Finite Group Databasebeta

← Group #13017515

Character table — Group #13017515

Order 1280.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92
size1111111122224444444444444444444488888888888888888888888888881010101010101010202020204040404040404040404040404040404040404040
order12222222444444445101010101010102020202020202020444420202020202020202020202020202020202020202020202022224444444444444444444488888888
χ111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ3111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1iiii−i−i−i−iiiii−i−i−i−i
χ4111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1−i−i−i−iiiii−i−i−i−iiiii
χ511111111111111111111111111111111-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-111111111-1-1-1-1-1-1-1-1
χ611111111111111111111111111111111-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-111111111
χ711111111111111111111111111111111-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111iiii−i−i−i−i−i−i−i−iiiii
χ811111111111111111111111111111111-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111−i−i−i−iiiiiiiii−i−i−i−i
χ911111111-1-1-1-111-1-111111111-1-1-1-1-1-1-1-111-1-11111-1-1-1-111111111-1-1-1-1-1-1-1-111111111-1-1-1-111-1-111-1-111-1-111-1-111-1-1
χ1011111111-1-1-1-111-1-111111111-1-1-1-1-1-1-1-111-1-11111-1-1-1-111111111-1-1-1-1-1-1-1-111111111-1-1-1-111-1-1-1-111-1-111-1-111-1-111
χ1111111111-1-1-1-111-1-111111111-1-1-1-1-1-1-1-111-1-11111-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-111ii−i−i−i−iiiii−i−i−i−iii
χ1211111111-1-1-1-111-1-111111111-1-1-1-1-1-1-1-111-1-11111-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-111−i−iiiii−i−i−i−iiiii−i−i
χ1311111111-1-1-1-111-1-111111111-1-1-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-11111111111111111-1-1-1-1-1-11111-1-111-1-1-1-111-1-111
χ1411111111-1-1-1-111-1-111111111-1-1-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-11111111111111111-1-1-1-1-1-111-1-111-1-11111-1-111-1-1
χ1511111111-1-1-1-111-1-111111111-1-1-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1111111-1-1ii−i−i−i−iii−i−iiiii−i−i
χ1611111111-1-1-1-111-1-111111111-1-1-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1111111-1-1−i−iiiii−i−iii−i−i−i−iii
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χ2022222222-2-2-2-2-2-22222222222-2-2-2-2-2-2-2-20000-2-2-2-222220000000000000000-2-2-2-2222222-2-200000000000000000000
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χ464444444444444444-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-4-4-4-4-1-1-1-1-1-1-1-1111111111111111100000000000000000000000000000000
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χ48444444444444-4-4-4-4-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1000011111111−5−555−5−555−5−555−5−55500000000000000000000000000000000
χ4944444444-4-4-4-444-4-4-1-1-1-1-1-1-1-11111111144-4-4-1-1-1-11111-1-1-1-1-1-1-1-11111111100000000000000000000000000000000
χ5044444444-4-4-4-444-4-4-1-1-1-1-1-1-1-111111111-4-444-1-1-1-1111111111111-1-1-1-1-1-1-1-100000000000000000000000000000000
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χ704-444-4-4-44000000−4i4i-11-1-1111-1i5−i5i5−i5i5−i5i5−i50000−555−5i−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−ζ38−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−ζ3600000000000000000000000000000000
χ714-444-4-4-44000000−4i4i-11-1-1111-1−i5i5−i5i5−i5i5−i5i500005−5−55i−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−ζ38ζ4−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−ζ3600000000000000000000000000000000
χ724-444-4-4-44000000−4i4i-11-1-1111-1−i5i5−i5i5−i5i5−i5i500005−5−55i−ii−i−ζ6+ζ14+ζ22−ζ38ζ6−ζ14−ζ22+ζ38−ζ6+ζ14−ζ22+ζ38ζ6−ζ14+ζ22−ζ38ζ6−ζ14−ζ22+ζ38−ζ6+ζ14+ζ22−ζ38ζ6−ζ14+ζ22−ζ38−ζ6+ζ14−ζ22+ζ38−ζ4+ζ12−ζ28+ζ36ζ4−ζ12+ζ28−ζ36−ζ4−ζ12+ζ28+ζ36ζ4+ζ12−ζ28−ζ36ζ4−ζ12+ζ28−ζ36−ζ4+ζ12−ζ28+ζ36ζ4+ζ12−ζ28−ζ36−ζ4−ζ12+ζ28+ζ3600000000000000000000000000000000
χ734-44-44-44-4000000004-44-44-44-400000000000000000000000000000000000000004i−4i−4i4i000000000000000000000000
χ744-44-44-44-4000000004-44-44-44-40000000000000000000000000000000000000000−4i4i4i−4i000000000000000000000000
χ754-4-4444-4-4000000004-4-4444-4-40000000000000000000000000000000000004-4-440000000000000000000000000000
χ764-4-4444-4-4000000004-4-4444-4-4000000000000000000000000000000000000-444-40000000000000000000000000000
χ774-4-4-4-444400004-400-11111-1-1-15−5−55−555−5004-4-1-1115−5−5555−5−5−5−555-1-1-1-1111100000000000000000000000000000000
χ784-4-4-4-444400004-400-11111-1-1-15−5−55−555−500-44-1-1115−5−55−5−55555−5−51111-1-1-1-100000000000000000000000000000000
χ794-4-4-4-444400004-400-11111-1-1-1−555−55−5−55004-4-1-111−555−5−5−55555−5−5-1-1-1-1111100000000000000000000000000000000
χ804-4-4-4-444400004-400-11111-1-1-1−555−55−5−5500-44-1-111−555−555−5−5−5−5551111-1-1-1-100000000000000000000000000000000
χ814-4-4-4-44440000-4400-11111-1-1-15−5−55−555−54-40011-1-1−555−5-1-1-1-1111155−5−5−5−55500000000000000000000000000000000
χ824-4-4-4-44440000-4400-11111-1-1-15−5−55−555−5-440011-1-1−555−51111-1-1-1-1−5−55555−5−500000000000000000000000000000000
χ834-4-4-4-44440000-4400-11111-1-1-1−555−55−5−554-40011-1-15−5−55-1-1-1-11111−5−55555−5−500000000000000000000000000000000
χ844-4-4-4-44440000-4400-11111-1-1-1−555−55−5−55-440011-1-15−5−551111-1-1-1-155−5−5−5−55500000000000000000000000000000000
χ85888-8-88-8-888-8-80000-2-2-222-222-2-2-2-22222000000000000000000000000000000000000000000000000000000000000
χ86888-8-88-8-8-8-8880000-2-2-222-2222222-2-2-2-2000000000000000000000000000000000000000000000000000000000000
χ8788-88-8-88-88i−8i8i−8i0000-2-22-222-22−2i−2i2i2i−2i−2i2i2i000000000000000000000000000000000000000000000000000000000000
χ8888-88-8-88-8−8i8i−8i8i0000-2-22-222-222i2i−2i−2i2i2i−2i−2i000000000000000000000000000000000000000000000000000000000000
χ898-88-88-88-800000000-22-22-22-222i5−2i52i5−2i5−2i52i5−2i52i5000000000000000000000000000000000000000000000000000000000000
χ908-88-88-88-800000000-22-22-22-22−2i52i5−2i52i52i5−2i52i5−2i5000000000000000000000000000000000000000000000000000000000000
χ918-8-8888-8-800000000-222-2-2-22225−25−252525−25−2525000000000000000000000000000000000000000000000000000000000000
χ928-8-8888-8-800000000-222-2-2-222−252525−25−252525−25000000000000000000000000000000000000000000000000000000000000

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