Finite Group Databasebeta

← Group #10692413

Character table — Group #10692413

Order 768.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63
size11112222222244444444444888888881212121216161616161616161616161616161616242424242424242424244848
order122234444666244441212121212122444612121288882466688121212121224242424888888888844
χ1111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111-1-11-1-1-1-1111-1-1-1-1-1-1-1-1-1-1111111-1-1
χ31111111111111111111111111111111-1-1-1-11111111111111111-1-1-1-1-1-1-1-1-1-1-1-1
χ41111111111111111111111111111111-1-1-1-1-1-11-1-1-1-1111-1-1-1-1-1-11111-1-1-1-1-1-111
χ511111111111111111111111-1-1-1-11111111111-111-1-1-1-1-111-1-1-1-1111111-1-1-1-1-1-1
χ611111111111111111111111-1-1-1-111111111-1-1-1-1-111-1-1-1-1-11111-1-1-1-111-1-1-1-111
χ711111111111111111111111-1-1-1-11111-1-1-1-111-111-1-1-1-1-111-1-1-1-1-1-1-1-1-1-1111111
χ811111111111111111111111-1-1-1-11111-1-1-1-1-1-1-1-1-111-1-1-1-1-111111111-1-11111-1-1
χ911111-1-1-1-1111-111-11-1-1-1-1111-1-11-111-1ii−i−i1-11111-1-1-11-1-111-1-1ii−i−ii−iii−i−ii−i
χ1011111-1-1-1-1111-111-11-1-1-1-1111-1-11-111-1ii−i−i-111-1-1-11-1-1111-1-111−i−iiii−iii−i−i−ii
χ1111111-1-1-1-1111-111-11-1-1-1-1111-1-11-111-1−i−iii1-11111-1-1-11-1-111-1-1−i−iii−ii−i−iii−ii
χ1211111-1-1-1-1111-111-11-1-1-1-1111-1-11-111-1−i−iii-111-1-1-11-1-1111-1-111ii−i−i−ii−i−iiii−i
χ1311111-1-1-1-1111-111-11-1-1-1-111-111-1-111-1ii−i−i1-1-111-1111-1-1-1-1-111ii−i−ii−i−i−iii−ii
χ1411111-1-1-1-1111-111-11-1-1-1-111-111-1-111-1ii−i−i-11-1-1-11-111-11111-1-1−i−iiii−i−i−iiii−i
χ1511111-1-1-1-1111-111-11-1-1-1-111-111-1-111-1−i−iii1-1-111-1111-1-1-1-1-111−i−iii−iiii−i−ii−i
χ1611111-1-1-1-1111-111-11-1-1-1-111-111-1-111-1−i−iii-11-1-1-11-111-11111-1-1ii−i−i−iiii−i−i−ii
χ17222222222222-22-2-2-22222-2-20000-22-2-2222200000000000000000000-2-2000000
χ18222222222222-22-2-2-22222-2-20000-22-2-2-2-2-2-20000000000000000000022000000
χ192222222-2-22222-2-2-22-2-2222222-2-22-2-2-2000000200002-2-2000000000000000000
χ202222222-2-22222-2-2-22-2-22222-2-2222-2-2-2000000-20000-222000000000000000000
χ212222222-2-2222-2-222-2-2-222-2-20000-2-222000000000000000000000000002i−2i2i−2i00
χ222222222-2-2222-2-222-2-2-222-2-20000-2-22200000000000000000000000000−2i2i−2i2i00
χ2322222-2-2222222-22-2-222-2-2-2-200002-22-2000000000000000000000000002-2-2200
χ2422222-2-2222222-22-2-222-2-2-2-200002-22-200000000000000000000000000-222-200
χ2522222-2-222222-2-2-22222-2-2222-22-2-2-2-2200000020000-22-2000000000000000000
χ2622222-2-222222-2-2-22222-2-222-22-22-2-2-22000000-200002-22000000000000000000
χ2722222-2-2-2-222222-22-2-2-2-2-2-2-2000022-222i2i−2i−2i00000000000000000000−2i2i000000
χ2822222-2-2-2-222222-22-2-2-2-2-2-2-2000022-22−2i−2i2i2i000000000000000000002i−2i000000
χ292222-12222-1-1-122222-1-1-1-1-1-12222-1-1-1-1000022-1-1-122-1-1-1-1-1-1-1-1-1000000000000
χ302222-12222-1-1-122222-1-1-1-1-1-12222-1-1-1-10000-2-2-111-2-2-1-1-1111111000000000000
χ312222-12222-1-1-122222-1-1-1-1-1-1-2-2-2-2-1-1-1-10000221-1-1-2-2111-1-11111000000000000
χ322222-12222-1-1-122222-1-1-1-1-1-1-2-2-2-2-1-1-1-10000-2-21112211111-1-1-1-1000000000000
χ332222-122-2-2-1-1-12-2-2-2211-1-1-1-122-2-2-1111000000-1−i3i300-111−i3i3−i3i3−i3i3000000000000
χ342222-122-2-2-1-1-12-2-2-2211-1-1-1-122-2-2-1111000000-1i3−i300-111i3−i3i3−i3i3−i3000000000000
χ352222-122-2-2-1-1-12-2-2-2211-1-1-1-1-2-222-11110000001−i3i3001-1-1−i3i3i3−i3i3−i3000000000000
χ362222-122-2-2-1-1-12-2-2-2211-1-1-1-1-2-222-11110000001i3−i3001-1-1i3−i3−i3i3−i3i3000000000000
χ372222-1-2-222-1-1-1-2-2-222-1-111-1-12-22-2111-1000000-1−i3i3001-11i3−i3−i3i3i3−i3000000000000
χ382222-1-2-222-1-1-1-2-2-222-1-111-1-12-22-2111-1000000-1i3−i3001-11−i3i3i3−i3−i3i3000000000000
χ392222-1-2-222-1-1-1-2-2-222-1-111-1-1-22-22111-10000001−i3i300-11-1i3−i3i3−i3−i3i3000000000000
χ402222-1-2-222-1-1-1-2-2-222-1-111-1-1-22-22111-10000001i3−i300-11-1−i3i3−i3i3i3−i3000000000000
χ412222-1-2-2-2-2-1-1-1-222-221111-1-12-2-221-1-1100002-2-1-1-12-211-111-1-111000000000000
χ422222-1-2-2-2-2-1-1-1-222-221111-1-12-2-221-1-110000-22-111-2211-1-1-111-1-1000000000000
χ432222-1-2-2-2-2-1-1-1-222-221111-1-1-222-21-1-1100002-21-1-1-22-1-111111-1-1000000000000
χ442222-1-2-2-2-2-1-1-1-222-221111-1-1-222-21-1-110000-221112-2-1-11-1-1-1-111000000000000
χ454444-24444-2-2-2-44-4-4-4-2-2-2-22200002-22200000000000000000000000000000000
χ464444-244-4-4-2-2-2-4-444-422-2-222000022-2-200000000000000000000000000000000
χ474444-2-4-444-2-2-24-44-4-4-2-222220000-22-2200000000000000000000000000000000
χ484444-2-4-4-4-4-2-2-244-44-42222220000-2-22-200000000000000000000000000000000
χ4944-4-44004i−4i4-4-4000004i−4i000000000000000000000000000000002ζ7+2ζ23−2ζ7−2ζ23−2ζ5−2ζ132ζ5+2ζ1300000000
χ5044-4-44004i−4i4-4-4000004i−4i00000000000000000000000000000000−2ζ7−2ζ232ζ7+2ζ232ζ5+2ζ13−2ζ5−2ζ1300000000
χ5144-4-4400−4i4i4-4-400000−4i4i00000000000000000000000000000000−2ζ5−2ζ132ζ5+2ζ132ζ7+2ζ23−2ζ7−2ζ2300000000
χ5244-4-4400−4i4i4-4-400000−4i4i000000000000000000000000000000002ζ5+2ζ13−2ζ5−2ζ13−2ζ7−2ζ232ζ7+2ζ2300000000
χ534-44-444i−4i00-44-400000004i−4i00000000002+2i−2−2i2−2i−2+2i0000000000000000000000000000
χ544-44-444i−4i00-44-400000004i−4i0000000000−2−2i2+2i−2+2i2−2i0000000000000000000000000000
χ554-44-44−4i4i00-44-40000000−4i4i00000000002−2i−2+2i2+2i−2−2i0000000000000000000000000000
χ564-44-44−4i4i00-44-40000000−4i4i0000000000−2+2i2−2i−2−2i2+2i0000000000000000000000000000
χ5788-8-8-4008i−8i-44400000−4i4i00000000000000000000000000000000000000000000
χ5888-8-8-400−8i8i-444000004i−4i00000000000000000000000000000000000000000000
χ598-88-8-48i−8i004-440000000−4i4i000000000000000000000000000000000000000000
χ608-88-8-4−8i8i004-4400000004i−4i000000000000000000000000000000000000000000
χ618-8-8880000-8-88000000000000000000000000000000000000000000000000000
χ628-8-88-4000044-4000000000−4i34i30000000000000000000000000000000000000000
χ638-8-88-4000044-40000000004i3−4i30000000000000000000000000000000000000000

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