Finite Group Databasebeta

← Group #13015043

Character table — Group #13015043

Order 1280.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86
size1111111122224444444444448888888888881010101010101010101010101616161616161616161620202020202020202020202020202020202040404040404040408080
order12222222444444445101010101010102020202020202020202020204444444444444420202020202020204488888888888888888888888844
χ111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111
χ3111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1111111111111111111-1-1-1-1-1-1-1-1-1-1
χ4111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1
χ5111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-11111111111-1-1iiiiiiii−i−i−i−i−i−i−i−iiiii−i−i−i−i-1-1
χ6111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-11111111111-1-1−i−i−i−i−i−i−i−iiiiiiiii−i−i−i−iiiii-1-1
χ7111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1iiiiiiii−i−i−i−i−i−i−i−i−i−i−i−iiiii11
χ8111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1−i−i−i−i−i−i−i−iiiiiiiiiiiii−i−i−i−i11
χ911111111-1-1-1-111-1-1111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-11-1-1-1-1-1111111iiii−i−i−i−iiiii−i−i−i−iii−i−iii−i−i1-1
χ1011111111-1-1-1-111-1-1111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-11-1-1-1-1-1111111−i−i−i−iiiii−i−i−i−iiiii−i−iii−i−iii1-1
χ1111111111-1-1-1-111-1-1111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-111111-1-1-1-111iiii−i−i−i−iiiii−i−i−i−i−i−iii−i−iii-11
χ1211111111-1-1-1-111-1-1111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-111111-1-1-1-111−i−i−i−iiiii−i−i−i−iiiiiii−i−iii−i−i-11
χ1311111111-1-1-1-111-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-1111111111-1-1-1-1-11111-1-11111-1-1-1-1-1-1-1-1111111-1-1-1-111-11
χ1411111111-1-1-1-111-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-1111111111-1-1-1-1-11111-1-1-1-1-1-111111111-1-1-1-1-1-11111-1-1-11
χ1511111111-1-1-1-111-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-111111111-111111-1-1-1-1-1-11111-1-1-1-1-1-1-1-11111-1-11111-1-11-1
χ1611111111-1-1-1-111-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-111111111-111111-1-1-1-1-1-1-1-1-1-111111111-1-1-1-111-1-1-1-1111-1
χ17222222222222-2-2-2-222222222-2-2-2-2-2-2-2-222222222-2-22222-2-20000000000-2-200000000000000000000000000
χ18222222222222-2-2-2-222222222-2-2-2-2-2-2-2-22222-2-2-2-222-2-2-2-22200000000002200000000000000000000000000
χ1922222222-2-2-2-2-2-22222222222-2-2-2-22222-2-2-2-2222222-2-2-2-2220000000000-2-200000000000000000000000000
χ2022222222-2-2-2-2-2-22222222222-2-2-2-22222-2-2-2-2-2-2-2-2-2-22222-2-200000000002200000000000000000000000000
χ21222-2-2-22-200002-2002-2-2-222-2222-2-20000000000002i−2i2i2i−2i−2i2i−2i0000000000000000−2ζ13−2ζ21−2ζ29−2ζ37−2ζ13−2ζ21−2ζ29−2ζ372ζ13+2ζ21+2ζ29+2ζ372ζ13+2ζ21+2ζ29+2ζ37−2ζ7−2ζ23−2ζ31−2ζ39−2ζ7−2ζ23−2ζ31−2ζ392ζ7+2ζ23+2ζ31+2ζ392ζ7+2ζ23+2ζ31+2ζ3900000000000000
χ22222-2-2-22-200002-2002-2-2-222-2222-2-20000000000002i−2i2i2i−2i−2i2i−2i00000000000000002ζ13+2ζ21+2ζ29+2ζ372ζ13+2ζ21+2ζ29+2ζ37−2ζ13−2ζ21−2ζ29−2ζ37−2ζ13−2ζ21−2ζ29−2ζ372ζ7+2ζ23+2ζ31+2ζ392ζ7+2ζ23+2ζ31+2ζ39−2ζ7−2ζ23−2ζ31−2ζ39−2ζ7−2ζ23−2ζ31−2ζ3900000000000000
χ23222-2-2-22-200002-2002-2-2-222-2222-2-2000000000000−2i2i−2i−2i2i2i−2i2i0000000000000000−2ζ7−2ζ23−2ζ31−2ζ39−2ζ7−2ζ23−2ζ31−2ζ392ζ7+2ζ23+2ζ31+2ζ392ζ7+2ζ23+2ζ31+2ζ39−2ζ13−2ζ21−2ζ29−2ζ37−2ζ13−2ζ21−2ζ29−2ζ372ζ13+2ζ21+2ζ29+2ζ372ζ13+2ζ21+2ζ29+2ζ3700000000000000
χ24222-2-2-22-200002-2002-2-2-222-2222-2-2000000000000−2i2i−2i−2i2i2i−2i2i00000000000000002ζ7+2ζ23+2ζ31+2ζ392ζ7+2ζ23+2ζ31+2ζ39−2ζ7−2ζ23−2ζ31−2ζ39−2ζ7−2ζ23−2ζ31−2ζ392ζ13+2ζ21+2ζ29+2ζ372ζ13+2ζ21+2ζ29+2ζ37−2ζ13−2ζ21−2ζ29−2ζ37−2ζ13−2ζ21−2ζ29−2ζ3700000000000000
χ25222-2-2-22-20000-22002-2-2-222-22-2-2220000000000002i−2i−2i−2i2i2i2i−2i000000000000−2ζ7−2ζ23−2ζ31−2ζ39−2ζ7−2ζ23−2ζ31−2ζ392ζ7+2ζ23+2ζ31+2ζ392ζ7+2ζ23+2ζ31+2ζ3900000000−2ζ13−2ζ21−2ζ29−2ζ37−2ζ13−2ζ21−2ζ29−2ζ372ζ13+2ζ21+2ζ29+2ζ372ζ13+2ζ21+2ζ29+2ζ370000000000
χ26222-2-2-22-20000-22002-2-2-222-22-2-2220000000000002i−2i−2i−2i2i2i2i−2i0000000000002ζ7+2ζ23+2ζ31+2ζ392ζ7+2ζ23+2ζ31+2ζ39−2ζ7−2ζ23−2ζ31−2ζ39−2ζ7−2ζ23−2ζ31−2ζ39000000002ζ13+2ζ21+2ζ29+2ζ372ζ13+2ζ21+2ζ29+2ζ37−2ζ13−2ζ21−2ζ29−2ζ37−2ζ13−2ζ21−2ζ29−2ζ370000000000
χ27222-2-2-22-20000-22002-2-2-222-22-2-222000000000000−2i2i2i2i−2i−2i−2i2i000000000000−2ζ13−2ζ21−2ζ29−2ζ37−2ζ13−2ζ21−2ζ29−2ζ372ζ13+2ζ21+2ζ29+2ζ372ζ13+2ζ21+2ζ29+2ζ3700000000−2ζ7−2ζ23−2ζ31−2ζ39−2ζ7−2ζ23−2ζ31−2ζ392ζ7+2ζ23+2ζ31+2ζ392ζ7+2ζ23+2ζ31+2ζ390000000000
χ28222-2-2-22-20000-22002-2-2-222-22-2-222000000000000−2i2i2i2i−2i−2i−2i2i0000000000002ζ13+2ζ21+2ζ29+2ζ372ζ13+2ζ21+2ζ29+2ζ37−2ζ13−2ζ21−2ζ29−2ζ37−2ζ13−2ζ21−2ζ29−2ζ37000000002ζ7+2ζ23+2ζ31+2ζ392ζ7+2ζ23+2ζ31+2ζ39−2ζ7−2ζ23−2ζ31−2ζ39−2ζ7−2ζ23−2ζ31−2ζ390000000000
χ2922-22-2-2-222i2i−2i−2i000022-2-22-22-2000000002i2i−2i−2i22-2-2002i−2i2i−2i0000000000000000000000000000001−i−1+i1+i−1−i1−i−1+i1+i−1−i00
χ3022-22-2-2-222i2i−2i−2i000022-2-22-22-2000000002i2i−2i−2i22-2-2002i−2i2i−2i000000000000000000000000000000−1+i1−i−1−i1+i−1+i1−i−1−i1+i00
χ3122-22-2-2-222i2i−2i−2i000022-2-22-22-2000000002i2i−2i−2i-2-22200−2i2i−2i2i0000000000000000000000000000001+i−1−i−1+i1−i−1−i1+i1−i−1+i00
χ3222-22-2-2-222i2i−2i−2i000022-2-22-22-2000000002i2i−2i−2i-2-22200−2i2i−2i2i000000000000000000000000000000−1−i1+i1−i−1+i1+i−1−i−1+i1−i00
χ3322-22-2-2-22−2i−2i2i2i000022-2-22-22-200000000−2i−2i2i2i22-2-200−2i2i−2i2i0000000000000000000000000000001+i−1−i1−i−1+i1+i−1−i1−i−1+i00
χ3422-22-2-2-22−2i−2i2i2i000022-2-22-22-200000000−2i−2i2i2i22-2-200−2i2i−2i2i000000000000000000000000000000−1−i1+i−1+i1−i−1−i1+i−1+i1−i00
χ3522-22-2-2-22−2i−2i2i2i000022-2-22-22-200000000−2i−2i2i2i-2-222002i−2i2i−2i0000000000000000000000000000001−i−1+i−1−i1+i−1+i1−i1+i−1−i00
χ3622-22-2-2-22−2i−2i2i2i000022-2-22-22-200000000−2i−2i2i2i-2-222002i−2i2i−2i000000000000000000000000000000−1+i1−i1+i−1−i1−i−1+i−1−i1+i00
χ372-2-222-22-20000002i−2i222-2-2-2-2200002i2i−2i−2i00002-22-22i−2i0000−2i2i0000000000001+i−1−i1+i−1−i1−i−1+i1−i−1+i1+i−1−i1+i−1−i1−i−1+i1−i−1+i0000000000
χ382-2-222-22-20000002i−2i222-2-2-2-2200002i2i−2i−2i00002-22-22i−2i0000−2i2i000000000000−1−i1+i−1−i1+i−1+i1−i−1+i1−i−1−i1+i−1−i1+i−1+i1−i−1+i1−i0000000000
χ392-2-222-22-20000002i−2i222-2-2-2-2200002i2i−2i−2i0000-22-22−2i2i00002i−2i0000000000001−i−1+i1−i−1+i−1−i1+i−1−i1+i−1+i1−i−1+i1−i1+i−1−i1+i−1−i0000000000
χ402-2-222-22-20000002i−2i222-2-2-2-2200002i2i−2i−2i0000-22-22−2i2i00002i−2i000000000000−1+i1−i−1+i1−i1+i−1−i1+i−1−i1−i−1+i1−i−1+i−1−i1+i−1−i1+i0000000000
χ412-2-222-22-2000000−2i2i222-2-2-2-220000−2i−2i2i2i00002-22-2−2i2i00002i−2i0000000000001−i−1+i1−i−1+i1+i−1−i1+i−1−i1−i−1+i1−i−1+i1+i−1−i1+i−1−i0000000000
χ422-2-222-22-2000000−2i2i222-2-2-2-220000−2i−2i2i2i00002-22-2−2i2i00002i−2i000000000000−1+i1−i−1+i1−i−1−i1+i−1−i1+i−1+i1−i−1+i1−i−1−i1+i−1−i1+i0000000000
χ432-2-222-22-2000000−2i2i222-2-2-2-220000−2i−2i2i2i0000-22-222i−2i0000−2i2i0000000000001+i−1−i1+i−1−i−1+i1−i−1+i1−i−1−i1+i−1−i1+i1−i−1+i1−i−1+i0000000000
χ442-2-222-22-2000000−2i2i222-2-2-2-220000−2i−2i2i2i0000-22-222i−2i0000−2i2i000000000000−1−i1+i−1−i1+i1−i−1+i1−i−1+i1+i−1−i1+i−1−i−1+i1−i−1+i1−i0000000000
χ452-2-2-2-22222-22-200002-2-22-2-222000000002-22-20000220000-2-200000000002-2i2−i2−i2i2i2−i2−i2i2i2−i2−i2i2i2−i2−i2i20000000000
χ462-2-2-2-22222-22-200002-2-22-2-222000000002-22-20000220000-2-200000000002-2−i2i2i2−i2−i2i2i2−i2−i2i2i2−i2−i2i2i2−i20000000000
χ472-2-2-2-22222-22-200002-2-22-2-222000000002-22-20000-2-20000220000000000-222−2−222−2−22−222−2−222−20000000000
χ482-2-2-2-22222-22-200002-2-22-2-222000000002-22-20000-2-20000220000000000-22−222−2−222−22−2−222−2−220000000000
χ492-2-2-2-2222-22-2200002-2-22-2-22200000000-22-220000220000-2-20000000000-22i2−i2−i2i2−i2i2i2−i2−i2i2i2−i2i2−i2−i2i20000000000
χ502-2-2-2-2222-22-2200002-2-22-2-22200000000-22-220000220000-2-20000000000-22−i2i2i2−i2i2−i2−i2i2i2−i2−i2i2−i2i2i2−i20000000000
χ512-2-2-2-2222-22-2200002-2-22-2-22200000000-22-220000-2-200002200000000002-22−2−22−222−22−2−22−222−20000000000
χ522-2-2-2-2222-22-2200002-2-22-2-22200000000-22-220000-2-200002200000000002-2−222−22−2−22−222−22−2−220000000000
χ534444444444444444-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-100000000000044-1-1-1-1-1-1-1-10000000000000000000000000000
χ544444444444444444-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1000000000000-4-4111111110000000000000000000000000000
χ55444444444444-4-4-4-4-1-1-1-1-1-1-1-111111111-1-1-1-10000000000000055−5−555−5−50000000000000000000000000000
χ56444444444444-4-4-4-4-1-1-1-1-1-1-1-111111111-1-1-1-100000000000000−5−555−5−5550000000000000000000000000000
χ5744444444-4-4-4-444-4-4-1-1-1-1-1-1-1-1-1-1-1-1111111110000000000004-41111-1-1-1-10000000000000000000000000000
χ5844444444-4-4-4-444-4-4-1-1-1-1-1-1-1-1-1-1-1-111111111000000000000-44-1-1-1-111110000000000000000000000000000
χ5944444444-4-4-4-4-4-444-1-1-1-1-1-1-1-11111-1-1-1-111110000000000000055−5−5−5−5550000000000000000000000000000
χ6044444444-4-4-4-4-4-444-1-1-1-1-1-1-1-11111-1-1-1-1111100000000000000−5−55555−5−50000000000000000000000000000
χ6144-4-444-4-4000000004-4444-4-4-40000000000000000004-4-440000000000000000000000000000000000000000
χ6244-4-444-4-4000000004-4444-4-4-4000000000000000000-444-40000000000000000000000000000000000000000
χ634-444-44-4-40000000044-44-44-4-40000000000004-4-440000000000000000000000000000000000000000000000
χ644-444-44-4-40000000044-44-44-4-4000000000000-444-40000000000000000000000000000000000000000000000
χ654-44-44-4-444i−4i−4i4i00004-44-4-444-4000000004i−4i−4i4i00000000000000000000000000000000000000000000000000
χ664-44-44-4-444i−4i−4i4i0000-11-111-1-115−55−5i5−i5i5−i5−iii−i00000000000000−ζ4+ζ12−ζ28+ζ36ζ4−ζ12+ζ28−ζ36−ζ4−ζ12+ζ28+ζ36ζ4+ζ12−ζ28−ζ36−ζ6+ζ14−ζ22+ζ38ζ6−ζ14+ζ22−ζ38ζ6−ζ14−ζ22+ζ38−ζ6+ζ14+ζ22−ζ380000000000000000000000000000
χ674-44-44-4-444i−4i−4i4i0000-11-111-1-115−55−5i5−i5i5−i5−iii−i00000000000000ζ4−ζ12+ζ28−ζ36−ζ4+ζ12−ζ28+ζ36ζ4+ζ12−ζ28−ζ36−ζ4−ζ12+ζ28+ζ36ζ6−ζ14+ζ22−ζ38−ζ6+ζ14−ζ22+ζ38−ζ6+ζ14+ζ22−ζ38ζ6−ζ14−ζ22+ζ380000000000000000000000000000
χ684-44-44-4-444i−4i−4i4i0000-11-111-1-11−55−55−i5i5−i5i5−iii−i00000000000000−ζ4−ζ12+ζ28+ζ36ζ4+ζ12−ζ28−ζ36ζ4−ζ12+ζ28−ζ36−ζ4+ζ12−ζ28+ζ36−ζ6+ζ14+ζ22−ζ38ζ6−ζ14−ζ22+ζ38−ζ6+ζ14−ζ22+ζ38ζ6−ζ14+ζ22−ζ380000000000000000000000000000
χ694-44-44-4-444i−4i−4i4i0000-11-111-1-11−55−55−i5i5−i5i5−iii−i00000000000000ζ4+ζ12−ζ28−ζ36−ζ4−ζ12+ζ28+ζ36−ζ4+ζ12−ζ28+ζ36ζ4−ζ12+ζ28−ζ36ζ6−ζ14−ζ22+ζ38−ζ6+ζ14+ζ22−ζ38ζ6−ζ14+ζ22−ζ38−ζ6+ζ14−ζ22+ζ380000000000000000000000000000
χ704-44-44-4-44−4i4i4i−4i00004-44-4-444-400000000−4i4i4i−4i00000000000000000000000000000000000000000000000000
χ714-44-44-4-44−4i4i4i−4i0000-11-111-1-115−55−5−i5i5−i5i5i−i−ii00000000000000−ζ4+ζ12−ζ28+ζ36ζ4−ζ12+ζ28−ζ36−ζ4−ζ12+ζ28+ζ36ζ4+ζ12−ζ28−ζ36ζ6−ζ14+ζ22−ζ38−ζ6+ζ14−ζ22+ζ38−ζ6+ζ14+ζ22−ζ38ζ6−ζ14−ζ22+ζ380000000000000000000000000000
χ724-44-44-4-44−4i4i4i−4i0000-11-111-1-115−55−5−i5i5−i5i5i−i−ii00000000000000ζ4−ζ12+ζ28−ζ36−ζ4+ζ12−ζ28+ζ36ζ4+ζ12−ζ28−ζ36−ζ4−ζ12+ζ28+ζ36−ζ6+ζ14−ζ22+ζ38ζ6−ζ14+ζ22−ζ38ζ6−ζ14−ζ22+ζ38−ζ6+ζ14+ζ22−ζ380000000000000000000000000000
χ734-44-44-4-44−4i4i4i−4i0000-11-111-1-11−55−55i5−i5i5−i5i−i−ii00000000000000−ζ4−ζ12+ζ28+ζ36ζ4+ζ12−ζ28−ζ36ζ4−ζ12+ζ28−ζ36−ζ4+ζ12−ζ28+ζ36ζ6−ζ14−ζ22+ζ38−ζ6+ζ14+ζ22−ζ38ζ6−ζ14+ζ22−ζ38−ζ6+ζ14−ζ22+ζ380000000000000000000000000000
χ744-44-44-4-44−4i4i4i−4i0000-11-111-1-11−55−55i5−i5i5−i5i−i−ii00000000000000ζ4+ζ12−ζ28−ζ36−ζ4−ζ12+ζ28+ζ36−ζ4+ζ12−ζ28+ζ36ζ4−ζ12+ζ28−ζ36−ζ6+ζ14+ζ22−ζ38ζ6−ζ14−ζ22+ζ38−ζ6+ζ14−ζ22+ζ38ζ6−ζ14+ζ22−ζ380000000000000000000000000000
χ75888-8-8-88-800008-800-2222-2-22-2-2-2220000000000000000000000000000000000000000000000000000000000
χ76888-8-8-88-80000-8800-2222-2-22-222-2-20000000000000000000000000000000000000000000000000000000000
χ7788-88-8-8-888i8i−8i−8i0000-2-222-22-2200000000−2i−2i2i2i00000000000000000000000000000000000000000000000000
χ7888-88-8-8-88−8i−8i8i8i0000-2-222-22-22000000002i2i−2i−2i00000000000000000000000000000000000000000000000000
χ7988-8-888-8-800000000-22-2-2-2222000025−25−2525000000000000000000000000000000000000000000000000000000
χ8088-8-888-8-800000000-22-2-2-22220000−252525−25000000000000000000000000000000000000000000000000000000
χ818-888-88-8-800000000-2-22-22-22225−25−25250000000000000000000000000000000000000000000000000000000000
χ828-888-88-8-800000000-2-22-22-222−252525−250000000000000000000000000000000000000000000000000000000000
χ838-8-888-88-80000008i−8i-2-2-22222-20000−2i−2i2i2i000000000000000000000000000000000000000000000000000000
χ848-8-888-88-8000000−8i8i-2-2-22222-200002i2i−2i−2i000000000000000000000000000000000000000000000000000000
χ858-8-8-8-88888-88-80000-222-222-2-200000000-22-2200000000000000000000000000000000000000000000000000
χ868-8-8-8-8888-88-880000-222-222-2-2000000002-22-200000000000000000000000000000000000000000000000000

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