Finite Group Databasebeta

← Group #10697413

Character table — Group #10697413

Order 768.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60
size11112222222222444444444488888888888888881616161616161616161616164848484848484848
order122234466612121212244444661212444412121212121212121212121224668812122424242444448888
χ1111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1
χ31111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-11-11-111-1-1
χ41111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-11-11-1-111
χ5111111111111111111111111-1-1-1-11111-1-1-1-1-1-1-1-11111-1-111-1-1-1-11-11-1-1-111
χ6111111111111111111111111-1-1-1-11111-1-1-1-1-1-1-1-11111-1-111-1-1-1-1-11-1111-1-1
χ7111111111111111111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-111-1-111111111-1-1-1-1
χ8111111111111111111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-111-1-11111-1-1-1-11111
χ9222222222222222-2-22-2-222220000-2-2-2-20000000000002-20022-2-200000000
χ10222222222222222-2-22-2-222220000-2-2-2-2000000000000-2200-2-22200000000
χ1122222222222222-22-2-22-2-2-2-2-2000022-2-200000000000000000000020-20000
χ1222222222222222-22-2-22-2-2-2-2-2000022-2-2000000000000000000000-2020000
χ1322222222222222-2-22-2-22-2-2-2-20000-2-2220000000000000000000020-200000
χ1422222222222222-2-22-2-22-2-2-2-20000-2-22200000000000000000000-20200000
χ1522222-2-2222-2-2-2-222-2-2-2222-2-200002-22-2000000000000000000000000002-2
χ1622222-2-2222-2-2-2-222-2-2-2222-2-200002-22-200000000000000000000000000-22
χ1722222-2-2222-2-2-2-22-22-22-222-2-20000-22-220000000000000000000000002-200
χ1822222-2-2222-2-2-2-22-22-22-222-2-20000-22-22000000000000000000000000-2200
χ1922222-2-2222-2-2-2-2-2222-2-2-2-2222i2i−2i−2i2-2-222i2i2i2i−2i−2i−2i−2i00000000000000000000
χ2022222-2-2222-2-2-2-2-2222-2-2-2-222−2i−2i2i2i2-2-22−2i−2i−2i−2i2i2i2i2i00000000000000000000
χ2122222-2-2222-2-2-2-2-2-2-2222-2-2220000-222-2000000002-22200-2-2000000000000
χ2222222-2-2222-2-2-2-2-2-2-2222-2-2220000-222-200000000-22-2-20022000000000000
χ232222-122-1-1-1-1-1-1-1222222-1-1-1-12222-1-1-1-1-1-1-1-1-1-1-1-122-1-122-1-1-1-1-1-100000000
χ242222-122-1-1-1-1-1-1-1222222-1-1-1-12222-1-1-1-1-1-1-1-1-1-1-1-1-2-211-2-211111100000000
χ252222-122-1-1-1-1-1-1-1222222-1-1-1-1-2-2-2-2-1-1-1-11111111122-1-1-2-2-1-1111100000000
χ262222-122-1-1-1-1-1-1-1222222-1-1-1-1-2-2-2-2-1-1-1-111111111-2-2112211-1-1-1-100000000
χ272222-122-1-1-1-1-1-1-12-2-22-2-2-1-1-1-100001111−i3−i3i3i3−i3−i3i3i300−i3i32-2−i3i3-1-11100000000
χ282222-122-1-1-1-1-1-1-12-2-22-2-2-1-1-1-100001111−i3−i3i3i3−i3−i3i3i300i3−i3-22i3−i311-1-100000000
χ292222-122-1-1-1-1-1-1-12-2-22-2-2-1-1-1-100001111i3i3−i3−i3i3i3−i3−i300−i3i3-22−i3i311-1-100000000
χ302222-122-1-1-1-1-1-1-12-2-22-2-2-1-1-1-100001111i3i3−i3−i3i3i3−i3−i300i3−i32-2i3−i3-1-11100000000
χ312222-1-2-2-1-1-11111-2222-2-211-1-12i2i−2i−2i-111-1−i−i−i−iiiii00−i3i300i3−i33−33−300000000
χ322222-1-2-2-1-1-11111-2222-2-211-1-12i2i−2i−2i-111-1−i−i−i−iiiii00i3−i300−i3i3−33−3300000000
χ332222-1-2-2-1-1-11111-2222-2-211-1-1−2i−2i2i2i-111-1iiii−i−i−i−i00−i3i300i3−i3−33−3300000000
χ342222-1-2-2-1-1-11111-2222-2-211-1-1−2i−2i2i2i-111-1iiii−i−i−i−i00i3−i300−i3i33−33−300000000
χ352222-1-2-2-1-1-11111-2-2-222211-1-100001-1-1133−3−3−3−3332-2-1-100113−3−3300000000
χ362222-1-2-2-1-1-11111-2-2-222211-1-100001-1-1133−3−3−3−333-221100-1-1−333−300000000
χ372222-1-2-2-1-1-11111-2-2-222211-1-100001-1-11−3−33333−3−32-2-1-10011−333−300000000
χ382222-1-2-2-1-1-11111-2-2-222211-1-100001-1-11−3−33333−3−3-221100-1-13−3−3300000000
χ394444-244-2-2-2-2-2-2-2-44-4-44-422220000-2-2220000000000000000000000000000
χ404444-244-2-2-2-2-2-2-2-4-44-4-442222000022-2-20000000000000000000000000000
χ414444-2-4-4-2-2-2222244-4-4-44-2-2220000-22-220000000000000000000000000000
χ424444-2-4-4-2-2-222224-44-44-4-2-22200002-22-20000000000000000000000000000
χ434-4-4444-4-4-4444-4-400000000002i−2i2i−2i00002i−2i2i−2i2i−2i2i−2i00000000000000000000
χ444-4-4444-4-4-4444-4-40000000000−2i2i−2i2i0000−2i2i−2i2i−2i2i−2i2i00000000000000000000
χ454-4-444-44-4-44-4-44400000000002-2-2200002-22-2-22-2200000000000000000000
χ464-4-444-44-4-44-4-4440000000000-222-20000-22-222-22-200000000000000000000
χ474-4-44-24-422-2-2-222000000−2i32i3−2i32i32i−2i2i−2i00002ζ7−2ζ72ζ11−2ζ112ζ7−2ζ72ζ11−2ζ1100000000000000000000
χ484-4-44-24-422-2-2-222000000−2i32i3−2i32i3−2i2i−2i2i0000−2ζ72ζ7−2ζ112ζ11−2ζ72ζ7−2ζ112ζ1100000000000000000000
χ494-4-44-24-422-2-2-2220000002i3−2i32i3−2i32i−2i2i−2i00002ζ11−2ζ112ζ7−2ζ72ζ11−2ζ112ζ7−2ζ700000000000000000000
χ504-4-44-24-422-2-2-2220000002i3−2i32i3−2i3−2i2i−2i2i0000−2ζ112ζ11−2ζ72ζ7−2ζ112ζ11−2ζ72ζ700000000000000000000
χ514-4-44-2-4422-222-2-2000000−2i32i32i3−2i32-2-220000−1−i31+i3−1+i31−i31+i3−1−i31−i3−1+i300000000000000000000
χ524-4-44-2-4422-222-2-2000000−2i32i32i3−2i3-222-200001+i3−1−i31−i3−1+i3−1−i31+i3−1+i31−i300000000000000000000
χ534-4-44-2-4422-222-2-20000002i3−2i3−2i32i32-2-220000−1+i31−i3−1−i31+i31−i3−1+i31+i3−1−i300000000000000000000
χ544-4-44-2-4422-222-2-20000002i3−2i3−2i32i3-222-200001−i3−1+i31+i3−1−i3−1+i31−i3−1−i31+i300000000000000000000
χ5588-8-88008-8-800000000000000000000000000000000000000000000000000
χ5688-8-8-400-44443−4343−430000000000000000000000000000000000000000000000
χ5788-8-8-400-444−4343−43430000000000000000000000000000000000000000000000
χ588-88-8800-88-800000000000000000000000000000000000000000000000000
χ598-88-8-4004-4443−43−43430000000000000000000000000000000000000000000000
χ608-88-8-4004-44−434343−430000000000000000000000000000000000000000000000

Here ζ is a primitive root of unity of order 12 (ζ12 = 1); i = ζ3.