Finite Group Databasebeta

← Group #11746772

Character table — Group #11746772

Order 960.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78
size11112222224444444444444444444455558888888888888888881010101010102020202020202020303030303030303060606060
order124423461212568810121515202024242424303060606060224410203030404040406060120120120120120120120120246612126881224242424888888888888
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1
χ3111111111111111111111111111111-1-1-1-1111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1iiii−i−i−i−iii−i−i
χ4111111111111111111111111111111-1-1-1-1111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1−i−i−i−iiiii−i−iii
χ5111111111111-1-1111111-1-1-1-111111111111111-1-1-1-111-1-1-1-1-1-1-1-11111111-1-11-1-1-1-111111111-1-1-1-1
χ6111111111111-1-1111111-1-1-1-111111111111111-1-1-1-111-1-1-1-1-1-1-1-11111111-1-11-1-1-1-1-1-1-1-1-1-1-1-11111
χ7111111111111-1-1111111-1-1-1-1111111-1-1-1-11111-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-11111iiii−i−i−i−i−i−iii
χ8111111111111-1-1111111-1-1-1-1111111-1-1-1-11111-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-11111−i−i−i−iiiiiii−i−i
χ911-1-1-1111-1-11-1i−i1111-1-1ii−i−i11-1-1-1-111-1-1-11-1-1ii−i−i11iiii−i−i−i−i-1111-1-1-1i−i1ii−i−i11-1-111-1-1i−ii−i
χ1011-1-1-1111-1-11-1i−i1111-1-1ii−i−i11-1-1-1-111-1-1-11-1-1ii−i−i11iiii−i−i−i−i-1111-1-1-1i−i1ii−i−i-1-111-1-111−ii−ii
χ1111-1-1-1111-1-11-1i−i1111-1-1ii−i−i11-1-1-1-1-1-111-11-1-1ii−i−i11iiii−i−i−i−i1-1-1-1111−ii-1−i−iiiii−i−i−i−iii-111-1
χ1211-1-1-1111-1-11-1i−i1111-1-1ii−i−i11-1-1-1-1-1-111-11-1-1ii−i−i11iiii−i−i−i−i1-1-1-1111−ii-1−i−iii−i−iiiii−i−i1-1-11
χ1311-1-1-1111-1-11-1−ii1111-1-1−i−iii11-1-1-1-111-1-1-11-1-1−i−iii11−i−i−i−iiiii-1111-1-1-1−ii1−i−iii11-1-111-1-1−ii−ii
χ1411-1-1-1111-1-11-1−ii1111-1-1−i−iii11-1-1-1-111-1-1-11-1-1−i−iii11−i−i−i−iiiii-1111-1-1-1−ii1−i−iii-1-111-1-111i−ii−i
χ1511-1-1-1111-1-11-1−ii1111-1-1−i−iii11-1-1-1-1-1-111-11-1-1−i−iii11−i−i−i−iiiii1-1-1-1111i−i-1ii−i−iii−i−i−i−iii1-1-11
χ1611-1-1-1111-1-11-1−ii1111-1-1−i−iii11-1-1-1-1-1-111-11-1-1−i−iii11−i−i−i−iiiii1-1-1-1111i−i-1ii−i−i−i−iiiii−i−i-111-1
χ1722222-12-1-1-12-1222-1-1-122-1-1-1-1-1-1-1-1-1-1222222-1-12222-1-1-1-1-1-1-1-1-1-122-1-1-1-1-122-1-1-1-1-1000000000000
χ1822222-12-1-1-12-1222-1-1-122-1-1-1-1-1-1-1-1-1-1-2-2-2-222-1-12222-1-1-1-1-1-1-1-1-1-1-2-211111-2-211111000000000000
χ1922222-12-1-1-12-1-2-22-1-1-1221111-1-1-1-1-1-1222222-1-1-2-2-2-2-1-11111111122-1-1-1-1-1-2-2-11111000000000000
χ2022222-12-1-1-12-1-2-22-1-1-1221111-1-1-1-1-1-1-2-2-2-222-1-1-2-2-2-2-1-111111111-2-211111221-1-1-1-1000000000000
χ212222-22-22222-2002-2222200002222222222-2-2-2-20000-2-200000000-2-22222-200-20000000000000000
χ222222-22-22222-2002-222220000222222-2-2-2-2-2-2-2-20000-2-20000000022-2-2-2-220020000000000000000
χ232222-2-1-2-1-1-1210021-1-122−i3i3−i3i3-1-1-1-1-1-12222-2-211000011−i3−i3i3i3−i3−i3i3i3-2-2-1-1-1-11001−i3i3−i3i3000000000000
χ242222-2-1-2-1-1-1210021-1-122−i3i3−i3i3-1-1-1-1-1-1-2-2-2-2-2-211000011−i3−i3i3i3−i3−i3i3i3221111-100-1i3−i3i3−i3000000000000
χ252222-2-1-2-1-1-1210021-1-122i3−i3i3−i3-1-1-1-1-1-12222-2-211000011i3i3−i3−i3i3i3−i3−i3-2-2-1-1-1-11001i3−i3i3−i3000000000000
χ262222-2-1-2-1-1-1210021-1-122i3−i3i3−i3-1-1-1-1-1-1-2-2-2-2-2-211000011i3i3−i3−i3i3i3−i3−i3221111-100-1−i3i3−i3i3000000000000
χ2722-2-222-22-2-222002-222-2-2000022-2-2-2-222-2-22-2220000-2-2000000002-222-2-2200-20000000000000000
χ2822-2-222-22-2-222002-222-2-2000022-2-2-2-2-2-2222-2220000-2-200000000-22-2-222-20020000000000000000
χ2922-2-22-1-2-1112-10021-1-1-2-23−3−33-1-1111122-2-22-2-1-100001133−3−3−3−3332-2-1-111-10013−3−33000000000000
χ3022-2-22-1-2-1112-10021-1-1-2-23−3−33-1-11111-2-2222-2-1-100001133−3−3−3−333-2211-1-1100-1−333−3000000000000
χ3122-2-22-1-2-1112-10021-1-1-2-2−333−3-1-1111122-2-22-2-1-1000011−3−33333−3−32-2-1-111-1001−333−3000000000000
χ3222-2-22-1-2-1112-10021-1-1-2-2−333−3-1-11111-2-2222-2-1-1000011−3−33333−3−3-2211-1-1100-13−3−33000000000000
χ3322-2-2-2-12-111212i−2i2-1-1-1-2-2−i−iii-1-1111122-2-2-22112i2i−2i−2i-1-1−i−i−i−iiiii-22-1-11112i−2i-1−i−iii000000000000
χ3422-2-2-2-12-111212i−2i2-1-1-1-2-2−i−iii-1-11111-2-222-22112i2i−2i−2i-1-1−i−i−i−iiiii2-211-1-1-1−2i2i1ii−i−i000000000000
χ3522-2-2-2-12-11121−2i2i2-1-1-1-2-2ii−i−i-1-1111122-2-2-2211−2i−2i2i2i-1-1iiii−i−i−i−i-22-1-1111−2i2i-1ii−i−i000000000000
χ3622-2-2-2-12-11121−2i2i2-1-1-1-2-2ii−i−i-1-11111-2-222-2211−2i−2i2i2i-1-1iiii−i−i−i−i2-211-1-1-12i−2i1−i−iii000000000000
χ372-22i−2i020-22i−2i2000-20222i−2i0000-2-22i2i−2i−2i2-22i−2i000000000000000000002-22i−2i000000002−2−i2i22−2−i2i20000
χ382-22i−2i020-22i−2i2000-20222i−2i0000-2-22i2i−2i−2i2-22i−2i000000000000000000002-22i−2i00000000−22i2−i2−22i2−i20000
χ392-22i−2i020-22i−2i2000-20222i−2i0000-2-22i2i−2i−2i-22−2i2i00000000000000000000-22−2i2i00000000−i2i2−22i2−i22−20000
χ402-22i−2i020-22i−2i2000-20222i−2i0000-2-22i2i−2i−2i-22−2i2i00000000000000000000-22−2i2i00000000i2−i22−2−i2i2−220000
χ412-2−2i2i020-2−2i2i2000-2022−2i2i0000-2-2−2i−2i2i2i2-2−2i2i000000000000000000002-2−2i2i000000002−2i2−i22−2i2−i20000
χ422-2−2i2i020-2−2i2i2000-2022−2i2i0000-2-2−2i−2i2i2i2-2−2i2i000000000000000000002-2−2i2i00000000−22−i2i2−22−i2i20000
χ432-2−2i2i020-2−2i2i2000-2022−2i2i0000-2-2−2i−2i2i2i-222i−2i00000000000000000000-222i−2i00000000−i2i22−2i2−i2−220000
χ442-2−2i2i020-2−2i2i2000-2022−2i2i0000-2-2−2i−2i2i2i-222i−2i00000000000000000000-222i−2i00000000i2−i2−22−i2i22−20000
χ454444444444-1444-14-1-1-1-14444-1-1-1-1-1-10000-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-100000000000000000000000000
χ464444444444-14-4-4-14-1-1-1-1-4-4-4-4-1-1-1-1-1-10000-1-1-1-11111-1-11111111100000000000000000000000000
χ4744444-24-2-2-2-1-244-1-21−i1521+i152-1-1-2-2-2-21−i1521+i1521−i1521+i1521−i1521+i1520000-1-11−i1521+i152-1-1-1-11−i1521+i1521−i1521+i1521−i1521+i1521−i1521+i1521−i1521+i15200000000000000000000000000
χ4844444-24-2-2-2-1-244-1-21+i1521−i152-1-1-2-2-2-21+i1521−i1521+i1521−i1521+i1521−i1520000-1-11+i1521−i152-1-1-1-11+i1521−i1521+i1521−i1521+i1521−i1521+i1521−i1521+i1521−i15200000000000000000000000000
χ4944444-24-2-2-2-1-2-4-4-1-21−i1521+i152-1-122221−i1521+i1521−i1521+i1521−i1521+i1520000-1-11−i1521+i15211111−i1521+i152−1+i152−1−i152−1+i152−1−i152−1+i152−1−i152−1+i152−1−i15200000000000000000000000000
χ5044444-24-2-2-2-1-2-4-4-1-21+i1521−i152-1-122221+i1521−i1521+i1521−i1521+i1521−i1520000-1-11+i1521−i15211111+i1521−i152−1−i152−1+i152−1−i152−1+i152−1−i152−1+i152−1−i152−1+i15200000000000000000000000000
χ514444-44-4444-1-400-1-4-1-1-1-10000-1-1-1-1-1-100001111−55−5511−555−5−555−500000000000000000000000000
χ524444-44-4444-1-400-1-4-1-1-1-10000-1-1-1-1-1-1000011115−55−5115−5−555−5−5500000000000000000000000000
χ534444-4-2-4-2-2-2-1200-121−i1521+i152-1-1−2i32i3−2i32i31−i1521+i1521−i1521+i1521−i1521+i152000011−1+i152−1−i1525−55−5−1+i152−1−i152ζ28−ζ44+ζ52−ζ116ζ4−ζ68+ζ76−ζ92−ζ28+ζ44−ζ52+ζ116−ζ4+ζ68−ζ76+ζ92ζ28−ζ44+ζ52−ζ116ζ4−ζ68+ζ76−ζ92−ζ28+ζ44−ζ52+ζ116−ζ4+ζ68−ζ76+ζ9200000000000000000000000000
χ544444-4-2-4-2-2-2-1200-121−i1521+i152-1-12i3−2i32i3−2i31−i1521+i1521−i1521+i1521−i1521+i152000011−1+i152−1−i152−55−55−1+i152−1−i152−ζ28+ζ44−ζ52+ζ116−ζ4+ζ68−ζ76+ζ92ζ28−ζ44+ζ52−ζ116ζ4−ζ68+ζ76−ζ92−ζ28+ζ44−ζ52+ζ116−ζ4+ζ68−ζ76+ζ92ζ28−ζ44+ζ52−ζ116ζ4−ζ68+ζ76−ζ9200000000000000000000000000
χ554444-4-2-4-2-2-2-1200-121+i1521−i152-1-1−2i32i3−2i32i31+i1521−i1521+i1521−i1521+i1521−i152000011−1−i152−1+i152−55−55−1−i152−1+i152ζ4−ζ68+ζ76−ζ92ζ28−ζ44+ζ52−ζ116−ζ4+ζ68−ζ76+ζ92−ζ28+ζ44−ζ52+ζ116ζ4−ζ68+ζ76−ζ92ζ28−ζ44+ζ52−ζ116−ζ4+ζ68−ζ76+ζ92−ζ28+ζ44−ζ52+ζ11600000000000000000000000000
χ564444-4-2-4-2-2-2-1200-121+i1521−i152-1-12i3−2i32i3−2i31+i1521−i1521+i1521−i1521+i1521−i152000011−1−i152−1+i1525−55−5−1−i152−1+i152−ζ4+ζ68−ζ76+ζ92−ζ28+ζ44−ζ52+ζ116ζ4−ζ68+ζ76−ζ92ζ28−ζ44+ζ52−ζ116−ζ4+ζ68−ζ76+ζ92−ζ28+ζ44−ζ52+ζ116ζ4−ζ68+ζ76−ζ92ζ28−ζ44+ζ52−ζ11600000000000000000000000000
χ5744-4-444-44-4-4-1400-1-4-1-1110000-1-111110000-11-1-1−i5i5i5−i511−i5i5i5−i5i5−i5−i5i500000000000000000000000000
χ5844-4-444-44-4-4-1400-1-4-1-1110000-1-111110000-11-1-1i5−i5−i5i511i5−i5−i5i5−i5i5i5−i500000000000000000000000000
χ5944-4-44-2-4-222-1-200-121−i1521+i1521123−23−23231−i1521+i152−1+i152−1−i152−1+i152−1−i1520000-111−i1521+i152i5−i5−i5i5−1+i152−1−i152ζ14−ζ22+ζ86−ζ118ζ38−ζ46+ζ62−ζ94−ζ14+ζ22−ζ86+ζ118−ζ38+ζ46−ζ62+ζ94−ζ14+ζ22−ζ86+ζ118−ζ38+ζ46−ζ62+ζ94ζ14−ζ22+ζ86−ζ118ζ38−ζ46+ζ62−ζ9400000000000000000000000000
χ6044-4-44-2-4-222-1-200-121−i1521+i15211−232323−231−i1521+i152−1+i152−1−i152−1+i152−1−i1520000-111−i1521+i152−i5i5i5−i5−1+i152−1−i152−ζ14+ζ22−ζ86+ζ118−ζ38+ζ46−ζ62+ζ94ζ14−ζ22+ζ86−ζ118ζ38−ζ46+ζ62−ζ94ζ14−ζ22+ζ86−ζ118ζ38−ζ46+ζ62−ζ94−ζ14+ζ22−ζ86+ζ118−ζ38+ζ46−ζ62+ζ9400000000000000000000000000
χ6144-4-44-2-4-222-1-200-121+i1521−i1521123−23−23231+i1521−i152−1−i152−1+i152−1−i152−1+i1520000-111+i1521−i152−i5i5i5−i5−1−i152−1+i152ζ38−ζ46+ζ62−ζ94ζ14−ζ22+ζ86−ζ118−ζ38+ζ46−ζ62+ζ94−ζ14+ζ22−ζ86+ζ118−ζ38+ζ46−ζ62+ζ94−ζ14+ζ22−ζ86+ζ118ζ38−ζ46+ζ62−ζ94ζ14−ζ22+ζ86−ζ11800000000000000000000000000
χ6244-4-44-2-4-222-1-200-121+i1521−i15211−232323−231+i1521−i152−1−i152−1+i152−1−i152−1+i1520000-111+i1521−i152i5−i5−i5i5−1−i152−1+i152−ζ38+ζ46−ζ62+ζ94−ζ14+ζ22−ζ86+ζ118ζ38−ζ46+ζ62−ζ94ζ14−ζ22+ζ86−ζ118ζ38−ζ46+ζ62−ζ94ζ14−ζ22+ζ86−ζ118−ζ38+ζ46−ζ62+ζ94−ζ14+ζ22−ζ86+ζ11800000000000000000000000000
χ6344-4-4-4444-4-4-1-44i−4i-14-1-1114i4i−4i−4i-1-1111100001-111−i−iii-1-1−i−i−i−iiiii00000000000000000000000000
χ6444-4-4-4444-4-4-1-4−4i4i-14-1-111−4i−4i4i4i-1-1111100001-111ii−i−i-1-1iiii−i−i−i−i00000000000000000000000000
χ6544-4-4-4-24-222-124i−4i-1-21−i1521+i15211−2i−2i2i2i1−i1521+i152−1+i152−1−i152−1+i152−1−i15200001-1−1+i152−1−i152−i−iii1−i1521+i152ζ14+ζ22+ζ86+ζ118ζ38+ζ46+ζ62+ζ94ζ14+ζ22+ζ86+ζ118ζ38+ζ46+ζ62+ζ94−ζ14−ζ22−ζ86−ζ118−ζ38−ζ46−ζ62−ζ94−ζ14−ζ22−ζ86−ζ118−ζ38−ζ46−ζ62−ζ9400000000000000000000000000
χ6644-4-4-4-24-222-124i−4i-1-21+i1521−i15211−2i−2i2i2i1+i1521−i152−1−i152−1+i152−1−i152−1+i15200001-1−1−i152−1+i152−i−iii1+i1521−i152ζ38+ζ46+ζ62+ζ94ζ14+ζ22+ζ86+ζ118ζ38+ζ46+ζ62+ζ94ζ14+ζ22+ζ86+ζ118−ζ38−ζ46−ζ62−ζ94−ζ14−ζ22−ζ86−ζ118−ζ38−ζ46−ζ62−ζ94−ζ14−ζ22−ζ86−ζ11800000000000000000000000000
χ6744-4-4-4-24-222-12−4i4i-1-21−i1521+i152112i2i−2i−2i1−i1521+i152−1+i152−1−i152−1+i152−1−i15200001-1−1+i152−1−i152ii−i−i1−i1521+i152−ζ14−ζ22−ζ86−ζ118−ζ38−ζ46−ζ62−ζ94−ζ14−ζ22−ζ86−ζ118−ζ38−ζ46−ζ62−ζ94ζ14+ζ22+ζ86+ζ118ζ38+ζ46+ζ62+ζ94ζ14+ζ22+ζ86+ζ118ζ38+ζ46+ζ62+ζ9400000000000000000000000000
χ6844-4-4-4-24-222-12−4i4i-1-21+i1521−i152112i2i−2i−2i1+i1521−i152−1−i152−1+i152−1−i152−1+i15200001-1−1−i152−1+i152ii−i−i1+i1521−i152−ζ38−ζ46−ζ62−ζ94−ζ14−ζ22−ζ86−ζ118−ζ38−ζ46−ζ62−ζ94−ζ14−ζ22−ζ86−ζ118ζ38+ζ46+ζ62+ζ94ζ14+ζ22+ζ86+ζ118ζ38+ζ46+ζ62+ζ94ζ14+ζ22+ζ86+ζ11800000000000000000000000000
χ694-44i−4i0-202−2i2i4000-40-2-24i−4i000022−2i−2i2i2i4-44i−4i00000000000000000000-22−2i2i00000000000000000000
χ704-44i−4i0-202−2i2i4000-40-2-24i−4i000022−2i−2i2i2i-44−4i4i000000000000000000002-22i−2i00000000000000000000
χ714-4−4i4i0-2022i−2i4000-40-2-2−4i4i0000222i2i−2i−2i4-4−4i4i00000000000000000000-222i−2i00000000000000000000
χ724-4−4i4i0-2022i−2i4000-40-2-2−4i4i0000222i2i−2i−2i-444i−4i000000000000000000002-2−2i2i00000000000000000000
χ738-88i−8i080-88i−8i-200020-2-2−2i2i000022−2i−2i2i2i000000000000000000000000000000000000000000000000
χ748-88i−8i0-404−4i4i-2000201−i151+i15−2i2i0000−1+i15−1−i152ζ14+2ζ22+2ζ86+2ζ1182ζ38+2ζ46+2ζ62+2ζ94−2ζ14−2ζ22−2ζ86−2ζ118−2ζ38−2ζ46−2ζ62−2ζ94000000000000000000000000000000000000000000000000
χ758-88i−8i0-404−4i4i-2000201+i151−i15−2i2i0000−1−i15−1+i152ζ38+2ζ46+2ζ62+2ζ942ζ14+2ζ22+2ζ86+2ζ118−2ζ38−2ζ46−2ζ62−2ζ94−2ζ14−2ζ22−2ζ86−2ζ118000000000000000000000000000000000000000000000000
χ768-8−8i8i080-8−8i8i-200020-2-22i−2i0000222i2i−2i−2i000000000000000000000000000000000000000000000000
χ778-8−8i8i0-4044i−4i-2000201−i151+i152i−2i0000−1+i15−1−i15−2ζ14−2ζ22−2ζ86−2ζ118−2ζ38−2ζ46−2ζ62−2ζ942ζ14+2ζ22+2ζ86+2ζ1182ζ38+2ζ46+2ζ62+2ζ94000000000000000000000000000000000000000000000000
χ788-8−8i8i0-4044i−4i-2000201+i151−i152i−2i0000−1−i15−1+i15−2ζ38−2ζ46−2ζ62−2ζ94−2ζ14−2ζ22−2ζ86−2ζ1182ζ38+2ζ46+2ζ62+2ζ942ζ14+2ζ22+2ζ86+2ζ118000000000000000000000000000000000000000000000000

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