Finite Group Databasebeta

← Group #10877179

Character table — Group #10877179

Order 768.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72
size11112222222222444444444444448888888888888888881212121216161616161616161616242424242424242424244848
order122222344446662244661212121212121212444466888812121212121212128888882424242424242424244444448888
χ1111111111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111111111-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-1-1-1
χ31111111111111111111111111111111111-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-1-11111-111-1-1
χ41111111111111111111111111111111111-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1111-1-1-1-11-1-111
χ51111111111111111111111111111-1-1-1-1111111-1-1-1-1-1-1-1-11111-1-11111-1-1-1-1111-1-1-1-1111-1-1
χ61111111111111111111111111111-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-11111-1-1-111
χ71111111111111111111111111111-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-1-11111-1-1-1-1-1-1-1-11111
χ81111111111111111111111111111-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-1111111111111-1-1-1-1
χ911111111111111-1-1-1-111-1-1-1-1111111-1-1-1-111-1-11111-1-1-1-111111-111-1-111-1-1-11-111-1-11-1-11-1
χ1011111111111111-1-1-1-111-1-1-1-1111111-1-1-1-111-1-11111-1-1-1-1-1-1-1-11-111-1-111-1-11-11-1-111-111-11
χ1111111111111111-1-1-1-111-1-1-1-1111111-1-1-1-1-1-1111111-1-1-1-11111-11-1-111-1-1111-1111-1-1-1-1-1-11
χ1211111111111111-1-1-1-111-1-1-1-1111111-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1-11-1-111-1-111-11-1-1-1111111-1
χ1311111111111111-1-1-1-111-1-1-1-11111-1-111-1-111-1-1-1-1-1-111111111-1111-1-1-1-111-11-1-1-1111-1-1-11
χ1411111111111111-1-1-1-111-1-1-1-11111-1-111-1-111-1-1-1-1-1-11111-1-1-1-1-1111-1-1-1-1111-1111-1-1-1111-1
χ1511111111111111-1-1-1-111-1-1-1-11111-1-111-1-1-1-111-1-1-1-1111111111-1-1-11111-1-11-11-1-111-1-1-11-1
χ1611111111111111-1-1-1-111-1-1-1-11111-1-111-1-1-1-111-1-1-1-11111-1-1-1-11-1-1-11111-1-1-11-111-1-1111-11
χ172222222-2-2-2-222222-2-222-2-2-2-2-2-2-2-20000222i−2i2i−2i000000000000002i−2i2i−2i0000000000000000
χ182222222-2-2-2-222222-2-222-2-2-2-2-2-2-2-2000022−2i2i−2i2i00000000000000−2i2i−2i2i0000000000000000
χ192222222-2-2-2-2222-2-222222222-2-2-2-20000-2-22i−2i−2i2i000000000000002i−2i−2i2i0000000000000000
χ202222222-2-2-2-2222-2-222222222-2-2-2-20000-2-2−2i2i2i−2i00000000000000−2i2i2i−2i0000000000000000
χ21222222-12222-1-1-12222-1-1-1-1-1-1-1-1-1-12222-1-12222-1-1-1-1-1-1-1-1000022-1-1-1-1-1-1-1-1000000000000
χ22222222-12222-1-1-12222-1-1-1-1-1-1-1-1-1-12222-1-1-2-2-2-2-1-1-1-1-1-1-1-10000-2-211111111000000000000
χ23222222-12222-1-1-12222-1-1-1-1-1-1-1-1-1-1-2-2-2-2-1-12222111111110000-2-2-1-1-1-11111000000000000
χ24222222-12222-1-1-12222-1-1-1-1-1-1-1-1-1-1-2-2-2-2-1-1-2-2-2-2111111110000221111-1-1-1-1000000000000
χ25222222-12222-1-1-1-2-2-2-2-1-11111-1-1-1-122-2-21122-2-2-1-1-1-1111100002-2-1-111-1-111000000000000
χ26222222-12222-1-1-1-2-2-2-2-1-11111-1-1-1-122-2-211-2-222-1-1-1-111110000-2211-1-111-1-1000000000000
χ27222222-12222-1-1-1-2-2-2-2-1-11111-1-1-1-1-2-2221122-2-21111-1-1-1-10000-22-1-11111-1-1000000000000
χ28222222-12222-1-1-1-2-2-2-2-1-11111-1-1-1-1-2-22211-2-2221111-1-1-1-100002-211-1-1-1-111000000000000
χ29222222-1-2-2-2-2-1-1-122-2-2-1-1111111110000-1-12i−2i2i−2i−i3−i3i3i3−i3−i3i3i3000000−ii−ii3−33−3000000000000
χ30222222-1-2-2-2-2-1-1-122-2-2-1-1111111110000-1-12i−2i2i−2ii3i3−i3−i3i3i3−i3−i3000000−ii−ii−33−33000000000000
χ31222222-1-2-2-2-2-1-1-122-2-2-1-1111111110000-1-1−2i2i−2i2i−i3−i3i3i3−i3−i3i3i3000000i−ii−i−33−33000000000000
χ32222222-1-2-2-2-2-1-1-122-2-2-1-1111111110000-1-1−2i2i−2i2ii3i3−i3−i3i3i3−i3−i3000000i−ii−i3−33−3000000000000
χ33222222-1-2-2-2-2-1-1-1-2-222-1-1-1-1-1-111110000112i−2i−2i2i−i3−i3i3i3i3i3−i3−i3000000−iii−i3−3−33000000000000
χ34222222-1-2-2-2-2-1-1-1-2-222-1-1-1-1-1-111110000112i−2i−2i2ii3i3−i3−i3−i3−i3i3i3000000−iii−i−333−3000000000000
χ35222222-1-2-2-2-2-1-1-1-2-222-1-1-1-1-1-11111000011−2i2i2i−2i−i3−i3i3i3i3i3−i3−i3000000i−i−ii−333−3000000000000
χ36222222-1-2-2-2-2-1-1-1-2-222-1-1-1-1-1-11111000011−2i2i2i−2ii3i3−i3−i3−i3−i3i3i3000000i−i−ii3−3−33000000000000
χ372222-2-222-2-222222-22-2-2-222-2-222-2-200002-200000000000022-2-20000000000000000002-200
χ382222-2-222-2-222222-22-2-2-222-2-222-2-200002-2000000000000-2-222000000000000000000-2200
χ392222-2-222-2-22222-22-22-2-2-2-22222-2-20000-2200000000000022-2-2000000000000000000-2200
χ402222-2-222-2-22222-22-22-2-2-2-22222-2-20000-22000000000000-2-2220000000000000000002-200
χ412222-2-22-222-22222-2-22-2-2-2-222-2-22200002-20000000000000000000000000022-20000-20000
χ422222-2-22-222-22222-2-22-2-2-2-222-2-22200002-200000000000000000000000000-2-22000020000
χ432222-2-22-222-2222-222-2-2-222-2-2-2-2220000-22000000000000000000000000002-2-2000020000
χ442222-2-22-222-2222-222-2-2-222-2-2-2-2220000-2200000000000000000000000000-2220000-20000
χ4522-2-22-22-22-222-2-200002-200002-22-2002i−2i00000000002i−2i2i−2i2-22-20000000000000002i−2i00000
χ4622-2-22-22-22-222-2-200002-200002-22-2002i−2i00000000002i−2i2i−2i-22-22000000000000000−2i2i00000
χ4722-2-22-22-22-222-2-200002-200002-22-200−2i2i0000000000−2i2i−2i2i2-22-2000000000000000−2i2i00000
χ4822-2-22-22-22-222-2-200002-200002-22-200−2i2i0000000000−2i2i−2i2i-22-220000000000000002i−2i00000
χ4922-2-2-222-2-2222-2-20000-2200002-2-222i−2i000000002i−2i2i−2i00002-2-2200000000000002i−2i0000000
χ5022-2-2-222-2-2222-2-20000-2200002-2-222i−2i000000002i−2i2i−2i0000-222-20000000000000−2i2i0000000
χ5122-2-2-222-2-2222-2-20000-2200002-2-22−2i2i00000000−2i2i−2i2i00002-2-220000000000000−2i2i0000000
χ5222-2-2-222-2-2222-2-20000-2200002-2-22−2i2i00000000−2i2i−2i2i0000-222-200000000000002i−2i0000000
χ534444-4-4-24-4-44-2-2-24-44-422-2-222-2-2220000-2200000000000000000000000000000000000000
χ544444-4-4-24-4-44-2-2-2-44-442222-2-2-2-22200002-200000000000000000000000000000000000000
χ554444-4-4-2-444-4-2-2-24-4-442222-2-222-2-20000-2200000000000000000000000000000000000000
χ564444-4-4-2-444-4-2-2-2-444-422-2-22222-2-200002-200000000000000000000000000000000000000
χ5744-4-44-444-44-44-4-400004-40000-44-4400000000000000000000000000000000000000000000
χ5844-4-44-4-24-44-4-2220000-2200002-22-20000000000000023−23−232300000000000000000000000000
χ5944-4-44-4-24-44-4-2220000-2200002-22-200000000000000−232323−2300000000000000000000000000
χ6044-4-44-4-2-44-44-2220000-220000-22-22004i−4i0000000000−2i2i−2i2i00000000000000000000000000
χ6144-4-44-4-2-44-44-2220000-220000-22-2200−4i4i00000000002i−2i2i−2i00000000000000000000000000
χ6244-4-4-44444-4-44-4-40000-440000-444-400000000000000000000000000000000000000000000
χ6344-4-4-44-244-4-4-22200002-200002-2-22000000000023−23−2323000000000000000000000000000000
χ6444-4-4-44-244-4-4-22200002-200002-2-220000000000−232323−23000000000000000000000000000000
χ6544-4-4-44-2-4-444-22200002-20000-222-24i−4i00000000−2i2i−2i2i000000000000000000000000000000
χ6644-4-4-44-2-4-444-22200002-20000-222-2−4i4i000000002i−2i2i−2i000000000000000000000000000000
χ678-88-80080000-88-80000000000000000000000000000000000000000000000000000000000
χ688-88-800-400004-440000000043−43000000000000000000000000000000000000000000000000
χ698-88-800-400004-4400000000−4343000000000000000000000000000000000000000000000000
χ708-8-880080000-8-880000000000000000000000000000000000000000000000000000000000
χ718-8-8800-4000044-400000043−4300000000000000000000000000000000000000000000000000
χ728-8-8800-4000044-4000000−434300000000000000000000000000000000000000000000000000

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