Finite Group Databasebeta

← Group #10714864

Character table — Group #10714864

Order 768.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63
size1111222222444444444444888888888888888888888816161616161616161624242424484848484848
order1222223666222244661212121244444466661212121212121212121212124881212242424244444444444
χ1111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1
χ311111111111111111111111111-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-1-111-1-11-111-1-1
χ411111111111111111111111111-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-11-1-111
χ51111111111111111111111-1-1-1-1111111-1-1-1-1-1-1-1-111111-1-111-1-1-1-1111111-1-1-1-1
χ61111111111111111111111-1-1-1-1111111-1-1-1-1-1-1-1-111111-1-111-1-1-1-1-1-1-1-1-1-11111
χ71111111111111111111111-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1111111-1-11-1-1-111
χ81111111111111111111111-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-111-1-11111-1-111-1111-1-1
χ922222222222-22-2-2-222-2-2-2-200000022-2-200000000000000000000000220-20000
χ1022222222222-22-2-2-222-2-2-2-200000022-2-200000000000000000000000-2-2020000
χ112222222222-22-22-2-222-2-2-2-2000000-2-2220000000000000000000002200-200000
χ122222222222-22-22-2-222-2-2-2-2000000-2-222000000000000000000000-2-200200000
χ132222222222-2-2-2-222222222000022-2-2-2-2000000002222-200-2-200000000000000
χ142222222222-2-2-2-2222222220000-2-2-2-2-2-200000000-2-2-2-22002200000000000000
χ15222222-1-1-1-1222222-1-1-1-1-1-1222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1222-1-1-1-1-1-10000000000
χ16222222-1-1-1-1222222-1-1-1-1-1-12222-2-2-1-1-1-1-1-1-1-1-1-1-1-11111-2-2-21111110000000000
χ17222222-1-1-1-1222222-1-1-1-1-1-1-2-2-2-222-1-1-1-111111111-1-1-1-12-2-2-1-111110000000000
χ18222222-1-1-1-1222222-1-1-1-1-1-1-2-2-2-2-2-2-1-1-1-1111111111111-22211-1-1-1-10000000000
χ19222222-1-1-1-1-2-2-2-222-1-1-1-1-1-10000221111−i3−i3i3i3−i3−i3i3i3-1-1-1-1-20011−i3−i3i3i30000000000
χ20222222-1-1-1-1-2-2-2-222-1-1-1-1-1-10000221111i3i3−i3−i3i3i3−i3−i3-1-1-1-1-20011i3i3−i3−i30000000000
χ21222222-1-1-1-1-2-2-2-222-1-1-1-1-1-10000-2-21111−i3−i3i3i3−i3−i3i3i31111200-1-1i3i3−i3−i30000000000
χ22222222-1-1-1-1-2-2-2-222-1-1-1-1-1-10000-2-21111i3i3−i3−i3i3i3−i3−i31111200-1-1−i3−i3i3i30000000000
χ2322-2-22-222-2-222-2-2-222-2-2-2220000002-22-200000000000002-2002-22-20000000000
χ2422-2-22-222-2-222-2-2-222-2-2-2220000002-22-20000000000000-2200-22-220000000000
χ2522-2-22-222-2-22-2-222-22-222-2-20000002-2-220000000000000000000000000002-200
χ2622-2-22-222-2-22-2-222-22-222-2-20000002-2-22000000000000000000000000000-2200
χ2722-2-22-222-2-2-222-22-22-222-2-2000000-222-2000000000000000000000000000002-2
χ2822-2-22-222-2-2-222-22-22-222-2-2000000-222-200000000000000000000000000000-22
χ2922-2-22-222-2-2-2-222-222-2-2-2222i−2i2i−2i00-22-222i−2i2i−2i2i−2i2i−2i00000000000000000000000
χ3022-2-22-222-2-2-2-222-222-2-2-222−2i2i−2i2i00-22-22−2i2i−2i2i−2i2i−2i2i00000000000000000000000
χ3122-2-22-2-1-11122-2-2-22-1111-1-1000000-11-113−3−333−3−3333−3−302-23−3-11-110000000000
χ3222-2-22-2-1-11122-2-2-22-1111-1-1000000-11-113−3−333−3−33−3−3330-22−331-11-10000000000
χ3322-2-22-2-1-11122-2-2-22-1111-1-1000000-11-11−333−3−333−333−3−30-223−31-11-10000000000
χ3422-2-22-2-1-11122-2-2-22-1111-1-1000000-11-11−333−3−333−3−3−33302-2−33-11-110000000000
χ3522-2-22-2-1-111-2-222-22-1111-1-12i−2i2i−2i001-11-1−ii−ii−ii−ii33−3−3000−33−i3i3i3−i30000000000
χ3622-2-22-2-1-111-2-222-22-1111-1-12i−2i2i−2i001-11-1−ii−ii−ii−ii−3−3330003−3i3−i3−i3i30000000000
χ3722-2-22-2-1-111-2-222-22-1111-1-1−2i2i−2i2i001-11-1i−ii−ii−ii−i33−3−3000−33i3−i3−i3i30000000000
χ3822-2-22-2-1-111-2-222-22-1111-1-1−2i2i−2i2i001-11-1i−ii−ii−ii−i−3−3330003−3−i3i3i3−i30000000000
χ39444444-2-2-2-24-44-4-4-4-2-22222000000-2-2220000000000000000000000000000000
χ40444444-2-2-2-2-44-44-4-4-2-2222200000022-2-20000000000000000000000000000000
χ414444-4-44444000000-4-4000022-2-20000002222-2-2-2-200000000000000000000000
χ424444-4-44444000000-4-40000-2-222000000-2-2-2-2222200000000000000000000000
χ434444-4-4-2-2-2-200000022−2i32i3−2i32i322-2-2000000−1−i3−1−i3−1+i3−1+i31+i31+i31−i31−i300000000000000000000000
χ444444-4-4-2-2-2-200000022−2i32i3−2i32i3-2-2220000001+i31+i31−i31−i3−1−i3−1−i3−1+i3−1+i300000000000000000000000
χ454444-4-4-2-2-2-2000000222i3−2i32i3−2i322-2-2000000−1+i3−1+i3−1−i3−1−i31−i31−i31+i31+i300000000000000000000000
χ464444-4-4-2-2-2-2000000222i3−2i32i3−2i3-2-2220000001−i31−i31+i31+i3−1+i3−1+i3−1−i3−1−i300000000000000000000000
χ4744-4-44-4-2-2224-4-444-4-22-2-222000000-222-20000000000000000000000000000000
χ4844-4-44-4-2-222-444-44-4-22-2-2220000002-2-220000000000000000000000000000000
χ4944-4-4-4444-4-4000000-4400002i−2i−2i2i0000002i−2i2i−2i−2i2i−2i2i00000000000000000000000
χ5044-4-4-4444-4-4000000-440000−2i2i2i−2i000000−2i2i−2i2i2i−2i2i−2i00000000000000000000000
χ5144-4-4-44-2-2220000002-2−2i32i32i3−2i32i−2i−2i2i0000002ζ7−2ζ72ζ11−2ζ11−2ζ72ζ7−2ζ112ζ1100000000000000000000000
χ5244-4-4-44-2-2220000002-2−2i32i32i3−2i3−2i2i2i−2i000000−2ζ72ζ7−2ζ112ζ112ζ7−2ζ72ζ11−2ζ1100000000000000000000000
χ5344-4-4-44-2-2220000002-22i3−2i3−2i32i32i−2i−2i2i0000002ζ11−2ζ112ζ7−2ζ7−2ζ112ζ11−2ζ72ζ700000000000000000000000
χ5444-4-4-44-2-2220000002-22i3−2i3−2i32i3−2i2i2i−2i000000−2ζ112ζ11−2ζ72ζ72ζ11−2ζ112ζ7−2ζ700000000000000000000000
χ554-44-4004-44-400000000000000002i−2i0000000000002i−2i2i−2i0000000002-22i−2i000000
χ564-44-4004-44-400000000000000002i−2i0000000000002i−2i2i−2i000000000-22−2i2i000000
χ574-44-4004-44-40000000000000000−2i2i000000000000−2i2i−2i2i0000000002-2−2i2i000000
χ584-44-4004-44-40000000000000000−2i2i000000000000−2i2i−2i2i000000000-222i−2i000000
χ598-88-800-44-4400000000000000004i−4i000000000000−2i2i−2i2i0000000000000000000
χ608-88-800-44-440000000000000000−4i4i0000000000002i−2i2i−2i0000000000000000000
χ618-8-88008-8-8800000000000000000000000000000000000000000000000000000
χ628-8-8800-444-4000000000000000000000000000000−2i32i32i3−2i30000000000000000000
χ638-8-8800-444-40000000000000000000000000000002i3−2i3−2i32i30000000000000000000

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