Finite Group Databasebeta

← Group #10768999

Character table — Group #10768999

Order 768.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72
size11112222222222444444444444448888888888888888881616161616161616161624242424242424242424242424242424
order1222223444466644446612121212121212122444888812122424242424242424688121212242424242224444444444444
χ1111111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ311111111111111111111111111111111-1-1-1-111-1-1-1-1-1-1-1-11-1-1111-1-1-1-111-111-1-1-1-1-1-1-11111
χ411111111111111111111111111111111-1-1-1-111-1-1-1-1-1-1-1-11-1-1111-1-1-1-1-1-11-1-11111111-1-1-1-1
χ51111111111111111111111111111-1-1-1-111111111111111-1-1-1-1-1-1-1-1-1-111-1111111-1-1-1-1-1-1-1
χ61111111111111111111111111111-1-1-1-111111111111111-1-1-1-1-1-1-1-1-1-1-1-11-1-1-1-1-1-11111111
χ71111111111111111111111111111-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1-111-1-1-1111111111-1-1-1-1111-1-1-1-1
χ81111111111111111111111111111-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1-111-1-1-11111-1-1-1-1-11111-1-1-11111
χ91111111-1-1-1-1111-1-11111-1-1-1-1111111-1-111-1-1-1-11111-1-1-1-111-11-1-111-1-1111-1-111-1-11-1-111-1-1
χ101111111-1-1-1-1111-1-11111-1-1-1-1111111-1-111-1-1-1-11111-1-1-1-111-11-1-111-1-1-1-1-111-1-111-111-1-111
χ111111111-1-1-1-1111-1-11111-1-1-1-1111111-1-1-1-111-1-1-1-1-1-111111-111-1-1-1-11111-1-1-1-1-111-11111-1-1
χ121111111-1-1-1-1111-1-11111-1-1-1-1111111-1-1-1-111-1-1-1-1-1-111111-111-1-1-1-111-1-111111-1-11-1-1-1-111
χ131111111-1-1-1-1111-1-11111-1-1-1-11111-1-11111-1-1-1-11111-1-1-1-1-1-11-111-1-11111-1-1-111-1-1-111-1-111
χ141111111-1-1-1-1111-1-11111-1-1-1-11111-1-11111-1-1-1-11111-1-1-1-1-1-11-111-1-111-1-1111-1-1111-1-111-1-1
χ151111111-1-1-1-1111-1-11111-1-1-1-11111-1-111-1-111-1-1-1-1-1-11111-11-1-11111-1-1111-1-1-1-1111-1-1-1-111
χ161111111-1-1-1-1111-1-11111-1-1-1-11111-1-111-1-111-1-1-1-1-1-11111-11-1-11111-1-1-1-1-11111-1-1-11111-1-1
χ17222222222-2-22222-2-2-22222-2-2-2-2-2-22-22-200002-200000000200-22-200000000000000000000
χ18222222222-2-22222-2-2-22222-2-2-2-2-2-2-22-2200002-200000000-2002-2200000000000000000000
χ192222222-2-222222-22-2-222-2-222-2-2-2-22-2-220000-2200000000200-2-2200000000000000000000
χ202222222-2-222222-22-2-222-2-222-2-2-2-2-222-20000-2200000000-20022-200000000000000000000
χ21222222-12222-1-1-12222-1-1-1-1-1-1-1-1-1-122222222-1-1-1-1-1-1-1-1-1-1-122-1-1-1-1-1-1-10000000000000000
χ22222222-12222-1-1-12222-1-1-1-1-1-1-1-1-1-12222-2-2-2-2-1-111111111-1-2-2-1-1-111110000000000000000
χ23222222-12222-1-1-12222-1-1-1-1-1-1-1-1-1-1-2-2-2-22222-1-1-1-1-1-1-1-1-1-11-2-211111110000000000000000
χ24222222-12222-1-1-12222-1-1-1-1-1-1-1-1-1-1-2-2-2-2-2-2-2-2-1-111111111122111-1-1-1-10000000000000000
χ25222222-122-2-2-1-1-12-2-2-2-1-1-1-11111112-22-20000-1133−3−333−3−3-1001-113−33−30000000000000000
χ26222222-122-2-2-1-1-12-2-2-2-1-1-1-11111112-22-20000-11−3−333−3−333-1001-11−33−330000000000000000
χ27222222-122-2-2-1-1-12-2-2-2-1-1-1-1111111-22-220000-1133−3−333−3−3100-11-1−33−330000000000000000
χ28222222-122-2-2-1-1-12-2-2-2-1-1-1-1111111-22-220000-11−3−333−3−333100-11-13−33−30000000000000000
χ29222222-1-2-222-1-1-1-22-2-2-1-111-1-111112-2-2200001-133−3−3−3−333-10011-13−3−330000000000000000
χ30222222-1-2-222-1-1-1-22-2-2-1-111-1-111112-2-2200001-1−3−33333−3−3-10011-1−333−30000000000000000
χ31222222-1-2-222-1-1-1-22-2-2-1-111-1-11111-222-200001-133−3−3−3−333100-1-11−333−30000000000000000
χ32222222-1-2-222-1-1-1-22-2-2-1-111-1-11111-222-200001-1−3−33333−3−3100-1-113−3−330000000000000000
χ33222222-1-2-2-2-2-1-1-1-2-222-1-11111-1-1-1-122-2-222-2-211-1-1-1-11111-12-2-111-1-1110000000000000000
χ34222222-1-2-2-2-2-1-1-1-2-222-1-11111-1-1-1-122-2-2-2-222111111-1-1-1-1-1-22-11111-1-10000000000000000
χ35222222-1-2-2-2-2-1-1-1-2-222-1-11111-1-1-1-1-2-22222-2-211-1-1-1-111111-221-1-111-1-10000000000000000
χ36222222-1-2-2-2-2-1-1-1-2-222-1-11111-1-1-1-1-2-222-2-222111111-1-1-1-112-21-1-1-1-1110000000000000000
χ372222-2-222222222-2-22-2-2-2222222-2-200000000-2-2000000000000000000000002-22-20000000
χ382222-2-222222222-2-22-2-2-2222222-2-200000000-2-200000000000000000000000-22-220000000
χ392222-2-2222-2-2222-22-22-2-222-2-2-2-22200000000-22000000000000000000002000000-22-20000
χ402222-2-2222-2-2222-22-22-2-222-2-2-2-22200000000-2200000000000000000000-20000002-220000
χ412222-2-22-2-2222222-2-22-2-2-2-222-2-222000000002-2000000000000000000002000000-2-220000
χ422222-2-22-2-2222222-2-22-2-2-2-222-2-222000000002-200000000000000000000-200000022-20000
χ432222-2-22-2-2-2-2222222-2-2-2-2-2-2-222-2-20000000022000000000000000000000002-2-220000000
χ442222-2-22-2-2-2-2222222-2-2-2-2-2-2-222-2-2000000002200000000000000000000000-222-20000000
χ454444-4-4-24444-2-2-2-4-44-422-2-2-2-2-2-22200000000220000000000000000000000000000000000
χ464444-4-4-244-4-4-2-2-2-44-4422-2-22222-2-2000000002-20000000000000000000000000000000000
χ474444-4-4-2-4-444-2-2-24-4-442222-2-222-2-200000000-220000000000000000000000000000000000
χ484444-4-4-2-4-4-4-4-2-2-2444-4222222-2-22200000000-2-20000000000000000000000000000000000
χ4944-4-4004004i−4i4-4-4000000004i−4i000000000000000000000000000000000000000000002-22i−2i
χ5044-4-4004004i−4i4-4-4000000004i−4i00000000000000000000000000000000000000000000-22−2i2i
χ5144-4-400400−4i4i4-4-400000000−4i4i000000000000000000000000000000000000000000002-2−2i2i
χ5244-4-400400−4i4i4-4-400000000−4i4i00000000000000000000000000000000000000000000-222i−2i
χ534-44-40044i−4i00-44-40000004i−4i00000000000000000000000000000000002-202i−2i00000000000
χ544-44-40044i−4i00-44-40000004i−4i0000000000000000000000000000000000-220−2i2i00000000000
χ554-44-4004−4i4i00-44-4000000−4i4i00000000000000000000000000000000002-20−2i2i00000000000
χ564-44-4004−4i4i00-44-4000000−4i4i0000000000000000000000000000000000-2202i−2i00000000000
χ574-4-444-440000-4-4400004-400000000000000−2i22i2000000−2i22i2−2i22i200000000000000000000000000
χ584-4-444-440000-4-4400004-4000000000000002i2−2i20000002i2−2i22i2−2i200000000000000000000000000
χ594-4-444-4-2000022-20000-22000023−2323−23000000−2i22i20000002ζ5+2ζ7−2ζ5−2ζ72ζ13+2ζ23−2ζ13−2ζ2300000000000000000000000000
χ604-4-444-4-2000022-20000-22000023−2323−230000002i2−2i2000000−2ζ5−2ζ72ζ5+2ζ7−2ζ13−2ζ232ζ13+2ζ2300000000000000000000000000
χ614-4-444-4-2000022-20000-220000−2323−2323000000−2i22i20000002ζ13+2ζ23−2ζ13−2ζ232ζ5+2ζ7−2ζ5−2ζ700000000000000000000000000
χ624-4-444-4-2000022-20000-220000−2323−23230000002i2−2i2000000−2ζ13−2ζ232ζ13+2ζ23−2ζ5−2ζ72ζ5+2ζ700000000000000000000000000
χ634-4-44-4440000-4-440000-44000000000000−2i22i20000−2i22i2−2i22i2000000000000000000000000000000
χ644-4-44-4440000-4-440000-440000000000002i2−2i200002i2−2i22i2−2i2000000000000000000000000000000
χ654-4-44-44-2000022-200002-2000023−23−23230000−2i22i200002ζ13+2ζ23−2ζ13−2ζ232ζ5+2ζ7−2ζ5−2ζ7000000000000000000000000000000
χ664-4-44-44-2000022-200002-2000023−23−232300002i2−2i20000−2ζ13−2ζ232ζ13+2ζ23−2ζ5−2ζ72ζ5+2ζ7000000000000000000000000000000
χ674-4-44-44-2000022-200002-20000−232323−230000−2i22i200002ζ5+2ζ7−2ζ5−2ζ72ζ13+2ζ23−2ζ13−2ζ23000000000000000000000000000000
χ684-4-44-44-2000022-200002-20000−232323−2300002i2−2i20000−2ζ5−2ζ72ζ5+2ζ7−2ζ13−2ζ232ζ13+2ζ23000000000000000000000000000000
χ6988-8-800-4008i−8i-44400000000−4i4i000000000000000000000000000000000000000000000000
χ7088-8-800-400−8i8i-444000000004i−4i000000000000000000000000000000000000000000000000
χ718-88-800-48i−8i004-44000000−4i4i00000000000000000000000000000000000000000000000000
χ728-88-800-4−8i8i004-440000004i−4i00000000000000000000000000000000000000000000000000

Here ζ is a primitive root of unity of order 24 (ζ24 = 1); i = ζ6.