Finite Group Databasebeta

← Group #10836674

Character table — Group #10836674

Order 768.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75
size11112222222222444444444444444466888888888888888881212121212161616161616161616162424242424242424244848
order12222234444666444466881212121224242424444488888121212122424242424244448848121212122424242424448888848
χ1111111111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111-1-1-1-1111111111111111111-1-1-1-1-1-1-1-1-1-111-1-1111-1-1-1-1
χ3111111111111111111111111111111-1-111111111111111111-1-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-1-1
χ4111111111111111111111111111111-1-1-1-1-1-11111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-11111
χ511111111111111111111-1-11111-1-1-1-1111111-1-1-11111-1-1-1-1-1-1111-1-1-1-111-1-111-1-11111-1-1-111-1-1
χ611111111111111111111-1-11111-1-1-1-111-1-1-1-1-1-1-11111-1-1-1-1-1-1111-1-111-1-111-1-11111-1-1-1-1-1-1-111
χ711111111111111111111-1-11111-1-1-1-1-1-11111-1-1-11111-1-1-1-1-1-1-1-1-111-1-111-1-111-1-1-1-1-1-1111-1-111
χ811111111111111111111-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-11111-1-111-1-111-1-11111111-1-1
χ911111111111111-1-1-1-11111111111111111-1-11-1-1-1-1-1-111-1-1-1-1111111-11111-1-1-1-1-1-1111-1-1-1-11-1
χ1011111111111111-1-1-1-111111111111111-1-1111-1-1-1-1-1-111-1-1-1-111111-11-1-1-1-11111-1-1-1-11-1-111-11
χ1111111111111111-1-1-1-1111111111111-1-111-1-11-1-1-1-1-1-111-1-1-1-1-1-1-1-1-11-11111-1-1-1-111-1-1-11111-11
χ1211111111111111-1-1-1-1111111111111-1-1-1-1111-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-11-1-1-1-111111111-111-1-11-1
χ1311111111111111-1-1-1-111-1-11111-1-1-1-11111-1-1-111-1-1-1-1-1-11111111-1-1-1111-1-1-1-111-1-111-111-1-1-11
χ1411111111111111-1-1-1-111-1-11111-1-1-1-111-1-111-111-1-1-1-1-1-11111111-1-11-1-1-11111-1-1-1-1-1-1-111111-1
χ1511111111111111-1-1-1-111-1-11111-1-1-1-1-1-111-1-1-111-1-1-1-1-1-11111-1-1-111-1111-1-1-1-11111-1-11-1-1111-1
χ1611111111111111-1-1-1-111-1-11111-1-1-1-1-1-1-1-111-111-1-1-1-1-1-11111-1-1-1111-1-1-11111-1-111111-1-1-1-1-11
χ172222222-2-2-2-222200002200-2-2-2-2000022000002i−2i0000002i2i−2i−2i-2-22000000000000000002i−2i0000
χ182222222-2-2-2-222200002200-2-2-2-200002200000−2i2i000000−2i−2i2i2i-2-2200000000000000000−2i2i0000
χ192222222-2-2-2-222200002200-2-2-2-20000-2-2000002i−2i0000002i2i−2i−2i22-200000000000000000−2i2i0000
χ202222222-2-2-2-222200002200-2-2-2-20000-2-200000−2i2i000000−2i−2i2i2i22-2000000000000000002i−2i0000
χ21222222-12222-1-1-12222-1-122-1-1-1-1-1-1-1-1002222222-1-1-1-1-1-1-1-1-1-10000022-1-1-1-1-1-1-1-100000000000
χ22222222-12222-1-1-12222-1-122-1-1-1-1-1-1-1-100-2-2-2-2222-1-1-1-1-1-1-1-1-1-100000-2-21111111100000000000
χ23222222-12222-1-1-12222-1-1-2-2-1-1-1-11111002222-2-2-2-1-1-1-111111100000-2-2-1-111-1-11100000000000
χ24222222-12222-1-1-12222-1-1-2-2-1-1-1-1111100-2-2-2-2-2-2-2-1-1-1-1111111000002211-1-111-1-100000000000
χ25222222-12222-1-1-1-2-2-2-2-1-122-1-1-1-1-1-1-1-10022-2-22-2-21111-1-11111000002-2-1-1-1-1111100000000000
χ26222222-12222-1-1-1-2-2-2-2-1-122-1-1-1-1-1-1-1-100-2-2222-2-21111-1-1111100000-221111-1-1-1-100000000000
χ27222222-12222-1-1-1-2-2-2-2-1-1-2-2-1-1-1-111110022-2-2-222111111-1-1-1-100000-22-1-11111-1-100000000000
χ28222222-12222-1-1-1-2-2-2-2-1-1-2-2-1-1-1-1111100-2-222-222111111-1-1-1-1000002-211-1-1-1-11100000000000
χ292222-2-222-2-2222222-2-2-2-20022-2-2000022000000022-2-20000002-2-2000000000000-22000000000
χ302222-2-222-2-2222222-2-2-2-20022-2-20000-2-2000000022-2-2000000-2220000000000002-2000000000
χ312222-2-222-2-22222-2-222-2-20022-2-20000220000000-2-2220000002-2-20000000000002-2000000000
χ322222-2-222-2-22222-2-222-2-20022-2-20000-2-20000000-2-222000000-222000000000000-22000000000
χ332222-2-22-222-22220000-2-222-2-2222222220000-2000000-2-20000-22-22200000000000000-2000000
χ342222-2-22-222-22220000-2-222-2-2222222-2-20000-2000000-2-200002-22-2-2000000000000002000000
χ352222-2-22-222-22220000-2-2-2-2-2-222-2-2-2-22200002000000220000-22-2-2-2000000000000002000000
χ362222-2-22-222-22220000-2-2-2-2-2-222-2-2-2-2-2-2000020000002200002-222200000000000000-2000000
χ3722-2-22-22-22-22-22-22i−2i2i−2i2-2002-22-200000000000002i−2i2i−2i000000000000000000000002i−2i0002-200
χ3822-2-22-22-22-22-22-22i−2i2i−2i2-2002-22-200000000000002i−2i2i−2i00000000000000000000000−2i2i000-2200
χ3922-2-22-22-22-22-22-2−2i2i−2i2i2-2002-22-20000000000000−2i2i−2i2i000000000000000000000002i−2i000-2200
χ4022-2-22-22-22-22-22-2−2i2i−2i2i2-2002-22-20000000000000−2i2i−2i2i00000000000000000000000−2i2i0002-200
χ4122-2-2-222-2-222-22-22i−2i−2i2i-22002-2-220000002-22i−2i0002i−2i−2i2i00000000000002-2002i−2i0000000000000
χ4222-2-2-222-2-222-22-22i−2i−2i2i-22002-2-22000000-22−2i2i0002i−2i−2i2i0000000000000-2200−2i2i0000000000000
χ4322-2-2-222-2-222-22-2−2i2i2i−2i-22002-2-220000002-2−2i2i000−2i2i2i−2i00000000000002-200−2i2i0000000000000
χ4422-2-2-222-2-222-22-2−2i2i2i−2i-22002-2-22000000-222i−2i000−2i2i2i−2i0000000000000-22002i−2i0000000000000
χ4522-2-2-22-1-2-2221-112i−2i−2i2i1-100-111-133−3−3002-22i−2i000−iii−i3−3−i3i3−i3i30000000-113−3−ii−i3i300000000000
χ4622-2-2-22-1-2-2221-112i−2i−2i2i1-100-111-133−3−300-22−2i2i000−iii−i3−3−i3i3−i3i300000001-1−33i−ii3−i300000000000
χ4722-2-2-22-1-2-2221-112i−2i−2i2i1-100-111-1−3−333002-22i−2i000−iii−i−33i3−i3i3−i30000000-11−33−iii3−i300000000000
χ4822-2-2-22-1-2-2221-112i−2i−2i2i1-100-111-1−3−33300-22−2i2i000−iii−i−33i3−i3i3−i300000001-13−3i−i−i3i300000000000
χ4922-2-2-22-1-2-2221-11−2i2i2i−2i1-100-111-133−3−3002-2−2i2i000i−i−ii3−3i3−i3i3−i30000000-113−3i−ii3−i300000000000
χ5022-2-2-22-1-2-2221-11−2i2i2i−2i1-100-111-133−3−300-222i−2i000i−i−ii3−3i3−i3i3−i300000001-1−33−ii−i3i300000000000
χ5122-2-2-22-1-2-2221-11−2i2i2i−2i1-100-111-1−3−333002-2−2i2i000i−i−ii−33−i3i3−i3i30000000-11−33i−i−i3i300000000000
χ5222-2-2-22-1-2-2221-11−2i2i2i−2i1-100-111-1−3−33300-222i−2i000i−i−ii−33−i3i3−i3i300000001-13−3−iii3−i300000000000
χ53444444-2-4-4-4-4-2-2-20000-2-2002222000000000004i−4i000000−2i−2i2i2i00000000000000000000000000
χ54444444-2-4-4-4-4-2-2-20000-2-200222200000000000−4i4i0000002i2i−2i−2i00000000000000000000000000
χ554444-4-4-24-4-44-2-2-244-4-42200-2-2220000000000000-2-22200000000000000000000000000000000
χ564444-4-4-24-4-44-2-2-2-4-4442200-2-222000000000000022-2-200000000000000000000000000000000
χ574444-4-4-2-444-4-2-2-20000224422-2-2-2-2-2-2000000-400000022000000000000000000000000000000
χ584444-4-4-2-444-4-2-2-2000022-4-422-2-222220000004000000-2-2000000000000000000000000000000
χ5944-4-44-444-44-4-44-400004-400-44-440000000000000000000000000000000000000000000000000
χ6044-4-44-4-24-44-42-220000-22002-22-22323−23−230000000000000−2323000000000000000000000000000000
χ6144-4-44-4-24-44-42-220000-22002-22-2−23−232323000000000000023−23000000000000000000000000000000
χ6244-4-44-4-2-44-442-224i−4i4i−4i-2200-22-220000000000000−2i2i−2i2i00000000000000000000000000000000
χ6344-4-44-4-2-44-442-22−4i4i−4i4i-2200-22-2200000000000002i−2i2i−2i00000000000000000000000000000000
χ6444-4-4-44444-4-4-44-40000-4400-444-40000000000000000000000000000000000000000000000000
χ6544-4-4-44-244-4-42-2200002-2002-2-22000000000000000000023−23−232300000000000000000000000000
χ6644-4-4-44-244-4-42-2200002-2002-2-220000000000000000000−232323−2300000000000000000000000000
χ674-4-440040000-4-44000000−2i22i20000−2i22i2−2i22i24-400000000000000000000−2i22i2000000000000000000000
χ684-4-440040000-4-44000000−2i22i20000−2i22i2−2i22i2-44000000000000000000002i2−2i2000000000000000000000
χ694-4-440040000-4-440000002i2−2i200002i2−2i22i2−2i24-4000000000000000000002i2−2i2000000000000000000000
χ704-4-440040000-4-440000002i2−2i200002i2−2i22i2−2i2-4400000000000000000000−2i22i2000000000000000000000
χ718-88-800800008-8-80000000000000000000000000000000000000000000000000000000000000
χ728-88-800-40000-4440000000000002i6−2i6−2i62i6000000000000000000000000000000000000000000000
χ738-88-800-40000-444000000000000−2i62i62i6−2i6000000000000000000000000000000000000000000000
χ748-8-8800-4000044-4000000−4i24i200002i2−2i22i2−2i2000000000000000000000000000000000000000000000
χ758-8-8800-4000044-40000004i2−4i20000−2i22i2−2i22i2000000000000000000000000000000000000000000000

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