Finite Group Databasebeta

← Group #13017025

Character table — Group #13017025

Order 1280.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96C97C98C99C100C101C102C103C104C105C106C107C108C109C110C111C112C113C114C115C116
size111144444888888810101010202020202020202040111144444888888810101010202020202020202040111144444888888810101010202020202020202040111144444888888810101010202020202020202040
order12224510101042020202020202244444488884444442020202042020202020204444444488884222241010101042020202020202244444488884444442020202042020202020204444444488884
χ111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111-1-1-1-1-1-1-1-1111111111111111111111-1-1-1-1-1-1-1-1111111111111111111111-1-1-1-1-1-1-1-1111111111111111111111-1-1-1-1-1-1-1-11
χ31111111111111111-1-1-1-1ii−i−iii−i−i-11111111111111111-1-1-1-1ii−i−iii−i−i-11111111111111111-1-1-1-1ii−i−iii−i−i-11111111111111111-1-1-1-1ii−i−iii−i−i-1
χ41111111111111111-1-1-1-1−i−iii−i−iii-11111111111111111-1-1-1-1−i−iii−i−iii-11111111111111111-1-1-1-1−i−iii−i−iii-11111111111111111-1-1-1-1−i−iii−i−iii-1
χ5111111111-111-1-1-1-111111111-1-1-1-1-1111111111-111-1-1-1-111111111-1-1-1-1-1111111111-111-1-1-1-111111111-1-1-1-1-1111111111-111-1-1-1-111111111-1-1-1-1-1
χ6111111111-111-1-1-1-11111-1-1-1-11111-1111111111-111-1-1-1-11111-1-1-1-11111-1111111111-111-1-1-1-11111-1-1-1-11111-1111111111-111-1-1-1-11111-1-1-1-11111-1
χ7111111111-111-1-1-1-1-1-1-1-1ii−i−i−i−iii1111111111-111-1-1-1-1-1-1-1-1ii−i−i−i−iii1111111111-111-1-1-1-1-1-1-1-1ii−i−i−i−iii1111111111-111-1-1-1-1-1-1-1-1ii−i−i−i−iii1
χ8111111111-111-1-1-1-1-1-1-1-1−i−iiiii−i−i1111111111-111-1-1-1-1-1-1-1-1−i−iiiii−i−i1111111111-111-1-1-1-1-1-1-1-1−i−iiiii−i−i1111111111-111-1-1-1-1-1-1-1-1−i−iiiii−i−i1
χ92222-222220-2-2000022-2-20000000002222-222220-2-2000022-2-20000000002222-222220-2-2000022-2-20000000002222-222220-2-2000022-2-2000000000
χ102222-222220-2-20000-2-2220000000002222-222220-2-20000-2-2220000000002222-222220-2-20000-2-2220000000002222-222220-2-20000-2-222000000000
χ1122-2-2022-2-200000002-20000002−22−2022-2-2022-2-200000002-20000002−22−2022-2-2022-2-200000002-20000002−22−2022-2-2022-2-200000002-20000002−22−20
χ1222-2-2022-2-200000002-2000000−22−22022-2-2022-2-200000002-2000000−22−22022-2-2022-2-200000002-2000000−22−22022-2-2022-2-200000002-2000000−22−220
χ1322-2-2022-2-20000000-22000000i2−i2−i2i2022-2-2022-2-20000000-22000000i2−i2−i2i2022-2-2022-2-20000000-22000000i2−i2−i2i2022-2-2022-2-20000000-22000000i2−i2−i2i20
χ1422-2-2022-2-20000000-22000000−i2i2i2−i2022-2-2022-2-20000000-22000000−i2i2i2−i2022-2-2022-2-20000000-22000000−i2i2i2−i2022-2-2022-2-20000000-22000000−i2i2i2−i20
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χ162-22-202-2-220000000002i−2i−1−i1+i−1+i1−i000002-22-202-2-220000000002i−2i−1−i1+i−1+i1−i000002-22-202-2-220000000002i−2i−1−i1+i−1+i1−i000002-22-202-2-220000000002i−2i−1−i1+i−1+i1−i00000
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χ182-22-202-2-22000000000−2i2i−1+i1−i−1−i1+i000002-22-202-2-22000000000−2i2i−1+i1−i−1−i1+i000002-22-202-2-22000000000−2i2i−1+i1−i−1−i1+i000002-22-202-2-22000000000−2i2i−1+i1−i−1−i1+i00000
χ1944444-1-1-1-14-1-1-1-1-1-1000000000000044444-1-1-1-14-1-1-1-1-1-1000000000000044444-1-1-1-14-1-1-1-1-1-1000000000000044444-1-1-1-14-1-1-1-1-1-10000000000000
χ2044444-1-1-1-1-4-1-11111000000000000044444-1-1-1-1-4-1-11111000000000000044444-1-1-1-1-4-1-11111000000000000044444-1-1-1-1-4-1-111110000000000000
χ214444-4-1-1-1-101155−5−500000000000004444-4-1-1-1-101155−5−500000000000004444-4-1-1-1-101155−5−500000000000004444-4-1-1-1-101155−5−50000000000000
χ224444-4-1-1-1-1011−5−55500000000000004444-4-1-1-1-1011−5−55500000000000004444-4-1-1-1-1011−5−55500000000000004444-4-1-1-1-1011−5−5550000000000000
χ234-4-4404-44-4000000000000000000004-4-4404-44-4000000000000000000004-4-4404-44-4000000000000000000004-4-4404-44-400000000000000000000
χ244-4-440-11-1105−5−ζ6+ζ14−ζ22+ζ38ζ6−ζ14+ζ22−ζ38ζ6−ζ14−ζ22+ζ38−ζ6+ζ14+ζ22−ζ3800000000000004-4-440-11-1105−5−ζ6+ζ14−ζ22+ζ38ζ6−ζ14+ζ22−ζ38ζ6−ζ14−ζ22+ζ38−ζ6+ζ14+ζ22−ζ3800000000000004-4-440-11-1105−5−ζ6+ζ14−ζ22+ζ38ζ6−ζ14+ζ22−ζ38ζ6−ζ14−ζ22+ζ38−ζ6+ζ14+ζ22−ζ3800000000000004-4-440-11-1105−5−ζ6+ζ14−ζ22+ζ38ζ6−ζ14+ζ22−ζ38ζ6−ζ14−ζ22+ζ38−ζ6+ζ14+ζ22−ζ380000000000000
χ254-4-440-11-1105−5ζ6−ζ14+ζ22−ζ38−ζ6+ζ14−ζ22+ζ38−ζ6+ζ14+ζ22−ζ38ζ6−ζ14−ζ22+ζ3800000000000004-4-440-11-1105−5ζ6−ζ14+ζ22−ζ38−ζ6+ζ14−ζ22+ζ38−ζ6+ζ14+ζ22−ζ38ζ6−ζ14−ζ22+ζ3800000000000004-4-440-11-1105−5ζ6−ζ14+ζ22−ζ38−ζ6+ζ14−ζ22+ζ38−ζ6+ζ14+ζ22−ζ38ζ6−ζ14−ζ22+ζ3800000000000004-4-440-11-1105−5ζ6−ζ14+ζ22−ζ38−ζ6+ζ14−ζ22+ζ38−ζ6+ζ14+ζ22−ζ38ζ6−ζ14−ζ22+ζ380000000000000
χ264-4-440-11-110−55ζ6−ζ14−ζ22+ζ38−ζ6+ζ14+ζ22−ζ38ζ6−ζ14+ζ22−ζ38−ζ6+ζ14−ζ22+ζ3800000000000004-4-440-11-110−55ζ6−ζ14−ζ22+ζ38−ζ6+ζ14+ζ22−ζ38ζ6−ζ14+ζ22−ζ38−ζ6+ζ14−ζ22+ζ3800000000000004-4-440-11-110−55ζ6−ζ14−ζ22+ζ38−ζ6+ζ14+ζ22−ζ38ζ6−ζ14+ζ22−ζ38−ζ6+ζ14−ζ22+ζ3800000000000004-4-440-11-110−55ζ6−ζ14−ζ22+ζ38−ζ6+ζ14+ζ22−ζ38ζ6−ζ14+ζ22−ζ38−ζ6+ζ14−ζ22+ζ380000000000000
χ274-4-440-11-110−55−ζ6+ζ14+ζ22−ζ38ζ6−ζ14−ζ22+ζ38−ζ6+ζ14−ζ22+ζ38ζ6−ζ14+ζ22−ζ3800000000000004-4-440-11-110−55−ζ6+ζ14+ζ22−ζ38ζ6−ζ14−ζ22+ζ38−ζ6+ζ14−ζ22+ζ38ζ6−ζ14+ζ22−ζ3800000000000004-4-440-11-110−55−ζ6+ζ14+ζ22−ζ38ζ6−ζ14−ζ22+ζ38−ζ6+ζ14−ζ22+ζ38ζ6−ζ14+ζ22−ζ3800000000000004-4-440-11-110−55−ζ6+ζ14+ζ22−ζ38ζ6−ζ14−ζ22+ζ38−ζ6+ζ14−ζ22+ζ38ζ6−ζ14+ζ22−ζ380000000000000
χ2888-8-80-2-2220000000000000000000088-8-80-2-2220000000000000000000088-8-80-2-2220000000000000000000088-8-80-2-22200000000000000000000
χ298-88-80-222-2000000000000000000008-88-80-222-2000000000000000000008-88-80-222-2000000000000000000008-88-80-222-200000000000000000000
χ3011111111111111111111111111111iiiiiiiiiiiiiiiiiiiiiiiiiiiii-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1−i−i−i−i−i−i−i−i−i−i−i−i−i−i−i−i−i−i−i−i−i−i−i−i−i−i−i−i−i
χ3111111111111111111111-1-1-1-1-1-1-1-11iiiiiiiiiiiiiiiiiiii−i−i−i−i−i−i−i−ii-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1−i−i−i−i−i−i−i−i−i−i−i−i−i−i−i−i−i−i−i−iiiiiiiii−i
χ321111111111111111-1-1-1-1ii−i−iii−i−i-1iiiiiiiiiiiiiiii−i−i−i−i-1-111-1-111−i-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111−i−iii−i−iii1−i−i−i−i−i−i−i−i−i−i−i−i−i−i−i−iiiii11-1-111-1-1i
χ331111111111111111-1-1-1-1−i−iii−i−iii-1iiiiiiiiiiiiiiii−i−i−i−i11-1-111-1-1−i-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111ii−i−iii−i−i1−i−i−i−i−i−i−i−i−i−i−i−i−i−i−i−iiiii-1-111-1-111i
χ34111111111-111-1-1-1-111111111-1-1-1-1-1iiiiiiiii−iii−i−i−i−iiiiiiiii−i−i−i−i−i-1-1-1-1-1-1-1-1-11-1-11111-1-1-1-1-1-1-1-111111−i−i−i−i−i−i−i−i−ii−i−iiiii−i−i−i−i−i−i−i−iiiiii
χ35111111111-111-1-1-1-11111-1-1-1-11111-1iiiiiiiii−iii−i−i−i−iiiii−i−i−i−iiiii−i-1-1-1-1-1-1-1-1-11-1-11111-1-1-1-11111-1-1-1-11−i−i−i−i−i−i−i−i−ii−i−iiiii−i−i−i−iiiii−i−i−i−ii
χ36111111111-111-1-1-1-1-1-1-1-1ii−i−i−i−iii1iiiiiiiii−iii−i−i−i−i−i−i−i−i-1-11111-1-1i-1-1-1-1-1-1-1-1-11-1-111111111−i−iiiii−i−i-1−i−i−i−i−i−i−i−i−ii−i−iiiiiiiii11-1-1-1-111−i
χ37111111111-111-1-1-1-1-1-1-1-1−i−iiiii−i−i1iiiiiiiii−iii−i−i−i−i−i−i−i−i11-1-1-1-111i-1-1-1-1-1-1-1-1-11-1-111111111ii−i−i−i−iii-1−i−i−i−i−i−i−i−i−ii−i−iiiiiiiii-1-11111-1-1−i
χ382222-222220-2-2000022-2-20000000002i2i2i2i−2i2i2i2i2i0−2i−2i00002i2i−2i−2i000000000-2-2-2-22-2-2-2-20220000-2-222000000000−2i−2i−2i−2i2i−2i−2i−2i−2i02i2i0000−2i−2i2i2i000000000
χ392222-222220-2-20000-2-2220000000002i2i2i2i−2i2i2i2i2i0−2i−2i0000−2i−2i2i2i000000000-2-2-2-22-2-2-2-2022000022-2-2000000000−2i−2i−2i−2i2i−2i−2i−2i−2i02i2i00002i2i−2i−2i000000000
χ4022-2-2022-2-200000002-20000002−22−202i2i−2i−2i02i2i−2i−2i00000002i−2i000000i2−i2i2−i20-2-2220-2-2220000000-22000000−22−220−2i−2i2i2i0−2i−2i2i2i0000000−2i2i000000−i2i2−i2i20
χ4122-2-2022-2-200000002-2000000−22−2202i2i−2i−2i02i2i−2i−2i00000002i−2i000000−i2i2−i2i20-2-2220-2-2220000000-220000002−22−20−2i−2i2i2i0−2i−2i2i2i0000000−2i2i000000i2−i2i2−i20
χ4222-2-2022-2-20000000-22000000i2−i2−i2i202i2i−2i−2i02i2i−2i−2i0000000−2i2i000000−222−20-2-2220-2-22200000002-2000000−i2i2i2−i20−2i−2i2i2i0−2i−2i2i2i00000002i−2i0000002−2−220
χ4322-2-2022-2-20000000-22000000−i2i2i2−i202i2i−2i−2i02i2i−2i−2i0000000−2i2i0000002−2−220-2-2220-2-22200000002-2000000i2−i2−i2i20−2i−2i2i2i0−2i−2i2i2i00000002i−2i000000−222−20
χ442-22-202-2-220000000002i−2i1+i−1−i1−i−1+i000002i−2i2i−2i02i−2i−2i2i000000000-22−1+i1−i1+i−1−i00000-22-220-222-2000000000−2i2i−1−i1+i−1+i1−i00000−2i2i−2i2i0−2i2i2i−2i0000000002-21−i−1+i−1−i1+i00000
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χ524-4-4404-44-4000000000000000000004i−4i−4i4i04i−4i4i−4i00000000000000000000-444-40-44-4400000000000000000000−4i4i4i−4i0−4i4i−4i4i00000000000000000000
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χ564-4-440-11-110−55−ζ6+ζ14+ζ22−ζ38ζ6−ζ14−ζ22+ζ38−ζ6+ζ14−ζ22+ζ38ζ6−ζ14+ζ22−ζ3800000000000004i−4i−4i4i0−ii−ii0−i5i5−ζ4−ζ12+ζ28+ζ36ζ4+ζ12−ζ28−ζ36−ζ4+ζ12−ζ28+ζ36ζ4−ζ12+ζ28−ζ360000000000000-444-401-11-105−5ζ6−ζ14−ζ22+ζ38−ζ6+ζ14+ζ22−ζ38ζ6−ζ14+ζ22−ζ38−ζ6+ζ14−ζ22+ζ380000000000000−4i4i4i−4i0i−ii−i0i5−i5ζ4+ζ12−ζ28−ζ36−ζ4−ζ12+ζ28+ζ36ζ4−ζ12+ζ28−ζ36−ζ4+ζ12−ζ28+ζ360000000000000
χ5788-8-80-2-222000000000000000000008i8i−8i−8i0−2i−2i2i2i00000000000000000000-8-888022-2-200000000000000000000−8i−8i8i8i02i2i−2i−2i00000000000000000000
χ588-88-80-222-2000000000000000000008i−8i8i−8i0−2i2i2i−2i00000000000000000000-88-8802-2-2200000000000000000000−8i8i−8i8i02i−2i−2i2i00000000000000000000
χ5911111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ6011111111111111111111-1-1-1-1-1-1-1-11-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-111111111111111111111-1-1-1-1-1-1-1-11-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1
χ611111111111111111-1-1-1-1ii−i−iii−i−i-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111−i−iii−i−iii11111111111111111-1-1-1-1ii−i−iii−i−i-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111−i−iii−i−iii1
χ621111111111111111-1-1-1-1−i−iii−i−iii-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111ii−i−iii−i−i11111111111111111-1-1-1-1−i−iii−i−iii-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111ii−i−iii−i−i1
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χ64111111111-111-1-1-1-11111-1-1-1-11111-1-1-1-1-1-1-1-1-1-11-1-11111-1-1-1-11111-1-1-1-11111111111-111-1-1-1-11111-1-1-1-11111-1-1-1-1-1-1-1-1-1-11-1-11111-1-1-1-11111-1-1-1-11
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χ8688-8-80-2-22200000000000000000000-8-888022-2-20000000000000000000088-8-80-2-22200000000000000000000-8-888022-2-200000000000000000000
χ878-88-80-222-200000000000000000000-88-8802-2-22000000000000000000008-88-80-222-200000000000000000000-88-8802-2-2200000000000000000000
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χ92111111111-111-1-1-1-111111111-1-1-1-1-1−i−i−i−i−i−i−i−i−ii−i−iiiii−i−i−i−i−i−i−i−iiiiii-1-1-1-1-1-1-1-1-11-1-11111-1-1-1-1-1-1-1-111111iiiiiiiii−iii−i−i−i−iiiiiiiii−i−i−i−i−i
χ93111111111-111-1-1-1-11111-1-1-1-11111-1−i−i−i−i−i−i−i−i−ii−i−iiiii−i−i−i−iiiii−i−i−i−ii-1-1-1-1-1-1-1-1-11-1-11111-1-1-1-11111-1-1-1-11iiiiiiiii−iii−i−i−i−iiiii−i−i−i−iiiii−i
χ94111111111-111-1-1-1-1-1-1-1-1ii−i−i−i−iii1−i−i−i−i−i−i−i−i−ii−i−iiiiiiiii11-1-1-1-111−i-1-1-1-1-1-1-1-1-11-1-111111111−i−iiiii−i−i-1iiiiiiiii−iii−i−i−i−i−i−i−i−i-1-11111-1-1i
χ95111111111-111-1-1-1-1-1-1-1-1−i−iiiii−i−i1−i−i−i−i−i−i−i−i−ii−i−iiiiiiiii-1-11111-1-1−i-1-1-1-1-1-1-1-1-11-1-111111111ii−i−i−i−iii-1iiiiiiiii−iii−i−i−i−i−i−i−i−i11-1-1-1-111i
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χ1124-4-440-11-1105−5ζ6−ζ14+ζ22−ζ38−ζ6+ζ14−ζ22+ζ38−ζ6+ζ14+ζ22−ζ38ζ6−ζ14−ζ22+ζ380000000000000−4i4i4i−4i0i−ii−i0−i5i5−ζ4+ζ12−ζ28+ζ36ζ4−ζ12+ζ28−ζ36ζ4+ζ12−ζ28−ζ36−ζ4−ζ12+ζ28+ζ360000000000000-444-401-11-10−55−ζ6+ζ14−ζ22+ζ38ζ6−ζ14+ζ22−ζ38ζ6−ζ14−ζ22+ζ38−ζ6+ζ14+ζ22−ζ3800000000000004i−4i−4i4i0−ii−ii0i5−i5ζ4−ζ12+ζ28−ζ36−ζ4+ζ12−ζ28+ζ36−ζ4−ζ12+ζ28+ζ36ζ4+ζ12−ζ28−ζ360000000000000
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χ11588-8-80-2-22200000000000000000000−8i−8i8i8i02i2i−2i−2i00000000000000000000-8-888022-2-2000000000000000000008i8i−8i−8i0−2i−2i2i2i00000000000000000000
χ1168-88-80-222-200000000000000000000−8i8i−8i8i02i−2i−2i2i00000000000000000000-88-8802-2-22000000000000000000008i−8i8i−8i0−2i2i2i−2i00000000000000000000

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