Finite Group Databasebeta

← Group #10900851

Character table — Group #10900851

Order 768.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72
size11111111222222222222444488888888888888888888881212121216161616161616161616242424242424242424244848
order12222222344446666666121212122244448888121212122424242424242424224424666612121212222244888844
χ1111111111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111111111-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-1-1-1
χ3111111111111111111111111111111-1-1-1-11111-1-1-1-1-1-1-1-11111-1-111-1-1-1-111111111-1-1-1-1-1-1
χ4111111111111111111111111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-111-1-1-1-1-1-1111111
χ511111111111111111111111111-1-1-1-111-1-1-1-1-1-11111-1-1-1-111111-11111-1-1-1-111-1-1-1-111-1-1-11
χ611111111111111111111111111-1-1-1-111-1-1-1-1-1-11111-1-1-1-1-1-1-1-11-11111-1-1-1-1-1-11111-1-1111-1
χ711111111111111111111111111-1-1-1-1-1-111-1-1-1-1-1-1-1-111111111-1111-1-111-1-111-1-1-1-1-1-1111-1
χ811111111111111111111111111-1-1-1-1-1-111-1-1-1-1-1-1-1-11111-1-1-1-1-1111-1-111-1-1-1-1111111-1-1-11
χ9111111111111111111111111-1-11-1-1111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1
χ10111111111111111111111111-1-11-1-111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-111
χ11111111111111111111111111-1-11-1-11-1-1-1-11111-1-1-1-1-1-1-1-1111111-1-11111-1-1-1-1-1-111-1-1-1-111
χ12111111111111111111111111-1-11-1-11-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-111-1-11111-1-11111-1-11111-1-1
χ13111111111111111111111111-1-1-111-111-1-1-1-1-1-11111-1-1-1-11111-11-1-1-1-11111-1-111-1-111-1-11-1
χ14111111111111111111111111-1-1-111-111-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-11-1-1-1-1111111-1-111-1-111-11
χ15111111111111111111111111-1-1-111-1-1-111-1-1-1-1-1-1-1-1111111111-1-1-111-1-111-1-111-1-1-1-111-11
χ16111111111111111111111111-1-1-111-1-1-111-1-1-1-1-1-1-1-11111-1-1-1-11-1-1-111-1-11111-1-11111-1-11-1
χ17222222222-2-2-2-22222222-2-2-2-200200-2000022-2-20000000022-2-200000000000000-22000000
χ18222222222-2-2-2-22222222-2-2-2-200200-2000022-2-200000000-2-222000000000000002-2000000
χ19222222222-2-2-2-22222222-2-2-2-200-20020000-2-2220000000022-2-2000000000000002-2000000
χ20222222222-2-2-2-22222222-2-2-2-200-20020000-2-22200000000-2-22200000000000000-22000000
χ2122222222-12222-1-1-1-1-1-1-1-1-1-1-12222222222-1-1-1-1-1-1-1-1-1-1-1-1000022-1-1-1-1-1-1-1-1000000000000
χ2222222222-12222-1-1-1-1-1-1-1-1-1-1-1222222-2-2-2-2-1-1-1-1111111110000-2-2-1-11111-1-1000000000000
χ2322222222-12222-1-1-1-1-1-1-1-1-1-1-122-2-2-2-222-2-21111-1-1-1-1111100002-2-1-1-1-11111000000000000
χ2422222222-12222-1-1-1-1-1-1-1-1-1-1-122-2-2-2-2-2-22211111111-1-1-1-10000-22-1-111-1-111000000000000
χ2522222222-12222-1-1-1-1-1-1-1-1-1-1-1-2-22-2-222222-1-1-1-1-1-1-1-1-1-1-1-10000-2-211111111000000000000
χ2622222222-12222-1-1-1-1-1-1-1-1-1-1-1-2-22-2-22-2-2-2-2-1-1-1-11111111100002211-1-1-1-111000000000000
χ2722222222-12222-1-1-1-1-1-1-1-1-1-1-1-2-2-222-222-2-21111-1-1-1-111110000-221111-1-1-1-1000000000000
χ2822222222-12222-1-1-1-1-1-1-1-1-1-1-1-2-2-222-2-2-22211111111-1-1-1-100002-211-1-111-1-1000000000000
χ292-2-2-222-2222-22-2-2-2-222-222-22-20002-2000000000000000002-22-2000000002-2002-200000000
χ302-2-2-222-2222-22-2-2-2-222-222-22-20002-200000000000000000-22-22000000002-200-2200000000
χ312-2-2-222-2222-22-2-2-2-222-222-22-2000-22000000000000000002-22-200000000-2200-2200000000
χ322-2-2-222-2222-22-2-2-2-222-222-22-2000-2200000000000000000-22-2200000000-22002-200000000
χ332-2-2-222-222-22-22-2-2-222-22-22-222-2000000000000000000002-2-22002-20000002-20000000000
χ342-2-2-222-222-22-22-2-2-222-22-22-222-200000000000000000000-222-2002-2000000-220000000000
χ352-2-2-222-222-22-22-2-2-222-22-22-22-22000000000000000000002-2-2200-22000000-220000000000
χ362-2-2-222-222-22-22-2-2-222-22-22-22-2200000000000000000000-222-200-220000002-20000000000
χ3744444444-2-4-4-4-4-2-2-2-2-2-2-2222200400-40000-2-2220000000000000000000000000000000000
χ3844444444-2-4-4-4-4-2-2-2-2-2-2-2222200-4004000022-2-20000000000000000000000000000000000
χ39444-44-4-4-44000044-44-4-4-4000000000000−2i22i200000000−2i2−2i22i22i200000000000000000000000000
χ40444-44-4-4-44000044-44-4-4-40000000000002i2−2i2000000002i22i2−2i2−2i200000000000000000000000000
χ41444-44-4-4-4-20000-2-22-2222000000000000−2i22i20023−23i6i6−i6−i6i2i2−i2−i200000000000000000000000000
χ42444-44-4-4-4-20000-2-22-2222000000000000−2i22i200−2323−i6−i6i6i6i2i2−i2−i200000000000000000000000000
χ43444-44-4-4-4-20000-2-22-22220000000000002i2−2i20023−23−i6−i6i6i6−i2−i2i2i200000000000000000000000000
χ44444-44-4-4-4-20000-2-22-22220000000000002i2−2i200−2323i6i6−i6−i6−i2−i2i2i200000000000000000000000000
χ4544-44-44-4-444-4-444-4-4-4-444-444-4000000000000000000000000000000000000000000000000
χ4644-44-44-4-44-444-44-4-4-4-4444-4-44000000000000000000000000000000000000000000000000
χ4744-44-44-4-4-24-4-44-22222-2-22-2-22000000000000000000−2i32i3−2i32i300000000000000000000000000
χ4844-44-44-4-4-24-4-44-22222-2-22-2-220000000000000000002i3−2i32i3−2i300000000000000000000000000
χ4944-44-44-4-4-2-444-4-22222-2-2-222-200000000000000−2i32i3−2i32i3000000000000000000000000000000
χ5044-44-44-4-4-2-444-4-22222-2-2-222-2000000000000002i3−2i32i3−2i3000000000000000000000000000000
χ5144-4-4-4-444400004-44-44-4-4000000000022−2200000022−22−2222000000000000000000000000000000
χ5244-4-4-4-444400004-44-44-4-40000000000−2222000000−222222−22000000000000000000000000000000
χ5344-4-4-4-444-20000-22-22-222000000000022−220023−2300−222−26−6−6600000000000000000000000000
χ5444-4-4-4-444-20000-22-22-222000000000022−2200−232300−222−2−666−600000000000000000000000000
χ5544-4-4-4-444-20000-22-22-2220000000000−22220023−23002−2−22−666−600000000000000000000000000
χ5644-4-4-4-444-20000-22-22-2220000000000−222200−2323002−2−226−6−6600000000000000000000000000
χ574-444-4-4-4440000-44-4-444-4000000000000000000000000000000000000000000000022−220000
χ584-444-4-4-4440000-44-4-444-40000000000000000000000000000000000000000000000−22220000
χ594-44-4-444-4444-4-4-444-4-4-44-4-444000000000000000000000000000000000000000000000000
χ604-44-4-444-44-4-444-444-4-4-4444-4-4000000000000000000000000000000000000000000000000
χ614-44-4-444-4-244-4-42-2-2222-222-2-2000000000000000000000000000000−2i32i30000000000000000
χ624-44-4-444-4-244-4-42-2-2222-222-2-20000000000000000000000000000002i3−2i30000000000000000
χ634-44-4-444-4-2-4-4442-2-2222-2-2-2220000000000000000000000000000000023−2300000000000000
χ644-44-4-444-4-2-4-4442-2-2222-2-2-22200000000000000000000000000000000−232300000000000000
χ654-4-444-44-440000-4-444-44-400000000000000000000000000000000000000000000000022−2200
χ664-4-444-44-440000-4-444-44-4000000000000000000000000000000000000000000000000−222200
χ674-4-4-444-44-24-44-4222-2-22-2-22-220004-400000000000000000000000000000-22000000000000
χ684-4-4-444-44-24-44-4222-2-22-2-22-22000-44000000000000000000000000000002-2000000000000
χ694-4-4-444-44-2-44-44222-2-22-22-22-24-400000000000000000000000000-22000000000000000000
χ704-4-4-444-44-2-44-44222-2-22-22-22-2-44000000000000000000000000002-2000000000000000000
χ718-888-8-8-88-400004-444-4-440000000000000000000000000000000000000000000000000000
χ728-8-888-88-8-4000044-4-44-440000000000000000000000000000000000000000000000000000

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