Finite Group Databasebeta

← Group #10697407

Character table — Group #10697407

Order 768.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60
size11112222222222444444444488888888888888881616161616161616161616164848484848484848
order12223446661212121224444466121244441212121212121212121212124488121212122424242424448888
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
χ5111111111111111111111111-1-1-1-11111-1-1-1-1-1-1-1-111-1-11111-1-1-1-11-11-1-1-111
χ6111111111111111111111111-1-1-1-11111-1-1-1-1-1-1-1-111-1-11111-1-1-1-1-11-1111-1-1
χ7111111111111111111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-111-1-1-1-111111111-1-1-1-1
χ8111111111111111111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-111-1-1-1-11111-1-1-1-11111
χ9222222222222222-22-2-2-222220000-2-2-2-200000000002-2000022-2-200000000
χ10222222222222222-22-2-2-222220000-2-2-2-20000000000-220000-2-22200000000
χ1122222222222222-22-2-2-22-2-2-2-2000022-2-20000000000000000000020-200000
χ1222222222222222-22-2-2-22-2-2-2-2000022-2-200000000000000000000-20200000
χ1322222222222222-2-2-222-2-2-2-2-20000-2-22200000000000000000000020-20000
χ1422222222222222-2-2-222-2-2-2-2-20000-2-222000000000000000000000-2020000
χ1522222-2-2222-2-2-2-222-2-22-222-2-200002-22-20000000000000000000000002-200
χ1622222-2-2222-2-2-2-222-2-22-222-2-200002-22-2000000000000000000000000-2200
χ1722222-2-2222-2-2-2-22-2-22-2222-2-20000-22-22000000000000000000000000002-2
χ1822222-2-2222-2-2-2-22-2-22-2222-2-20000-22-2200000000000000000000000000-22
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
χ2122222-2-2222-2-2-2-2-2-22-222-2-2220000-222-2000000002-20022-2-2000000000000
χ2222222-2-2222-2-2-2-2-2-22-222-2-2220000-222-200000000-2200-2-222000000000000
χ232222-122-1-1-1-1-1-1-1222222-1-1-1-12222-1-1-1-1-1-1-1-1-1-1-1-12222-1-1-1-1-1-1-1-100000000
χ242222-122-1-1-1-1-1-1-1222222-1-1-1-12222-1-1-1-1-1-1-1-1-1-1-1-1-2-2-2-21111111100000000
χ252222-122-1-1-1-1-1-1-1222222-1-1-1-1-2-2-2-2-1-1-1-11111111122-2-2-1-1-1-1111100000000
χ262222-122-1-1-1-1-1-1-1222222-1-1-1-1-2-2-2-2-1-1-1-111111111-2-2221111-1-1-1-100000000
χ272222-122-1-1-1-1-1-1-12-22-2-2-2-1-1-1-100001111−i3−i3i3i3−i3−i3i3i3002-2−i3i3−i3i3-1-11100000000
χ282222-122-1-1-1-1-1-1-12-22-2-2-2-1-1-1-100001111−i3−i3i3i3−i3−i3i3i300-22i3−i3i3−i311-1-100000000
χ292222-122-1-1-1-1-1-1-12-22-2-2-2-1-1-1-100001111i3i3−i3−i3i3i3−i3−i3002-2i3−i3i3−i3-1-11100000000
χ302222-122-1-1-1-1-1-1-12-22-2-2-2-1-1-1-100001111i3i3−i3−i3i3i3−i3−i300-22−i3i3−i3i311-1-100000000
χ312222-1-2-2-1-1-11111-2222-2-211-1-12i2i−2i−2i-111-1−i−i−i−iiiii0000−i3i3i3−i33−33−300000000
χ322222-1-2-2-1-1-11111-2222-2-211-1-12i2i−2i−2i-111-1−i−i−i−iiiii0000i3−i3−i3i3−33−3300000000
χ332222-1-2-2-1-1-11111-2222-2-211-1-1−2i−2i2i2i-111-1iiii−i−i−i−i0000−i3i3i3−i3−33−3300000000
χ342222-1-2-2-1-1-11111-2222-2-211-1-1−2i−2i2i2i-111-1iiii−i−i−i−i0000i3−i3−i3i33−33−300000000
χ352222-1-2-2-1-1-11111-2-22-22211-1-100001-1-1133−3−3−3−3332-200-1-1113−3−3300000000
χ362222-1-2-2-1-1-11111-2-22-22211-1-100001-1-1133−3−3−3−333-220011-1-1−333−300000000
χ372222-1-2-2-1-1-11111-2-22-22211-1-100001-1-11−3−33333−3−32-200-1-111−333−300000000
χ382222-1-2-2-1-1-11111-2-22-22211-1-100001-1-11−3−33333−3−3-220011-1-13−3−3300000000
χ394444-244-2-2-2-2-2-2-2-44-4-4-4422220000-2-2220000000000000000000000000000
χ404444-244-2-2-2-2-2-2-2-4-4-444-42222000022-2-20000000000000000000000000000
χ414444-2-4-4-2-2-2222244-4-44-4-2-2220000-22-220000000000000000000000000000
χ424444-2-4-4-2-2-222224-4-44-44-2-22200002-22-20000000000000000000000000000
χ434-44-444-44-4-444-4-400000000002-22-200002-22-22-22-200000000000000000000
χ444-44-444-44-4-444-4-40000000000-22-220000-22-22-22-2200000000000000000000
χ454-44-44-444-4-4-4-44400000000002i−2i−2i2i00002i−2i2i−2i−2i2i−2i2i00000000000000000000
χ464-44-44-444-4-4-4-4440000000000−2i2i2i−2i0000−2i2i−2i2i2i−2i2i−2i00000000000000000000
χ474-44-4-24-4-222-2-222000000−2i32i3−2i32i32-22-20000−1−i31+i3−1+i31−i3−1−i31+i3−1+i31−i300000000000000000000
χ484-44-4-24-4-222-2-222000000−2i32i3−2i32i3-22-2200001+i3−1−i31−i3−1+i31+i3−1−i31−i3−1+i300000000000000000000
χ494-44-4-24-4-222-2-2220000002i3−2i32i3−2i32-22-20000−1+i31−i3−1−i31+i3−1+i31−i3−1−i31+i300000000000000000000
χ504-44-4-24-4-222-2-2220000002i3−2i32i3−2i3-22-2200001−i3−1+i31+i3−1−i31−i3−1+i31+i3−1−i300000000000000000000
χ514-44-4-2-44-22222-2-2000000−2i32i32i3−2i32i−2i−2i2i00002ζ7−2ζ72ζ11−2ζ11−2ζ72ζ7−2ζ112ζ1100000000000000000000
χ524-44-4-2-44-22222-2-2000000−2i32i32i3−2i3−2i2i2i−2i0000−2ζ72ζ7−2ζ112ζ112ζ7−2ζ72ζ11−2ζ1100000000000000000000
χ534-44-4-2-44-22222-2-20000002i3−2i3−2i32i32i−2i−2i2i00002ζ11−2ζ112ζ7−2ζ7−2ζ112ζ11−2ζ72ζ700000000000000000000
χ544-44-4-2-44-22222-2-20000002i3−2i3−2i32i3−2i2i2i−2i0000−2ζ112ζ11−2ζ72ζ72ζ11−2ζ112ζ7−2ζ700000000000000000000
χ5588-8-8800-88-800000000000000000000000000000000000000000000000000
χ5688-8-8-4004-4443−4343−430000000000000000000000000000000000000000000000
χ5788-8-8-4004-44−4343−43430000000000000000000000000000000000000000000000
χ588-8-88800-8-8800000000000000000000000000000000000000000000000000
χ598-8-88-40044-443−43−43430000000000000000000000000000000000000000000000
χ608-8-88-40044-4−434343−430000000000000000000000000000000000000000000000

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