Finite Group Databasebeta

← Group #10692434

Character table — Group #10692434

Order 768.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63
size11112222222244444444444888888881212121216161616161616161616161616161616242424242424242424244848
order1222344446662444412121212121222446121212888844668812121212121224242424888888888888
χ1111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111-1-111-1-1-1-111-1-1-1-1-1-1111111-1-1-1-1-1-1
χ31111111111111111111111111111111-1-1-1-11111111111111111-1-1-1-1-1-1-1-1-1-1-1-1
χ41111111111111111111111111111111-1-1-1-1-1-111-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1111111
χ511111111111111111111111-1-1-1-11111111111-1-1-1-111-1-111-1-1-1-111-1-1-1-11111-1-1
χ611111111111111111111111-1-1-1-111111111-1-1-1-111-1-1-1-1-1-1111111-1-1-1-1-1-1-1-111
χ711111111111111111111111-1-1-1-11111-1-1-1-111-1-1-1-111-1-111-1-1-1-1-1-11111-1-1-1-111
χ811111111111111111111111-1-1-1-11111-1-1-1-1-1-1-1-111-1-1-1-1-1-11111-1-111111111-1-1
χ911111-1-1-1-1111-1111-1-1-1-1-1111-11-1-111-1ii−i−i1-11-11-1111-1-1-111-1-1i−iii−i−iii−i−ii−i
χ1011111-1-1-1-1111-1111-1-1-1-1-1111-11-1-111-1ii−i−i-111-1-11-1-11-111-1-111i−iii−i−i−i−iii−ii
χ1111111-1-1-1-1111-1111-1-1-1-1-1111-11-1-111-1−i−iii1-11-11-1111-1-1-111-1-1−ii−i−iii−i−iii−ii
χ1211111-1-1-1-1111-1111-1-1-1-1-1111-11-1-111-1−i−iii-111-1-11-1-11-111-1-111−ii−i−iiiii−i−ii−i
χ1311111-1-1-1-1111-1111-1-1-1-1-111-11-11-111-1ii−i−i1-1-11-1111-11-1-1-1-111i−i−i−iiiii−i−i−ii
χ1411111-1-1-1-1111-1111-1-1-1-1-111-11-11-111-1ii−i−i-11-111-1-1-1-111111-1-1i−i−i−iii−i−iiii−i
χ1511111-1-1-1-1111-1111-1-1-1-1-111-11-11-111-1−i−iii1-1-11-1111-11-1-1-1-111−iiii−i−i−i−iiii−i
χ1611111-1-1-1-1111-1111-1-1-1-1-111-11-11-111-1−i−iii-11-111-1-1-1-111111-1-1−iiii−i−iii−i−i−ii
χ17222222222222-2-22-2-22222-2-20000-2-22-222220000000000000000-2-20000000000
χ18222222222222-2-22-2-22222-2-20000-2-22-2-2-2-2-20000000000000000220000000000
χ192222222-2-222222-2-2-222-2-2-2-2000022-2-200000000000000000000002i−2i2i−2i000000
χ202222222-2-222222-2-2-222-2-2-2-2000022-2-20000000000000000000000−2i2i−2i2i000000
χ212222222-2-2222-2-2-22222-2-22222-2-2-2-2-22000000220000-2-2000000000000000000
χ222222222-2-2222-2-2-22222-2-222-2-222-2-2-22000000-2-2000022000000000000000000
χ2322222-2-2222222-2-22-2-2-222222-2-222-2-2-20000002-20000-22000000000000000000
χ2422222-2-2222222-2-22-2-2-22222-222-22-2-2-2000000-2200002-2000000000000000000
χ2522222-2-222222-22-2-22-2-222-2-20000-22-2200000000000000000000002-2-22000000
χ2622222-2-222222-22-2-22-2-222-2-20000-22-220000000000000000000000-222-2000000
χ2722222-2-2-2-22222-22-22-2-2-2-2-2-200002-2222i2i−2i−2i0000000000000000−2i2i0000000000
χ2822222-2-2-2-22222-22-22-2-2-2-2-2-200002-222−2i−2i2i2i00000000000000002i−2i0000000000
χ292222-12222-1-1-122222-1-1-1-1-1-12222-1-1-1-1000022-1-122-1-1-1-1-1-1-1-1-1-1000000000000
χ302222-12222-1-1-122222-1-1-1-1-1-12222-1-1-1-10000-2-2-1-1-2-211-1-1111111000000000000
χ312222-12222-1-1-122222-1-1-1-1-1-1-2-2-2-2-1-1-1-100002211-2-2-1-111-1-11111000000000000
χ322222-12222-1-1-122222-1-1-1-1-1-1-2-2-2-2-1-1-1-10000-2-21122111111-1-1-1-1000000000000
χ332222-122-2-2-1-1-1-2-2-222-1-111-1-122-2-2111-1000000-1-100−i3i311−i3i3−i3i3−i3i3000000000000
χ342222-122-2-2-1-1-1-2-2-222-1-111-1-122-2-2111-1000000-1-100i3−i311i3−i3i3−i3i3−i3000000000000
χ352222-122-2-2-1-1-1-2-2-222-1-111-1-1-2-222111-10000001100−i3i3-1-1−i3i3i3−i3i3−i3000000000000
χ362222-122-2-2-1-1-1-2-2-222-1-111-1-1-2-222111-10000001100i3−i3-1-1i3−i3−i3i3−i3i3000000000000
χ372222-1-2-222-1-1-12-2-22-211-1-1-1-12-2-22-1111000000-1100−i3i31-1i3−i3−i3i3i3−i3000000000000
χ382222-1-2-222-1-1-12-2-22-211-1-1-1-12-2-22-1111000000-1100i3−i31-1−i3i3i3−i3−i3i3000000000000
χ392222-1-2-222-1-1-12-2-22-211-1-1-1-1-222-2-11110000001-100−i3i3-11i3−i3i3−i3−i3i3000000000000
χ402222-1-2-222-1-1-12-2-22-211-1-1-1-1-222-2-11110000001-100i3−i3-11−i3i3−i3i3i3−i3000000000000
χ412222-1-2-2-2-2-1-1-1-2222-21111-1-12-22-21-1-1100002-2-112-2-1-1-1111-1-111000000000000
χ422222-1-2-2-2-2-1-1-1-2222-21111-1-12-22-21-1-110000-22-11-2211-11-1-111-1-1000000000000
χ432222-1-2-2-2-2-1-1-1-2222-21111-1-1-22-221-1-1100002-21-1-22-1-11-11111-1-1000000000000
χ442222-1-2-2-2-2-1-1-1-2222-21111-1-1-22-221-1-110000-221-12-2111-1-1-1-1-111000000000000
χ454444-24444-2-2-2-4-44-4-4-2-2-2-222000022-2200000000000000000000000000000000
χ464444-244-4-4-2-2-244-4-4-4-2-222220000-2-22200000000000000000000000000000000
χ474444-2-4-444-2-2-2-44-4-4422-2-22200002-22-200000000000000000000000000000000
χ484444-2-4-4-4-4-2-2-24-44-442222220000-22-2-200000000000000000000000000000000
χ4944-4-444-4004-4-4000004-400000000000022−2222−220000000000000000000000000000
χ5044-4-444-4004-4-4000004-4000000000000−2222−22220000000000000000000000000000
χ5144-4-44-44004-4-400000-44000000000000−2i22i22i2−2i20000000000000000000000000000
χ5244-4-44-44004-4-400000-440000000000002i2−2i2−2i22i20000000000000000000000000000
χ534-44-44004i−4i-44-400000004i−4i0000000000000000000000000000000000002ζ7+2ζ23−2ζ7−2ζ23−2ζ5−2ζ132ζ5+2ζ1300
χ544-44-44004i−4i-44-400000004i−4i000000000000000000000000000000000000−2ζ7−2ζ232ζ7+2ζ232ζ5+2ζ13−2ζ5−2ζ1300
χ554-44-4400−4i4i-44-40000000−4i4i000000000000000000000000000000000000−2ζ5−2ζ132ζ5+2ζ132ζ7+2ζ23−2ζ7−2ζ2300
χ564-44-4400−4i4i-44-40000000−4i4i0000000000000000000000000000000000002ζ5+2ζ13−2ζ5−2ζ13−2ζ7−2ζ232ζ7+2ζ2300
χ5788-8-8-48-800-44400000-4400000000000000000000000000000000000000000000
χ5888-8-8-4-8800-444000004-400000000000000000000000000000000000000000000
χ598-88-8-4008i−8i4-440000000−4i4i000000000000000000000000000000000000000000
χ608-88-8-400−8i8i4-4400000004i−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.