Finite Group Databasebeta

← Group #10704760

Character table — Group #10704760

Order 768.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63
size111122222244444444668888888888888888121212161616161616161616161616162424242424242424484848
order122222366644444466224488881212121212121212121224426688242424242424242444448888488
χ1111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111-1-1-1-11111111111111111-1-1-1-1-1-1-1-1-1-11111-1-1-1-11-1-1
χ311111111111111111111-1-1111111-1-1-1-11111111-1-1-1-1-11111-1-1-1-111-1-11111-1-1-1
χ411111111111111111111-1-1-1-1-1-111-1-1-1-11111111-1-1-111-1-1-1-1111111-1-1-1-1-1-1-111
χ5111111111111111111-1-11111111111111111-1-1-11111111111111-1-1-1-1-1-1-1-1-1-1-1
χ6111111111111111111-1-111-1-1-1-11111111111-1-1-1111-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-111
χ7111111111111111111-1-1-1-1111111-1-1-1-11111-1-1-1-1-1-1-1-11111-1-1-1-1-1-111-1-1-1-1111
χ8111111111111111111-1-1-1-1-1-1-1-111-1-1-1-11111-1-1-1-1-1-111-1-1-1-11111-1-11111111-1-1
χ9111111111111-1-1-1-1111111ii−i−i111111-1-1-1-11-1-1-1-1-1i−iii−i−iii−i−i1-111ii−i−i-1i−i
χ10111111111111-1-1-1-1111111−i−iii111111-1-1-1-11-1-1-1-1-1−ii−i−iii−i−iii1-111−i−iii-1−ii
χ11111111111111-1-1-1-11111-1-1ii−i−i11-1-1-1-1-1-1-1-11-1-1111−iiii−i−i−i−iii1-1-1-1ii−i−i1−ii
χ12111111111111-1-1-1-11111-1-1−i−iii11-1-1-1-1-1-1-1-11-1-1111i−i−i−iiiii−i−i1-1-1-1−i−iii1i−i
χ13111111111111-1-1-1-111-1-111ii−i−i111111-1-1-1-1-111-1-1-1i−iii−i−iii−i−i-11-1-1−i−iii1−ii
χ14111111111111-1-1-1-111-1-111−i−iii111111-1-1-1-1-111-1-1-1−ii−i−iii−i−iii-11-1-1ii−i−i1i−i
χ15111111111111-1-1-1-111-1-1-1-1ii−i−i11-1-1-1-1-1-1-1-1-111111−iiii−i−i−i−iii-1111−i−iii-1i−i
χ16111111111111-1-1-1-111-1-1-1-1−i−iii11-1-1-1-1-1-1-1-1-111111i−i−i−iiiii−i−i-1111ii−i−i-1−ii
χ172222222222-2-222-2-22222000000-2-2000022-2-22220000000000000-2-2000000000
χ182222222222-2-222-2-222-2-2000000-2-2000022-2-2-2-2-2000000000000022000000000
χ192222222222-2-2-2-2222222000000-2-20000-2-2222-2-20000000000000-22000000000
χ202222222222-2-2-2-22222-2-2000000-2-20000-2-222-22200000000000002-2000000000
χ21222222-1-1-1-1222222-1-100222222-1-1-1-1-1-1-1-1-1-10002-1-122-1-1-1-1-1-1-1-100000000000
χ22222222-1-1-1-1222222-1-10022-2-2-2-2-1-1-1-1-1-1-1-1-1-10002-1-1-2-21111111100000000000
χ23222222-1-1-1-1222222-1-100-2-22222-1-11111-1-1-1-1000-211-2-2-1-1-1-1111100000000000
χ24222222-1-1-1-1222222-1-100-2-2-2-2-2-2-1-11111-1-1-1-1000-211221111-1-1-1-100000000000
χ25222222-1-1-1-122-2-2-2-2-1-100222i2i−2i−2i-1-1-1-1-1-11111000-2112i−2i−i−iii−i−iii00000000000
χ26222222-1-1-1-122-2-2-2-2-1-10022−2i−2i2i2i-1-1-1-1-1-11111000-211−2i2iii−i−iii−i−i00000000000
χ27222222-1-1-1-122-2-2-2-2-1-100-2-22i2i−2i−2i-1-1111111110002-1-1−2i2i−i−iiiii−i−i00000000000
χ28222222-1-1-1-122-2-2-2-2-1-100-2-2−2i−2i2i2i-1-1111111110002-1-12i−2iii−i−i−i−iii00000000000
χ2922-2-2-222-22-22-22i−2i2i−2i2-2000000002-200002i−2i2i−2i000000000000000000002ζ7+2ζ23−2ζ7−2ζ23−2ζ5−2ζ132ζ5+2ζ13000
χ3022-2-2-222-22-22-22i−2i2i−2i2-2000000002-200002i−2i2i−2i00000000000000000000−2ζ7−2ζ232ζ7+2ζ232ζ5+2ζ13−2ζ5−2ζ13000
χ3122-2-2-222-22-22-2−2i2i−2i2i2-2000000002-20000−2i2i−2i2i00000000000000000000−2ζ5−2ζ132ζ5+2ζ132ζ7+2ζ23−2ζ7−2ζ23000
χ3222-2-2-222-22-22-2−2i2i−2i2i2-2000000002-20000−2i2i−2i2i000000000000000000002ζ5+2ζ13−2ζ5−2ζ13−2ζ7−2ζ232ζ7+2ζ23000
χ3322-2-2-222-22-2-222i−2i−2i2i2-200002ζ7+2ζ23−2ζ7−2ζ23−2ζ5−2ζ132ζ5+2ζ13-2200002i−2i−2i2i000000002ζ7+2ζ23−2ζ7−2ζ23−2ζ5−2ζ132ζ5+2ζ13000000000000000
χ3422-2-2-222-22-2-222i−2i−2i2i2-20000−2ζ7−2ζ232ζ7+2ζ232ζ5+2ζ13−2ζ5−2ζ13-2200002i−2i−2i2i00000000−2ζ7−2ζ232ζ7+2ζ232ζ5+2ζ13−2ζ5−2ζ13000000000000000
χ3522-2-2-222-22-2-22−2i2i2i−2i2-20000−2ζ5−2ζ132ζ5+2ζ132ζ7+2ζ23−2ζ7−2ζ23-220000−2i2i2i−2i00000000−2ζ5−2ζ132ζ5+2ζ132ζ7+2ζ23−2ζ7−2ζ23000000000000000
χ3622-2-2-222-22-2-22−2i2i2i−2i2-200002ζ5+2ζ13−2ζ5−2ζ13−2ζ7−2ζ232ζ7+2ζ23-220000−2i2i2i−2i000000002ζ5+2ζ13−2ζ5−2ζ13−2ζ7−2ζ232ζ7+2ζ23000000000000000
χ3722-2-2-22-11-11-222i−2i−2i2i-1100002ζ7+2ζ23−2ζ7−2ζ23−2ζ5−2ζ132ζ5+2ζ131-133−3−3−iii−i0000−i3i300−ζ7−ζ23ζ7+ζ23ζ5+ζ13−ζ5−ζ13ζ5−ζ13−ζ5+ζ13−ζ7+ζ23ζ7−ζ2300000000000
χ3822-2-2-22-11-11-222i−2i−2i2i-1100002ζ7+2ζ23−2ζ7−2ζ23−2ζ5−2ζ132ζ5+2ζ131-1−3−333−iii−i0000i3−i300−ζ7−ζ23ζ7+ζ23ζ5+ζ13−ζ5−ζ13−ζ5+ζ13ζ5−ζ13ζ7−ζ23−ζ7+ζ2300000000000
χ3922-2-2-22-11-11-222i−2i−2i2i-110000−2ζ7−2ζ232ζ7+2ζ232ζ5+2ζ13−2ζ5−2ζ131-133−3−3−iii−i0000−i3i300ζ7+ζ23−ζ7−ζ23−ζ5−ζ13ζ5+ζ13−ζ5+ζ13ζ5−ζ13ζ7−ζ23−ζ7+ζ2300000000000
χ4022-2-2-22-11-11-222i−2i−2i2i-110000−2ζ7−2ζ232ζ7+2ζ232ζ5+2ζ13−2ζ5−2ζ131-1−3−333−iii−i0000i3−i300ζ7+ζ23−ζ7−ζ23−ζ5−ζ13ζ5+ζ13ζ5−ζ13−ζ5+ζ13−ζ7+ζ23ζ7−ζ2300000000000
χ4122-2-2-22-11-11-22−2i2i2i−2i-110000−2ζ5−2ζ132ζ5+2ζ132ζ7+2ζ23−2ζ7−2ζ231-133−3−3i−i−ii0000i3−i300ζ5+ζ13−ζ5−ζ13−ζ7−ζ23ζ7+ζ23−ζ7+ζ23ζ7−ζ23ζ5−ζ13−ζ5+ζ1300000000000
χ4222-2-2-22-11-11-22−2i2i2i−2i-110000−2ζ5−2ζ132ζ5+2ζ132ζ7+2ζ23−2ζ7−2ζ231-1−3−333i−i−ii0000−i3i300ζ5+ζ13−ζ5−ζ13−ζ7−ζ23ζ7+ζ23ζ7−ζ23−ζ7+ζ23−ζ5+ζ13ζ5−ζ1300000000000
χ4322-2-2-22-11-11-22−2i2i2i−2i-1100002ζ5+2ζ13−2ζ5−2ζ13−2ζ7−2ζ232ζ7+2ζ231-133−3−3i−i−ii0000i3−i300−ζ5−ζ13ζ5+ζ13ζ7+ζ23−ζ7−ζ23ζ7−ζ23−ζ7+ζ23−ζ5+ζ13ζ5−ζ1300000000000
χ4422-2-2-22-11-11-22−2i2i2i−2i-1100002ζ5+2ζ13−2ζ5−2ζ13−2ζ7−2ζ232ζ7+2ζ231-1−3−333i−i−ii0000−i3i300−ζ5−ζ13ζ5+ζ13ζ7+ζ23−ζ7−ζ23−ζ7+ζ23ζ7−ζ23ζ5−ζ13−ζ5+ζ1300000000000
χ45444444-2-2-2-2-4-444-4-4-2-200000000220000-2-222000000000000000000000000000
χ46444444-2-2-2-2-4-4-4-444-2-20000000022000022-2-2000000000000000000000000000
χ474444-4-44444000000-4-4440000000000000000-400000000000000000000000000
χ484444-4-44444000000-4-4-4-40000000000000000400000000000000000000000000
χ4944-4-44-44-44-4000000-4400000000000000000004i−4i000000000000000000000000
χ5044-4-44-44-44-4000000-440000000000000000000−4i4i000000000000000000000000
χ5144-4-4-44-22-224-44i−4i4i−4i-2200000000-220000−2i2i−2i2i000000000000000000000000000
χ5244-4-4-44-22-224-4−4i4i−4i4i-2200000000-2200002i−2i2i−2i000000000000000000000000000
χ534-44-40044-4-4000000004-42i−2i0000002i−2i2i−2i00000000000000000000002i−2i0000000
χ544-44-40044-4-4000000004-4−2i2i000000−2i2i−2i2i0000000000000000000000−2i2i0000000
χ554-44-40044-4-400000000-442i−2i0000002i−2i2i−2i0000000000000000000000−2i2i0000000
χ564-44-40044-4-400000000-44−2i2i000000−2i2i−2i2i00000000000000000000002i−2i0000000
χ578888-8-8-4-4-4-400000044000000000000000000000000000000000000000000000
χ5888-8-88-8-44-440000004-4000000000000000000000000000000000000000000000
χ598-88-800-4-44400000000004i−4i000000−2i2i−2i2i0000000000000000000000000000000
χ608-88-800-4-4440000000000−4i4i0000002i−2i2i−2i0000000000000000000000000000000
χ618-8-88008-8-8800000000000000000000000000000000000000000000000000000
χ628-8-8800-444-4000000000000000000−2i32i32i3−2i30000000000000000000000000000000
χ638-8-8800-444-40000000000000000002i3−2i3−2i32i30000000000000000000000000000000

Here ζ is a primitive root of unity of order 24 (ζ24 = 1); i = ζ6.