Finite Group Databasebeta

← Group #10692142

Character table — Group #10692142

Order 768.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60
size111122222244444444444488888888161616161616161616161616161616162424242424242424242424244848
order122234466622244466661212688881212122444661212121212122424242424448888888888
χ1111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ3111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1
χ4111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1111111
χ511111111111111111111111-1-1-1-111111-1-11111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-111
χ611111111111111111111111-1-1-1-111111-1-11111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1
χ711111111111111111111111-1-1-1-1111-1-111-1-1-1-11111-1-1-1-11111-1-1-1-11111-1-1
χ811111111111111111111111-1-1-1-1111-1-111-1-1-1-11111-1-1-1-1-1-1-1-11111-1-1-1-111
χ911111-1-11111-1-111-111-1-1-1-1-1ii−i−i11-11-1i−i11-1-1ii−i−iii−i−i1-11-1ii−i−iii−i−i1-1
χ1011111-1-11111-1-111-111-1-1-1-1-1ii−i−i11-11-1i−i11-1-1ii−i−iii−i−i-11-11−i−iii−i−iii-11
χ1111111-1-11111-1-111-111-1-1-1-1-1ii−i−i11-1-11−ii-1-111−i−iiiii−i−i1-11-1ii−i−i−i−iii-11
χ1211111-1-11111-1-111-111-1-1-1-1-1ii−i−i11-1-11−ii-1-111−i−iiiii−i−i-11-11−i−iiiii−i−i1-1
χ1311111-1-11111-1-111-111-1-1-1-1-1−i−iii11-11-1−ii11-1-1−i−iii−i−iii1-11-1−i−iii−i−iii1-1
χ1411111-1-11111-1-111-111-1-1-1-1-1−i−iii11-11-1−ii11-1-1−i−iii−i−iii-11-11ii−i−iii−i−i-11
χ1511111-1-11111-1-111-111-1-1-1-1-1−i−iii11-1-11i−i-1-111ii−i−i−i−iii1-11-1−i−iiiii−i−i-11
χ1611111-1-11111-1-111-111-1-1-1-1-1−i−iii11-1-11i−i-1-111ii−i−i−i−iii-11-11ii−i−i−i−iii1-1
χ1722222222222-2-2-2-2222-2-222-20000-2-22000000000000000000002-22-2000000
χ1822222222222-2-2-2-2222-2-222-20000-2-2200000000000000000000-22-22000000
χ192222222222-22-2-22-2-2-2-2-222200002-2-200000000000000002-2-220000000000
χ202222222222-22-2-22-2-2-2-2-222200002-2-20000000000000000-222-20000000000
χ212222222222-2-222-2-2-2-22222-22-22-2-22-20000000000002-22-200000000000000
χ222222222222-2-222-2-2-2-22222-2-22-22-22-2000000000000-22-2200000000000000
χ2322222-2-2222222-2-2-22222-2-220000-2-2-2000000000000000000002i−2i−2i2i000000
χ2422222-2-2222222-2-2-22222-2-220000-2-2-200000000000000000000−2i2i2i−2i000000
χ2522222-2-2222-22-22-22-2-2-2-2-2-222i−2i−2i2i-2220000000000002i−2i−2i2i00000000000000
χ2622222-2-2222-22-22-22-2-2-2-2-2-22−2i2i2i−2i-222000000000000−2i2i2i−2i00000000000000
χ2722222-2-2222-2-22-222-2-222-2-2-200002-22000000000000000022-2-20000000000
χ2822222-2-2222-2-22-222-2-222-2-2-200002-220000000000000000-2-2220000000000
χ292222-122-1-1-1222222-1-1-1-1-1-1-12222-1-1-12222-1-1-1-1-1-1-1-1-1-1-1-100000000000000
χ302222-122-1-1-1222222-1-1-1-1-1-1-12222-1-1-1-2-2-2-211111111-1-1-1-100000000000000
χ312222-122-1-1-1222222-1-1-1-1-1-1-1-2-2-2-2-1-1-122-2-2-1-1-1-11111111100000000000000
χ322222-122-1-1-1222222-1-1-1-1-1-1-1-2-2-2-2-1-1-1-2-2221111-1-1-1-1111100000000000000
χ332222-122-1-1-1-2-222-2-211-1-1-1-112-22-21-110000−i3i3−i3i3−i3i3−i3i3-11-1100000000000000
χ342222-122-1-1-1-2-222-2-211-1-1-1-112-22-21-110000i3−i3i3−i3i3−i3i3−i3-11-1100000000000000
χ352222-122-1-1-1-2-222-2-211-1-1-1-11-22-221-110000−i3i3−i3i3i3−i3i3−i31-11-100000000000000
χ362222-122-1-1-1-2-222-2-211-1-1-1-11-22-221-110000i3−i3i3−i3−i3i3−i3i31-11-100000000000000
χ372222-1-2-2-1-1-12-2-222-2-1-1111112i2i−2i−2i-1-112-22i−2i-1-111−i−iii−i−iii00000000000000
χ382222-1-2-2-1-1-12-2-222-2-1-1111112i2i−2i−2i-1-11-22−2i2i11-1-1ii−i−i−i−iii00000000000000
χ392222-1-2-2-1-1-12-2-222-2-1-111111−2i−2i2i2i-1-112-2−2i2i-1-111ii−i−iii−i−i00000000000000
χ402222-1-2-2-1-1-12-2-222-2-1-111111−2i−2i2i2i-1-11-222i−2i11-1-1−i−iiiii−i−i00000000000000
χ412222-1-2-2-1-1-1-22-22-22111111-12i−2i−2i2i1-1-10000−i3i3i3−i33−3−33−iii−i00000000000000
χ422222-1-2-2-1-1-1-22-22-22111111-12i−2i−2i2i1-1-10000i3−i3−i3i3−333−3−iii−i00000000000000
χ432222-1-2-2-1-1-1-22-22-22111111-1−2i2i2i−2i1-1-10000−i3i3i3−i3−333−3i−i−ii00000000000000
χ442222-1-2-2-1-1-1-22-22-22111111-1−2i2i2i−2i1-1-10000i3−i3−i3i33−3−33i−i−ii00000000000000
χ454444-244-2-2-24-4-4-4-44-2-222-2-22000022-2000000000000000000000000000000
χ464444-244-2-2-2-44-4-44-42222-2-2-20000-222000000000000000000000000000000
χ474444-2-4-4-2-2-2444-4-4-4-2-2-2-222-20000222000000000000000000000000000000
χ484444-2-4-4-2-2-2-4-44-44422-2-22220000-22-2000000000000000000000000000000
χ4944-4-444i−4i4-4-400000000004i−4i000000000000000000000000000000002ζ7+2ζ23−2ζ7−2ζ23−2ζ5−2ζ132ζ5+2ζ1300
χ5044-4-444i−4i4-4-400000000004i−4i00000000000000000000000000000000−2ζ7−2ζ232ζ7+2ζ232ζ5+2ζ13−2ζ5−2ζ1300
χ5144-4-44−4i4i4-4-40000000000−4i4i00000000000000000000000000000000−2ζ5−2ζ132ζ5+2ζ132ζ7+2ζ23−2ζ7−2ζ2300
χ5244-4-44−4i4i4-4-40000000000−4i4i000000000000000000000000000000002ζ5+2ζ13−2ζ5−2ζ13−2ζ7−2ζ232ζ7+2ζ2300
χ5388-8-8-48i−8i-4440000000000−4i4i00000000000000000000000000000000000000
χ5488-8-8-4−8i8i-44400000000004i−4i00000000000000000000000000000000000000
χ558-88-8800-88-800000000000000000000000000000000000000000000000000
χ568-88-8-4004-44000000−4i34i3000000000000000000000000000000000000000000
χ578-88-8-4004-440000004i3−4i3000000000000000000000000000000000000000000
χ588-8-88800-8-8800000000000000000000000000000000000000000000000000
χ598-8-88-40044-400000000−4i34i30000000000000000000000000000000000000000
χ608-8-88-40044-4000000004i3−4i30000000000000000000000000000000000000000

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