Finite Group Databasebeta

← Group #12002428

Character table — Group #12002428

Order 1280.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96C97C98C99C100C101C102C103C104
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order1222444422445510101010101020202020202020204444101010102020202044442020202020202020202020202020202020202020202020202488101010102020202040404040404040404444444488888888
χ111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ311111111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1
χ411111111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111
χ51111111111111111111111111111111111111111-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-111111111-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1-1-1
χ61111111111111111111111111111111111111111-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-11111
χ71111111111111111111111111111111111111111-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-11111
χ81111111111111111111111111111111111111111-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-111111111-1-1-1-111111111-1-1-1-1
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χ23222222222222−1−52−1+52−1−52−1−52−1+52−1+52−1−52−1+52−1−52−1−52−1+52−1+52−1−52−1−52−1+52−1+52-2-2-2-2−1−52−1−52−1+52−1+52−1−52−1−52−1+52−1+5222-2-21+521+521+521+521−521−521−521−52−1−52−1−52−1−52−1−52−1+52−1+52−1+52−1+521+521+521+521+521−521−521−521−520000−ζ4+ζ36ζ4−ζ36−ζ12+ζ28ζ12−ζ28−ζ4+ζ36ζ4−ζ36−ζ12+ζ28ζ12−ζ28−ζ4+ζ36−ζ4+ζ36ζ4−ζ36ζ4−ζ36−ζ12+ζ28−ζ12+ζ28ζ12−ζ28ζ12−ζ280000000000000000
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χ25222222222222−1−52−1+52−1−52−1−52−1+52−1+52−1−52−1+52−1−52−1−52−1+52−1+52−1−52−1−52−1+52−1+52-2-2-2-2−1−52−1−52−1+52−1+52−1−52−1−52−1+52−1+52-2-2221+521+521+521+521−521−521−521−521+521+521+521+521−521−521−521−52−1−52−1−52−1−52−1−52−1+52−1+52−1+52−1+520000−ζ4+ζ36ζ4−ζ36−ζ12+ζ28ζ12−ζ28−ζ4+ζ36ζ4−ζ36−ζ12+ζ28ζ12−ζ28ζ4−ζ36ζ4−ζ36−ζ4+ζ36−ζ4+ζ36ζ12−ζ28ζ12−ζ28−ζ12+ζ28−ζ12+ζ280000000000000000
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χ2822222222-2-2-2-222222222222222222-22-2-2-2-2-2-2-2-2-2000022-2-222-2-2000000000000000000000000000000000000000000000000−2i−2i2i2i
χ2922222222-2-2-2-22222222222222222-22-22-2-2-2-2-2-2-2-20000-2-222-2-222000000000000000000000000000000000000000000002i2i−2i−2i0000
χ3022222222-2-2-2-22222222222222222-22-22-2-2-2-2-2-2-2-20000-2-222-2-22200000000000000000000000000000000000000000000−2i−2i2i2i0000
χ312222-2-2-2-222-2-222222222-2-2-2-2-2-2-2-22-2-222222-2-2-2-200002-22-22-22-2000000000000000000000000000000000000000022-2-200000000
χ322222-2-2-2-222-2-222222222-2-2-2-2-2-2-2-22-2-222222-2-2-2-200002-22-22-22-20000000000000000000000000000000000000000-2-22200000000
χ332222-2-2-2-222-2-222222222-2-2-2-2-2-2-2-2-222-22222-2-2-2-20000-22-22-22-2200000000000000000000000000000000000022-2-2000000000000
χ342222-2-2-2-222-2-222222222-2-2-2-2-2-2-2-2-222-22222-2-2-2-20000-22-22-22-22000000000000000000000000000000000000-2-222000000000000
χ352222-2-2-2-2-2-22222222222-2-2-2-2-2-2-2-222-2-2-2-2-2-2222200002-2-222-2-2200000000000000002-2002222-2-2-2-2000000000000000000000000
χ362222-2-2-2-2-2-22222222222-2-2-2-2-2-2-2-222-2-2-2-2-2-2222200002-2-222-2-220000000000000000-2200-2-2-2-22222000000000000000000000000
χ372222-2-2-2-2-2-22222222222-2-2-2-2-2-2-2-2-2-222-2-2-2-222220000-222-2-222-20000000000000000002i−2i000000002i−2i2i−2i2i−2i2i−2i0000000000000000
χ382222-2-2-2-2-2-22222222222-2-2-2-2-2-2-2-2-2-222-2-2-2-222220000-222-2-222-2000000000000000000−2i2i00000000−2i2i−2i2i−2i2i−2i2i0000000000000000
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χ402222-2-2-2-2-2-222−1+52−1−52−1+52−1+52−1−52−1−52−1+52−1−521−521−521+521+521−521−521+521+5222-2-21−521−521+521+52−1+52−1+52−1−52−1−520000−1+521−521−52−1+52−1−521+521+52−1−52−ζ22+ζ38−ζ22+ζ38ζ22−ζ38ζ22−ζ38ζ6−ζ14ζ6−ζ14−ζ6+ζ14−ζ6+ζ14−ζ22+ζ38−ζ22+ζ38ζ22−ζ38ζ22−ζ38ζ6−ζ14ζ6−ζ14−ζ6+ζ14−ζ6+ζ14-22001−521−521+521+52−1+52−1+52−1−52−1−52ζ22−ζ38−ζ22+ζ38−ζ22+ζ38ζ22−ζ38ζ6−ζ14−ζ6+ζ14−ζ6+ζ14ζ6−ζ140000000000000000
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χ432222-2-2-2-2-2-222−1+52−1−52−1+52−1+52−1−52−1−52−1+52−1−521−521−521+521+521−521−521+521+52-2-2221−521−521+521+52−1+52−1+52−1−52−1−5200001−52−1+52−1+521−521+52−1−52−1−521+52−ζ22+ζ38−ζ22+ζ38ζ22−ζ38ζ22−ζ38ζ6−ζ14ζ6−ζ14−ζ6+ζ14−ζ6+ζ14ζ22−ζ38ζ22−ζ38−ζ22+ζ38−ζ22+ζ38−ζ6+ζ14−ζ6+ζ14ζ6−ζ14ζ6−ζ14002i−2i−ζ12+ζ28ζ12−ζ28ζ4−ζ36−ζ4+ζ36ζ12−ζ28−ζ12+ζ28−ζ4+ζ36ζ4−ζ36−ζ22−ζ38ζ22+ζ38−ζ22−ζ38ζ22+ζ38−ζ6−ζ14ζ6+ζ14−ζ6−ζ14ζ6+ζ140000000000000000
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χ1018-88-88i−8i−8i8i0000−2+25−2−252−25−2+252+25−2−252−252+25−4ζ22−4ζ384ζ22+4ζ38−4ζ6−4ζ144ζ6+4ζ144ζ22+4ζ38−4ζ22−4ζ384ζ6+4ζ14−4ζ6−4ζ140000000000000000000000000000000000000000000000000000000000000000000000000000
χ1028-88-88i−8i−8i8i0000−2−25−2+252+25−2−252−25−2+252+252−25−4ζ6−4ζ144ζ6+4ζ14−4ζ22−4ζ384ζ22+4ζ384ζ6+4ζ14−4ζ6−4ζ144ζ22+4ζ38−4ζ22−4ζ380000000000000000000000000000000000000000000000000000000000000000000000000000
χ1038-88-8−8i8i8i−8i0000−2+25−2−252−25−2+252+25−2−252−252+254ζ22+4ζ38−4ζ22−4ζ384ζ6+4ζ14−4ζ6−4ζ14−4ζ22−4ζ384ζ22+4ζ38−4ζ6−4ζ144ζ6+4ζ140000000000000000000000000000000000000000000000000000000000000000000000000000
χ1048-88-8−8i8i8i−8i0000−2−25−2+252+25−2−252−25−2+252+252−254ζ6+4ζ14−4ζ6−4ζ144ζ22+4ζ38−4ζ22−4ζ38−4ζ6−4ζ144ζ6+4ζ14−4ζ22−4ζ384ζ22+4ζ380000000000000000000000000000000000000000000000000000000000000000000000000000

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