Finite Group Databasebeta

← Group #10944158

Character table — Group #10944158

Order 768.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81
size1111222222222222444444444444444444444888888888812121212121212121212121212121212161616161616161616161616242424244848
order12222234444446662244444444466121212121212121266121212121212121222222244444444442266668824242424444488
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ311111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1
χ411111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111
χ51111111111111111-1-111-1-1-1-11-1-11111111111-1-111-1-1-1-1-1-11111-1-1-1-1-1-11111-1-1111111-1-1-1-1-1-11111-1-1
χ61111111111111111-1-111-1-1-1-11-1-11111111111-1-111-1-1-1-1-1-11111-1-1-1-1-1-11111-1-1-1-1-1-1-1-1111111-1-1-1-111
χ71111111111111111-1-111-1-1-1-11-1-11111111111-1-111-1-1-1-1-1-1-1-1-1-1111111-1-1-1-111111111-1-1-1-1-1-1-1-1-1-111
χ81111111111111111-1-111-1-1-1-11-1-11111111111-1-111-1-1-1-1-1-1-1-1-1-1111111-1-1-1-111-1-1-1-1-1-11111111111-1-1
χ9111111111-1-11111111-1-111-1-1-1-1-111111-1-1-1-1111-1-111-1-1-1-111111111-1-1-1-1-1-1-1-11-111-1-11-111-1-111-1-11-1
χ10111111111-1-11111111-1-111-1-1-1-1-111111-1-1-1-1111-1-111-1-1-1-111111111-1-1-1-1-1-1-1-1-11-1-111-11-1-111-1-111-11
χ11111111111-1-11111111-1-111-1-1-1-1-111111-1-1-1-1111-1-111-1-1-1-1-1-1-1-1-1-1-1-1111111111-111-1-11-111-1-1-1-111-11
χ12111111111-1-11111111-1-111-1-1-1-1-111111-1-1-1-1111-1-111-1-1-1-1-1-1-1-1-1-1-1-111111111-11-1-111-11-1-11111-1-11-1
χ13111111111-1-111111-1-1-1-1-1-111-11111111-1-1-1-11-1-1-1-1-1-111111111-1-1-1-111-1-1-1-1111-111-1-1-11-1-11111-1-1-11
χ14111111111-1-111111-1-1-1-1-1-111-11111111-1-1-1-11-1-1-1-1-1-111111111-1-1-1-111-1-1-1-111-11-1-1111-111-1-1-1-1111-1
χ15111111111-1-111111-1-1-1-1-1-111-11111111-1-1-1-11-1-1-1-1-1-11111-1-1-1-11111-1-11111-1-11-111-1-1-11-1-111-1-1111-1
χ16111111111-1-111111-1-1-1-1-1-111-11111111-1-1-1-11-1-1-1-1-1-11111-1-1-1-11111-1-11111-1-1-11-1-1111-111-1-111-1-1-11
χ172222222-2-222-2-222200-2-2000020022-2-2-222-2-2-2002-200000022-2-200000022-2-200000000000000000000
χ182222222-2-222-2-222200-2-2000020022-2-2-222-2-2-2002-2000000-2-222000000-2-22200000000000000000000
χ192222222-2-2-2-2-2-222200220000-20022-2-2-2-2-222-200-2200000022-2-2000000-2-22200000000000000000000
χ202222222-2-2-2-2-2-222200220000-20022-2-2-2-2-222-200-22000000-2-22200000022-2-200000000000000000000
χ21222222-1222222-1-1-122222222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1000000000000000022-1-1-1-122-1-1-1-1000000
χ22222222-1222222-1-1-122222222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-10000000000000000-2-21111-2-21111000000
χ23222222-1222222-1-1-1-2-222-2-2-2-22-2-2-1-1-1-1-1-1-1-1-1-111-1-1111111000000000000000022-1-1-1-1-2-21111000000
χ24222222-1222222-1-1-1-2-222-2-2-2-22-2-2-1-1-1-1-1-1-1-1-1-111-1-11111110000000000000000-2-2111122-1-1-1-1000000
χ25222222-122-2-222-1-1-122-2-222-2-2-2-2-2-1-1-1-1-11111-1-1-111-1-1111100000000000000002-2-1-1112-2-1-111000000
χ26222222-122-2-222-1-1-122-2-222-2-2-2-2-2-1-1-1-1-11111-1-1-111-1-111110000000000000000-2211-1-1-2211-1-1000000
χ27222222-122-2-222-1-1-1-2-2-2-2-2-222-222-1-1-1-1-11111-1111111-1-1-1-100000000000000002-2-1-111-2211-1-1000000
χ28222222-122-2-222-1-1-1-2-2-2-2-2-222-222-1-1-1-1-11111-1111111-1-1-1-10000000000000000-2211-1-12-2-1-111000000
χ292222-2-222-2222-2222222-2-2-2-2-2-222-2-22-2-222-2-2222-22-2-222-2-20000000000000000000000000000000000
χ302222-2-222-2222-2222-2-22-22222-2-2-2-2-22-2-222-2-22-2-2-2222-2-2220000000000000000000000000000000000
χ312222-2-222-2-2-22-222222-22-2-2222-2-2-2-22-2-2-2-2222222-2-2-2-2-2220000000000000000000000000000000000
χ322222-2-222-2-2-22-2222-2-2-2222-2-2222-2-22-2-2-2-2222-2-22-22222-2-20000000000000000000000000000000000
χ332222-2-22-2222-2222200-220000-200-2-2-2222222-200-2-2000000000022-2-2-2-2000022000000000000000000
χ342222-2-22-2222-2222200-220000-200-2-2-2222222-200-2-20000000000-2-222220000-2-2000000000000000000
χ352222-2-22-22-2-2-22222002-20000200-2-2-222-2-2-2-2-20022000000000022-2-2220000-2-2000000000000000000
χ362222-2-22-22-2-2-22222002-20000200-2-2-222-2-2-2-2-200220000000000-2-222-2-2000022000000000000000000
χ372222-2-2-12-2222-2-1-1-1222-2-2-2-2-2-22211-111-1-111-1-1-11-111-1-111000000000000000000−i3i3−i3i300−i3i3−i3i3000000
χ382222-2-2-12-2222-2-1-1-1222-2-2-2-2-2-22211-111-1-111-1-1-11-111-1-111000000000000000000i3−i3i3−i300i3−i3i3−i3000000
χ392222-2-2-12-2222-2-1-1-1-2-22-22222-2-2-211-111-1-111-1111-1-1-111-1-1000000000000000000−i3i3−i3i300i3−i3i3−i3000000
χ402222-2-2-12-2222-2-1-1-1-2-22-22222-2-2-211-111-1-111-1111-1-1-111-1-1000000000000000000i3−i3i3−i300−i3i3−i3i3000000
χ412222-2-2-12-2-2-22-2-1-1-122-22-2-2222-2-211-11111-1-1-1-1-1-111111-1-1000000000000000000−i3i3i3−i300−i3i3i3−i3000000
χ422222-2-2-12-2-2-22-2-1-1-122-22-2-2222-2-211-11111-1-1-1-1-1-111111-1-1000000000000000000i3−i3−i3i300i3−i3−i3i3000000
χ432222-2-2-12-2-2-22-2-1-1-1-2-2-2222-2-222211-11111-1-1-111-11-1-1-1-111000000000000000000−i3i3i3−i300i3−i3−i3i3000000
χ442222-2-2-12-2-2-22-2-1-1-1-2-2-2222-2-222211-11111-1-1-111-11-1-1-1-111000000000000000000i3−i3−i3i300−i3i3i3−i3000000
χ4522-2-22-222-200-222-2-20000002i−2i02i−2i2-222-20000-20000002i−2i2i−2i00002-22-2002i−2i2i−2i00000000000000000000
χ4622-2-22-222-200-222-2-20000002i−2i02i−2i2-222-20000-20000002i−2i2i−2i0000-22-2200−2i2i−2i2i00000000000000000000
χ4722-2-22-222-200-222-2-2000000−2i2i0−2i2i2-222-20000-2000000−2i2i−2i2i00002-22-200−2i2i−2i2i00000000000000000000
χ4822-2-22-222-200-222-2-2000000−2i2i0−2i2i2-222-20000-2000000−2i2i−2i2i0000-22-22002i−2i2i−2i00000000000000000000
χ4922-2-22-22-22002-22-2-22-2002-2000002-2-2-22000022-2002-20000000000002i−2i2i−2i−2i2i2i−2i000000000000000000
χ5022-2-22-22-22002-22-2-22-2002-2000002-2-2-22000022-2002-2000000000000−2i2i−2i2i2i−2i−2i2i000000000000000000
χ5122-2-22-22-22002-22-2-2-2200-22000002-2-2-2200002-2200-220000000000002i−2i−2i2i2i−2i2i−2i000000000000000000
χ5222-2-22-22-22002-22-2-2-2200-22000002-2-2-2200002-2200-22000000000000−2i2i2i−2i−2i2i−2i2i000000000000000000
χ5322-2-2-2222200-2-22-2-20000002i−2i0−2i2i-222-220000-2000000−2i2i2i−2i2-22-200002i−2i0000−2i2i000000000000000000
χ5422-2-2-2222200-2-22-2-20000002i−2i0−2i2i-222-220000-2000000−2i2i2i−2i-22-220000−2i2i00002i−2i000000000000000000
χ5522-2-2-2222200-2-22-2-2000000−2i2i02i−2i-222-220000-20000002i−2i−2i2i2-22-20000−2i2i00002i−2i000000000000000000
χ5622-2-2-2222200-2-22-2-2000000−2i2i02i−2i-222-220000-20000002i−2i−2i2i-22-2200002i−2i0000−2i2i000000000000000000
χ5722-2-2-222-2-200222-2-22-200-2200000-22-22-2000022-200-2200002-2-222-2-2200000000000000000000000000
χ5822-2-2-222-2-200222-2-22-200-2200000-22-22-2000022-200-220000-222-2-222-200000000000000000000000000
χ5922-2-2-222-2-200222-2-2-22002-200000-22-22-200002-22002-200002-2-22-222-200000000000000000000000000
χ6022-2-2-222-2-200222-2-2-22002-200000-22-22-200002-22002-20000-222-22-2-2200000000000000000000000000
χ61444444-2-4-444-4-4-2-2-200-4-40000400-2-2222-2-222200-220000000000000000000000000000000000000000
χ62444444-2-4-4-4-4-4-4-2-2-200440000-400-2-222222-2-22002-20000000000000000000000000000000000000000
χ634444-4-4-2-4444-44-2-2-200-440000-400222-2-2-2-2-2-2200220000000000000000000000000000000000000000
χ644444-4-4-2-44-4-4-44-2-2-2004-40000400222-2-22222200-2-20000000000000000000000000000000000000000
χ6544-4-44-4-24-400-44-2220000004i−4i04i−4i-22-2-2200002000000−2i2i−2i2i0000000000000000000000000000000000
χ6644-4-44-4-24-400-44-222000000−4i4i0−4i4i-22-2-22000020000002i−2i2i−2i0000000000000000000000000000000000
χ6744-4-44-4-2-44004-4-2224-4004-400000-2222-20000-2-2200-2200000000000000000000000000000000000000
χ6844-4-44-4-2-44004-4-222-4400-4400000-2222-20000-22-2002-200000000000000000000000000000000000000
χ6944-4-4-44-24400-4-4-2220000004i−4i0−4i4i2-2-22-2000020000002i−2i−2i2i0000000000000000000000000000000000
χ7044-4-4-44-24400-4-4-222000000−4i4i04i−4i2-2-22-200002000000−2i2i2i−2i0000000000000000000000000000000000
χ7144-4-4-44-2-4-40044-2224-400-44000002-22-220000-2-22002-200000000000000000000000000000000000000
χ7244-4-4-44-2-4-40044-222-44004-4000002-22-220000-22-200-2200000000000000000000000000000000000000
χ734-4-44004004-400-44-400000000000000004-4000000000000000000000000000000000000000002-22-200
χ744-4-44004004-400-44-400000000000000004-400000000000000000000000000000000000000000-22-2200
χ754-4-4400400-4400-44-40000000000000000-44000000000000000000000000000000000000000002-2-2200
χ764-4-4400400-4400-44-40000000000000000-4400000000000000000000000000000000000000000-222-200
χ778-88-8008000000-8-8800000000000000000000000000000000000000000000000000000000000000000
χ788-88-800-400000044-4000000000000000000−4i34i3000000000000000000000000000000000000000000000
χ798-88-800-400000044-40000000000000000004i3−4i3000000000000000000000000000000000000000000000
χ808-8-8800-4008-8004-440000000000000000-4400000000000000000000000000000000000000000000000
χ818-8-8800-400-88004-4400000000000000004-400000000000000000000000000000000000000000000000

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