Finite Group Databasebeta

← Group #14313975

Character table — Group #14313975

Order 1920.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96C97C98C99C100C101C102
size11222222222444444444444444444455888888888888888888888888101010101010101010161616161616161616161616202020202020204040404040406060606060606060120120120120
order12234466688581010101212151524242424303030303030224412121212202040404040606060601201201201201201201201202446666882020202060606060606060608121224242424441212121216161616161616164444
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1
χ311111111111111111111111111111111-1-1-1-1-1-1111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-11111111-1-1-1-1-1-111111111-1-1-1-1
χ411111111111111111111111111111111-1-1-1-1-1-1111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-11111111-1-1-1-1-1-1-1-1-1-1-1-1-1-11111
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
χ7111111111111111111111111111111-1-1-1-1-1-1-1-1111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111iiii−i−i−i−i−i−iii
χ8111111111111111111111111111111-1-1-1-1-1-1-1-1111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111−i−i−i−iiiiiii−i−i
χ911-11-11-1-11111-1-1-11-111111-1-1-1-1-1-111111-111-1-1-1111-1-1-1-1111111-1-1-1-1-11-111-1-11111-1-11111-1-1-1-1-11-111-1-11-111-1-111-1-111-1-11-11-1
χ1011-11-11-1-11111-1-1-11-111111-1-1-1-1-1-111111-111-1-1-1111-1-1-1-1111111-1-1-1-1-11-111-1-11111-1-11111-1-1-1-1-11-111-1-11-111-1-1-1-111-1-111-11-11
χ1111-11-11-1-11111-1-1-11-111111-1-1-1-1-1-11111-11-1-111-1111-1-1-1-1111111-1-1-1-1-11-111-1-111-1-111-1-1-1-11111-11-111-1-1-11-1-11111-1-111-1-1-11-11
χ1211-11-11-1-11111-1-1-11-111111-1-1-1-1-1-11111-11-1-111-1111-1-1-1-1111111-1-1-1-1-11-111-1-111-1-111-1-1-1-11111-11-111-1-1-11-1-111-1-111-1-1111-11-1
χ1311-11-11-1-11111-1-1-11-111111-1-1-1-1-1-111-1-11-111-1-1-1111-1-1-1-1111111-1-1-1-11-11-1-111-1-111-1-11111-1-1-1-11-11-1-111-11-1-111ii−i−i−i−iiii−i−ii
χ1411-11-11-1-11111-1-1-11-111111-1-1-1-1-1-111-1-11-111-1-1-1111-1-1-1-1111111-1-1-1-11-11-1-111-1-111-1-11111-1-1-1-11-11-1-111-11-1-111−i−iiiii−i−i−iii−i
χ1511-11-11-1-11111-1-1-11-111111-1-1-1-1-1-111-1-1-11-1-111-1111-1-1-1-1111111-1-1-1-11-11-1-111-1-1-1-111-1-1-1-111111-11-1-1111-111-1-1ii−i−i−i−iii−iii−i
χ1611-11-11-1-11111-1-1-11-111111-1-1-1-1-1-111-1-1-11-1-111-1111-1-1-1-1111111-1-1-1-11-11-1-111-1-1-1-111-1-1-1-111111-11-1-1111-111-1-1−i−iiiii−i−ii−i−ii
χ17222222222-2-22-22222222-2-2-2-22222222200000022-2-2-2-22222-2-2-2-2-2-2-2-22222222-2-2000000000000-222-2-2-2-2000000000000000000
χ18222222222-2-22-22222222-2-2-2-2222222-2-200000022-2-2-2-22222-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2220000000000002-2-22222000000000000000000
χ192222-2-22220020222-2-222000022222222000000-2-20000-2-2-2-2000000002-2-22222000000000000000-2-200000000002−22−22−22−20000
χ202222-2-22220020222-2-222000022222222000000-2-20000-2-2-2-2000000002-2-22222000000000000000-2-20000000000−22−22−22−220000
χ212222-2-22220020222-2-2220000222222-2-2000000-2-20000-2-2-2-200000000-222-2-2-2-2000000000000000220000000000−i2i2−i2i2i2−i2i2−i20000
χ222222-2-22220020222-2-2220000222222-2-2000000-2-20000-2-2-2-200000000-222-2-2-2-2000000000000000220000000000i2−i2i2−i2−i2i2−i2i20000
χ23222-122-1-1-12222222-1-1-1-1-1-1-1-1-1-1-1-1-1-12222-1-1-1-1222222-1-1-1-1-1-1-1-1-1-1-1-1222-1-1-1-1222222-1-1-1-1-1-1-1-12-1-1-1-1-1-122-1-1-1-1000000000000
χ24222-122-1-1-12222222-1-1-1-1-1-1-1-1-1-1-1-1-1-122-2-21111222222-1-1-1-1-1-1-1-1-1-1-1-1222-1-1-1-122-2-2-2-2111111112-1-1-1-1-1-1-2-21111000000000000
χ25222-122-1-1-12222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-2-222-1-1-1-1222222-1-1-1-1-1-1-1-1-1-1-1-1-2-2-21111-2-22222-1-1-1-1-1-1-1-1-2111111-2-21111000000000000
χ26222-122-1-1-12222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-2-2-2-21111222222-1-1-1-1-1-1-1-1-1-1-1-1-2-2-21111-2-2-2-2-2-211111111-211111122-1-1-1-1000000000000
χ27222-122-1-1-1-2-22-2222-1-1-1-11111-1-1-1-1-1-12200−i3i3−i3i322-2-2-2-2-1-1-1-111111111222-1-1-1-1-2-20000−i3−i3i3i3−i3−i3i3i3-2-1-1111100−i3i3−i3i3000000000000
χ28222-122-1-1-1-2-22-2222-1-1-1-11111-1-1-1-1-1-12200i3−i3i3−i322-2-2-2-2-1-1-1-111111111222-1-1-1-1-2-20000i3i3−i3−i3i3i3−i3−i3-2-1-1111100i3−i3i3−i3000000000000
χ29222-122-1-1-1-2-22-2222-1-1-1-11111-1-1-1-1-1-1-2-200−i3i3−i3i322-2-2-2-2-1-1-1-111111111-2-2-21111220000−i3−i3i3i3−i3−i3i3i3211-1-1-1-100i3−i3i3−i3000000000000
χ30222-122-1-1-1-2-22-2222-1-1-1-11111-1-1-1-1-1-1-2-200i3−i3i3−i322-2-2-2-2-1-1-1-111111111-2-2-21111220000i3i3−i3−i3i3i3−i3−i3211-1-1-1-100−i3i3−i3i3000000000000
χ3122-222-2-2-220020-2-222-2220000-2-2-2-222220000002-2000022-2-200000000-2-2222-2-2000000000000000-2200000000002−2−222−2−220000
χ3222-222-2-2-220020-2-222-2220000-2-2-2-222220000002-2000022-2-200000000-2-2222-2-2000000000000000-220000000000−222−2−222−20000
χ3322-222-2-2-220020-2-222-2220000-2-2-2-222-2-20000002-2000022-2-20000000022-2-2-2220000000000000002-20000000000−i2i2i2−i2i2−i2−i2i20000
χ3422-222-2-2-220020-2-222-2220000-2-2-2-222-2-20000002-2000022-2-20000000022-2-2-2220000000000000002-20000000000i2−i2−i2i2−i2i2i2−i20000
χ3522-22-22-2-22-2-222-2-22-2222-2-222-2-2-2-22222000000-22-2-222-2-222-2-2-2-22222-22-222-2-2-2-200000000000022-2-2-222000000000000000000
χ3622-22-22-2-22-2-222-2-22-2222-2-222-2-2-2-222-2-2000000-22-2-222-2-222-2-2-2-222222-22-2-22222000000000000-2-2222-2-2000000000000000000
χ3722-2-1-2211-1222-2-2-221-1-1-1-1-1111111-1-1222-2-1-111-2222-2-211-1-1-1-1-1-11111-22-2-1-1112222-2-2-1-1-1-11111-2-11-1-1112-2-1-111000000000000
χ3822-2-1-2211-1222-2-2-221-1-1-1-1-1111111-1-122-2211-1-1-2222-2-211-1-1-1-1-1-11111-22-2-1-11122-2-2221111-1-1-1-1-2-11-1-111-2211-1-1000000000000
χ3922-2-1-2211-1222-2-2-221-1-1-1-1-1111111-1-1-2-22-2-1-111-2222-2-211-1-1-1-1-1-111112-2211-1-1-2-222-2-2-1-1-1-1111121-111-1-1-2211-1-1000000000000
χ4022-2-1-2211-1222-2-2-221-1-1-1-1-1111111-1-1-2-2-2211-1-1-2222-2-211-1-1-1-1-1-111112-2211-1-1-2-2-2-2221111-1-1-1-121-111-1-12-2-1-111000000000000
χ4122-2-1-2211-1-2-222-2-221-1-1-111-1-11111-1-12200−i3i3i3−i3-22-2-22211-1-11111-1-1-1-1-22-2-1-111-2-20000−i3−i3i3i3i3i3−i3−i32-1111-1-100−i3i3i3−i3000000000000
χ4222-2-1-2211-1-2-222-2-221-1-1-111-1-11111-1-12200i3−i3−i3i3-22-2-22211-1-11111-1-1-1-1-22-2-1-111-2-20000i3i3−i3−i3−i3−i3i3i32-1111-1-100i3−i3−i3i3000000000000
χ4322-2-1-2211-1-2-222-2-221-1-1-111-1-11111-1-1-2-200−i3i3i3−i3-22-2-22211-1-11111-1-1-1-12-2211-1-1220000−i3−i3i3i3i3i3−i3−i3-21-1-1-11100i3−i3−i3i3000000000000
χ4422-2-1-2211-1-2-222-2-221-1-1-111-1-11111-1-1-2-200i3−i3−i3i3-22-2-22211-1-11111-1-1-1-12-2211-1-1220000i3i3−i3−i3−i3−i3i3i3-21-1-1-11100−i3i3i3−i3000000000000
χ4544444444444-14-1-1-144-1-14444-1-1-1-1-1-100444444-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1000000000-1-1-1-1-1-1-1-1-1-1-1-10000000000000000000000000
χ4644444444444-14-1-1-144-1-14444-1-1-1-1-1-100-4-4-4-4-4-4-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-10000000001111111111110000000000000000000000000
χ47444444444-4-4-1-4-1-1-144-1-1-4-4-4-4-1-1-1-1-1-100000000-1-11111-1-1-1-111111111000000000−55−55−55−55−55−550000000000000000000000000
χ48444444444-4-4-1-4-1-1-144-1-1-4-4-4-4-1-1-1-1-1-100000000-1-11111-1-1-1-1111111110000000005−55−55−55−55−55−50000000000000000000000000
χ49444-244-2-2-244-14-1-1-1-2-21−i1521+i152-2-2-2-21−i1521−i1521+i1521+i1521−i1521+i1520044-2-2-2-2-1-1-1-1-1-11−i1521+i1521−i1521+i1521−i1521−i1521+i1521+i1521−i1521−i1521+i1521+i152000000000-1-1-1-11−i1521+i1521+i1521−i1521−i1521+i1521+i1521−i1520000000000000000000000000
χ50444-244-2-2-244-14-1-1-1-2-21−i1521+i152-2-2-2-21−i1521−i1521+i1521+i1521−i1521+i15200-4-42222-1-1-1-1-1-11−i1521+i1521−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
χ51444-244-2-2-244-14-1-1-1-2-21+i1521−i152-2-2-2-21+i1521+i1521−i1521−i1521+i1521−i1520044-2-2-2-2-1-1-1-1-1-11+i1521−i1521+i1521−i1521+i1521+i1521−i1521−i1521+i1521+i1521−i1521−i152000000000-1-1-1-11+i1521−i1521−i1521+i1521+i1521−i1521−i1521+i1520000000000000000000000000
χ52444-244-2-2-244-14-1-1-1-2-21+i1521−i152-2-2-2-21+i1521+i1521−i1521−i1521+i1521−i15200-4-42222-1-1-1-1-1-11+i1521−i1521+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
χ53444-244-2-2-2-4-4-1-4-1-1-1-2-21−i1521+i15222221−i1521−i1521+i1521+i1521−i1521+i1520000−2i32i3−2i32i3-1-111111−i1521+i1521−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
χ54444-244-2-2-2-4-4-1-4-1-1-1-2-21−i1521+i15222221−i1521−i1521+i1521+i1521−i1521+i15200002i3−2i32i3−2i3-1-111111−i1521+i1521−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
χ55444-244-2-2-2-4-4-1-4-1-1-1-2-21+i1521−i15222221+i1521+i1521−i1521−i1521+i1521−i1520000−2i32i3−2i32i3-1-111111+i1521−i1521+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
χ56444-244-2-2-2-4-4-1-4-1-1-1-2-21+i1521−i15222221+i1521+i1521−i1521−i1521+i1521−i15200002i3−2i32i3−2i3-1-111111+i1521−i1521+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
χ57444-2-4-4-2-2-2004044422-2-20000-2-2-2-2-2-244000000-4-400002222000000004-4-4-2-2-2-2000000000000000220000000000000000000000
χ58444-2-4-4-2-2-2004044422-2-20000-2-2-2-2-2-2-4-4000000-4-40000222200000000-4442222000000000000000-2-20000000000000000000000
χ5944-44-44-4-4444-1-411-1-44-1-144-4-41111-1-1004-444-4-41-1-1-11111-1-1-1-1-1-11111000000000-1-111-1-1-1-111110000000000000000000000000
χ6044-44-44-4-4444-1-411-1-44-1-144-4-41111-1-100-44-4-4441-1-1-11111-1-1-1-1-1-1111100000000011-1-11111-1-1-1-10000000000000000000000000
χ6144-44-44-4-44-4-4-1411-1-44-1-1-4-4441111-1-1000000001-111-1-111-1-11111-1-1-1-1000000000−555−5−55−555−55−50000000000000000000000000
χ6244-44-44-4-44-4-4-1411-1-44-1-1-4-4441111-1-1000000001-111-1-111-1-11111-1-1-1-10000000005−5−555−55−5−55−550000000000000000000000000
χ6344-4-24-422-20040-4-44-22-2-200002222-2-2440000004-40000-2-22200000000-4-44-2-2220000000000000002-20000000000000000000000
χ6444-4-24-422-20040-4-44-22-2-200002222-2-2-4-40000004-40000-2-2220000000044-422-2-2000000000000000-220000000000000000000000
χ6544-4-2-4422-244-1-411-12-21−i1521+i152-2-222−1+i152−1+i152−1−i152−1−i1521−i1521+i152004-4-2-2221-1-1-111−1+i152−1−i1521−i1521+i1521−i1521−i1521+i1521+i152−1+i152−1+i152−1−i152−1−i152000000000-1-1111−i1521+i1521+i1521−i152−1+i152−1−i152−1−i152−1+i1520000000000000000000000000
χ6644-4-2-4422-244-1-411-12-21−i1521+i152-2-222−1+i152−1+i152−1−i152−1−i1521−i1521+i15200-4422-2-21-1-1-111−1+i152−1−i1521−i1521+i1521−i1521−i1521+i1521+i152−1+i152−1+i152−1−i152−1−i15200000000011-1-1−1+i152−1−i152−1−i152−1+i1521−i1521+i1521+i1521−i1520000000000000000000000000
χ6744-4-2-4422-244-1-411-12-21+i1521−i152-2-222−1−i152−1−i152−1+i152−1+i1521+i1521−i152004-4-2-2221-1-1-111−1−i152−1+i1521+i1521−i1521+i1521+i1521−i1521−i152−1−i152−1−i152−1+i152−1+i152000000000-1-1111+i1521−i1521−i1521+i152−1−i152−1+i152−1+i152−1−i1520000000000000000000000000
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Here ζ is a primitive root of unity of order 120 (ζ120 = 1); i = ζ30.