-1-1-1-14-400-1-1-1-111115−5−555−5−5555−5−5−5−55500000000000000000000000000000000
χ784-4-4-4-44444-4-440000-11111-1-1-11111-1-1-1-14-400-1-1-1-11111−555−5−555−5−5−55555−5−500000000000000000000000000000000
χ794-4-4-4-44444-4-440000-11111-1-1-11111-1-1-1-1-44001111-1-1-1-15−5−555−5−55−5−55555−5−500000000000000000000000000000000
χ804-4-4-4-44444-4-440000-11111-1-1-11111-1-1-1-1-44001111-1-1-1-1−555−5−555−555−5−5−5−55500000000000000000000000000000000
χ814-4-4-4-4444-444-40000-11111-111-1-1-1-111-1-1004-455−5−5−5−5555−5−55−555−5-1-1-1-1111100000000000000000000000000000000
χ824-4-4-4-4444-444-40000-11111-111-1-1-1-111-1-1004-4−5−55555−5−5−555−55−5−55-1-1-1-1111100000000000000000000000000000000
χ834-4-4-4-4444-444-40000-11111-111-1-1-1-111-1-100-4455−5−5−5−555−555−55−5−551111-1-1-1-100000000000000000000000000000000
χ844-4-4-4-4444-444-40000-11111-111-1-1-1-111-1-100-44−5−55555−5−55−5−55−555−51111-1-1-1-100000000000000000000000000000000
χ85888-8-88-8-888-8-80000-2-2-2222-2-2-2-22222-22000000000000000000000000000000000000000000000000000000000000
χ86888-8-88-8-8-8-8880000-2-2-22222222-2-2-2-2-22000000000000000000000000000000000000000000000000000000000000
χ8788-88-8-88-800000000-2-22-22225−2525−25−2525−25252-2000000000000000000000000000000000000000000000000000000000000
χ8888-88-8-88-800000000-2-22-222−2525−252525−2525−252-2000000000000000000000000000000000000000000000000000000000000
χ898-88-88-88-800000000-22-22-2225−25−252525−25−25252-2000000000000000000000000000000000000000000000000000000000000
χ908-88-88-88-800000000-22-22-22−252525−25−252525−252-2000000000000000000000000000000000000000000000000000000000000
χ918-8-8888-8-88-88-80000-222-2-22-2-222-2-222-22000000000000000000000000000000000000000000000000000000000000
χ928-8-8888-8-8-88-880000-222-2-2222-2-222-2-2-22000000000000000000000000000000000000000000000000000000000000

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