Finite Group Databasebeta

← Group #14278129

Character table — Group #14278129

Order 1920.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96C97C98C99C100C101C102C103C104C105
size111122222222224444444444444444444444448888888888888888888888888888888888888888888882020202040404040404040404040120120120120120120120120
order122222366666665101010101010101515303030303030303030303030303044412121212121220202020202020202020202060606060606060606060606060606060606060606060606044442266661212121288888888
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
χ5111111111111111111111111111111111111111-1-1-1-1-1-1111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-111111111-1-1-1-1
χ6111111111111111111111111111111111111111-1-1-1-1-1-1111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-11111-1-1-1-11111
χ7111111111111111111111111111111111111111-1-1-1-1-1-1111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-1-1ii−i−i−i−iii
χ8111111111111111111111111111111111111111-1-1-1-1-1-1111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-1-1−i−iiiii−i−i
χ922222222222222222222222222222222222222-2000000-2-2-2-2-2-200000000-2-2-2-2-2-2-2-200000000000000002-2-2200000022-2-200000000
χ1022222222222222222222222222222222222222-2000000-2-2-2-2-2-200000000-2-2-2-2-2-2-2-20000000000000000-222-2000000-2-22200000000
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
χ13222222-1-1-1-1-1-1-1-122222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-12-2-21111-1-12222-2-2-2-2-2-2-2-2-1-1-1-1-1-1-1-111111111111111112222-2-21111-1-1-1-100000000
χ14222222-1-1-1-1-1-1-1-122222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-12-2-21111-1-12222-2-2-2-2-2-2-2-2-1-1-1-1-1-1-1-11111111111111111-2-2-2-222-1-1-1-1111100000000
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−i3i3i3i3i3i3i3i3i32-2-2200−i3−i3i3i3-1-11100000000
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−i3i3i3i3i3i3i3i3i3-222-200i3i3−i3−i311-1-100000000
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−i32-2-2200i3i3−i3−i3-1-11100000000
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−i3-222-200−i3−i3i3i311-1-100000000
χ192-22-22-2222-2-2-22-22222-2-2-2-222222222-2-2-2-2-2-2-2-200000000000000000000000000000000000000000000002i−2i0000000002i−2i00001−i−1+i1+i−1−i
χ202-22-22-2222-2-2-22-22222-2-2-2-222222222-2-2-2-2-2-2-2-200000000000000000000000000000000000000000000002i−2i0000000002i−2i0000−1+i1−i−1−i1+i
χ212-22-22-2222-2-2-22-22222-2-2-2-222222222-2-2-2-2-2-2-2-20000000000000000000000000000000000000000000000−2i2i000000000−2i2i00001+i−1−i1−i−1+i
χ222-22-22-2222-2-2-22-22222-2-2-2-222222222-2-2-2-2-2-2-2-20000000000000000000000000000000000000000000000−2i2i000000000−2i2i0000−1−i1+i−1+i1−i
χ232-22-2-222-2-2-2222-222-2-2-222-22222-2-2-2-2-2-22222-2-2000000000000000000000000000000000000000000000200-20000002-200−i2i2−i2i20000
χ242-22-2-222-2-2-2222-222-2-2-222-22222-2-2-2-2-2-22222-2-2000000000000000000000000000000000000000000000200-20000002-200i2−i2i2−i20000
χ252-22-2-222-2-2-2222-222-2-2-222-22222-2-2-2-2-2-22222-2-2000000000000000000000000000000000000000000000-2002000000-22002−2−220000
χ262-22-2-222-2-2-2222-222-2-2-222-22222-2-2-2-2-2-22222-2-2000000000000000000000000000000000000000000000-2002000000-2200−222−20000
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
χ394444-4-44-4-44-4-44444-4-44-4-444444-4-4-4-444-4-4-4-4440000000000000000000000000000000000000000000000000000000000000000000
χ404444-4-44-4-44-4-444-1-111-111-1-1-1-1-11111-1-11111-1-1000000000−5−555ζ14+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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χ998-88-8-88-4444-4-4-44-2-2222-2-221+i151−i151+i151−i15−1−i15−1−i15−1+i15−1+i15−1−i15−1+i151+i151+i151−i151−i15−1−i15−1+i150000000000000000000000000000000000000000000000000000000000000000000
χ1008-8-8800800-800-88-22−2525225−25-2-2-222−2525−25252225−2525−25-2-20000000000000000000000000000000000000000000000000000000000000000000
χ1018-8-8800800-800-88-2225−252−2525-2-2-22225−2525−2522−2525−2525-2-20000000000000000000000000000000000000000000000000000000000000000000
χ1028-8-8800-4−4i34i344i3−4i34-4-22−2525225−25-21+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
χ1038-8-8800-4−4i34i344i3−4i34-4-2225−252−2525-21−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
χ1048-8-8800-44i3−4i34−4i34i34-4-22−2525225−25-21−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
χ1058-8-8800-44i3−4i34−4i34i34-4-2225−252−2525-21+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.