Finite Group Databasebeta

← Group #14278925

Character table — Group #14278925

Order 1920.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96C97C98C99C100C101C102
size11222222222444444444444444444455888888888888888888888888101010101010101010161616161616161616161616202020202020204040404040406060606060606060120120120120
order122344688121256810121515202024242424303060606060448810202424242430304040404060601201201201201201201201202246688121240404040120120120120120120120120681224242424882424242416161616161616168888
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1
χ311111111111111111111111111111111-1-111-1-1-1-11111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-11111111-1-1-1-1-1-111111111-1-1-1-1
χ411111111111111111111111111111111-1-111-1-1-1-11111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-11111111-1-1-1-1-1-1-1-1-1-1-1-1-1-11111
χ5111111111111111111111111111111-1-1111111111111111111111111-1-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1iiii−i−i−i−iii−i−i
χ6111111111111111111111111111111-1-1111111111111111111111111-1-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1−i−i−i−iiiii−i−iii
χ7111111111111111111111111111111-1-1-1-111-1-1-1-11111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111iiii−i−i−i−i−i−iii
χ8111111111111111111111111111111-1-1-1-111-1-1-1-11111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111−i−i−i−iiiiiii−i−i
χ911-111-1111-1-11-1-11111-1-111-1-111-1-1-1-111i−i-11ii−i−i-1-111-1-1111111-1-1-1-11-1-1-1-11111ii−i−iiiii−i−i−i−i1-1-111-1-1i−iii−i−i11-1-111-1-1i−ii−i
χ1011-111-1111-1-11-1-11111-1-111-1-111-1-1-1-111i−i-11ii−i−i-1-111-1-1111111-1-1-1-11-1-1-1-11111ii−i−iiiii−i−i−i−i1-1-111-1-1i−iii−i−i-1-111-1-111−ii−ii
χ1111-111-1111-1-11-1-11111-1-111-1-111-1-1-1-111−ii-11−i−iii-1-111-1-1111111-1-1-1-11-1-1-1-11111−i−iii−i−i−i−iiiii1-1-111-1-1−ii−i−iii11-1-111-1-1−ii−ii
χ1211-111-1111-1-11-1-11111-1-111-1-111-1-1-1-111−ii-11−i−iii-1-111-1-1111111-1-1-1-11-1-1-1-11111−i−iii−i−i−i−iiiii1-1-111-1-1−ii−i−iii-1-111-1-111i−ii−i
χ1311-111-1111-1-11-1-11111-1-111-1-111-1-1-1-1-1-1i−i-11ii−i−i-1-111-1-1111111-1-1-1-1-11111-1-1-1-1ii−i−iiiii−i−i−i−i-111-1-111−ii−i−iiiii−i−i−i−iii-111-1
χ1411-111-1111-1-11-1-11111-1-111-1-111-1-1-1-1-1-1i−i-11ii−i−i-1-111-1-1111111-1-1-1-1-11111-1-1-1-1ii−i−iiiii−i−i−i−i-111-1-111−ii−i−iii−i−iiiii−i−i1-1-11
χ1511-111-1111-1-11-1-11111-1-111-1-111-1-1-1-1-1-1−ii-11−i−iii-1-111-1-1111111-1-1-1-1-11111-1-1-1-1−i−iii−i−i−i−iiiii-111-1-111i−iii−i−iii−i−i−i−iii1-1-11
χ1611-111-1111-1-11-1-11111-1-111-1-111-1-1-1-1-1-1−ii-11−i−iii-1-111-1-1111111-1-1-1-1-11111-1-1-1-1−i−iii−i−i−i−iiiii-111-1-111i−iii−i−i−i−iiiii−i−i-111-1
χ172222222-2-22222-2222222-2-2-2-2222222220022000022-2-2-2-222-2-2-2-2-2-2-2-222222-2-2220000000000002-22-2-2-2-2000000000000000000
χ182222222-2-22222-2222222-2-2-2-2222222-2-20022000022-2-2-2-222-2-2-2-2-2-2-2-2-2-2-2-2-222-2-2000000000000-22-22222000000000000000000
χ192222-2-2200-2-22202-222-2-2000022-2-2-2-222002-20000220000-2-200000000-2-22-2-20022000000000000-2020000000000−i2i2−i2i2−i2i2−i2i20000
χ202222-2-2200-2-22202-222-2-2000022-2-2-2-222002-20000220000-2-200000000-2-22-2-20022000000000000-2020000000000i2−i2i2−i2i2−i2i2−i20000
χ212222-2-2200-2-22202-222-2-2000022-2-2-2-2-2-2002-20000220000-2-20000000022-22200-2-200000000000020-200000000002−22−2−22−220000
χ222222-2-2200-2-22202-222-2-2000022-2-2-2-2-2-2002-20000220000-2-20000000022-22200-2-200000000000020-20000000000−22−222−22−20000
χ23222-122-122-1-12-122-1-1-122-1-1-1-1-1-1-1-1-1-1222222-1-1-1-1-1-12222-1-1-1-1-1-1-1-1-1-1222-1-122-1-12222-1-1-1-1-1-1-1-1-12-1-1-1-1-122-1-1-1-1000000000000
χ24222-122-122-1-12-122-1-1-122-1-1-1-1-1-1-1-1-1-122-2-2221111-1-12222-1-1-1-1-1-1-1-1-1-1222-1-122-1-1-2-2-2-211111111-12-1-1-1-1-1-2-21111000000000000
χ25222-122-122-1-12-122-1-1-122-1-1-1-1-1-1-1-1-1-1-2-22222-1-1-1-1-1-12222-1-1-1-1-1-1-1-1-1-1-2-2-211-2-2112222-1-1-1-1-1-1-1-11-211111-2-21111000000000000
χ26222-122-122-1-12-122-1-1-122-1-1-1-1-1-1-1-1-1-1-2-2-2-2221111-1-12222-1-1-1-1-1-1-1-1-1-1-2-2-211-2-211-2-2-2-2111111111-21111122-1-1-1-1000000000000
χ27222-122-1-2-2-1-12-1-22-1-1-1221111-1-1-1-1-1-1220022−i3i3−i3i3-1-1-2-2-2-2-1-111111111222-1-1-2-2-1-10000−i3−i3i3i3−i3−i3i3i3-1-2-1111100−i3i3−i3i3000000000000
χ28222-122-1-2-2-1-12-1-22-1-1-1221111-1-1-1-1-1-1220022i3−i3i3−i3-1-1-2-2-2-2-1-111111111222-1-1-2-2-1-10000i3i3−i3−i3i3i3−i3−i3-1-2-1111100i3−i3i3−i3000000000000
χ29222-122-1-2-2-1-12-1-22-1-1-1221111-1-1-1-1-1-1-2-20022−i3i3−i3i3-1-1-2-2-2-2-1-111111111-2-2-21122110000−i3−i3i3i3−i3−i3i3i3121-1-1-1-100i3−i3i3−i3000000000000
χ30222-122-1-2-2-1-12-1-22-1-1-1221111-1-1-1-1-1-1-2-20022i3−i3i3−i3-1-1-2-2-2-2-1-111111111-2-2-21122110000i3i3−i3−i3i3i3−i3−i3121-1-1-1-100−i3i3−i3i3000000000000
χ3122-222-22-2-2-2-22-222222-2-2-2-22222-2-2-2-22200-220000-2-2-2-22222-2-2-2-222222-2-2-2-2-2-22200000000000022-2-2-222000000000000000000
χ3222-222-22-2-2-2-22-222222-2-2-2-22222-2-2-2-2-2-200-220000-2-2-2-22222-2-2-2-22222-2222222-2-2000000000000-2-2222-2-2000000000000000000
χ3322-22-22200222-202-2222200002222222200-2-20000-2-20000-2-200000000-22-2220022000000000000-20-20000000000−i2i2i2−i2−i2i2i2−i20000
χ3422-22-22200222-202-2222200002222222200-2-20000-2-20000-2-200000000-22-2220022000000000000-20-20000000000i2−i2−i2i2i2−i2−i2i20000
χ3522-22-22200222-202-222220000222222-2-200-2-20000-2-20000-2-2000000002-22-2-200-2-200000000000020200000000002−2−22−222−20000
χ3622-22-22200222-202-222220000222222-2-200-2-20000-2-20000-2-2000000002-22-2-200-2-20000000000002020000000000−222−22−2−220000
χ3722-2-12-2-1221121-22-1-1-1-2-2-1-111-1-11111222i−2i-22−i−iii1122-2-2-1-1-1-1-1-111112-2-21122-1-12i2i−2i−2i−i−i−i−iiiii-1-21-1-1112i−2i−i−iii000000000000
χ3822-2-12-2-1221121-22-1-1-1-2-2-1-111-1-1111122−2i2i-22ii−i−i1122-2-2-1-1-1-1-1-111112-2-21122-1-1−2i−2i2i2iiiii−i−i−i−i-1-21-1-111−2i2iii−i−i000000000000
χ3922-2-12-2-1221121-22-1-1-1-2-2-1-111-1-11111-2-22i−2i-22−i−iii1122-2-2-1-1-1-1-1-11111-222-1-1-2-2112i2i−2i−2i−i−i−i−iiiii12-111-1-1−2i2iii−i−i000000000000
χ4022-2-12-2-1221121-22-1-1-1-2-2-1-111-1-11111-2-2−2i2i-22ii−i−i1122-2-2-1-1-1-1-1-11111-222-1-1-2-211−2i−2i2i2iiiii−i−i−i−i12-111-1-12i−2i−i−iii000000000000
χ4122-2-12-2-1-2-2112122-1-1-1-2-211-1-1-1-111112200-223−3−3311-2-222-1-11111-1-1-1-12-2-211-2-2-1-1000033−3−3−3−333-12111-1-1003−3−33000000000000
χ4222-2-12-2-1-2-2112122-1-1-1-2-211-1-1-1-111112200-22−333−311-2-222-1-11111-1-1-1-12-2-211-2-2-1-10000−3−33333−3−3-12111-1-100−333−3000000000000
χ4322-2-12-2-1-2-2112122-1-1-1-2-211-1-1-1-11111-2-200-223−3−3311-2-222-1-11111-1-1-1-1-222-1-12211000033−3−3−3−3331-2-1-1-11100−333−3000000000000
χ4422-2-12-2-1-2-2112122-1-1-1-2-211-1-1-1-11111-2-200-22−333−311-2-222-1-11111-1-1-1-1-222-1-122110000−3−33333−3−31-2-1-1-111003−3−33000000000000
χ4544444444444-144-14-1-1-1-14444-1-1-1-1-1-10044-1-14444-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1000000000-1-1-1-1-1-1-1-1-1-1-1-10000000000000000000000000
χ4644444444444-144-14-1-1-1-14444-1-1-1-1-1-100-4-4-1-1-4-4-4-4-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-10000000001111111111110000000000000000000000000
χ474444444-4-444-14-4-14-1-1-1-1-4-4-4-4-1-1-1-1-1-10000-1-10000-1-11111-1-111111111000000000−55−55−55−55−55−550000000000000000000000000
χ484444444-4-444-14-4-14-1-1-1-1-4-4-4-4-1-1-1-1-1-10000-1-10000-1-11111-1-1111111110000000005−55−55−55−55−55−50000000000000000000000000
χ49444-244-244-2-2-1-24-1-21−i1521+i152-1-1-2-2-2-21−i1521+i1521−i1521−i1521+i1521+i1520044-1-1-2-2-2-21−i1521+i152-1-1-1-11−i1521+i1521−i1521−i1521+i1521+i1521−i1521−i1521+i1521+i152000000000-1-1-1-11−i1521+i1521+i1521−i1521−i1521+i1521+i1521−i1520000000000000000000000000
χ50444-244-244-2-2-1-24-1-21−i1521+i152-1-1-2-2-2-21−i1521+i1521−i1521−i1521+i1521+i15200-4-4-1-122221−i1521+i152-1-1-1-11−i1521+i1521−i1521−i1521+i1521+i1521−i1521−i1521+i1521+i1520000000001111−1+i152−1−i152−1−i152−1+i152−1+i152−1−i152−1−i152−1+i1520000000000000000000000000
χ51444-244-244-2-2-1-24-1-21+i1521−i152-1-1-2-2-2-21+i1521−i1521+i1521+i1521−i1521−i1520044-1-1-2-2-2-21+i1521−i152-1-1-1-11+i1521−i1521+i1521+i1521−i1521−i1521+i1521+i1521−i1521−i152000000000-1-1-1-11+i1521−i1521−i1521+i1521+i1521−i1521−i1521+i1520000000000000000000000000
χ52444-244-244-2-2-1-24-1-21+i1521−i152-1-1-2-2-2-21+i1521−i1521+i1521+i1521−i1521−i15200-4-4-1-122221+i1521−i152-1-1-1-11+i1521−i1521+i1521+i1521−i1521−i1521+i1521+i1521−i1521−i1520000000001111−1−i152−1+i152−1+i152−1−i152−1−i152−1+i152−1+i152−1−i1520000000000000000000000000
χ53444-244-2-4-4-2-2-1-2-4-1-21−i1521+i152-1-122221−i1521+i1521−i1521−i1521+i1521+i1520000-1-1−2i32i3−2i32i31−i1521+i15211111−i1521+i152−1+i152−1+i152−1−i152−1−i152−1+i152−1+i152−1−i152−1−i1520000000005−55−5ζ28−ζ44+ζ52−ζ116ζ4−ζ68+ζ76−ζ92−ζ4+ζ68−ζ76+ζ92−ζ28+ζ44−ζ52+ζ116ζ28−ζ44+ζ52−ζ116ζ4−ζ68+ζ76−ζ92−ζ4+ζ68−ζ76+ζ92−ζ28+ζ44−ζ52+ζ1160000000000000000000000000
χ54444-244-2-4-4-2-2-1-2-4-1-21−i1521+i152-1-122221−i1521+i1521−i1521−i1521+i1521+i1520000-1-12i3−2i32i3−2i31−i1521+i15211111−i1521+i152−1+i152−1+i152−1−i152−1−i152−1+i152−1+i152−1−i152−1−i152000000000−55−55−ζ28+ζ44−ζ52+ζ116−ζ4+ζ68−ζ76+ζ92ζ4−ζ68+ζ76−ζ92ζ28−ζ44+ζ52−ζ116−ζ28+ζ44−ζ52+ζ116−ζ4+ζ68−ζ76+ζ92ζ4−ζ68+ζ76−ζ92ζ28−ζ44+ζ52−ζ1160000000000000000000000000
χ55444-244-2-4-4-2-2-1-2-4-1-21+i1521−i152-1-122221+i1521−i1521+i1521+i1521−i1521−i1520000-1-1−2i32i3−2i32i31+i1521−i15211111+i1521−i152−1−i152−1−i152−1+i152−1+i152−1−i152−1−i152−1+i152−1+i152000000000−55−55ζ4−ζ68+ζ76−ζ92ζ28−ζ44+ζ52−ζ116−ζ28+ζ44−ζ52+ζ116−ζ4+ζ68−ζ76+ζ92ζ4−ζ68+ζ76−ζ92ζ28−ζ44+ζ52−ζ116−ζ28+ζ44−ζ52+ζ116−ζ4+ζ68−ζ76+ζ920000000000000000000000000
χ56444-244-2-4-4-2-2-1-2-4-1-21+i1521−i152-1-122221+i1521−i1521+i1521+i1521−i1521−i1520000-1-12i3−2i32i3−2i31+i1521−i15211111+i1521−i152−1−i152−1−i152−1+i152−1+i152−1−i152−1−i152−1+i152−1+i1520000000005−55−5−ζ4+ζ68−ζ76+ζ92−ζ28+ζ44−ζ52+ζ116ζ28−ζ44+ζ52−ζ116ζ4−ζ68+ζ76−ζ92−ζ4+ζ68−ζ76+ζ92−ζ28+ζ44−ζ52+ζ116ζ28−ζ44+ζ52−ζ116ζ4−ζ68+ζ76−ζ920000000000000000000000000
χ57444-2-4-4-200224-2042-2-2-4-40000-2-2222244004-40000-2-200002200000000-4-442200-2-200000000000020-20000000000000000000000
χ58444-2-4-4-200224-2042-2-2-4-40000-2-22222-4-4004-40000-2-20000220000000044-4-2-20022000000000000-2020000000000000000000000
χ5944-444-4444-4-4-1-4-4-14-1-11144-4-4-1-11111004i−4i1-14i4i−4i−4i11-1-111-1-1-1-1-1-11111000000000−i−iii−i−i−i−iiiii0000000000000000000000000
χ6044-444-4444-4-4-1-4-4-14-1-11144-4-4-1-1111100−4i4i1-1−4i−4i4i4i11-1-111-1-1-1-1-1-11111000000000ii−i−iiiii−i−i−i−i0000000000000000000000000
χ6144-444-44-4-4-4-4-1-44-14-1-111-4-444-1-1111100001-100001111-1-1-1-11111-1-1-1-1000000000−i5i5i5−i5−i5i5−i5i5i5−i5i5−i50000000000000000000000000
χ6244-444-44-4-4-4-4-1-44-14-1-111-4-444-1-1111100001-100001111-1-1-1-11111-1-1-1-1000000000i5−i5−i5i5i5−i5i5−i5−i5i5−i5i50000000000000000000000000
χ6344-4-24-4-24422-12-4-1-21−i1521+i15211-2-2221−i1521+i152−1+i152−1+i152−1−i152−1−i152004i−4i1-1−2i−2i2i2i−1+i152−1−i152-1-1111−i1521+i1521−i1521−i1521+i1521+i152−1+i152−1+i152−1−i152−1−i152000000000−i−iiiζ14+ζ22+ζ86+ζ118ζ38+ζ46+ζ62+ζ94ζ38+ζ46+ζ62+ζ94ζ14+ζ22+ζ86+ζ118−ζ14−ζ22−ζ86−ζ118−ζ38−ζ46−ζ62−ζ94−ζ38−ζ46−ζ62−ζ94−ζ14−ζ22−ζ86−ζ1180000000000000000000000000
χ6444-4-24-4-24422-12-4-1-21−i1521+i15211-2-2221−i1521+i152−1+i152−1+i152−1−i152−1−i15200−4i4i1-12i2i−2i−2i−1+i152−1−i152-1-1111−i1521+i1521−i1521−i1521+i1521+i152−1+i152−1+i152−1−i152−1−i152000000000ii−i−i−ζ14−ζ22−ζ86−ζ118−ζ38−ζ46−ζ62−ζ94−ζ38−ζ46−ζ62−ζ94−ζ14−ζ22−ζ86−ζ118ζ14+ζ22+ζ86+ζ118ζ38+ζ46+ζ62+ζ94ζ38+ζ46+ζ62+ζ94ζ14+ζ22+ζ86+ζ1180000000000000000000000000
χ6544-4-24-4-24422-12-4-1-21+i1521−i15211-2-2221+i1521−i152−1−i152−1−i152−1+i152−1+i152004i−4i1-1−2i−2i2i2i−1−i152−1+i152-1-1111+i1521−i1521+i1521+i1521−i1521−i152−1−i152−1−i152−1+i152−1+i152000000000−i−iiiζ38+ζ46+ζ62+ζ94ζ14+ζ22+ζ86+ζ118ζ14+ζ22+ζ86+ζ118ζ38+ζ46+ζ62+ζ94−ζ38−ζ46−ζ62−ζ94−ζ14−ζ22−ζ86−ζ118−ζ14−ζ22−ζ86−ζ118−ζ38−ζ46−ζ62−ζ940000000000000000000000000
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Here ζ is a primitive root of unity of order 120 (ζ120 = 1); i = ζ30.