Finite Group Databasebeta

← Group #11746796

Character table — Group #11746796

Order 960.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63
size1111222244444444444444488888888888888888888810101010202020204040406060606060606060
order12223666451010101212151530303030303026610101010202030303030303030306060606044441212121226688888888
χ1111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1
χ311111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1iiii−i−i−i−i
χ411111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1−i−i−i−iiiii
χ511111111111111111111111-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1111111111111-1-1-111-1-111-1-1
χ611111111111111111111111-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1111111111111-1-1-1-1-111-1-111
χ711111111111111111111111-1-1-1-1-1-1-111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1111ii−i−i−i−iii
χ811111111111111111111111-1-1-1-1-1-1-111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1111−i−iiiii−i−i
χ922222222-22222-2-2222222220000000-2-200000000-2-2-2-22-22-222-2-200000000000
χ1022222222-22222-2-2222222220000000-2-200000000-2-2-2-2-22-22-2-22200000000000
χ112222-1-1-1-122222-1-1-1-1-1-1-1-1-1-12-1-1222222-1-1-1-1-1-1-1-1-1-1-1-12222-1-1-1-12-1-100000000
χ122222-1-1-1-122222-1-1-1-1-1-1-1-1-1-12-1-1222222-1-1-1-1-1-1-1-1-1-1-1-1-2-2-2-21111-21100000000
χ132222-1-1-1-122222-1-1-1-1-1-1-1-1-1-1-211-2-2-2-22211111111-1-1-1-12222-1-1-1-1-21100000000
χ142222-1-1-1-122222-1-1-1-1-1-1-1-1-1-1-211-2-2-2-22211111111-1-1-1-1-2-2-2-211112-1-100000000
χ152222-1-1-1-1-2222211-1-1-1-1-1-1-1-10−i3i30000-2-2−i3−i3−i3−i3i3i3i3i311112-22-2-1-1110−i3i300000000
χ162222-1-1-1-1-2222211-1-1-1-1-1-1-1-10−i3i30000-2-2−i3−i3−i3−i3i3i3i3i31111-22-2211-1-10i3−i300000000
χ172222-1-1-1-1-2222211-1-1-1-1-1-1-1-10i3−i30000-2-2i3i3i3i3−i3−i3−i3−i311112-22-2-1-1110i3−i300000000
χ182222-1-1-1-1-2222211-1-1-1-1-1-1-1-10i3−i30000-2-2i3i3i3i3−i3−i3−i3−i31111-22-2211-1-10−i3i300000000
χ192-22-22-22-2022-2-2002222-2-2-2-2000000000000000000000020-2002-2000−i2i200−i2i200
χ202-22-22-22-2022-2-2002222-2-2-2-2000000000000000000000020-2002-2000i2−i200i2−i200
χ212-22-22-22-2022-2-2002222-2-2-2-20000000000000000000000-20200-220002−200−2200
χ222-22-22-22-2022-2-2002222-2-2-2-20000000000000000000000-20200-22000−22002−200
χ232-2-222-2-2202-22-20022-2-222-2-200000000000000000000020-202-20000000−i2i200−i2i2
χ242-2-222-2-2202-22-20022-2-222-2-200000000000000000000020-202-20000000i2−i200i2−i2
χ252-2-222-2-2202-22-20022-2-222-2-2000000000000000000000-2020-2200000002−200−22
χ262-2-222-2-2202-22-20022-2-222-2-2000000000000000000000-2020-220000000−22002−2
χ27444444444-1-1-1-144-1-1-1-1-1-1-1-1444-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-10000000000000000000
χ28444444444-1-1-1-144-1-1-1-1-1-1-1-1-4-4-41111-1-111111111-1-1-1-10000000000000000000
χ2944444444-4-1-1-1-1-4-4-1-1-1-1-1-1-1-1000−5−55511−5−555−5−55511110000000000000000000
χ3044444444-4-1-1-1-1-4-4-1-1-1-1-1-1-1-100055−5−51155−5−555−5−511110000000000000000000
χ314444-2-2-2-24-1-1-1-1-2-21−i1521+i1521−i1521+i1521−i1521+i1521−i1521+i1524-2-2-1-1-1-1-1-11−i1521−i1521+i1521+i1521+i1521+i1521−i1521−i1521−i1521−i1521+i1521+i1520000000000000000000
χ324444-2-2-2-24-1-1-1-1-2-21−i1521+i1521−i1521+i1521−i1521+i1521−i1521+i152-4221111-1-1−1+i152−1+i152−1−i152−1−i152−1−i152−1−i152−1+i152−1+i1521−i1521−i1521+i1521+i1520000000000000000000
χ334444-2-2-2-24-1-1-1-1-2-21+i1521−i1521+i1521−i1521+i1521−i1521+i1521−i1524-2-2-1-1-1-1-1-11+i1521+i1521−i1521−i1521−i1521−i1521+i1521+i1521+i1521+i1521−i1521−i1520000000000000000000
χ344444-2-2-2-24-1-1-1-1-2-21+i1521−i1521+i1521−i1521+i1521−i1521+i1521−i152-4221111-1-1−1−i152−1−i152−1+i152−1+i152−1+i152−1+i152−1−i152−1−i1521+i1521+i1521−i1521−i1520000000000000000000
χ354444-2-2-2-2-4-1-1-1-1221−i1521+i1521−i1521+i1521−i1521+i1521−i1521+i1520−2i32i355−5−511ζ28−ζ44+ζ52−ζ116ζ28−ζ44+ζ52−ζ116ζ4−ζ68+ζ76−ζ92ζ4−ζ68+ζ76−ζ92−ζ4+ζ68−ζ76+ζ92−ζ4+ζ68−ζ76+ζ92−ζ28+ζ44−ζ52+ζ116−ζ28+ζ44−ζ52+ζ116−1+i152−1+i152−1−i152−1−i1520000000000000000000
χ364444-2-2-2-2-4-1-1-1-1221−i1521+i1521−i1521+i1521−i1521+i1521−i1521+i15202i3−2i3−5−55511−ζ28+ζ44−ζ52+ζ116−ζ28+ζ44−ζ52+ζ116−ζ4+ζ68−ζ76+ζ92−ζ4+ζ68−ζ76+ζ92ζ4−ζ68+ζ76−ζ92ζ4−ζ68+ζ76−ζ92ζ28−ζ44+ζ52−ζ116ζ28−ζ44+ζ52−ζ116−1+i152−1+i152−1−i152−1−i1520000000000000000000
χ374444-2-2-2-2-4-1-1-1-1221+i1521−i1521+i1521−i1521+i1521−i1521+i1521−i1520−2i32i3−5−55511ζ4−ζ68+ζ76−ζ92ζ4−ζ68+ζ76−ζ92ζ28−ζ44+ζ52−ζ116ζ28−ζ44+ζ52−ζ116−ζ28+ζ44−ζ52+ζ116−ζ28+ζ44−ζ52+ζ116−ζ4+ζ68−ζ76+ζ92−ζ4+ζ68−ζ76+ζ92−1−i152−1−i152−1+i152−1+i1520000000000000000000
χ384444-2-2-2-2-4-1-1-1-1221+i1521−i1521+i1521−i1521+i1521−i1521+i1521−i15202i3−2i355−5−511−ζ4+ζ68−ζ76+ζ92−ζ4+ζ68−ζ76+ζ92−ζ28+ζ44−ζ52+ζ116−ζ28+ζ44−ζ52+ζ116ζ28−ζ44+ζ52−ζ116ζ28−ζ44+ζ52−ζ116ζ4−ζ68+ζ76−ζ92ζ4−ζ68+ζ76−ζ92−1−i152−1−i152−1+i152−1+i1520000000000000000000
χ3944-4-444-4-404-4-440044-4-4-4-4440000000000000000000000000000000000000000
χ4044-4-444-4-40-111-100-1-11111-1-1000ζ4−ζ28+ζ44+ζ52−ζ68−ζ76+ζ92−ζ116−ζ4+ζ28−ζ44−ζ52+ζ68+ζ76−ζ92+ζ116ζ4+ζ28+ζ44−ζ52+ζ68−ζ76−ζ92−ζ116−ζ4−ζ28−ζ44+ζ52−ζ68+ζ76+ζ92+ζ116−55ζ4−ζ28+ζ44+ζ52−ζ68−ζ76+ζ92−ζ116−ζ4+ζ28−ζ44−ζ52+ζ68+ζ76−ζ92+ζ116ζ4+ζ28+ζ44−ζ52+ζ68−ζ76−ζ92−ζ116−ζ4−ζ28−ζ44+ζ52−ζ68+ζ76+ζ92+ζ116ζ4−ζ28+ζ44+ζ52−ζ68−ζ76+ζ92−ζ116−ζ4+ζ28−ζ44−ζ52+ζ68+ζ76−ζ92+ζ116ζ4+ζ28+ζ44−ζ52+ζ68−ζ76−ζ92−ζ116−ζ4−ζ28−ζ44+ζ52−ζ68+ζ76+ζ92+ζ116−55−550000000000000000000
χ4144-4-444-4-40-111-100-1-11111-1-1000−ζ4+ζ28−ζ44−ζ52+ζ68+ζ76−ζ92+ζ116ζ4−ζ28+ζ44+ζ52−ζ68−ζ76+ζ92−ζ116−ζ4−ζ28−ζ44+ζ52−ζ68+ζ76+ζ92+ζ116ζ4+ζ28+ζ44−ζ52+ζ68−ζ76−ζ92−ζ116−55−ζ4+ζ28−ζ44−ζ52+ζ68+ζ76−ζ92+ζ116ζ4−ζ28+ζ44+ζ52−ζ68−ζ76+ζ92−ζ116−ζ4−ζ28−ζ44+ζ52−ζ68+ζ76+ζ92+ζ116ζ4+ζ28+ζ44−ζ52+ζ68−ζ76−ζ92−ζ116−ζ4+ζ28−ζ44−ζ52+ζ68+ζ76−ζ92+ζ116ζ4−ζ28+ζ44+ζ52−ζ68−ζ76+ζ92−ζ116−ζ4−ζ28−ζ44+ζ52−ζ68+ζ76+ζ92+ζ116ζ4+ζ28+ζ44−ζ52+ζ68−ζ76−ζ92−ζ116−55−550000000000000000000
χ4244-4-444-4-40-111-100-1-11111-1-1000ζ4+ζ28+ζ44−ζ52+ζ68−ζ76−ζ92−ζ116−ζ4−ζ28−ζ44+ζ52−ζ68+ζ76+ζ92+ζ116−ζ4+ζ28−ζ44−ζ52+ζ68+ζ76−ζ92+ζ116ζ4−ζ28+ζ44+ζ52−ζ68−ζ76+ζ92−ζ1165−5ζ4+ζ28+ζ44−ζ52+ζ68−ζ76−ζ92−ζ116−ζ4−ζ28−ζ44+ζ52−ζ68+ζ76+ζ92+ζ116−ζ4+ζ28−ζ44−ζ52+ζ68+ζ76−ζ92+ζ116ζ4−ζ28+ζ44+ζ52−ζ68−ζ76+ζ92−ζ116ζ4+ζ28+ζ44−ζ52+ζ68−ζ76−ζ92−ζ116−ζ4−ζ28−ζ44+ζ52−ζ68+ζ76+ζ92+ζ116−ζ4+ζ28−ζ44−ζ52+ζ68+ζ76−ζ92+ζ116ζ4−ζ28+ζ44+ζ52−ζ68−ζ76+ζ92−ζ1165−55−50000000000000000000
χ4344-4-444-4-40-111-100-1-11111-1-1000−ζ4−ζ28−ζ44+ζ52−ζ68+ζ76+ζ92+ζ116ζ4+ζ28+ζ44−ζ52+ζ68−ζ76−ζ92−ζ116ζ4−ζ28+ζ44+ζ52−ζ68−ζ76+ζ92−ζ116−ζ4+ζ28−ζ44−ζ52+ζ68+ζ76−ζ92+ζ1165−5−ζ4−ζ28−ζ44+ζ52−ζ68+ζ76+ζ92+ζ116ζ4+ζ28+ζ44−ζ52+ζ68−ζ76−ζ92−ζ116ζ4−ζ28+ζ44+ζ52−ζ68−ζ76+ζ92−ζ116−ζ4+ζ28−ζ44−ζ52+ζ68+ζ76−ζ92+ζ116−ζ4−ζ28−ζ44+ζ52−ζ68+ζ76+ζ92+ζ116ζ4+ζ28+ζ44−ζ52+ζ68−ζ76−ζ92−ζ116ζ4−ζ28+ζ44+ζ52−ζ68−ζ76+ζ92−ζ116−ζ4+ζ28−ζ44−ζ52+ζ68+ζ76−ζ92+ζ1165−55−50000000000000000000
χ4444-4-4-2-22204-4-44−2i32i3-2-22222-2-200000000000000000−2i32i32i3−2i30000000000000000000
χ4544-4-4-2-22204-4-442i3−2i3-2-22222-2-2000000000000000002i3−2i3−2i32i30000000000000000000
χ4644-4-4-2-2220-111-1−2i32i31−i1521+i152−1+i152−1−i152−1+i152−1−i1521−i1521+i152000ζ4+ζ28+ζ44−ζ52+ζ68−ζ76−ζ92−ζ116−ζ4−ζ28−ζ44+ζ52−ζ68+ζ76+ζ92+ζ116−ζ4+ζ28−ζ44−ζ52+ζ68+ζ76−ζ92+ζ116ζ4−ζ28+ζ44+ζ52−ζ68−ζ76+ζ92−ζ1165−5−ζ28−ζ44+ζ52+ζ116ζ28+ζ44−ζ52−ζ116ζ4−ζ68−ζ76+ζ92−ζ4+ζ68+ζ76−ζ92−ζ4−ζ68+ζ76+ζ92ζ4+ζ68−ζ76−ζ92−ζ28+ζ44+ζ52−ζ116ζ28−ζ44−ζ52+ζ116ζ28−ζ44+ζ52−ζ116−ζ28+ζ44−ζ52+ζ116−ζ4+ζ68−ζ76+ζ92ζ4−ζ68+ζ76−ζ920000000000000000000
χ4744-4-4-2-2220-111-1−2i32i31−i1521+i152−1+i152−1−i152−1+i152−1−i1521−i1521+i152000−ζ4−ζ28−ζ44+ζ52−ζ68+ζ76+ζ92+ζ116ζ4+ζ28+ζ44−ζ52+ζ68−ζ76−ζ92−ζ116ζ4−ζ28+ζ44+ζ52−ζ68−ζ76+ζ92−ζ116−ζ4+ζ28−ζ44−ζ52+ζ68+ζ76−ζ92+ζ1165−5ζ28+ζ44−ζ52−ζ116−ζ28−ζ44+ζ52+ζ116−ζ4+ζ68+ζ76−ζ92ζ4−ζ68−ζ76+ζ92ζ4+ζ68−ζ76−ζ92−ζ4−ζ68+ζ76+ζ92ζ28−ζ44−ζ52+ζ116−ζ28+ζ44+ζ52−ζ116ζ28−ζ44+ζ52−ζ116−ζ28+ζ44−ζ52+ζ116−ζ4+ζ68−ζ76+ζ92ζ4−ζ68+ζ76−ζ920000000000000000000
χ4844-4-4-2-2220-111-1−2i32i31+i1521−i152−1−i152−1+i152−1−i152−1+i1521+i1521−i152000ζ4−ζ28+ζ44+ζ52−ζ68−ζ76+ζ92−ζ116−ζ4+ζ28−ζ44−ζ52+ζ68+ζ76−ζ92+ζ116ζ4+ζ28+ζ44−ζ52+ζ68−ζ76−ζ92−ζ116−ζ4−ζ28−ζ44+ζ52−ζ68+ζ76+ζ92+ζ116−55−ζ4+ζ68+ζ76−ζ92ζ4−ζ68−ζ76+ζ92−ζ28−ζ44+ζ52+ζ116ζ28+ζ44−ζ52−ζ116ζ28−ζ44−ζ52+ζ116−ζ28+ζ44+ζ52−ζ116−ζ4−ζ68+ζ76+ζ92ζ4+ζ68−ζ76−ζ92ζ4−ζ68+ζ76−ζ92−ζ4+ζ68−ζ76+ζ92−ζ28+ζ44−ζ52+ζ116ζ28−ζ44+ζ52−ζ1160000000000000000000
χ4944-4-4-2-2220-111-1−2i32i31+i1521−i152−1−i152−1+i152−1−i152−1+i1521+i1521−i152000−ζ4+ζ28−ζ44−ζ52+ζ68+ζ76−ζ92+ζ116ζ4−ζ28+ζ44+ζ52−ζ68−ζ76+ζ92−ζ116−ζ4−ζ28−ζ44+ζ52−ζ68+ζ76+ζ92+ζ116ζ4+ζ28+ζ44−ζ52+ζ68−ζ76−ζ92−ζ116−55ζ4−ζ68−ζ76+ζ92−ζ4+ζ68+ζ76−ζ92ζ28+ζ44−ζ52−ζ116−ζ28−ζ44+ζ52+ζ116−ζ28+ζ44+ζ52−ζ116ζ28−ζ44−ζ52+ζ116ζ4+ζ68−ζ76−ζ92−ζ4−ζ68+ζ76+ζ92ζ4−ζ68+ζ76−ζ92−ζ4+ζ68−ζ76+ζ92−ζ28+ζ44−ζ52+ζ116ζ28−ζ44+ζ52−ζ1160000000000000000000
χ5044-4-4-2-2220-111-12i3−2i31−i1521+i152−1+i152−1−i152−1+i152−1−i1521−i1521+i152000ζ4−ζ28+ζ44+ζ52−ζ68−ζ76+ζ92−ζ116−ζ4+ζ28−ζ44−ζ52+ζ68+ζ76−ζ92+ζ116ζ4+ζ28+ζ44−ζ52+ζ68−ζ76−ζ92−ζ116−ζ4−ζ28−ζ44+ζ52−ζ68+ζ76+ζ92+ζ116−55ζ28−ζ44−ζ52+ζ116−ζ28+ζ44+ζ52−ζ116−ζ4−ζ68+ζ76+ζ92ζ4+ζ68−ζ76−ζ92−ζ4+ζ68+ζ76−ζ92ζ4−ζ68−ζ76+ζ92−ζ28−ζ44+ζ52+ζ116ζ28+ζ44−ζ52−ζ116−ζ28+ζ44−ζ52+ζ116ζ28−ζ44+ζ52−ζ116ζ4−ζ68+ζ76−ζ92−ζ4+ζ68−ζ76+ζ920000000000000000000
χ5144-4-4-2-2220-111-12i3−2i31−i1521+i152−1+i152−1−i152−1+i152−1−i1521−i1521+i152000−ζ4+ζ28−ζ44−ζ52+ζ68+ζ76−ζ92+ζ116ζ4−ζ28+ζ44+ζ52−ζ68−ζ76+ζ92−ζ116−ζ4−ζ28−ζ44+ζ52−ζ68+ζ76+ζ92+ζ116ζ4+ζ28+ζ44−ζ52+ζ68−ζ76−ζ92−ζ116−55−ζ28+ζ44+ζ52−ζ116ζ28−ζ44−ζ52+ζ116ζ4+ζ68−ζ76−ζ92−ζ4−ζ68+ζ76+ζ92ζ4−ζ68−ζ76+ζ92−ζ4+ζ68+ζ76−ζ92ζ28+ζ44−ζ52−ζ116−ζ28−ζ44+ζ52+ζ116−ζ28+ζ44−ζ52+ζ116ζ28−ζ44+ζ52−ζ116ζ4−ζ68+ζ76−ζ92−ζ4+ζ68−ζ76+ζ920000000000000000000
χ5244-4-4-2-2220-111-12i3−2i31+i1521−i152−1−i152−1+i152−1−i152−1+i1521+i1521−i152000ζ4+ζ28+ζ44−ζ52+ζ68−ζ76−ζ92−ζ116−ζ4−ζ28−ζ44+ζ52−ζ68+ζ76+ζ92+ζ116−ζ4+ζ28−ζ44−ζ52+ζ68+ζ76−ζ92+ζ116ζ4−ζ28+ζ44+ζ52−ζ68−ζ76+ζ92−ζ1165−5−ζ4−ζ68+ζ76+ζ92ζ4+ζ68−ζ76−ζ92−ζ28+ζ44+ζ52−ζ116ζ28−ζ44−ζ52+ζ116−ζ28−ζ44+ζ52+ζ116ζ28+ζ44−ζ52−ζ116ζ4−ζ68−ζ76+ζ92−ζ4+ζ68+ζ76−ζ92−ζ4+ζ68−ζ76+ζ92ζ4−ζ68+ζ76−ζ92ζ28−ζ44+ζ52−ζ116−ζ28+ζ44−ζ52+ζ1160000000000000000000
χ5344-4-4-2-2220-111-12i3−2i31+i1521−i152−1−i152−1+i152−1−i152−1+i1521+i1521−i152000−ζ4−ζ28−ζ44+ζ52−ζ68+ζ76+ζ92+ζ116ζ4+ζ28+ζ44−ζ52+ζ68−ζ76−ζ92−ζ116ζ4−ζ28+ζ44+ζ52−ζ68−ζ76+ζ92−ζ116−ζ4+ζ28−ζ44−ζ52+ζ68+ζ76−ζ92+ζ1165−5ζ4+ζ68−ζ76−ζ92−ζ4−ζ68+ζ76+ζ92ζ28−ζ44−ζ52+ζ116−ζ28+ζ44+ζ52−ζ116ζ28+ζ44−ζ52−ζ116−ζ28−ζ44+ζ52+ζ116−ζ4+ζ68+ζ76−ζ92ζ4−ζ68−ζ76+ζ92−ζ4+ζ68−ζ76+ζ92ζ4−ζ68+ζ76−ζ92ζ28−ζ44+ζ52−ζ116−ζ28+ζ44−ζ52+ζ1160000000000000000000
χ544-44-4-22-22044-4-400-2-2-2-22222000000000000000000000040-400-2200000000000
χ554-44-4-22-22044-4-400-2-2-2-222220000000000000000000000-404002-200000000000
χ564-4-44-222-204-44-400-2-222-2-22200000000000000000000040-40-220000000000000
χ574-4-44-222-204-44-400-2-222-2-222000000000000000000000-40402-20000000000000
χ588-88-88-88-80-2-22200-2-2-2-222220000000000000000000000000000000000000000
χ598-88-8-44-440-2-222001−i151+i151−i151+i15−1+i15−1−i15−1+i15−1−i150000000000000000000000000000000000000000
χ608-88-8-44-440-2-222001+i151−i151+i151−i15−1−i15−1+i15−1−i15−1+i150000000000000000000000000000000000000000
χ618-8-888-8-880-22-2200-2-222-2-2220000000000000000000000000000000000000000
χ628-8-88-444-40-22-22001−i151+i15−1+i15−1−i151−i151+i15−1+i15−1−i150000000000000000000000000000000000000000
χ638-8-88-444-40-22-22001+i151−i15−1−i15−1+i151+i151−i15−1−i15−1+i150000000000000000000000000000000000000000

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