Finite Group Databasebeta

← Group #10692161

Character table — Group #10692161

Order 768.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60
size111122222244444444444488888888161616161616161616161616161616162424242424242424242424244848
order122234466624444466121212124444121212122466881212121212122424242488888888888888
χ1111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ3111111111111111111111111111111-1-1-1-1-1-11111-1-1-1-1-1-111111111-1-1-1-1-1-1
χ4111111111111111111111111111111-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111
χ51111111111111111111111-1-1-1-111111111-1-1-1-1-1-111-1-1-1-11111-1-1-1-11111-1-1
χ61111111111111111111111-1-1-1-111111111-1-1-1-1-1-111-1-1-1-1-1-1-1-11111-1-1-1-111
χ71111111111111111111111-1-1-1-11111-1-1-1-111-1-1-1-1-1-111111111-1-1-1-1-1-1-1-111
χ81111111111111111111111-1-1-1-11111-1-1-1-111-1-1-1-1-1-11111-1-1-1-111111111-1-1
χ911111-1-11111-111-1-111-1-1111-11-1-1-1-111-1111-11-11-1-1-111-1-1ii−i−iii−i−iii−i−ii−i
χ1011111-1-11111-111-1-111-1-1111-11-1-1-1-111-1111-11-11-1-1-111-1-1−i−iii−i−iii−i−iii−ii
χ1111111-1-11111-111-1-111-1-1111-11-1-1-1-11-11-1-1-111-11-111-1-111ii−i−iii−i−i−i−iii−ii
χ1211111-1-11111-111-1-111-1-1111-11-1-1-1-11-11-1-1-111-11-111-1-111−i−iii−i−iiiii−i−ii−i
χ1311111-1-11111-111-1-111-1-111-11-11-1-1-111-111-11-11-11-1-1-1-111ii−i−i−i−iiiii−i−i−ii
χ1411111-1-11111-111-1-111-1-111-11-11-1-1-111-111-11-11-11-1-1-1-111−i−iiiii−i−i−i−iiii−i
χ1511111-1-11111-111-1-111-1-111-11-11-1-1-11-11-1-11-1-11-111111-1-1ii−i−i−i−iii−i−iiii−i
χ1611111-1-11111-111-1-111-1-111-11-11-1-1-11-11-1-11-1-11-111111-1-1−i−iiiii−i−iii−i−i−ii
χ1722222222222-2-2-22-22222-2-200002-2-2-200000000000000002-22-20000000000
χ1822222222222-2-2-22-22222-2-200002-2-2-20000000000000000-22-220000000000
χ192222222222-22-22-2-2-2-222222-2-22-22-2-20000002-2-2200000000000000000000
χ202222222222-22-22-2-2-2-22222-222-2-22-2-2000000-222-200000000000000000000
χ212222222222-2-22-2-22-2-222-2-20000-2-222000000000000000000002-22-2000000
χ222222222222-2-22-2-22-2-222-2-20000-2-22200000000000000000000-22-22000000
χ2322222-2-222222-2-2-2222-2-2-2-20000-222-200000000000000002i−2i−2i2i0000000000
χ2422222-2-222222-2-2-2222-2-2-2-20000-222-20000000000000000−2i2i2i−2i0000000000
χ2522222-2-2222-222-22-2-2-2-2-2-2-2000022-22000000000000000000002i−2i−2i2i000000
χ2622222-2-2222-222-22-2-2-2-2-2-2-2000022-2200000000000000000000−2i2i2i−2i000000
χ2722222-2-2222-2-2-2222-2-2-2-22222-2-22-22-200000022-2-200000000000000000000
χ2822222-2-2222-2-2-2222-2-2-2-222-2-2222-22-2000000-2-22200000000000000000000
χ292222-122-1-1-1222222-1-1-1-1-1-12222-1-1-1-122-1-122-1-1-1-1-1-1-1-1-1-100000000000000
χ302222-122-1-1-1222222-1-1-1-1-1-12222-1-1-1-1-2-211-2-2-1-1-1-111111100000000000000
χ312222-122-1-1-1222222-1-1-1-1-1-1-2-2-2-2-1-1-1-122-1-1-2-21111-1-1111100000000000000
χ322222-122-1-1-1222222-1-1-1-1-1-1-2-2-2-2-1-1-1-1-2-21122111111-1-1-1-100000000000000
χ332222-122-1-1-1-22-22-2-211-1-1-1-12-2-221-11100−i3i300-111-1−i3i3−i3i3−i3i300000000000000
χ342222-122-1-1-1-22-22-2-211-1-1-1-12-2-221-11100i3−i300-111-1i3−i3i3−i3i3−i300000000000000
χ352222-122-1-1-1-22-22-2-211-1-1-1-1-222-21-11100−i3i3001-1-11−i3i3i3−i3i3−i300000000000000
χ362222-122-1-1-1-22-22-2-211-1-1-1-1-222-21-11100i3−i3001-1-11i3−i3−i3i3−i3i300000000000000
χ372222-1-2-2-1-1-12-222-2-2-1-111-1-12-22-2111-12-2-1-12-2-11-1111-1-11100000000000000
χ382222-1-2-2-1-1-12-222-2-2-1-111-1-12-22-2111-1-2211-22-11-11-1-111-1-100000000000000
χ392222-1-2-2-1-1-12-222-2-2-1-111-1-1-22-22111-12-2-1-1-221-11-11111-1-100000000000000
χ402222-1-2-2-1-1-12-222-2-2-1-111-1-1-22-22111-1-22112-21-11-1-1-1-1-11100000000000000
χ412222-1-2-2-1-1-1-2-2-22221111-1-122-2-2-11-1100−i3i300-1-111i3−i3−i3i3i3−i300000000000000
χ422222-1-2-2-1-1-1-2-2-22221111-1-122-2-2-11-1100i3−i300-1-111−i3i3i3−i3−i3i300000000000000
χ432222-1-2-2-1-1-1-2-2-22221111-1-1-2-222-11-1100−i3i30011-1-1i3−i3i3−i3−i3i300000000000000
χ442222-1-2-2-1-1-1-2-2-22221111-1-1-2-222-11-1100i3−i30011-1-1−i3i3−i3i3i3−i300000000000000
χ454444-244-2-2-24-4-4-44-4-2-2-2-2220000-2222000000000000000000000000000000
χ464444-244-2-2-2-4-44-4-4422-2-222000022-2-2000000000000000000000000000000
χ474444-2-4-4-2-2-244-4-4-44-2-2222200002-2-22000000000000000000000000000000
χ484444-2-4-4-2-2-2-444-44-42222220000-2-22-2000000000000000000000000000000
χ494-44-444i−4i-44-4000000004i−4i00000000000000000000000000000000002ζ7+2ζ23−2ζ7−2ζ23−2ζ5−2ζ132ζ5+2ζ1300
χ504-44-444i−4i-44-4000000004i−4i0000000000000000000000000000000000−2ζ7−2ζ232ζ7+2ζ232ζ5+2ζ13−2ζ5−2ζ1300
χ514-44-44−4i4i-44-400000000−4i4i0000000000000000000000000000000000−2ζ5−2ζ132ζ5+2ζ132ζ7+2ζ23−2ζ7−2ζ2300
χ524-44-44−4i4i-44-400000000−4i4i00000000000000000000000000000000002ζ5+2ζ13−2ζ5−2ζ13−2ζ7−2ζ232ζ7+2ζ2300
χ5388-8-88008-8-800000000000000000000000000000000000000000000000000
χ5488-8-8-400-444000000−4i34i3000000000000000000000000000000000000000000
χ5588-8-8-400-4440000004i3−4i3000000000000000000000000000000000000000000
χ568-88-8-48i−8i4-4400000000−4i4i0000000000000000000000000000000000000000
χ578-88-8-4−8i8i4-44000000004i−4i0000000000000000000000000000000000000000
χ588-8-88800-8-8800000000000000000000000000000000000000000000000000
χ598-8-88-40044-40000000000−4i34i300000000000000000000000000000000000000
χ608-8-88-40044-400000000004i3−4i300000000000000000000000000000000000000

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