Finite Group Databasebeta

← Group #10768912

Character table — Group #10768912

Order 768.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72
size11112222222222444444444444448888888888888888881616161616161616161624242424242424242424242424242424
order122222344446664444661212121212121212224488881212242424242424242466881212242424242444444444444444
χ1111111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ311111111111111111111111111111111-1-1-1-111-1-1-1-1-1-1-1-111-1-111-1-1-1-111-1-1111111-1-1-1-1-1-1
χ411111111111111111111111111111111-1-1-1-111-1-1-1-1-1-1-1-111-1-111-1-1-1-1-1-111-1-1-1-1-1-1111111
χ51111111111111111111111111111-1-1-1-111111111111111-1-1-1-1-1-1-1-1-1-111111-1-11-1-111-1-1-1-1
χ61111111111111111111111111111-1-1-1-111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-111-1-11111
χ71111111111111111111111111111-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-111-1-1111111-1-11-1-11-1-1-1-11111
χ81111111111111111111111111111-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-111-1-11111-1-111-111-11111-1-1-1-1
χ91111111-1-1-1-1111-1-11111-1-1-1-111111-11-111-1-1-1-11111-1-1-1-11-11-11-111-1-11111-11-1-11-1-1-111-1-1
χ101111111-1-1-1-1111-1-11111-1-1-1-111111-11-111-1-1-1-11111-1-1-1-11-11-11-111-1-1-1-1-1-11-111-1111-1-111
χ111111111-1-1-1-1111-1-11111-1-1-1-111111-11-1-1-111-1-1-1-1-1-111111-1-111-1-1-11111-1-1-11-1-11-111-1-111
χ121111111-1-1-1-1111-1-11111-1-1-1-111111-11-1-1-111-1-1-1-1-1-111111-1-111-1-1-111-1-1111-111-11-1-111-1-1
χ131111111-1-1-1-1111-1-11111-1-1-1-11111-11-1111-1-1-1-11111-1-1-1-1-11-11-11-1-1111111-1-11-1-11-1-1-1-111
χ141111111-1-1-1-1111-1-11111-1-1-1-11111-11-1111-1-1-1-11111-1-1-1-1-11-11-11-1-111-1-1-1-111-111-11111-1-1
χ151111111-1-1-1-1111-1-11111-1-1-1-11111-11-11-1-111-1-1-1-1-1-11111-111-1-1111-1-111-1-1-1-11-1-111111-1-1
χ161111111-1-1-1-1111-1-11111-1-1-1-11111-11-11-1-111-1-1-1-1-1-11111-111-1-1111-1-1-1-11111-111-1-1-1-1-111
χ17222222222-2-22222-2-2-22222-2-2-2-2-2-22-2-2200002-2000000002-200-2200000000000000000000
χ18222222222-2-22222-2-2-22222-2-2-2-2-2-2-222-200002-200000000-22002-200000000000000000000
χ192222222-2-222222-22-2-222-2-222-2-2-2-222-2-20000-22000000002200-2-200000000000000000000
χ202222222-2-222222-22-2-222-2-222-2-2-2-2-2-2220000-2200000000-2-2002200000000000000000000
χ21222222-12222-1-1-12222-1-1-1-1-1-1-1-1-1-122222222-1-1-1-1-1-1-1-1-1-1-1-122-1-1-1-1-1-10000000000000000
χ22222222-12222-1-1-12222-1-1-1-1-1-1-1-1-1-12222-2-2-2-2-1-111111111-1-1-2-2-1-111110000000000000000
χ23222222-12222-1-1-12222-1-1-1-1-1-1-1-1-1-1-2-2-2-22222-1-1-1-1-1-1-1-1-1-111-2-21111110000000000000000
χ24222222-12222-1-1-12222-1-1-1-1-1-1-1-1-1-1-2-2-2-2-2-2-2-2-1-111111111112211-1-1-1-10000000000000000
χ25222222-122-2-2-1-1-12-2-2-2-1-1-1-11111112-2-220000-1133−3−333−3−3-11001-13−33−30000000000000000
χ26222222-122-2-2-1-1-12-2-2-2-1-1-1-11111112-2-220000-11−3−333−3−333-11001-1−33−330000000000000000
χ27222222-122-2-2-1-1-12-2-2-2-1-1-1-1111111-222-20000-1133−3−333−3−31-100-11−33−330000000000000000
χ28222222-122-2-2-1-1-12-2-2-2-1-1-1-1111111-222-20000-11−3−333−3−3331-100-113−33−30000000000000000
χ29222222-1-2-222-1-1-1-22-2-2-1-111-1-1111122-2-200001-133−3−3−3−333-1-100113−3−330000000000000000
χ30222222-1-2-222-1-1-1-22-2-2-1-111-1-1111122-2-200001-1−3−33333−3−3-1-10011−333−30000000000000000
χ31222222-1-2-222-1-1-1-22-2-2-1-111-1-11111-2-22200001-133−3−3−3−3331100-1-1−333−30000000000000000
χ32222222-1-2-222-1-1-1-22-2-2-1-111-1-11111-2-22200001-1−3−33333−3−31100-1-13−3−330000000000000000
χ33222222-1-2-2-2-2-1-1-1-2-222-1-11111-1-1-1-12-22-222-2-211-1-1-1-11111-112-2-11-1-1110000000000000000
χ34222222-1-2-2-2-2-1-1-1-2-222-1-11111-1-1-1-12-22-2-2-222111111-1-1-1-1-11-22-1111-1-10000000000000000
χ35222222-1-2-2-2-2-1-1-1-2-222-1-11111-1-1-1-1-22-2222-2-211-1-1-1-111111-1-221-111-1-10000000000000000
χ36222222-1-2-2-2-2-1-1-1-2-222-1-11111-1-1-1-1-22-22-2-222111111-1-1-1-11-12-21-1-1-1110000000000000000
χ372222-2-222222222-2-22-2-2-2222222-2-200000000-2-20000000000000000002-200200-200000000
χ382222-2-222222222-2-22-2-2-2222222-2-200000000-2-2000000000000000000-2200-200200000000
χ392222-2-2222-2-2222-22-22-2-222-2-2-2-22200000000-22000000000000000000000002-20-22000000
χ402222-2-2222-2-2222-22-22-2-222-2-2-2-22200000000-2200000000000000000000000-2202-2000000
χ412222-2-22-2-2222222-2-22-2-2-2-222-2-222000000002-200000000000000000000000220-2-2000000
χ422222-2-22-2-2222222-2-22-2-2-2-222-2-222000000002-200000000000000000000000-2-2022000000
χ432222-2-22-2-2-2-2222222-2-2-2-2-2-2-222-2-200000000220000000000000000002-200-200200000000
χ442222-2-22-2-2-2-2222222-2-2-2-2-2-2-222-2-20000000022000000000000000000-2200200-200000000
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
χ4944-4-44-4400004-4-400004-400000000000022−22000022−2222−22000000000000000000000000000000
χ5044-4-44-4400004-4-400004-4000000000000−22220000−2222−2222000000000000000000000000000000
χ5144-4-44-4-20000-2220000-22000023−2323−23000022−2200002ζ5−2ζ7−2ζ5+2ζ72ζ13−2ζ23−2ζ13+2ζ23000000000000000000000000000000
χ5244-4-44-4-20000-2220000-22000023−2323−230000−22220000−2ζ5+2ζ72ζ5−2ζ7−2ζ13+2ζ232ζ13−2ζ23000000000000000000000000000000
χ5344-4-44-4-20000-2220000-220000−2323−2323000022−2200002ζ13−2ζ23−2ζ13+2ζ232ζ5−2ζ7−2ζ5+2ζ7000000000000000000000000000000
χ5444-4-44-4-20000-2220000-220000−2323−23230000−22220000−2ζ13+2ζ232ζ13−2ζ23−2ζ5+2ζ72ζ5−2ζ7000000000000000000000000000000
χ5544-4-4-44400004-4-40000-4400000000000000−2i22i2000000−2i22i2−2i22i200000000000000000000000000
χ5644-4-4-44400004-4-40000-44000000000000002i2−2i20000002i2−2i22i2−2i200000000000000000000000000
χ5744-4-4-44-20000-22200002-2000023−23−2323000000−2i22i20000002ζ5+2ζ7−2ζ5−2ζ72ζ13+2ζ23−2ζ13−2ζ2300000000000000000000000000
χ5844-4-4-44-20000-22200002-2000023−23−23230000002i2−2i2000000−2ζ5−2ζ72ζ5+2ζ7−2ζ13−2ζ232ζ13+2ζ2300000000000000000000000000
χ5944-4-4-44-20000-22200002-20000−232323−23000000−2i22i20000002ζ13+2ζ23−2ζ13−2ζ232ζ5+2ζ7−2ζ5−2ζ700000000000000000000000000
χ6044-4-4-44-20000-22200002-20000−232323−230000002i2−2i2000000−2ζ13−2ζ232ζ13+2ζ23−2ζ5−2ζ72ζ5+2ζ700000000000000000000000000
χ614-44-4004004-4-4-44000000004-4000000000000000000000000000000000000000000002i−2i2i−2i
χ624-44-4004004-4-4-44000000004-400000000000000000000000000000000000000000000−2i2i−2i2i
χ634-44-400400-44-4-4400000000-44000000000000000000000000000000000000000000002i−2i−2i2i
χ644-44-400400-44-4-4400000000-4400000000000000000000000000000000000000000000−2i2i2i−2i
χ654-4-440044i−4i00-44-40000004i−4i0000000000000000000000000000000000002i−2i0000002-20000
χ664-4-440044i−4i00-44-40000004i−4i000000000000000000000000000000000000−2i2i000000-220000
χ674-4-44004−4i4i00-44-4000000−4i4i0000000000000000000000000000000000002i−2i000000-220000
χ684-4-44004−4i4i00-44-4000000−4i4i000000000000000000000000000000000000−2i2i0000002-20000
χ698-88-800-4008-844-400000000-44000000000000000000000000000000000000000000000000
χ708-88-800-400-8844-4000000004-4000000000000000000000000000000000000000000000000
χ718-8-8800-48i−8i004-44000000−4i4i00000000000000000000000000000000000000000000000000
χ728-8-8800-4−8i8i004-440000004i−4i00000000000000000000000000000000000000000000000000

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