Finite Group Databasebeta

← Group #10877178

Character table — Group #10877178

Order 768.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72
size11112222222222444444444444448888888888888888881212121216161616161616161616242424242424242424244848
order12222234444666668888121212122424242444444488121212122424242424242244881212121224242424244444888888
χ1111111111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111111111-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-1-1-1
χ3111111111111111111111111111111-111-1-1-1-1-1-1-111-1-1-1-11111-1-11111-1-1-1-1-1-1111111-1-1-1-1
χ4111111111111111111111111111111-111-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-11111-1-1-1-111-1-1-1-1-1-11111
χ51111111111111111111111111111-1-11-1-111111111111111111-1-1-1-1-1-1-1-1-1-111-1-1-1-11111-1-1
χ61111111111111111111111111111-1-11-1-11111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-111
χ71111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-1111111-1-1-1-11111-1-1-1-1-1-111-1-111
χ81111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-111-1-1-1-11111111111-1-111-1-1
χ91111111111111111-1-1-1-11111-1-1-1-1111-1-11-1-11111-1-1-1-1-1-111111-111-1-111-1-11111-1-1-1-1-1-11-1
χ101111111111111111-1-1-1-11111-1-1-1-1111-1-11-1-11111-1-1-1-1-1-1-1-1-1-11-111-1-111-1-1-1-1-1-1111111-11
χ111111111111111111-1-1-1-11111-1-1-1-111-1-1-1-111-1-1-1-1-1-111111111-1111-1-1-1-111-1-111-1-1-1-111-11
χ121111111111111111-1-1-1-11111-1-1-1-111-1-1-1-111-1-1-1-1-1-11111-1-1-1-1-1111-1-1-1-11111-1-11111-1-11-1
χ131111111111111111-1-1-1-11111-1-1-1-1-1-11111-1-11111-1-1-1-1-1-11111-11-1-111-1-11111-1-111-1-1-1-1-11
χ141111111111111111-1-1-1-11111-1-1-1-1-1-11111-1-11111-1-1-1-1-1-1-1-1-1-1-11-1-111-1-111-1-111-1-111111-1
χ151111111111111111-1-1-1-11111-1-1-1-1-1-1-111-111-1-1-1-1-1-1111111111-1-1-11111-1-1-1-1-1-111-1-1111-1
χ161111111111111111-1-1-1-11111-1-1-1-1-1-1-111-111-1-1-1-1-1-11111-1-1-1-11-1-1-11111-1-11111-1-111-1-1-11
χ172222222-2-2-2-2222220000-2-2-2-200000000002i−2i0000002i2i−2i−2i22-2-20000000000000000002i−2i00
χ182222222-2-2-2-2222220000-2-2-2-200000000002i−2i0000002i2i−2i−2i-2-222000000000000000000−2i2i00
χ192222222-2-2-2-2222220000-2-2-2-20000000000−2i2i000000−2i−2i2i2i22-2-2000000000000000000−2i2i00
χ202222222-2-2-2-2222220000-2-2-2-20000000000−2i2i000000−2i−2i2i2i-2-2220000000000000000002i−2i00
χ21222222-12222-1-1-1-1-12222-1-1-1-1-1-1-1-122222222-1-1-1-1-1-1-1-1-1-1000022-1-1-1-1-1-1-1-1000000000000
χ22222222-12222-1-1-1-1-12222-1-1-1-1-1-1-1-122-222-2-2-21111-1-111110000-2-2-1-1-1-11111000000000000
χ23222222-12222-1-1-1-1-12222-1-1-1-1-1-1-1-1-2-22-2-2222-1-1-1-1-1-1-1-1-1-10000-2-211111111000000000000
χ24222222-12222-1-1-1-1-12222-1-1-1-1-1-1-1-1-2-2-2-2-2-2-2-21111-1-111110000221111-1-1-1-1000000000000
χ25222222-12222-1-1-1-1-1-2-2-2-2-1-1-1-11111222-2-22-2-2-1-1-1-111111100002-2-1-111-1-111000000000000
χ26222222-12222-1-1-1-1-1-2-2-2-2-1-1-1-1111122-2-2-2-222111111-1-1-1-10000-22-1-11111-1-1000000000000
χ27222222-12222-1-1-1-1-1-2-2-2-2-1-1-1-11111-2-22222-2-2-1-1-1-11111110000-2211-1-111-1-1000000000000
χ28222222-12222-1-1-1-1-1-2-2-2-2-1-1-1-11111-2-2-222-222111111-1-1-1-100002-211-1-1-1-111000000000000
χ292222-2-222-2-22222-2-222-2-2-222-22222000000000000-2-200002-22-200000000000000002-20000
χ302222-2-222-2-22222-2-222-2-2-222-22222000000000000-2-20000-22-220000000000000000-220000
χ312222-2-222-2-22222-2-2-2-222-222-2-2-2-2-20000000000002200002-22-20000000000000000-220000
χ322222-2-222-2-22222-2-2-2-222-222-2-2-2-2-2000000000000220000-22-2200000000000000002-20000
χ332222-2-22-222-2222-2-200002-2-22000000200-20022-2-20000002-2-2200000000002-20000000000
χ342222-2-22-222-2222-2-200002-2-22000000200-20022-2-2000000-222-20000000000-220000000000
χ352222-2-22-222-2222-2-200002-2-22000000-200200-2-2220000002-2-220000000000-220000000000
χ362222-2-22-222-2222-2-200002-2-22000000-200200-2-222000000-222-200000000002-20000000000
χ372-22-22-22-22-222-2-22-22-22-2-22-2222-2-22i−2i02i−2i00000002-200000000002i−2i2i−2i0000000000000000
χ382-22-22-22-22-222-2-22-22-22-2-22-2222-2-2−2i2i0−2i2i00000002-20000000000−2i2i−2i2i0000000000000000
χ392-22-22-22-22-222-2-22-2-22-22-22-22-2-2222i−2i0−2i2i0000000-2200000000002i−2i−2i2i0000000000000000
χ402-22-22-22-22-222-2-22-2-22-22-22-22-2-222−2i2i02i−2i0000000-220000000000−2i2i2i−2i0000000000000000
χ412-22-22-2-1-22-22-111-112-22-21-11-1-1-1112i−2i02i−2i0003−33−3-113−33−3000000−ii−ii−i3i3−i3i3000000000000
χ422-22-22-2-1-22-22-111-112-22-21-11-1-1-1112i−2i02i−2i000−33−33-11−33−33000000−ii−iii3−i3i3−i3000000000000
χ432-22-22-2-1-22-22-111-112-22-21-11-1-1-111−2i2i0−2i2i0003−33−3-113−33−3000000i−ii−ii3−i3i3−i3000000000000
χ442-22-22-2-1-22-22-111-112-22-21-11-1-1-111−2i2i0−2i2i000−33−33-11−33−33000000i−ii−i−i3i3−i3i3000000000000
χ452-22-22-2-1-22-22-111-11-22-221-11-111-1-12i−2i0−2i2i0003−33−31-1−33−33000000−iii−i−i3i3i3−i3000000000000
χ462-22-22-2-1-22-22-111-11-22-221-11-111-1-12i−2i0−2i2i000−33−331-13−33−3000000−iii−ii3−i3−i3i3000000000000
χ472-22-22-2-1-22-22-111-11-22-221-11-111-1-1−2i2i02i−2i0003−33−31-1−33−33000000i−i−iii3−i3−i3i3000000000000
χ482-22-22-2-1-22-22-111-11-22-221-11-111-1-1−2i2i02i−2i000−33−331-13−33−3000000i−i−ii−i3i3i3−i3000000000000
χ492-22-2-222-2-2222-2-2-222-2-2222-2-222-2-2000000000000-22000000000000000000002i−2i2i−2i000000
χ502-22-2-222-2-2222-2-2-222-2-2222-2-222-2-2000000000000-2200000000000000000000−2i2i−2i2i000000
χ512-22-2-222-2-2222-2-2-22-222-222-2-2-2-2220000000000002-2000000000000000000002i−2i−2i2i000000
χ522-22-2-222-2-2222-2-2-22-222-222-2-2-2-2220000000000002-200000000000000000000−2i2i2i−2i000000
χ53444444-2-4-4-4-4-2-2-2-2-20000222200000000004i−4i000000−2i−2i2i2i00000000000000000000000000
χ54444444-2-4-4-4-4-2-2-2-2-2000022220000000000−4i4i0000002i2i−2i−2i00000000000000000000000000
χ554444-4-4-24-4-44-2-2-22244-4-42-2-22-2-2-2-200000000000022000000000000000000000000000000
χ564444-4-4-24-4-44-2-2-222-4-4442-2-222222000000000000-2-2000000000000000000000000000000
χ574444-4-4-2-444-4-2-2-2220000-222-2000000400-400-2-22200000000000000000000000000000000
χ584444-4-4-2-444-4-2-2-2220000-222-2000000-40040022-2-200000000000000000000000000000000
χ594-44-44-444-44-44-4-44-400004-44-4000000000000000000000000000000000000000000000000
χ604-44-44-4-24-44-4-222-220000-22-22000000000000000000−2i32i32i3−2i300000000000000000000000000
χ614-44-44-4-24-44-4-222-220000-22-220000000000000000002i3−2i3−2i32i300000000000000000000000000
χ624-44-4-44444-4-44-4-4-440000-4-444000000000000000000000000000000000000000000000000
χ634-44-4-44-244-4-4-2222-2000022-2-200000000000023−23−232300000000000000000000000000000000
χ644-44-4-44-244-4-4-2222-2000022-2-2000000000000−232323−2300000000000000000000000000000000
χ654-44-4-44-2-4-444-2222-24-4-44-2-222-2-2220000000000002-2000000000000000000000000000000
χ664-44-4-44-2-4-444-2222-2-444-4-2-22222-2-2000000000000-22000000000000000000000000000000
χ6788-8-80080000-88-80000000000000000000000000000000000000000000000000000000000
χ6888-8-800-400004-44000000000026−2626−2600000000000000000000000000000000000000000000
χ6988-8-800-400004-440000000000−2626−262600000000000000000000000000000000000000000000
χ708-8-880080000-8-880000000000000000000000000000000000000000000000000000000000
χ718-8-8800-4000044-4000000000026−26−262600000000000000000000000000000000000000000000
χ728-8-8800-4000044-40000000000−262626−2600000000000000000000000000000000000000000000

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