Finite Group Databasebeta

← Group #10833504

Character table — Group #10833504

Order 768.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69
size112222222224444444444488888888888888888888121212121212161616161616161616162424242424242424244848
order1222234444622446661212121244668888881212242424242424242422444448121212122424242422444448848
χ1111111111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111111111111-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-1-1
χ31111111111111111111111111111-1-1-1-111-1-1-1-1-1-1-1-1111111-1-1-1-11111-1-11-11-1-1-1111-1-1
χ41111111111111111111111111111-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-11-1111-1-1-111
χ51111111111111111111111-1-111-1-1111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-1-1-1
χ61111111111111111111111-1-111-1-111111111111111-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111
χ71111111111111111111111-1-111-1-1-1-1-1-111-1-1-1-1-1-1-1-11111-1-11111-1-1-1-1111-11-1-1-1-1-1-111
χ81111111111111111111111-1-111-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-1-111-11-1111111-1-1
χ911111111111-1-1-1-1111111111-1-1-1-111-1-1-1-11111-1-1-1-11111111-11111-1-1-1-1-1-1-111-11-1-1-11
χ1011111111111-1-1-1-1111111111-1-1-1-111-1-1-1-11111-1-1-1-1-1-1-1-1-1-11-11111-1-1-1-1111-1-11-1111-1
χ1111111111111-1-1-1-1111111111-1-1-1-1-1-111-1-1-1-1-1-11111111111-11-1-111-1-111-11-1-1-111-1-11-1
χ1211111111111-1-1-1-1111111111-1-1-1-1-1-111-1-1-1-1-1-11111-1-1-1-1-1-1-11-1-111-1-1111-1111-1-111-11
χ1311111111111-1-1-1-11111111-1-1-1-11111-1-1-1-11111-1-1-1-11111-1-1-11-1-1-1-11111-1-1-111-1-1111-1
χ1411111111111-1-1-1-11111111-1-1-1-11111-1-1-1-11111-1-1-1-1-1-1-1-111-11-1-1-1-11111111-1-111-1-1-11
χ1511111111111-1-1-1-11111111-1-1-1-111-1-111-1-1-1-1-1-111111111-1-11-111-1-111-1-1-11-1-1-11-111-11
χ1611111111111-1-1-1-11111111-1-1-1-111-1-111-1-1-1-1-1-11111-1-1-1-1111-111-1-111-1-11-1111-11-1-11-1
χ1722222-12222-12222-1-1-1-1-1-1-122-1-1222222-1-1-1-1-1-1-1-1-1-100000022-1-1-1-1-1-1-1-100000000000
χ1822222-12222-12222-1-1-1-1-1-1-122-1-122-2-2-2-2-1-111111111000000-2-211-1-1-1-11100000000000
χ1922222-12222-12222-1-1-1-1-1-1-1-2-2-1-1-2-22222-1-1-1-1-1-1-1-1-1-1000000-2-21111111100000000000
χ2022222-12222-12222-1-1-1-1-1-1-1-2-2-1-1-2-2-2-2-2-2-1-11111111100000022-1-11111-1-100000000000
χ2122222-12222-1-2-2-2-2-1-1-1-1-1-1-12211-2-222-2-211-1-1-1-111110000002-2-1-1-1-1111100000000000
χ2222222-12222-1-2-2-2-2-1-1-1-1-1-1-12211-2-2-2-222111111-1-1-1-1000000-2211-1-111-1-100000000000
χ2322222-12222-1-2-2-2-2-1-1-1-1-1-1-1-2-2112222-2-211-1-1-1-11111000000-221111-1-1-1-100000000000
χ2422222-12222-1-2-2-2-2-1-1-1-1-1-1-1-2-21122-2-222111111-1-1-1-10000002-2-1-111-1-11100000000000
χ25222-2-2222-2-2222-2-22-2-222-2-22i−2i222i−2i0000-2-20000000000000000002i−2i2i−2i0000000000000
χ26222-2-2222-2-2222-2-22-2-222-2-2−2i2i22−2i2i0000-2-2000000000000000000−2i2i−2i2i0000000000000
χ27222-2-2222-2-22-2-2222-2-222-2-22i−2i-2-2−2i2i0000220000000000000000002i−2i−2i2i0000000000000
χ28222-2-2222-2-22-2-2222-2-222-2-2−2i2i-2-22i−2i000022000000000000000000−2i2i2i−2i0000000000000
χ29222-2-22-2-222200002-2-2-2-222000000002-200000022-2-22-22-200000000000002000-200000
χ30222-2-22-2-222200002-2-2-2-222000000002-200000022-2-2-22-220000000000000-2000200000
χ31222-2-22-2-222200002-2-2-2-22200000000-22000000-2-2222-22-20000000000000-2000200000
χ32222-2-22-2-222200002-2-2-2-22200000000-22000000-2-222-22-2200000000000002000-200000
χ33222-2-2-122-2-2-122-2-2-111-1-1112i−2i-1-12i−2i00001133−3−33−33−300000000−i3i3−ii−ii−i3i300000000000
χ34222-2-2-122-2-2-122-2-2-111-1-1112i−2i-1-12i−2i000011−3−333−33−3300000000i3−i3−ii−iii3−i300000000000
χ35222-2-2-122-2-2-122-2-2-111-1-111−2i2i-1-1−2i2i00001133−3−33−33−300000000i3−i3i−ii−ii3−i300000000000
χ36222-2-2-122-2-2-122-2-2-111-1-111−2i2i-1-1−2i2i000011−3−333−33−3300000000−i3i3i−ii−i−i3i300000000000
χ37222-2-2-122-2-2-1-2-222-111-1-1112i−2i11−2i2i0000-1-133−3−3−33−3300000000−i3i3−iii−ii3−i300000000000
χ38222-2-2-122-2-2-1-2-222-111-1-1112i−2i11−2i2i0000-1-1−3−3333−33−300000000i3−i3−iii−i−i3i300000000000
χ39222-2-2-122-2-2-1-2-222-111-1-111−2i2i112i−2i0000-1-133−3−3−33−3300000000i3−i3i−i−ii−i3i300000000000
χ40222-2-2-122-2-2-1-2-222-111-1-111−2i2i112i−2i0000-1-1−3−3333−33−300000000−i3i3i−i−iii3−i300000000000
χ4122-22-22-22-2222-22-2-22-2-22-22002-20000002-2000000002-2-2200000000000020-200000000
χ4222-22-22-22-2222-22-2-22-2-22-22002-20000002-200000000-222-2000000000000-20200000000
χ4322-22-22-22-222-22-22-22-2-22-2200-22000000-22000000002-2-22000000000000-20200000000
χ4422-22-22-22-222-22-22-22-2-22-2200-22000000-2200000000-222-200000000000020-200000000
χ4522-2-2222-2-2220000-2-222-2-220000002-200002-22-2000022-2-20000000000000002-2000000
χ4622-2-2222-2-2220000-2-222-2-220000002-200002-22-20000-2-222000000000000000-22000000
χ4722-2-2222-2-2220000-2-222-2-22000000-220000-22-22000022-2-2000000000000000-22000000
χ4822-2-2222-2-2220000-2-222-2-22000000-220000-22-220000-2-2220000000000000002-2000000
χ4922-2-222-222-222-2-22-2-22-222-2002-2000000-22000000000000220000000000000000-22-200
χ5022-2-222-222-222-2-22-2-22-222-2002-2000000-22000000000000-2-200000000000000002-2200
χ5122-2-222-222-22-222-2-2-22-222-200-220000002-2000000000000220000000000000000-2-2200
χ5222-2-222-222-22-222-2-2-22-222-200-220000002-2000000000000-2-2000000000000000022-200
χ53444444-4-4-4-440000444-4-4-4-400000000000000000000000000000000000000000000000
χ5444444-2-4-4-4-4-20000-2-2-22222000000000000000023−23−2323000000000000000000000000000
χ5544444-2-4-4-4-4-20000-2-2-222220000000000000000−232323−23000000000000000000000000000
χ56444-4-4-2-4-444-20000-22222-2-2000000004-4000000-2-222000000000000000000000000000
χ57444-4-4-2-4-444-20000-22222-2-200000000-4400000022-2-2000000000000000000000000000
χ5844-44-444-44-440000-44-44-44-400000000000000000000000000000000000000000000000
χ5944-44-4-24-44-4-200002-22-22-2200000000000023−23−23230000000000000000000000000000000
χ6044-44-4-24-44-4-200002-22-22-22000000000000−232323−230000000000000000000000000000000
χ6144-44-4-2-44-44-24-44-42-222-22-200-22000000-2200000000000000000000000000000000000
χ6244-44-4-2-44-44-2-44-442-222-22-2002-20000002-200000000000000000000000000000000000
χ6344-4-44-24-4-44-2000022-2-222-20000004-40000-22-220000000000000000000000000000000
χ6444-4-44-24-4-44-2000022-2-222-2000000-4400002-22-20000000000000000000000000000000
χ6544-4-44-2-444-4-24-4-4422-22-2-2200-220000002-200000000000000000000000000000000000
χ6644-4-44-2-444-4-2-444-422-22-2-22002-2000000-2200000000000000000000000000000000000
χ678-800080000-8000000000000000000000000000000000004-4000000000000000000000
χ688-800080000-800000000000000000000000000000000000-44000000000000000000000
χ6916-16000-8000080000000000000000000000000000000000000000000000000000000000

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