Finite Group Databasebeta

← Group #10692415

Character table — Group #10692415

Order 768.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63
size11112222222244444444444888888881212121216161616161616161616161616161616242424242424242424244848
order1222344446662444412121212121268888121212888824668812122424242424242424224488888888
χ1111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-1111111-1-1-1-1-1-1
χ31111111111111111111111111111111-1-1-1-11111111111111111-1-1-1-1-1-1-1-1-1-1-1-1
χ41111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1111111
χ5111111111111111111111111-1-1-1-111111111111-1-111-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1
χ6111111111111111111111111-1-1-1-11111111-1-1-1-111-1-1-1-1-1-11111-1-1-1-111-1-1-1-111
χ7111111111111111111111111-1-1-1-1111-1-1-1-11111-1-111-1-1-1-1-1-1-1-11111-1-1-1-1-1-111
χ8111111111111111111111111-1-1-1-1111-1-1-1-1-1-1-1-111-1-1-1-1-1-111111111-1-11111-1-1
χ911111-1-1-1-1111-111-11-1-1-1-1-1-1-1ii−i−i111ii−i−i1-111i−i-1-1ii−i−iii−i−i1-11-1i−iii−i−i1-1
χ1011111-1-1-1-1111-111-11-1-1-1-1-1-1-1ii−i−i111ii−i−i-11-1-1−ii11ii−i−i−i−iii1-11-1i−i−i−iii-11
χ1111111-1-1-1-1111-111-11-1-1-1-1-1-1-1ii−i−i111−i−iii1-111i−i-1-1ii−i−iii−i−i-11-11−ii−i−iii-11
χ1211111-1-1-1-1111-111-11-1-1-1-1-1-1-1ii−i−i111−i−iii-11-1-1−ii11ii−i−i−i−iii-11-11−iiii−i−i1-1
χ1311111-1-1-1-1111-111-11-1-1-1-1-1-1-1−i−iii111ii−i−i1-111−ii-1-1−i−iii−i−iii-11-11i−iii−i−i-11
χ1411111-1-1-1-1111-111-11-1-1-1-1-1-1-1−i−iii111ii−i−i-11-1-1i−i11−i−iiiii−i−i-11-11i−i−i−iii1-1
χ1511111-1-1-1-1111-111-11-1-1-1-1-1-1-1−i−iii111−i−iii1-111−ii-1-1−i−iii−i−iii1-11-1−ii−i−iii1-1
χ1611111-1-1-1-1111-111-11-1-1-1-1-1-1-1−i−iii111−i−iii-11-1-1i−i11−i−iiiii−i−i1-11-1−iiii−i−i-11
χ17222222222222-22-2-2-22222-2-2-200002-2-2222200000000000000000000-2-2000000
χ18222222222222-22-2-2-22222-2-2-200002-2-2-2-2-2-20000000000000000000022000000
χ19222222-2-222222-22-2-222-2-2-2-222i−2i2i−2i-2-220000000000002i−2i2i−2i0000000000000000
χ20222222-2-222222-22-2-222-2-2-2-22−2i2i−2i2i-2-22000000000000−2i2i−2i2i0000000000000000
χ21222222-2-22222-2-2-22222-2-222-20000-22-20000000000000000000022-2-200000000
χ22222222-2-22222-2-2-22222-2-222-20000-22-200000000000000000000-2-22200000000
χ2322222-222-22222-2-2-22-2-222-2-220000-22-2000000000000000000002-2-2200000000
χ2422222-222-22222-2-2-22-2-222-2-220000-22-200000000000000000000-222-200000000
χ2522222-222-2222-2-222-2-2-22222-22-2-22-2-220000000000002-2-220000000000000000
χ2622222-222-2222-2-222-2-2-22222-2-222-2-2-22000000000000-222-20000000000000000
χ2722222-2-2-2-222222-22-2-2-2-2-222200002-2-22i2i−2i−2i00000000000000000000−2i2i000000
χ2822222-2-2-2-222222-22-2-2-2-2-222200002-2-2−2i−2i2i2i000000000000000000002i−2i000000
χ292222-12222-1-1-122222-1-1-1-1-1-1-12222-1-1-1000022-1-122-1-1-1-1-1-1-1-1-1-1000000000000
χ302222-12222-1-1-122222-1-1-1-1-1-1-12222-1-1-10000-2-211-2-211-1-1-1-11111000000000000
χ312222-12222-1-1-122222-1-1-1-1-1-1-1-2-2-2-2-1-1-1000022-1-1-2-2-1-111111111000000000000
χ322222-12222-1-1-122222-1-1-1-1-1-1-1-2-2-2-2-1-1-10000-2-21122111111-1-1-1-1000000000000
χ332222-12-2-22-1-1-12-22-2-2-1-11111-12i−2i2i−2i11-1000000−i3i300−i3i3−ii−ii3−33−3000000000000
χ342222-12-2-22-1-1-12-22-2-2-1-11111-12i−2i2i−2i11-1000000i3−i300i3−i3−ii−ii−33−33000000000000
χ352222-12-2-22-1-1-12-22-2-2-1-11111-1−2i2i−2i2i11-1000000−i3i300−i3i3i−ii−i−33−33000000000000
χ362222-12-2-22-1-1-12-22-2-2-1-11111-1−2i2i−2i2i11-1000000i3−i300i3−i3i−ii−i3−33−3000000000000
χ372222-1-222-2-1-1-1-2-222-211-1-1-1-112-2-2211-1000000−i3i300i3−i3-111-1−i3i3i3−i3000000000000
χ382222-1-222-2-1-1-1-2-222-211-1-1-1-112-2-2211-1000000i3−i300−i3i3-111-1i3−i3−i3i3000000000000
χ392222-1-222-2-1-1-1-2-222-211-1-1-1-11-222-211-1000000−i3i300i3−i31-1-11i3−i3−i3i3000000000000
χ402222-1-222-2-1-1-1-2-222-211-1-1-1-11-222-211-1000000i3−i300−i3i31-1-11−i3i3i3−i3000000000000
χ412222-1-2-2-2-2-1-1-1-222-2211111112i2i−2i−2i-1-1-100002-2-1-12i−2i11−i−iii−i−iii000000000000
χ422222-1-2-2-2-2-1-1-1-222-2211111112i2i−2i−2i-1-1-10000-2211−2i2i-1-1−i−iiiii−i−i000000000000
χ432222-1-2-2-2-2-1-1-1-222-221111111−2i−2i2i2i-1-1-100002-2-1-1−2i2i11ii−i−iii−i−i000000000000
χ442222-1-2-2-2-2-1-1-1-222-221111111−2i−2i2i2i-1-1-10000-22112i−2i-1-1ii−i−i−i−iii000000000000
χ454444-24444-2-2-2-44-4-4-4-2-2-2-22220000-22200000000000000000000000000000000
χ464444-24-4-44-2-2-2-4-4-444-2-222-2-2200002-2200000000000000000000000000000000
χ474444-2-444-4-2-2-24-4-4-4422-2-222-200002-2200000000000000000000000000000000
χ484444-2-4-4-4-4-2-2-244-44-42222-2-2-20000-22200000000000000000000000000000000
χ4944-4-4404i−4i04-4-400000004i−4i0000000000000000000000000000000000002ζ7+2ζ23−2ζ7−2ζ23−2ζ5−2ζ132ζ5+2ζ1300
χ5044-4-4404i−4i04-4-400000004i−4i000000000000000000000000000000000000−2ζ7−2ζ232ζ7+2ζ232ζ5+2ζ13−2ζ5−2ζ1300
χ5144-4-440−4i4i04-4-40000000−4i4i000000000000000000000000000000000000−2ζ5−2ζ132ζ5+2ζ132ζ7+2ζ23−2ζ7−2ζ2300
χ5244-4-440−4i4i04-4-40000000−4i4i0000000000000000000000000000000000002ζ5+2ζ13−2ζ5−2ζ13−2ζ7−2ζ232ζ7+2ζ2300
χ534-44-44400-4-4-44000004-4000000000000−2i22i2−2i22i20000000000000000000000000000
χ544-44-44400-4-4-44000004-40000000000002i2−2i22i2−2i20000000000000000000000000000
χ554-44-44-4004-4-4400000-4400000000000022−22−22220000000000000000000000000000
χ564-44-44-4004-4-4400000-44000000000000−222222−220000000000000000000000000000
χ5788-8-8-408i−8i0-4440000000−4i4i000000000000000000000000000000000000000000
χ5888-8-8-40−8i8i0-44400000004i−4i000000000000000000000000000000000000000000
χ598-88-8-4800-844-400000-4400000000000000000000000000000000000000000000
χ608-88-8-4-800844-4000004-400000000000000000000000000000000000000000000
χ618-8-8880000-88-8000000000000000000000000000000000000000000000000000
χ628-8-88-400004-4400000000043−430000000000000000000000000000000000000000
χ638-8-88-400004-44000000000−43430000000000000000000000000000000000000000

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