Finite Group Databasebeta

← Group #10714874

Character table — Group #10714874

Order 768.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63
size1111222222222244444488888888888888888888888816161616161616161624242424484848484848
order122222366666664444444444441212121212121212121212121212121212124441212121212124444888888
χ1111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1
χ31111111111111111111111-1-1-1-11111111111-1-1-1-1-1-1-1-11-1-111-1-1-1-1111111-1-1-1-1
χ41111111111111111111111-1-1-1-11111111111-1-1-1-1-1-1-1-11-1-111-1-1-1-1-1-1-1-1-1-11111
χ511111111111111111111-1-111-1-1111111-1-1-1-11111-1-1-1-1-11-1-1-111-1-11111-1-111-1-1
χ611111111111111111111-1-111-1-1111111-1-1-1-11111-1-1-1-1-11-1-1-111-1-1-1-1-1-111-1-111
χ711111111111111111111-1-1-1-111111111-1-1-1-1-1-1-1-11111-1-11-1-1-1-1111111-1-1-1-111
χ811111111111111111111-1-1-1-111111111-1-1-1-1-1-1-1-11111-1-11-1-1-1-111-1-1-1-11111-1-1
χ9222222222222222-2-22-2-200002222-2-2-2-200000000222200-20000-2-20000000000
χ10222222222222222-2-22-2-20000-2-222-2-2-2-200000000-2-2-2-20020000220000000000
χ1122222222222222-22-2-22-2002200-2-222-2-20000222200000-2000-2-2000000000000
χ1222222222222222-22-2-22-200-2-200-2-222-2-20000-2-2-2-200000200022000000000000
χ1322222222222222-2-22-2-22220000-2-2-2-222222200000000-200-2-200000000000000
χ1422222222222222-2-22-2-22-2-20000-2-2-2-222-2-2-2-2000000002002200000000000000
χ15222222-1-1-1-1-1-1-1-1222222222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1222-1-1-1-1-1-10000000000
χ16222222-1-1-1-1-1-1-1-122222222-2-2-2-2-1-1-1-1-1-1-1-1-1-1111111112-2-2-1-111110000000000
χ17222222-1-1-1-1-1-1-1-1222222-2-222-2-2-1-1-1-1-1-11111-1-1-1-11111-22-211-1-1110000000000
χ18222222-1-1-1-1-1-1-1-1222222-2-2-2-222-1-1-1-1-1-111111111-1-1-1-1-2-221111-1-10000000000
χ19222222-1-1-1-1-1-1-1-12-2-22-2-2000022-1-11111−i3−i3i3i3−i3−i3i3i3-1-1-1-100-2−i3i3−i3i3110000000000
χ20222222-1-1-1-1-1-1-1-12-2-22-2-2000022-1-11111i3i3−i3−i3i3i3−i3−i3-1-1-1-100-2i3−i3i3−i3110000000000
χ21222222-1-1-1-1-1-1-1-12-2-22-2-20000-2-2-1-11111−i3−i3i3i3i3i3−i3−i31111002−i3i3i3−i3-1-10000000000
χ22222222-1-1-1-1-1-1-1-12-2-22-2-20000-2-2-1-11111i3i3−i3−i3−i3−i3i3i31111002i3−i3−i3i3-1-10000000000
χ23222222-1-1-1-1-1-1-1-1-22-2-22-200220011-1-111−i3−i3i3i3-1-1-1-1−i3−i3i3i30-20i3−i311−i3i30000000000
χ24222222-1-1-1-1-1-1-1-1-22-2-22-200220011-1-111i3i3−i3−i3-1-1-1-1i3i3−i3−i30-20−i3i311i3−i30000000000
χ25222222-1-1-1-1-1-1-1-1-22-2-22-200-2-20011-1-111−i3−i3i3i31111i3i3−i3−i3020i3−i3-1-1i3−i30000000000
χ26222222-1-1-1-1-1-1-1-1-22-2-22-200-2-20011-1-111i3i3−i3−i31111−i3−i3i3i3020−i3i3-1-1−i3i30000000000
χ27222222-1-1-1-1-1-1-1-1-2-22-2-222200001111-1-1-1-1-1-1−i3−i3i3i3−i3−i3i3i3-20011i3−i3i3−i30000000000
χ28222222-1-1-1-1-1-1-1-1-2-22-2-222200001111-1-1-1-1-1-1i3i3−i3−i3i3i3−i3−i3-20011−i3i3−i3i30000000000
χ29222222-1-1-1-1-1-1-1-1-2-22-2-22-2-200001111-1-11111−i3−i3i3i3i3i3−i3−i3200-1-1i3−i3−i3i30000000000
χ30222222-1-1-1-1-1-1-1-1-2-22-2-22-2-200001111-1-11111i3i3−i3−i3−i3−i3i3i3200-1-1−i3i3i3−i30000000000
χ3122-2-22-2222-22-2-2-222-2-2-220000002-22-22-200000000000000000000000002-20000
χ3222-2-22-2222-22-2-2-222-2-2-220000002-22-22-20000000000000000000000000-220000
χ3322-2-22-2222-22-2-2-22-22-22-20000002-2-22-220000000000000000000000000002-200
χ3422-2-22-2222-22-2-2-22-22-22-20000002-2-22-22000000000000000000000000000-2200
χ3522-2-22-2222-22-2-2-2-2222-2-2000000-222-2-22000000000000000000000000000002-2
χ3622-2-22-2222-22-2-2-2-2222-2-2000000-222-2-2200000000000000000000000000000-22
χ3722-2-22-2222-22-2-2-2-2-2-2222000000-22-222-20000000000000000000002i−2i2i−2i000000
χ3822-2-22-2222-22-2-2-2-2-2-2222000000-22-222-2000000000000000000000−2i2i−2i2i000000
χ394444-4-44-4-444-4-4400000000000000000000000000000000000000022-2-2000000
χ404444-4-44-4-444-4-44000000000000000000000000000000000000000-2-222000000
χ4144-4-44-4-2-2-22-222244-4-4-44000000-22-22-220000000000000000000000000000000
χ4244-4-44-4-2-2-22-22224-44-44-4000000-222-22-20000000000000000000000000000000
χ4344-4-44-4-2-2-22-2222-4444-4-40000002-2-222-20000000000000000000000000000000
χ4444-4-44-4-2-2-22-2222-4-4-44440000002-22-2-220000000000000000000000000000000
χ4544-4-4-444-4-4-4444-40000000000000000000000000000000000000002i−2i−2i2i000000
χ4644-4-4-444-4-4-4444-4000000000000000000000000000000000000000−2i2i2i−2i000000
χ474-4-4400400-4-40040000002-22i−2i2i−2i0000002-22-22i−2i2i−2i2i−2i2i−2i0000000000000000000
χ484-4-4400400-4-40040000002-2−2i2i−2i2i0000002-22-2−2i2i−2i2i−2i2i−2i2i0000000000000000000
χ494-4-4400400-4-4004000000-222i−2i−2i2i000000-22-222i−2i2i−2i−2i2i−2i2i0000000000000000000
χ504-4-4400400-4-4004000000-22−2i2i2i−2i000000-22-22−2i2i−2i2i2i−2i2i−2i0000000000000000000
χ514-4-4400-2−2i32i322−2i32i3-20000002-22i−2i2i−2i000000−1−i31+i3−1+i31−i32ζ11−2ζ112ζ7−2ζ72ζ11−2ζ112ζ7−2ζ70000000000000000000
χ524-4-4400-2−2i32i322−2i32i3-20000002-2−2i2i−2i2i000000−1−i31+i3−1+i31−i3−2ζ112ζ11−2ζ72ζ7−2ζ112ζ11−2ζ72ζ70000000000000000000
χ534-4-4400-2−2i32i322−2i32i3-2000000-222i−2i−2i2i0000001+i3−1−i31−i3−1+i32ζ11−2ζ112ζ7−2ζ7−2ζ112ζ11−2ζ72ζ70000000000000000000
χ544-4-4400-2−2i32i322−2i32i3-2000000-22−2i2i2i−2i0000001+i3−1−i31−i3−1+i3−2ζ112ζ11−2ζ72ζ72ζ11−2ζ112ζ7−2ζ70000000000000000000
χ554-4-4400-22i3−2i3222i3−2i3-20000002-22i−2i2i−2i000000−1+i31−i3−1−i31+i32ζ7−2ζ72ζ11−2ζ112ζ7−2ζ72ζ11−2ζ110000000000000000000
χ564-4-4400-22i3−2i3222i3−2i3-20000002-2−2i2i−2i2i000000−1+i31−i3−1−i31+i3−2ζ72ζ7−2ζ112ζ11−2ζ72ζ7−2ζ112ζ110000000000000000000
χ574-4-4400-22i3−2i3222i3−2i3-2000000-222i−2i−2i2i0000001−i3−1+i31+i3−1−i32ζ7−2ζ72ζ11−2ζ11−2ζ72ζ7−2ζ112ζ110000000000000000000
χ584-4-4400-22i3−2i3222i3−2i3-2000000-22−2i2i2i−2i0000001−i3−1+i31+i3−1−i3−2ζ72ζ7−2ζ112ζ112ζ7−2ζ72ζ11−2ζ110000000000000000000
χ598888-8-8-444-4-444-40000000000000000000000000000000000000000000000000
χ6088-8-8-88-4444-4-4-440000000000000000000000000000000000000000000000000
χ618-88-8008008-800-80000000000000000000000000000000000000000000000000
χ628-88-800-4−4i34i3-444i3−4i340000000000000000000000000000000000000000000000000
χ638-88-800-44i3−4i3-44−4i34i340000000000000000000000000000000000000000000000000

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