Finite Group Databasebeta

← Group #10693268

Character table — Group #10693268

Order 768.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63
size11112222222244444444444888888881212121216161616161616161616161616161616242424242424242424244848
order122234444666244441212121212126888812121288888888242424242424242424242424444444448888
χ1111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111-1-1-1-11111-1-1-1-1-1-1-1-111-1-111-1-111-1-1
χ31111111111111111111111111111111-1-1-1-11111111111111111-1-1-1-1-1-1-1-1-1-1-1-1
χ41111111111111111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-111-1-111-1-111
χ5111111111111111111111111-1-1-1-1111111111-1-1-1-1-1-1-1-1-1-11111-1-111-1-11111-1-1
χ6111111111111111111111111-1-1-1-11111111-1-111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-11111
χ7111111111111111111111111-1-1-1-1111-1-1-1-111-1-1-1-1-1-1-1-1-1-1111111-1-111-1-1-1-111
χ8111111111111111111111111-1-1-1-1111-1-1-1-1-1-111-1-1-1-11111-1-1-1-111111111-1-1-1-1
χ911111-1-1-1-11111-111-1-111-1-1-11ii−i−i1-1-1ii−i−ii−i1-1ii−i−i11-1-1ii−i−i1-1111-1-1-1i−ii−i
χ1011111-1-1-1-11111-111-1-111-1-1-11ii−i−i1-1-1ii−i−i−ii-11ii−i−i-1-111−i−iii1-1-1-11-111i−i−ii
χ1111111-1-1-1-11111-111-1-111-1-1-11ii−i−i1-1-1−i−iiii−i1-1ii−i−i11-1-1ii−i−i-11-1-1-1111−ii−ii
χ1211111-1-1-1-11111-111-1-111-1-1-11ii−i−i1-1-1−i−iii−ii-11ii−i−i-1-111−i−iii-1111-11-1-1−iii−i
χ1311111-1-1-1-11111-111-1-111-1-1-11−i−iii1-1-1ii−i−ii−i-11−i−iii-1-111ii−i−i-1111-11-1-1i−i−ii
χ1411111-1-1-1-11111-111-1-111-1-1-11−i−iii1-1-1ii−i−i−ii1-1−i−iii11-1-1−i−iii-11-1-1-1111i−ii−i
χ1511111-1-1-1-11111-111-1-111-1-1-11−i−iii1-1-1−i−iiii−i-11−i−iii-1-111ii−i−i1-1-1-11-111−iii−i
χ1611111-1-1-1-11111-111-1-111-1-1-11−i−iii1-1-1−i−iii−ii1-1−i−iii11-1-1−i−iii1-1111-1-1-1−ii−ii
χ17222222222222-2-22-2-22-2-2222-200002-2-22222000000000000000000000000-2-200
χ18222222222222-2-22-2-22-2-2222-200002-2-2-2-2-2-20000000000000000000000002200
χ192222222-2-222222-2-2-22-2-2-2-2222i−2i2i−2i-22-2000000002i−2i2i−2i00000000000000000000
χ202222222-2-222222-2-2-22-2-2-2-222−2i2i−2i2i-22-200000000−2i2i−2i2i00000000000000000000
χ212222222-2-2222-2-2-222222-2-22-20000-2-22000000000000000000002200-2-2000000
χ222222222-2-2222-2-2-222222-2-22-20000-2-2200000000000000000000-2-20022000000
χ2322222-2-2222222-2-2-22-2-2-222-222-2-22-2-22000000002-2-2200000000000000000000
χ2422222-2-2222222-2-2-22-2-2-222-22-222-2-2-2200000000-222-200000000000000000000
χ2522222-2-222222-22-22-2-22222-2-20000-22-2000000000000000000002-200-22000000
χ2622222-2-222222-22-22-2-22222-2-20000-22-200000000000000000000-22002-2000000
χ2722222-2-2-2-2222-222-22-2-2-2-2-2-2-200002222i2i−2i−2i000000000000000000000000−2i2i00
χ2822222-2-2-2-2222-222-22-2-2-2-2-2-2-20000222−2i−2i2i2i0000000000000000000000002i−2i00
χ292222-12222-1-1-122222-1-1-1-1-1-1-12222-1-1-100002222-1-1-1-1-1-1-1-1-1-1-1-1000000000000
χ302222-12222-1-1-122222-1-1-1-1-1-1-12222-1-1-10000-2-2-2-2-1-1-1-111111111000000000000
χ312222-12222-1-1-122222-1-1-1-1-1-1-1-2-2-2-2-1-1-1000022-2-211111111-1-1-1-1000000000000
χ322222-12222-1-1-122222-1-1-1-1-1-1-1-2-2-2-2-1-1-10000-2-2221111-1-1-1-11111000000000000
χ332222-122-2-2-1-1-122-2-2-2-11111-1-12i−2i2i−2i1-1100000000−ii−ii3−33−3−i3i3−i3i3000000000000
χ342222-122-2-2-1-1-122-2-2-2-11111-1-12i−2i2i−2i1-1100000000−ii−ii−33−33i3−i3i3−i3000000000000
χ352222-122-2-2-1-1-122-2-2-2-11111-1-1−2i2i−2i2i1-1100000000i−ii−i3−33−3i3−i3i3−i3000000000000
χ362222-122-2-2-1-1-122-2-2-2-11111-1-1−2i2i−2i2i1-1100000000i−ii−i−33−33−i3i3−i3i3000000000000
χ372222-1-2-222-1-1-12-2-2-22111-1-11-12-2-2211-100000000-111-13−3−33−333−3000000000000
χ382222-1-2-222-1-1-12-2-2-22111-1-11-12-2-2211-100000000-111-1−333−33−3−33000000000000
χ392222-1-2-222-1-1-12-2-2-22111-1-11-1-222-211-1000000001-1-113−3−333−3−33000000000000
χ402222-1-2-222-1-1-12-2-2-22111-1-11-1-222-211-1000000001-1-11−333−3−333−3000000000000
χ412222-1-2-2-2-2-1-1-12-222-21-1-1111-12i2i−2i−2i-11100002i−2i2-2−i−iii-1-111−i−iii000000000000
χ422222-1-2-2-2-2-1-1-12-222-21-1-1111-12i2i−2i−2i-1110000−2i2i-22−i−iii11-1-1ii−i−i000000000000
χ432222-1-2-2-2-2-1-1-12-222-21-1-1111-1−2i−2i2i2i-11100002i−2i-22ii−i−i11-1-1−i−iii000000000000
χ442222-1-2-2-2-2-1-1-12-222-21-1-1111-1−2i−2i2i2i-1110000−2i2i2-2ii−i−i-1-111ii−i−i000000000000
χ454444-24444-2-2-2-4-44-4-4-222-2-2-220000-22200000000000000000000000000000000
χ464444-244-4-4-2-2-2-4-4-444-2-2-222-22000022-200000000000000000000000000000000
χ474444-2-4-444-2-2-2-44-44-42-2-2-2-22200002-2200000000000000000000000000000000
χ484444-2-4-4-4-4-2-2-2-444-4422222220000-2-2-200000000000000000000000000000000
χ4944-4-444-4004-4-40000040000-40000000022−2222−220000000000000000000000000000
χ5044-4-444-4004-4-40000040000-400000000−2222−22220000000000000000000000000000
χ5144-4-44-44004-4-400000-40000400000000−2i22i22i2−2i20000000000000000000000000000
χ5244-4-44-44004-4-400000-400004000000002i2−2i2−2i22i20000000000000000000000000000
χ534-4-444004i−4i-44-4000000004i−4i00000000000000000000000000000002i−2i002-20000
χ544-4-444004i−4i-44-4000000004i−4i0000000000000000000000000000000−2i2i00-220000
χ554-4-44400−4i4i-44-400000000−4i4i00000000000000000000000000000002i−2i00-220000
χ564-4-44400−4i4i-44-400000000−4i4i0000000000000000000000000000000−2i2i002-20000
χ5788-8-8-48-800-44400000-4000040000000000000000000000000000000000000000
χ5888-8-8-4-8800-4440000040000-40000000000000000000000000000000000000000
χ598-88-880000-8-88000000000000000000000000000000000000000000000000000
χ608-88-8-4000044-400000043−430000000000000000000000000000000000000000000
χ618-88-8-4000044-4000000−43430000000000000000000000000000000000000000000
χ628-8-88-4008i−8i4-4400000000−4i4i00000000000000000000000000000000000000000
χ638-8-88-400−8i8i4-44000000004i−4i00000000000000000000000000000000000000000

Here i is the imaginary unit (i² = −1).