Finite Group Databasebeta

← Group #11752449

Character table — Group #11752449

Order 960.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78
size11112222224444444444444444444455558888888888888888881010101010102020202020202020303030303030303060606060
order12223446664451010101212121212121515303030303030222220202020202060606060606060606060606044666644121212121212444444444444
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
χ51111111111-1-1111111-1-1-1-111111111111111-1-1-1-11111-1-1-1-1-1-1-1-1111111-1-111-1-1-1-111111111-1-1-1-1
χ61111111111-1-1111111-1-1-1-111111111111111-1-1-1-11111-1-1-1-1-1-1-1-1111111-1-111-1-1-1-1-1-1-1-1-1-1-1-11111
χ71111111111-1-1111111-1-1-1-111111111-1-1-1-111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-11111iiii−i−i−i−i−i−iii
χ81111111111-1-1111111-1-1-1-111111111-1-1-1-111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-11111−i−i−i−iiiiiii−i−i
χ911111-1-11111-11111-1-111-1-1111111111111-1-111-1-1-1-1-1-11111-1-1-1-1-1-111111-1-1-111-1-111-1-111-1-11-11-1
χ1011111-1-11111-11111-1-111-1-1111111111111-1-111-1-1-1-1-1-11111-1-1-1-1-1-111111-1-1-111-1-1-1-111-1-111-11-11
χ1111111-1-11111-11111-1-111-1-111111111-1-1-1-1-1-111-1-1-1-1-1-11111-1-1-1-111-1-1-1-1-1111-1-111ii−i−i−i−iiii−i−ii
χ1211111-1-11111-11111-1-111-1-111111111-1-1-1-1-1-111-1-1-1-1-1-11111-1-1-1-111-1-1-1-1-1111-1-111−i−iiiii−i−i−iii−i
χ1311111-1-1111-111111-1-1-1-111111111111111-1-1-1-111-1-1-1-1-1-1-1-11111-1-11111-11-1-1-1-11111-1-111-1-1-11-11
χ1411111-1-1111-111111-1-1-1-111111111111111-1-1-1-111-1-1-1-1-1-1-1-11111-1-11111-11-1-1-1-111-1-111-1-1111-11-1
χ1511111-1-1111-111111-1-1-1-11111111111-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1111111-1-1-1-11-11111-1-1ii−i−i−i−iii−iii−i
χ1611111-1-1111-111111-1-1-1-11111111111-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1111111-1-1-1-11-11111-1-1−i−iiiii−i−ii−i−ii
χ172222-122-1-1-1222222-1-1-1-1-1-1-1-1-1-1-1-1-1-12222222222-1-1-1-1-1-1-1-1-1-1-1-122-1-1-1-122-1-1-1-1-1-1000000000000
χ182222-122-1-1-1222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-2-2-2-2222222-1-1-1-1-1-1-1-1-1-1-1-1-2-21111-2-2111111000000000000
χ192222-122-1-1-1-2-22222-1-11111-1-1-1-1-1-1-1-1222222-2-2-2-2-1-1-1-11111111122-1-1-1-1-2-2-1-11111000000000000
χ202222-122-1-1-1-2-22222-1-11111-1-1-1-1-1-1-1-1-2-2-2-222-2-2-2-2-1-1-1-111111111-2-211112211-1-1-1-1000000000000
χ212222-1-2-2-1-1-12-2222211-1-111-1-1-1-1-1-1-1-12222-2-222-2-21111-1-1-1-11111-2-2-1-1-1-12-211-1-111000000000000
χ222222-1-2-2-1-1-12-2222211-1-111-1-1-1-1-1-1-1-1-2-2-2-2-2-222-2-21111-1-1-1-11111221111-22-1-111-1-1000000000000
χ232222-1-2-2-1-1-1-2222221111-1-1-1-1-1-1-1-1-1-12222-2-2-2-22211111111-1-1-1-1-2-2-1-1-1-1-221111-1-1000000000000
χ242222-1-2-2-1-1-1-2222221111-1-1-1-1-1-1-1-1-1-1-2-2-2-2-2-2-2-22211111111-1-1-1-12211112-2-1-1-1-111000000000000
χ2522-2-22002-2-20022-2-20000002222-2-2-2-222-2-20000000000000000000022-2-200000000002-2002-20000
χ2622-2-22002-2-20022-2-20000002222-2-2-2-222-2-20000000000000000000022-2-20000000000-2200-220000
χ2722-2-22002-2-20022-2-20000002222-2-2-2-2-2-22200000000000000000000-2-22200000000002i−2i00−2i2i0000
χ2822-2-22002-2-20022-2-20000002222-2-2-2-2-2-22200000000000000000000-2-2220000000000−2i2i002i−2i0000
χ292-22-2200-22-2002-22-200000022-2-222-2-22-22-2000000000000000000002-22-2000000002-2002-2000000
χ302-22-2200-22-2002-22-200000022-2-222-2-22-22-2000000000000000000002-22-200000000-2200-22000000
χ312-22-2200-22-2002-22-200000022-2-222-2-2-22-2200000000000000000000-22-22000000002i−2i00−2i2i000000
χ322-22-2200-22-2002-22-200000022-2-222-2-2-22-2200000000000000000000-22-2200000000−2i2i002i−2i000000
χ332-2-2222-2-2-22002-2-222-2000022-2-2-2-2222-2-222-2000022-2-2000000002-22-2-22002-20000000000000000
χ342-2-2222-2-2-22002-2-222-2000022-2-2-2-222-222-22-2000022-2-200000000-22-222-200-220000000000000000
χ352-2-222-22-2-22002-2-22-22000022-2-2-2-2222-2-22-220000-2-22200000000-222-2-2200-220000000000000000
χ362-2-222-22-2-22002-2-22-22000022-2-2-2-222-222-2-220000-2-222000000002-2-222-2002-20000000000000000
χ372-2-22-12-211-1002-2-22-11−i3i3−i3i3-1-11111-1-12-2-222-20000-1-111−i3−i3i3i3−i3−i3i3i32-2-111-100-11−i3i3−i3i3000000000000
χ382-2-22-12-211-1002-2-22-11−i3i3−i3i3-1-11111-1-1-222-22-20000-1-111−i3−i3i3i3−i3−i3i3i3-221-1-11001-1i3−i3i3−i3000000000000
χ392-2-22-12-211-1002-2-22-11i3−i3i3−i3-1-11111-1-12-2-222-20000-1-111i3i3−i3−i3i3i3−i3−i32-2-111-100-11i3−i3i3−i3000000000000
χ402-2-22-12-211-1002-2-22-11i3−i3i3−i3-1-11111-1-1-222-22-20000-1-111i3i3−i3−i3i3i3−i3−i3-221-1-11001-1−i3i3−i3i3000000000000
χ412-2-22-1-2211-1002-2-221-1−i3i3i3−i3-1-11111-1-12-2-22-22000011-1-1−i3−i3i3i3i3i3−i3−i3-22-111-1001-1−i3i3i3−i3000000000000
χ422-2-22-1-2211-1002-2-221-1−i3i3i3−i3-1-11111-1-1-222-2-22000011-1-1−i3−i3i3i3i3i3−i3−i32-21-1-1100-11i3−i3−i3i3000000000000
χ432-2-22-1-2211-1002-2-221-1i3−i3−i3i3-1-11111-1-12-2-22-22000011-1-1i3i3−i3−i3−i3−i3i3i3-22-111-1001-1i3−i3−i3i3000000000000
χ442-2-22-1-2211-1002-2-221-1i3−i3−i3i3-1-11111-1-1-222-2-22000011-1-1i3i3−i3−i3−i3−i3i3i32-21-1-1100-11−i3i3i3−i3000000000000
χ45444444444444-1-1-1-1444444-1-1-1-1-1-1-1-10000-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-100000000000000000000000000
χ464444444444-4-4-1-1-1-144-4-4-4-4-1-1-1-1-1-1-1-10000-1-11111-1-1-1-11111111100000000000000000000000000
χ4744444-4-44444-4-1-1-1-1-4-444-4-4-1-1-1-1-1-1-1-1000011-1-1111111-1-1-1-1111100000000000000000000000000
χ4844444-4-4444-44-1-1-1-1-4-4-4-444-1-1-1-1-1-1-1-100001111-1-111111111-1-1-1-100000000000000000000000000
χ494444-244-2-2-244-1-1-1-1-2-2-2-2-2-21−i1521+i1521−i1521+i1521−i1521+i1521−i1521+i1520000-1-1-1-1-1-11−i1521+i1521−i1521+i1521−i1521+i1521−i1521+i1521−i1521+i1521−i1521+i15200000000000000000000000000
χ504444-244-2-2-244-1-1-1-1-2-2-2-2-2-21+i1521−i1521+i1521−i1521+i1521−i1521+i1521−i1520000-1-1-1-1-1-11+i1521−i1521+i1521−i1521+i1521−i1521+i1521−i1521+i1521−i1521+i1521−i15200000000000000000000000000
χ514444-244-2-2-2-4-4-1-1-1-1-2-222221−i1521+i1521−i1521+i1521−i1521+i1521−i1521+i1520000-1-111111−i1521+i1521−i1521+i152−1+i152−1−i152−1+i152−1−i152−1+i152−1−i152−1+i152−1−i15200000000000000000000000000
χ524444-244-2-2-2-4-4-1-1-1-1-2-222221+i1521−i1521+i1521−i1521+i1521−i1521+i1521−i1520000-1-111111+i1521−i1521+i1521−i152−1−i152−1+i152−1−i152−1+i152−1−i152−1+i152−1−i152−1+i15200000000000000000000000000
χ534444-2-4-4-2-2-24-4-1-1-1-122-2-2221−i1521+i1521−i1521+i1521−i1521+i1521−i1521+i152000011-1-111−1+i152−1−i152−1+i152−1−i1521−i1521+i1521−i1521+i152−1+i152−1−i152−1+i152−1−i15200000000000000000000000000
χ544444-2-4-4-2-2-24-4-1-1-1-122-2-2221+i1521−i1521+i1521−i1521+i1521−i1521+i1521−i152000011-1-111−1−i152−1+i152−1−i152−1+i1521+i1521−i1521+i1521−i152−1−i152−1+i152−1−i152−1+i15200000000000000000000000000
χ554444-2-4-4-2-2-2-44-1-1-1-12222-2-21−i1521+i1521−i1521+i1521−i1521+i1521−i1521+i15200001111-1-1−1+i152−1−i152−1+i152−1−i152−1+i152−1−i152−1+i152−1−i1521−i1521+i1521−i1521+i15200000000000000000000000000
χ564444-2-4-4-2-2-2-44-1-1-1-12222-2-21+i1521−i1521+i1521−i1521+i1521−i1521+i1521−i15200001111-1-1−1−i152−1+i152−1−i152−1+i152−1−i152−1+i152−1−i152−1+i1521+i1521−i1521+i1521−i15200000000000000000000000000
χ5744-4-4-200-2220044-4-4000000-2-2-2-2222244-4-400000000000000000000-2-22200000000000000000000
χ5844-4-4-200-2220044-4-4000000-2-2-2-22222-4-4440000000000000000000022-2-200000000000000000000
χ594-44-4-2002-22004-44-4000000-2-222-2-2224-44-400000000000000000000-22-2200000000000000000000
χ604-44-4-2002-22004-44-4000000-2-222-2-222-44-44000000000000000000002-22-200000000000000000000
χ614-4-4444-4-4-4400-111-14-40000-1-11111-1-10000-11−55−55-1-111−555−5−555−500000000000000000000000000
χ624-4-4444-4-4-4400-111-14-40000-1-11111-1-10000-115−55−5-1-1115−5−555−5−5500000000000000000000000000
χ634-4-444-44-4-4400-111-1-440000-1-11111-1-100001-1−555−511-1-1−555−55−5−5500000000000000000000000000
χ644-4-444-44-4-4400-111-1-440000-1-11111-1-100001-15−5−5511-1-15−5−55−555−500000000000000000000000000
χ654-4-44-24-422-200-111-1-22−2i32i3−2i32i31−i1521+i152−1+i152−1−i152−1+i152−1−i1521−i1521+i1520000-115−55−51−i1521+i152−1+i152−1−i152ζ14−ζ22+ζ26−ζ58ζ2−ζ34+ζ38−ζ46−ζ14+ζ22−ζ26+ζ58−ζ2+ζ34−ζ38+ζ46ζ14−ζ22+ζ26−ζ58ζ2−ζ34+ζ38−ζ46−ζ14+ζ22−ζ26+ζ58−ζ2+ζ34−ζ38+ζ4600000000000000000000000000
χ664-4-44-24-422-200-111-1-22−2i32i3−2i32i31+i1521−i152−1−i152−1+i152−1−i152−1+i1521+i1521−i1520000-11−55−551+i1521−i152−1−i152−1+i152ζ2−ζ34+ζ38−ζ46ζ14−ζ22+ζ26−ζ58−ζ2+ζ34−ζ38+ζ46−ζ14+ζ22−ζ26+ζ58ζ2−ζ34+ζ38−ζ46ζ14−ζ22+ζ26−ζ58−ζ2+ζ34−ζ38+ζ46−ζ14+ζ22−ζ26+ζ5800000000000000000000000000
χ674-4-44-24-422-200-111-1-222i3−2i32i3−2i31−i1521+i152−1+i152−1−i152−1+i152−1−i1521−i1521+i1520000-11−55−551−i1521+i152−1+i152−1−i152−ζ14+ζ22−ζ26+ζ58−ζ2+ζ34−ζ38+ζ46ζ14−ζ22+ζ26−ζ58ζ2−ζ34+ζ38−ζ46−ζ14+ζ22−ζ26+ζ58−ζ2+ζ34−ζ38+ζ46ζ14−ζ22+ζ26−ζ58ζ2−ζ34+ζ38−ζ4600000000000000000000000000
χ684-4-44-24-422-200-111-1-222i3−2i32i3−2i31+i1521−i152−1−i152−1+i152−1−i152−1+i1521+i1521−i1520000-115−55−51+i1521−i152−1−i152−1+i152−ζ2+ζ34−ζ38+ζ46−ζ14+ζ22−ζ26+ζ58ζ2−ζ34+ζ38−ζ46ζ14−ζ22+ζ26−ζ58−ζ2+ζ34−ζ38+ζ46−ζ14+ζ22−ζ26+ζ58ζ2−ζ34+ζ38−ζ46ζ14−ζ22+ζ26−ζ5800000000000000000000000000
χ694-4-44-2-4422-200-111-12-2−2i32i32i3−2i31−i1521+i152−1+i152−1−i152−1+i152−1−i1521−i1521+i15200001-15−5−55−1+i152−1−i1521−i1521+i152ζ14−ζ22+ζ26−ζ58ζ2−ζ34+ζ38−ζ46−ζ14+ζ22−ζ26+ζ58−ζ2+ζ34−ζ38+ζ46−ζ14+ζ22−ζ26+ζ58−ζ2+ζ34−ζ38+ζ46ζ14−ζ22+ζ26−ζ58ζ2−ζ34+ζ38−ζ4600000000000000000000000000
χ704-4-44-2-4422-200-111-12-2−2i32i32i3−2i31+i1521−i152−1−i152−1+i152−1−i152−1+i1521+i1521−i15200001-1−555−5−1−i152−1+i1521+i1521−i152ζ2−ζ34+ζ38−ζ46ζ14−ζ22+ζ26−ζ58−ζ2+ζ34−ζ38+ζ46−ζ14+ζ22−ζ26+ζ58−ζ2+ζ34−ζ38+ζ46−ζ14+ζ22−ζ26+ζ58ζ2−ζ34+ζ38−ζ46ζ14−ζ22+ζ26−ζ5800000000000000000000000000
χ714-4-44-2-4422-200-111-12-22i3−2i3−2i32i31−i1521+i152−1+i152−1−i152−1+i152−1−i1521−i1521+i15200001-1−555−5−1+i152−1−i1521−i1521+i152−ζ14+ζ22−ζ26+ζ58−ζ2+ζ34−ζ38+ζ46ζ14−ζ22+ζ26−ζ58ζ2−ζ34+ζ38−ζ46ζ14−ζ22+ζ26−ζ58ζ2−ζ34+ζ38−ζ46−ζ14+ζ22−ζ26+ζ58−ζ2+ζ34−ζ38+ζ4600000000000000000000000000
χ724-4-44-2-4422-200-111-12-22i3−2i3−2i32i31+i1521−i152−1−i152−1+i152−1−i152−1+i1521+i1521−i15200001-15−5−55−1−i152−1+i1521+i1521−i152−ζ2+ζ34−ζ38+ζ46−ζ14+ζ22−ζ26+ζ58ζ2−ζ34+ζ38−ζ46ζ14−ζ22+ζ26−ζ58ζ2−ζ34+ζ38−ζ46ζ14−ζ22+ζ26−ζ58−ζ2+ζ34−ζ38+ζ46−ζ14+ζ22−ζ26+ζ5800000000000000000000000000
χ7388-8-88008-8-800-2-222000000-2-2-2-22222000000000000000000000000000000000000000000000000
χ7488-8-8-400-44400-2-2220000001−i151+i151−i151+i15−1+i15−1−i15−1+i15−1−i15000000000000000000000000000000000000000000000000
χ7588-8-8-400-44400-2-2220000001+i151−i151+i151−i15−1−i15−1+i15−1−i15−1+i15000000000000000000000000000000000000000000000000
χ768-88-8800-88-800-22-22000000-2-222-2-222000000000000000000000000000000000000000000000000
χ778-88-8-4004-4400-22-220000001−i151+i15−1+i15−1−i151−i151+i15−1+i15−1−i15000000000000000000000000000000000000000000000000
χ788-88-8-4004-4400-22-220000001+i151−i15−1−i15−1+i151+i151−i15−1−i15−1+i15000000000000000000000000000000000000000000000000

Here ζ is a primitive root of unity of order 60 (ζ60 = 1); i = ζ15.