Finite Group Databasebeta

← Group #10847331

Character table — Group #10847331

Order 768.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75
size11112222222222444444444444444466888888888888888881212121212161616161616161616162424242424242424244848
order12222234444666668888881212121224242424444444888121212122424242424244448848121212122424242444448888848
χ1111111111111111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111-1-11-1-11111111111111111-1-1-1-1-1-1-1-1-1-1-1-111-1-1111-1-1
χ3111111111111111111111111111111-1-111111111111111111-1-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-1-1
χ4111111111111111111111111111111-1-11-1-11-1-111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-111-1-1-111
χ511111111111111111111-1-11111-1-1-1-111-111-111-1-1-1-1-11111-1-1111-1-1-1-111-1-111-1-111-1-11111-1-1-1
χ611111111111111111111-1-11111-1-1-1-111-1-1-1-1-1-1-1-1-1-1-11111-1-1111-1-111-1-111-1-111-1-1-1-1-1-111-111
χ711111111111111111111-1-11111-1-1-1-1-1-1-111-111-1-1-1-1-11111-1-1-1-1-111-1-111-1-111-1-1-1-111-1-1-1-1111
χ811111111111111111111-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-11111-1-111-1-111111111-1-11-1-1
χ91111111111111111-1-1-1-1111111111111-111-1-1-11-1-1-1-1-1-1-1-111111111-11111-1-1-1-111-1-1-1-1-1-111-1
χ101111111111111111-1-1-1-1111111111111-1-1-1-1111-1-1-1-1-1-1-1-11111111-11-1-1-1-11111-1-1-1-111-1-11-11
χ111111111111111111-1-1-1-11111111111-1-1-111-1-1-11-1-1-1-1-1-1-1-111-1-1-1-1-11-11111-1-1-1-1-1-1111111-1-11
χ121111111111111111-1-1-1-11111111111-1-1-1-1-1-1111-1-1-1-1-1-1-1-111-1-1-1-1-1-11-1-1-1-111111111-1-111-11-1
χ131111111111111111-1-1-1-1-1-11111-1-1-1-1111111-1-1-11111-1-1-1-1-1-1111-1-1-1111-1-1-1-1111111-1-1-1-1-1-11
χ141111111111111111-1-1-1-1-1-11111-1-1-1-1111-1-1111-11111-1-1-1-1-1-1111-1-11-1-1-11111-1-1-1-11111-1-1-11-1
χ151111111111111111-1-1-1-1-1-11111-1-1-1-1-1-11111-1-1-11111-1-1-1-1-1-1-1-1-111-1111-1-1-1-111-1-1-1-1111111-1
χ161111111111111111-1-1-1-1-1-11111-1-1-1-1-1-11-1-1111-11111-1-1-1-1-1-1-1-1-1111-1-1-11111-1-111-1-1-1-1111-11
χ172222222-2-2-2-2222222i2i−2i−2i00-2-2-2-2000022000000000002i2i−2i−2i00-2-220000000000000000002i−2i000
χ182222222-2-2-2-2222222i2i−2i−2i00-2-2-2-20000-2-2000000000002i2i−2i−2i0022-2000000000000000000−2i2i000
χ192222222-2-2-2-222222−2i−2i2i2i00-2-2-2-200002200000000000−2i−2i2i2i00-2-22000000000000000000−2i2i000
χ202222222-2-2-2-222222−2i−2i2i2i00-2-2-2-20000-2-200000000000−2i−2i2i2i0022-20000000000000000002i−2i000
χ21222222-12222-1-1-1-1-1222222-1-1-1-1-1-1-1-1002222222-1-1-1-1-1-1-1-1-1-10000022-1-1-1-1-1-1-1-100000000000
χ22222222-12222-1-1-1-1-1222222-1-1-1-1-1-1-1-1002-2-22-2-22-1-1-1-1-1-1-1-1-1-100000-2-21111111100000000000
χ23222222-12222-1-1-1-1-12222-2-2-1-1-1-1111100-222-222-21111-1-1-1-11100000-2-2-1-111-1-11100000000000
χ24222222-12222-1-1-1-1-12222-2-2-1-1-1-1111100-2-2-2-2-2-2-21111-1-1-1-111000002211-1-111-1-100000000000
χ25222222-12222-1-1-1-1-1-2-2-2-222-1-1-1-1-1-1-1-100-222-2-2-2211111111-1-1000002-2-1-1-1-1111100000000000
χ26222222-12222-1-1-1-1-1-2-2-2-222-1-1-1-1-1-1-1-100-2-2-2-222211111111-1-100000-221111-1-1-1-100000000000
χ27222222-12222-1-1-1-1-1-2-2-2-2-2-2-1-1-1-11111002222-2-2-2-1-1-1-111111100000-22-1-11111-1-100000000000
χ28222222-12222-1-1-1-1-1-2-2-2-2-2-2-1-1-1-11111002-2-2222-2-1-1-1-1111111000002-211-1-1-1-11100000000000
χ292222-2-222-2-22222-2-2000022-222-2222222000000-200000000-2-22-2-222000000000000000000-200
χ302222-2-222-2-22222-2-2000022-222-22222-2-2000000-200000000-2-2-222-2-2000000000000000000200
χ312222-2-222-2-22222-2-20000-2-2-222-2-2-2-2-222000000200000000222-2-2-2-2000000000000000000200
χ322222-2-222-2-22222-2-20000-2-2-222-2-2-2-2-2-2-200000020000000022-22222000000000000000000-200
χ332222-2-22-222-2222-2-20000002-2-22000022200-200022-2-2000000-22-2000000000000002-20000000
χ342222-2-22-222-2222-2-20000002-2-22000022-2002000-2-222000000-22-200000000000000-220000000
χ352222-2-22-222-2222-2-20000002-2-220000-2-2200-200022-2-20000002-2200000000000000-220000000
χ362222-2-22-222-2222-2-20000002-2-220000-2-2-2002000-2-2220000002-22000000000000002-20000000
χ3722-2-22-2222-2-22-2-22-22-22-20022-2-2000000000000000002-22-2000000000000000002-2002-200000
χ3822-2-22-2222-2-22-2-22-22-22-20022-2-2000000000000000002-22-200000000000000000-2200-2200000
χ3922-2-22-2222-2-22-2-22-2-22-220022-2-200000000000000000-22-22000000000000000002-200-2200000
χ4022-2-22-2222-2-22-2-22-2-22-220022-2-200000000000000000-22-2200000000000000000-22002-200000
χ4122-2-22-22-2-2222-2-22-22i−2i−2i2i00-2-22200000002i−2i02-2000002i−2i−2i2i0000000002i−2i002-20000000000000
χ4222-2-22-22-2-2222-2-22-22i−2i−2i2i00-2-2220000000−2i2i0-22000002i−2i−2i2i000000000−2i2i00-220000000000000
χ4322-2-22-22-2-2222-2-22-2−2i2i2i−2i00-2-22200000002i−2i0-2200000−2i2i2i−2i0000000002i−2i00-220000000000000
χ4422-2-22-22-2-2222-2-22-2−2i2i2i−2i00-2-2220000000−2i2i02-200000−2i2i2i−2i000000000−2i2i002-20000000000000
χ4522-2-22-2-1-2-222-111-112i−2i−2i2i0011-1-1−i3−i3i3i30002i−2i02-203−33−3−iii−i−i3i30000000−ii3−3-11−i3i300000000000
χ4622-2-22-2-1-2-222-111-112i−2i−2i2i0011-1-1−i3−i3i3i3000−2i2i0-2203−33−3−iii−i−i3i30000000i−i−331-1i3−i300000000000
χ4722-2-22-2-1-2-222-111-112i−2i−2i2i0011-1-1i3i3−i3−i30002i−2i02-20−33−33−iii−ii3−i30000000−ii−33-11i3−i300000000000
χ4822-2-22-2-1-2-222-111-112i−2i−2i2i0011-1-1i3i3−i3−i3000−2i2i0-220−33−33−iii−ii3−i30000000i−i3−31-1−i3i300000000000
χ4922-2-22-2-1-2-222-111-11−2i2i2i−2i0011-1-1−i3−i3i3i30002i−2i0-220−33−33i−i−ii−i3i30000000−ii3−31-1i3−i300000000000
χ5022-2-22-2-1-2-222-111-11−2i2i2i−2i0011-1-1−i3−i3i3i3000−2i2i02-20−33−33i−i−ii−i3i30000000i−i−33-11−i3i300000000000
χ5122-2-22-2-1-2-222-111-11−2i2i2i−2i0011-1-1i3i3−i3−i30002i−2i0-2203−33−3i−i−iii3−i30000000−ii−331-1−i3i300000000000
χ5222-2-22-2-1-2-222-111-11−2i2i2i−2i0011-1-1i3i3−i3−i3000−2i2i02-203−33−3i−i−iii3−i30000000i−i3−3-11i3−i300000000000
χ53444444-2-4-4-4-4-2-2-2-2-24i4i−4i−4i00222200000000000000000−2i−2i2i2i0000000000000000000000000000
χ54444444-2-4-4-4-4-2-2-2-2-2−4i−4i4i4i002222000000000000000002i2i−2i−2i0000000000000000000000000000
χ554444-4-4-24-4-44-2-2-2220000442-2-22-2-2-2-200000000-4000000002200000000000000000000000000
χ564444-4-4-24-4-44-2-2-2220000-4-42-2-22222200000000400000000-2-200000000000000000000000000
χ574444-4-4-2-444-4-2-2-222000000-222-2000000400-4000-2-22200000000000000000000000000000000
χ584444-4-4-2-444-4-2-2-222000000-222-2000000-400400022-2-200000000000000000000000000000000
χ5944-4-44-4-244-4-4-222-224-44-400-2-22200000000000000000-22-220000000000000000000000000000
χ6044-4-44-4-244-4-4-222-22-44-4400-2-222000000000000000002-22-20000000000000000000000000000
χ6144-4-4-4444-44-44-4-4-44000000-44-440000000000000000000000000000000000000000000000000
χ6244-4-4-444-44-444-4-4-440000004-44-40000000000000000000000000000000000000000000000000
χ6344-4-4-44-24-44-4-2222-20000002-22-2000000000000023−23−232300000000000000000000000000000000
χ6444-4-4-44-24-44-4-2222-20000002-22-20000000000000−232323−2300000000000000000000000000000000
χ6544-4-4-44-2-44-44-2222-2000000-22-22−2i3−2i32i32i3000000000000000002i3−2i300000000000000000000000000
χ6644-4-4-44-2-44-44-2222-2000000-22-222i32i3−2i3−2i300000000000000000−2i32i300000000000000000000000000
χ674-4-440040000-44-4000000−2i22i20000−2i22i2−2i22i24-400000000000000000000−2i22i2000000000000000000000
χ684-4-440040000-44-4000000−2i22i20000−2i22i2−2i22i2-44000000000000000000002i2−2i2000000000000000000000
χ694-4-440040000-44-40000002i2−2i200002i2−2i22i2−2i24-4000000000000000000002i2−2i2000000000000000000000
χ704-4-440040000-44-40000002i2−2i200002i2−2i22i2−2i2-4400000000000000000000−2i22i2000000000000000000000
χ718-88-80080000-8-880000000000000000000000000000000000000000000000000000000000000
χ728-88-800-4000044-400000000000026−26−2626000000000000000000000000000000000000000000000
χ738-88-800-4000044-4000000000000−262626−26000000000000000000000000000000000000000000000
χ748-8-8800-400004-44000000−4i24i200002i2−2i22i2−2i2000000000000000000000000000000000000000000000
χ758-8-8800-400004-440000004i2−4i20000−2i22i2−2i22i2000000000000000000000000000000000000000000000

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