Finite Group Databasebeta

← Group #14278265

Character table — Group #14278265

Order 1920.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96C97C98C99C100C101C102C103C104C105
size111122222222224444444444444444444444448888888888888888888888888888888888888888888882020202040404040404040404040120120120120120120120120
order12222236666666510101010101010151530303030303030303030303030304441212121212122020202020202020202020206060606060606060606060606060606060606060606060602244446612121212121244448888
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1
χ311111111111111111111111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1ii−i−iii−i−i
χ411111111111111111111111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1−i−iii−i−iii
χ5111111111111111111111111111111111111111-1-1-1-1-1-1111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-11111-1-1-1-11111-1-1-1-1
χ6111111111111111111111111111111111111111-1-1-1-1-1-1111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-11111-1-1-1-1-1-1-1-11111
χ7111111111111111111111111111111111111111-1-1-1-1-1-1111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-11111ii−i−i−i−iii
χ8111111111111111111111111111111111111111-1-1-1-1-1-1111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-11111−i−iiiii−i−i
χ922222222222222222222222222222222222222-2000000-2-2-2-2-2-200000000-2-2-2-2-2-2-2-2000000000000000022-2-20022-2-2000000000000
χ1022222222222222222222222222222222222222-2000000-2-2-2-2-2-200000000-2-2-2-2-2-2-2-20000000000000000-2-22200-2-222000000000000
χ11222222-1-1-1-1-1-1-1-122222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1222-1-1-1-1-1-1222222222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1222222-1-1-1-1-1-1-1-100000000
χ12222222-1-1-1-1-1-1-1-122222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1222-1-1-1-1-1-1222222222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-2-2-2-2-2-21111111100000000
χ13222222-1-1-1-1-1-1-1-122222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-12-2-21111-1-12222-2-2-2-2-2-2-2-2-1-1-1-1-1-1-1-111111111111111112222-2-2-1-1-1-1111100000000
χ14222222-1-1-1-1-1-1-1-122222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-12-2-21111-1-12222-2-2-2-2-2-2-2-2-1-1-1-1-1-1-1-11111111111111111-2-2-2-2221111-1-1-1-100000000
χ15222222-1-1-1-1-1-1-1-122222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-200−i3−i3i3i311-2-2-2-20000000011111111−i3−i3−i3−i3−i3−i3−i3−i3i3i3i3i3i3i3i3i322-2-200-1-111−i3−i3i3i300000000
χ16222222-1-1-1-1-1-1-1-122222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-200−i3−i3i3i311-2-2-2-20000000011111111−i3−i3−i3−i3−i3−i3−i3−i3i3i3i3i3i3i3i3i3-2-2220011-1-1i3i3−i3−i300000000
χ17222222-1-1-1-1-1-1-1-122222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-200i3i3−i3−i311-2-2-2-20000000011111111i3i3i3i3i3i3i3i3−i3−i3−i3−i3−i3−i3−i3−i322-2-200-1-111i3i3−i3−i300000000
χ18222222-1-1-1-1-1-1-1-122222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-200i3i3−i3−i311-2-2-2-20000000011111111i3i3i3i3i3i3i3i3−i3−i3−i3−i3−i3−i3−i3−i3-2-2220011-1-1−i3−i3i3i300000000
χ1922-2-22-22222-2-2-2-22222-2-2-2-222222222-2-2-2-2-2-2-2-20000000000000000000000000000000000000000000002-200002-200000000002−22−2
χ2022-2-22-22222-2-2-2-22222-2-2-2-222222222-2-2-2-2-2-2-2-20000000000000000000000000000000000000000000002-200002-20000000000−22−22
χ2122-2-22-22222-2-2-2-22222-2-2-2-222222222-2-2-2-2-2-2-2-2000000000000000000000000000000000000000000000-220000-220000000000−i2i2i2−i2
χ2222-2-22-22222-2-2-2-22222-2-2-2-222222222-2-2-2-2-2-2-2-2000000000000000000000000000000000000000000000-220000-220000000000i2−i2−i2i2
χ2322-2-2-2222-2-222-2-222-2-2-222-22222-2-2-2-2-2-22222-2-2000000000000000000000000000000000000000000000002i−2i00002i−2i00001+i−1−i1−i−1+i0000
χ2422-2-2-2222-2-222-2-222-2-2-222-22222-2-2-2-2-2-22222-2-2000000000000000000000000000000000000000000000002i−2i00002i−2i0000−1−i1+i−1+i1−i0000
χ2522-2-2-2222-2-222-2-222-2-2-222-22222-2-2-2-2-2-22222-2-200000000000000000000000000000000000000000000000−2i2i0000−2i2i00001−i−1+i1+i−1−i0000
χ2622-2-2-2222-2-222-2-222-2-2-222-22222-2-2-2-2-2-22222-2-200000000000000000000000000000000000000000000000−2i2i0000−2i2i0000−1+i1−i−1−i1+i0000
χ2744444444444444-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1444444444-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-10000000000000000000000
χ2844444444444444-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-14-4-4-4-4-4-444-1-1-1-111111111-1-1-1-1-1-1-1-111111111111111110000000000000000000000
χ2944444444444444-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-4000000-4-41111−5−5−5−5555511111111−5−5−5−55555−5−5−5−555550000000000000000000000
χ3044444444444444-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-4000000-4-411115555−5−5−5−5111111115555−5−5−5−55555−5−5−5−50000000000000000000000
χ31444444-2-2-2-2-2-2-2-2-1-1-1-1-1-1-1-11−i1521+i1521−i1521+i1521−i1521−i1521+i1521+i1521−i1521+i1521−i1521−i1521+i1521+i1521−i1521+i152444-2-2-2-2-2-2-1-1-1-1-1-1-1-1-1-1-1-11−i1521−i1521−i1521−i1521+i1521+i1521+i1521+i1521−i1521−i1521−i1521−i1521+i1521+i1521+i1521+i1521+i1521+i1521+i1521+i1521−i1521−i1521−i1521−i1520000000000000000000000
χ32444444-2-2-2-2-2-2-2-2-1-1-1-1-1-1-1-11−i1521+i1521−i1521+i1521−i1521−i1521+i1521+i1521−i1521+i1521−i1521−i1521+i1521+i1521−i1521+i1524-4-42222-2-2-1-1-1-1111111111−i1521−i1521−i1521−i1521+i1521+i1521+i1521+i152−1+i152−1+i152−1+i152−1+i152−1−i152−1−i152−1−i152−1−i152−1−i152−1−i152−1−i152−1−i152−1+i152−1+i152−1+i152−1+i1520000000000000000000000
χ33444444-2-2-2-2-2-2-2-2-1-1-1-1-1-1-1-11−i1521+i1521−i1521+i1521−i1521−i1521+i1521+i1521−i1521+i1521−i1521−i1521+i1521+i1521−i1521+i152-400−2i3−2i32i32i32211115555−5−5−5−5−1+i152−1+i152−1+i152−1+i152−1−i152−1−i152−1−i152−1−i152ζ28−ζ44+ζ52−ζ116ζ28−ζ44+ζ52−ζ116ζ28−ζ44+ζ52−ζ116ζ28−ζ44+ζ52−ζ116ζ4−ζ68+ζ76−ζ92ζ4−ζ68+ζ76−ζ92ζ4−ζ68+ζ76−ζ92ζ4−ζ68+ζ76−ζ92−ζ4+ζ68−ζ76+ζ92−ζ4+ζ68−ζ76+ζ92−ζ4+ζ68−ζ76+ζ92−ζ4+ζ68−ζ76+ζ92−ζ28+ζ44−ζ52+ζ116−ζ28+ζ44−ζ52+ζ116−ζ28+ζ44−ζ52+ζ116−ζ28+ζ44−ζ52+ζ1160000000000000000000000
χ34444444-2-2-2-2-2-2-2-2-1-1-1-1-1-1-1-11−i1521+i1521−i1521+i1521−i1521−i1521+i1521+i1521−i1521+i1521−i1521−i1521+i1521+i1521−i1521+i152-4002i32i3−2i3−2i3221111−5−5−5−55555−1+i152−1+i152−1+i152−1+i152−1−i152−1−i152−1−i152−1−i152−ζ28+ζ44−ζ52+ζ116−ζ28+ζ44−ζ52+ζ116−ζ28+ζ44−ζ52+ζ116−ζ28+ζ44−ζ52+ζ116−ζ4+ζ68−ζ76+ζ92−ζ4+ζ68−ζ76+ζ92−ζ4+ζ68−ζ76+ζ92−ζ4+ζ68−ζ76+ζ92ζ4−ζ68+ζ76−ζ92ζ4−ζ68+ζ76−ζ92ζ4−ζ68+ζ76−ζ92ζ4−ζ68+ζ76−ζ92ζ28−ζ44+ζ52−ζ116ζ28−ζ44+ζ52−ζ116ζ28−ζ44+ζ52−ζ116ζ28−ζ44+ζ52−ζ1160000000000000000000000
χ35444444-2-2-2-2-2-2-2-2-1-1-1-1-1-1-1-11+i1521−i1521+i1521−i1521+i1521+i1521−i1521−i1521+i1521−i1521+i1521+i1521−i1521−i1521+i1521−i152444-2-2-2-2-2-2-1-1-1-1-1-1-1-1-1-1-1-11+i1521+i1521+i1521+i1521−i1521−i1521−i1521−i1521+i1521+i1521+i1521+i1521−i1521−i1521−i1521−i1521−i1521−i1521−i1521−i1521+i1521+i1521+i1521+i1520000000000000000000000
χ36444444-2-2-2-2-2-2-2-2-1-1-1-1-1-1-1-11+i1521−i1521+i1521−i1521+i1521+i1521−i1521−i1521+i1521−i1521+i1521+i1521−i1521−i1521+i1521−i1524-4-42222-2-2-1-1-1-1111111111+i1521+i1521+i1521+i1521−i1521−i1521−i1521−i152−1−i152−1−i152−1−i152−1−i152−1+i152−1+i152−1+i152−1+i152−1+i152−1+i152−1+i152−1+i152−1−i152−1−i152−1−i152−1−i1520000000000000000000000
χ37444444-2-2-2-2-2-2-2-2-1-1-1-1-1-1-1-11+i1521−i1521+i1521−i1521+i1521+i1521−i1521−i1521+i1521−i1521+i1521+i1521−i1521−i1521+i1521−i152-400−2i3−2i32i32i3221111−5−5−5−55555−1−i152−1−i152−1−i152−1−i152−1+i152−1+i152−1+i152−1+i152ζ4−ζ68+ζ76−ζ92ζ4−ζ68+ζ76−ζ92ζ4−ζ68+ζ76−ζ92ζ4−ζ68+ζ76−ζ92ζ28−ζ44+ζ52−ζ116ζ28−ζ44+ζ52−ζ116ζ28−ζ44+ζ52−ζ116ζ28−ζ44+ζ52−ζ116−ζ28+ζ44−ζ52+ζ116−ζ28+ζ44−ζ52+ζ116−ζ28+ζ44−ζ52+ζ116−ζ28+ζ44−ζ52+ζ116−ζ4+ζ68−ζ76+ζ92−ζ4+ζ68−ζ76+ζ92−ζ4+ζ68−ζ76+ζ92−ζ4+ζ68−ζ76+ζ920000000000000000000000
χ38444444-2-2-2-2-2-2-2-2-1-1-1-1-1-1-1-11+i1521−i1521+i1521−i1521+i1521+i1521−i1521−i1521+i1521−i1521+i1521+i1521−i1521−i1521+i1521−i152-4002i32i3−2i3−2i32211115555−5−5−5−5−1−i152−1−i152−1−i152−1−i152−1+i152−1+i152−1+i152−1+i152−ζ4+ζ68−ζ76+ζ92−ζ4+ζ68−ζ76+ζ92−ζ4+ζ68−ζ76+ζ92−ζ4+ζ68−ζ76+ζ92−ζ28+ζ44−ζ52+ζ116−ζ28+ζ44−ζ52+ζ116−ζ28+ζ44−ζ52+ζ116−ζ28+ζ44−ζ52+ζ116ζ28−ζ44+ζ52−ζ116ζ28−ζ44+ζ52−ζ116ζ28−ζ44+ζ52−ζ116ζ28−ζ44+ζ52−ζ116ζ4−ζ68+ζ76−ζ92ζ4−ζ68+ζ76−ζ92ζ4−ζ68+ζ76−ζ92ζ4−ζ68+ζ76−ζ920000000000000000000000
χ394444-4-444-4-4-4-44444-4-44-4-444444-4-4-4-444-4-4-4-4440000000000000000000000000000000000000000000000000000000000000000000
χ404444-4-444-4-4-4-444-1-111-111-1-1-1-1-11111-1-11111-1-1000000000−5−555ζ14+ζ22−ζ38−ζ46+ζ62−ζ86+ζ94−ζ118ζ14+ζ22−ζ38−ζ46+ζ62−ζ86+ζ94−ζ118−ζ14−ζ22+ζ38+ζ46−ζ62+ζ86−ζ94+ζ118−ζ14−ζ22+ζ38+ζ46−ζ62+ζ86−ζ94+ζ118ζ14−ζ22+ζ38−ζ46−ζ62−ζ86+ζ94+ζ118ζ14−ζ22+ζ38−ζ46−ζ62−ζ86+ζ94+ζ118−ζ14+ζ22−ζ38+ζ46+ζ62+ζ86−ζ94−ζ118−ζ14+ζ22−ζ38+ζ46+ζ62+ζ86−ζ94−ζ118−5−555−5−555ζ14+ζ22−ζ38−ζ46+ζ62−ζ86+ζ94−ζ118ζ14+ζ22−ζ38−ζ46+ζ62−ζ86+ζ94−ζ118−ζ14−ζ22+ζ38+ζ46−ζ62+ζ86−ζ94+ζ118−ζ14−ζ22+ζ38+ζ46−ζ62+ζ86−ζ94+ζ118ζ14−ζ22+ζ38−ζ46−ζ62−ζ86+ζ94+ζ118ζ14−ζ22+ζ38−ζ46−ζ62−ζ86+ζ94+ζ118−ζ14+ζ22−ζ38+ζ46+ζ62+ζ86−ζ94−ζ118−ζ14+ζ22−ζ38+ζ46+ζ62+ζ86−ζ94−ζ118ζ14+ζ22−ζ38−ζ46+ζ62−ζ86+ζ94−ζ118ζ14+ζ22−ζ38−ζ46+ζ62−ζ86+ζ94−ζ118−ζ14−ζ22+ζ38+ζ46−ζ62+ζ86−ζ94+ζ118−ζ14−ζ22+ζ38+ζ46−ζ62+ζ86−ζ94+ζ118ζ14−ζ22+ζ38−ζ46−ζ62−ζ86+ζ94+ζ118ζ14−ζ22+ζ38−ζ46−ζ62−ζ86+ζ94+ζ118−ζ14+ζ22−ζ38+ζ46+ζ62+ζ86−ζ94−ζ118−ζ14+ζ22−ζ38+ζ46+ζ62+ζ86−ζ94−ζ1180000000000000000000000
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χ424444-4-444-4-4-4-444-1-111-111-1-1-1-1-11111-1-11111-1-100000000055−5−5ζ14−ζ22+ζ38−ζ46−ζ62−ζ86+ζ94+ζ118ζ14−ζ22+ζ38−ζ46−ζ62−ζ86+ζ94+ζ118−ζ14+ζ22−ζ38+ζ46+ζ62+ζ86−ζ94−ζ118−ζ14+ζ22−ζ38+ζ46+ζ62+ζ86−ζ94−ζ118−ζ14−ζ22+ζ38+ζ46−ζ62+ζ86−ζ94+ζ118−ζ14−ζ22+ζ38+ζ46−ζ62+ζ86−ζ94+ζ118ζ14+ζ22−ζ38−ζ46+ζ62−ζ86+ζ94−ζ118ζ14+ζ22−ζ38−ζ46+ζ62−ζ86+ζ94−ζ11855−5−555−5−5ζ14−ζ22+ζ38−ζ46−ζ62−ζ86+ζ94+ζ118ζ14−ζ22+ζ38−ζ46−ζ62−ζ86+ζ94+ζ118−ζ14+ζ22−ζ38+ζ46+ζ62+ζ86−ζ94−ζ118−ζ14+ζ22−ζ38+ζ46+ζ62+ζ86−ζ94−ζ118−ζ14−ζ22+ζ38+ζ46−ζ62+ζ86−ζ94+ζ118−ζ14−ζ22+ζ38+ζ46−ζ62+ζ86−ζ94+ζ118ζ14+ζ22−ζ38−ζ46+ζ62−ζ86+ζ94−ζ118ζ14+ζ22−ζ38−ζ46+ζ62−ζ86+ζ94−ζ118ζ14−ζ22+ζ38−ζ46−ζ62−ζ86+ζ94+ζ118ζ14−ζ22+ζ38−ζ46−ζ62−ζ86+ζ94+ζ118−ζ14+ζ22−ζ38+ζ46+ζ62+ζ86−ζ94−ζ118−ζ14+ζ22−ζ38+ζ46+ζ62+ζ86−ζ94−ζ118−ζ14−ζ22+ζ38+ζ46−ζ62+ζ86−ζ94+ζ118−ζ14−ζ22+ζ38+ζ46−ζ62+ζ86−ζ94+ζ118ζ14+ζ22−ζ38−ζ46+ζ62−ζ86+ζ94−ζ118ζ14+ζ22−ζ38−ζ46+ζ62−ζ86+ζ94−ζ1180000000000000000000000
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χ1018-8-88008-80000-88-2225−252−2525-2-2-22225−2525−2522−2525−2525-2-20000000000000000000000000000000000000000000000000000000000000000000
χ1028-8-8800-44−4i34i34i3−4i34-4-22−2525225−25-21+i151−i15−1−i15−1+i152ζ4−2ζ68+2ζ76−2ζ92−2ζ4+2ζ68−2ζ76+2ζ92−2ζ28+2ζ44−2ζ52+2ζ1162ζ28−2ζ44+2ζ52−2ζ116−1−i15−1+i15−2ζ4+2ζ68−2ζ76+2ζ922ζ4−2ζ68+2ζ76−2ζ922ζ28−2ζ44+2ζ52−2ζ116−2ζ28+2ζ44−2ζ52+2ζ1161+i151−i150000000000000000000000000000000000000000000000000000000000000000000
χ1038-8-8800-44−4i34i34i3−4i34-4-2225−252−2525-21−i151+i15−1+i15−1−i152ζ28−2ζ44+2ζ52−2ζ116−2ζ28+2ζ44−2ζ52+2ζ116−2ζ4+2ζ68−2ζ76+2ζ922ζ4−2ζ68+2ζ76−2ζ92−1+i15−1−i15−2ζ28+2ζ44−2ζ52+2ζ1162ζ28−2ζ44+2ζ52−2ζ1162ζ4−2ζ68+2ζ76−2ζ92−2ζ4+2ζ68−2ζ76+2ζ921−i151+i150000000000000000000000000000000000000000000000000000000000000000000
χ1048-8-8800-444i3−4i3−4i34i34-4-22−2525225−25-21−i151+i15−1+i15−1−i15−2ζ28+2ζ44−2ζ52+2ζ1162ζ28−2ζ44+2ζ52−2ζ1162ζ4−2ζ68+2ζ76−2ζ92−2ζ4+2ζ68−2ζ76+2ζ92−1+i15−1−i152ζ28−2ζ44+2ζ52−2ζ116−2ζ28+2ζ44−2ζ52+2ζ116−2ζ4+2ζ68−2ζ76+2ζ922ζ4−2ζ68+2ζ76−2ζ921−i151+i150000000000000000000000000000000000000000000000000000000000000000000
χ1058-8-8800-444i3−4i3−4i34i34-4-2225−252−2525-21+i151−i15−1−i15−1+i15−2ζ4+2ζ68−2ζ76+2ζ922ζ4−2ζ68+2ζ76−2ζ922ζ28−2ζ44+2ζ52−2ζ116−2ζ28+2ζ44−2ζ52+2ζ116−1−i15−1+i152ζ4−2ζ68+2ζ76−2ζ92−2ζ4+2ζ68−2ζ76+2ζ92−2ζ28+2ζ44−2ζ52+2ζ1162ζ28−2ζ44+2ζ52−2ζ1161+i151−i150000000000000000000000000000000000000000000000000000000000000000000

Here ζ is a primitive root of unity of order 120 (ζ120 = 1); i = ζ30.