Finite Group Databasebeta

← Group #13014792

Character table — Group #13014792

Order 1280.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92
size1111111122224444444444444444444488888888888888888888888888881010101010101010202020204040404040404040404040404040404040404040
order12222222222244445101010101010101010101010101010444420202020202020202020202020202020202020202020202044444444444444448888888888888888
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
χ911111111-1-1-1-111-1-1111111-1-1-1-1-1-1-1-11111-1-11111-1-1-1-111111111-1-1-1-1-1-1-1-111111111-1-1-1-111-1-111-1-111-1-111-1-111-1-1
χ1011111111-1-1-1-111-1-1111111-1-1-1-1-1-1-1-11111-1-11111-1-1-1-111111111-1-1-1-1-1-1-1-111111111-1-1-1-111-1-1-1-111-1-111-1-111-1-111
χ1111111111-1-1-1-111-1-1111111-1-1-1-1-1-1-1-11111-1-11111-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-111ii−i−i−i−iiiii−i−i−i−iii
χ1211111111-1-1-1-111-1-1111111-1-1-1-1-1-1-1-11111-1-11111-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-111−i−iiiii−i−i−i−iiiii−i−i
χ1311111111-1-1-1-111-1-1111111-1-1-1-1-1-1-1-111-1-1111111-1-1-1-1-1-1-1-1-1-1-1-11111111111111111-1-1-1-1-1-11111-1-111-1-1-1-111-1-111
χ1411111111-1-1-1-111-1-1111111-1-1-1-1-1-1-1-111-1-1111111-1-1-1-1-1-1-1-1-1-1-1-11111111111111111-1-1-1-1-1-111-1-111-1-11111-1-111-1-1
χ1511111111-1-1-1-111-1-1111111-1-1-1-1-1-1-1-111-1-1111111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1111111-1-1ii−i−i−i−iii−i−iiiii−i−i
χ1611111111-1-1-1-111-1-1111111-1-1-1-1-1-1-1-111-1-1111111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1111111-1-1−i−iiiii−i−iii−i−i−i−iii
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χ1922222222-2-2-2-2-2-222222222-2-2-2-2-2-2-2-2220000-2-2-2-22222000000000000000022-2-2-2-222-2-22200000000000000000000
χ2022222222-2-2-2-2-2-222222222-2-2-2-2-2-2-2-2220000-2-2-2-222220000000000000000-2-22222-2-222-2-200000000000000000000
χ21222-2-22-2-222-2-200002222-2-22222-2-2-2-2-2-20000000000000000000000000000220000-2-22-20000002−22−22−22−200000000
χ22222-2-22-2-222-2-200002222-2-22222-2-2-2-2-2-20000000000000000000000000000220000-2-22-2000000−22−22−22−2200000000
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χ25222-2-22-2-2-2-22200002222-2-2-2-2-2-22222-2-20000000000000000000000000000220000-2-2-220000002−2−222−2−2200000000
χ26222-2-22-2-2-2-22200002222-2-2-2-2-2-22222-2-20000000000000000000000000000220000-2-2-22000000−222−2−222−200000000
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χ2922-22-2-2-2200002-20022-2-22-2000000002-2002i−2i22-2-20000000000002i2i2i2i−2i−2i−2i−2i2i−2i2i2i−2i−2i2i−2i0000002-20000000000000000
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χ432-2-2222-2-2-22-2200002-22-22-2-2-222-2-222-22000000000000000000000000000000−2i2i−2i2i00002i−2i0000000000001−i−1+i−1+i1−i1+i−1−i−1−i1+i
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χ454444444444444444-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-14444-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-100000000000000000000000000000000
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χ47444444444444-4-4-4-4-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-100001111111155−5−555−5−555−5−555−5−500000000000000000000000000000000
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
χ4944444444-4-4-4-444-4-4-1-1-1-1-1-111111111-1-144-4-4-1-1-1-11111-1-1-1-1-1-1-1-11111111100000000000000000000000000000000
χ5044444444-4-4-4-444-4-4-1-1-1-1-1-111111111-1-1-4-444-1-1-1-1111111111111-1-1-1-1-1-1-1-100000000000000000000000000000000
χ5144444444-4-4-4-4-4-444-1-1-1-1-1-111111111-1-100001111-1-1-1-155−5−555−5−5−5−555−5−55500000000000000000000000000000000
χ5244444444-4-4-4-4-4-444-1-1-1-1-1-111111111-1-100001111-1-1-1-1−5−555−5−55555−5−555−5−500000000000000000000000000000000
χ5344-44-4-4-4400004-400-1-111-115−55−55−55−5-11004i−4i-1-11155−5−5i5i5−i5−i5−i5−i5i5i5−i−i−i−iiiii00000000000000000000000000000000
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χ5544-44-4-4-4400004-400-1-111-11−55−55−55−55-11004i−4i-1-111−5−555−i5−i5i5i5i5i5−i5−i5−i−i−i−iiiii00000000000000000000000000000000
χ5644-44-4-4-4400004-400-1-111-11−55−55−55−55-1100−4i4i-1-111−5−555i5i5−i5−i5−i5−i5i5i5iiii−i−i−i−i00000000000000000000000000000000
χ5744-44-4-4-440000-4400-1-111-115−55−55−55−5-114i−4i0011-1-1−5−555−i−i−i−iiiiii5i5−i5−i5−i5−i5i5i500000000000000000000000000000000
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χ5944-44-4-4-440000-4400-1-111-11−55−55−55−55-114i−4i0011-1-155−5−5−i−i−i−iiiii−i5−i5i5i5i5i5−i5−i500000000000000000000000000000000
χ6044-44-4-4-440000-4400-1-111-11−55−55−55−55-11−4i4i0011-1-155−5−5iiii−i−i−i−ii5i5−i5−i5−i5−i5i5i500000000000000000000000000000000
χ6144-4-44-44-40000000044-4-4-4400000000-4400000000000000000000000000004i−4i0000−4i4i000000000000000000000000
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χ804-4-4-4-4444-444-400004-44-4-44-4-44444-4-44-4000000000000000000000000000000000000000000000000000000000000
χ814-4-4-4-4444-444-40000-11-111-111-1-1-1-111-1100005−5−55−555−5ζ6−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+ζ38ζ6−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
χ824-4-4-4-4444-444-40000-11-111-111-1-1-1-111-1100005−5−55−555−5−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−ζ38−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+ζ3800000000000000000000000000000000
χ834-4-4-4-4444-444-40000-11-111-111-1-1-1-111-110000−555−55−5−55−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−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
χ844-4-4-4-4444-444-40000-11-111-111-1-1-1-111-110000−555−55−5−55ζ6−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+ζ38ζ6−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
χ85888-8-88-8-888-8-80000-2-2-2-222-2-2-2-2222222000000000000000000000000000000000000000000000000000000000000
χ86888-8-88-8-8-8-8880000-2-2-2-2222222-2-2-2-222000000000000000000000000000000000000000000000000000000000000
χ8788-8-88-88-800000000-2-2222-225−2525−25−2525−25252-2000000000000000000000000000000000000000000000000000000000000
χ8888-8-88-88-800000000-2-2222-2−2525−252525−2525−252-2000000000000000000000000000000000000000000000000000000000000
χ898-888-8-88-800000000-222-2-2-225−25−252525−25−252522000000000000000000000000000000000000000000000000000000000000
χ908-888-8-88-800000000-222-2-2-2−252525−25−252525−2522000000000000000000000000000000000000000000000000000000000000
χ918-8-8888-8-88-88-80000-22-22-22-2-222-2-2222-2000000000000000000000000000000000000000000000000000000000000
χ928-8-8888-8-8-88-880000-22-22-2222-2-222-2-22-2000000000000000000000000000000000000000000000000000000000000

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