Finite Group Databasebeta

← Group #10849412

Character table — Group #10849412

Order 768.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78
size111122222222222222444444444444888888888888888888121212121212121212121212161616161616161616162424242424244848
order122222344444444666446612121212121212122244888812122424242424242424444444444444446612121212121224444488
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-1
χ31111111111111111111111111111111111-1-1-1-111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-11111-1-1-1-1111111-1-1
χ41111111111111111111111111111111111-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-11111-1-1-1-1-1-1-1-1-1-111
χ5111111111111111111111111111111-1-1-1-111111111111111111111111111-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-1
χ6111111111111111111111111111111-1-1-1-111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111
χ7111111111111111111111111111111-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-111-1-1-1-1111111-1-1-1-111
χ8111111111111111111111111111111-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-11111111111-1-1-1-11111-1-11111-1-1
χ911111111-1-1-1-1111111-1-111-1-111-1-1111-11-111-1-1-1-11111-1-1-1-111111111-1-1-1-11-11-11-111-1-1-1-111-1-11-1
χ1011111111-1-1-1-1111111-1-111-1-111-1-1111-11-111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-111111-11-11-111-1-111-1-111-11
χ1111111111-1-1-1-1111111-1-111-1-111-1-1111-11-1-1-111-1-1-1-1-1-111111111-1-1-1-11111-111-11-1-1-111-1-111-1-1-11
χ1211111111-1-1-1-1111111-1-111-1-111-1-1111-11-1-1-111-1-1-1-1-1-11111-1-1-1-11111-1-1-1-1-111-11-1-1-11111-1-1111-1
χ1311111111-1-1-1-1111111-1-111-1-111-1-111-11-1111-1-1-1-11111-1-1-1-111111111-1-1-1-1-11-11-11-1-111-1-1-1-111-11
χ1411111111-1-1-1-1111111-1-111-1-111-1-111-11-1111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-11111-11-11-11-1-1111111-1-11-1
χ1511111111-1-1-1-1111111-1-111-1-111-1-111-11-11-1-111-1-1-1-1-1-111111111-1-1-1-111111-1-11-1111-1-1-1-1-1-1111-1
χ1611111111-1-1-1-1111111-1-111-1-111-1-111-11-11-1-111-1-1-1-1-1-11111-1-1-1-11111-1-1-1-11-1-11-1111-1-11111-1-1-11
χ172222222-222-2-2-2-2-22222-222-2-2-2-222-2-200000000-22000000000000000000000000000000002-22-200
χ182222222-222-2-2-2-2-22222-222-2-2-2-222-2-200000000-2200000000000000000000000000000000-22-2200
χ192222222-2-2-222-2-2-2222-222222-2-2-2-2-2-2000000002-2000000000000000000000000000000002-2-2200
χ202222222-2-2-222-2-2-2222-222222-2-2-2-2-2-2000000002-200000000000000000000000000000000-222-200
χ21222222-122222222-1-1-122-1-1-1-1-1-1-1-1-1-122222222-1-1-1-1-1-1-1-1-1-100000000000022-1-1-1-1-1-1-1-100000000
χ22222222-122222222-1-1-122-1-1-1-1-1-1-1-1-1-12222-2-2-2-2-1-111111111000000000000-2-2-1-1-1-1111100000000
χ23222222-122222222-1-1-122-1-1-1-1-1-1-1-1-1-1-2-2-2-22222-1-1-1-1-1-1-1-1-1-1000000000000-2-21111111100000000
χ24222222-122222222-1-1-122-1-1-1-1-1-1-1-1-1-1-2-2-2-2-2-2-2-2-1-111111111000000000000221111-1-1-1-100000000
χ25222222-12-2-2-2-2222-1-1-1-2-2-1-111-1-111-1-12-22-222-2-211-1-1-1-111110000000000002-2-11-11-1-11100000000
χ26222222-12-2-2-2-2222-1-1-1-2-2-1-111-1-111-1-12-22-2-2-222111111-1-1-1-1000000000000-22-11-1111-1-100000000
χ27222222-12-2-2-2-2222-1-1-1-2-2-1-111-1-111-1-1-22-2222-2-211-1-1-1-11111000000000000-221-11-111-1-100000000
χ28222222-12-2-2-2-2222-1-1-1-2-2-1-111-1-111-1-1-22-22-2-222111111-1-1-1-10000000000002-21-11-1-1-11100000000
χ292222-2-22222-2-2-2-22222-22-2-2-2-22222-2-2000000002-20000000022-2-20000000000000000002-2000000
χ302222-2-22222-2-2-2-22222-22-2-2-2-22222-2-2000000002-200000000-2-222000000000000000000-22000000
χ312222-2-222-2-222-2-222222-2-2-22222-2-2-2-200000000-220000000022-2-2000000000000000000-22000000
χ322222-2-222-2-222-2-222222-2-2-22222-2-2-2-200000000-2200000000-2-2220000000000000000002-2000000
χ332222-2-22-2222222-2222-2-2-2-222-2-2222222-2-20000-2-2000000000000000000000022-2-2000000000000
χ342222-2-22-2222222-2222-2-2-2-222-2-22222-2-2220000-2-20000000000000000000000-2-222000000000000
χ352222-2-22-2-2-2-2-222-222222-2-2-2-2-2-2-2-2222-2-2200002200000000000000000000002-2-22000000000000
χ362222-2-22-2-2-2-2-222-222222-2-2-2-2-2-2-2-222-222-20000220000000000000000000000-222-2000000000000
χ372222-2-2-1-2222222-2-1-1-1-2-211-1-111-1-1-1-122-2-2000011−i3−i3i3i3−i3−i3i3i300000000000000-1-111−i3i3−i3i300000000
χ382222-2-2-1-2222222-2-1-1-1-2-211-1-111-1-1-1-122-2-2000011i3i3−i3−i3i3i3−i3−i300000000000000-1-111i3−i3i3−i300000000
χ392222-2-2-1-2222222-2-1-1-1-2-211-1-111-1-1-1-1-2-222000011−i3−i3i3i3−i3−i3i3i30000000000000011-1-1i3−i3i3−i300000000
χ402222-2-2-1-2222222-2-1-1-1-2-211-1-111-1-1-1-1-2-222000011i3i3−i3−i3i3i3−i3−i30000000000000011-1-1−i3i3−i3i300000000
χ412222-2-2-1-2-2-2-2-222-2-1-1-12211111111-1-12-2-220000-1-1−i3−i3i3i3i3i3−i3−i300000000000000-111-1−i3i3i3−i300000000
χ422222-2-2-1-2-2-2-2-222-2-1-1-12211111111-1-12-2-220000-1-1i3i3−i3−i3−i3−i3i3i300000000000000-111-1i3−i3−i3i300000000
χ432222-2-2-1-2-2-2-2-222-2-1-1-12211111111-1-1-222-20000-1-1−i3−i3i3i3i3i3−i3−i3000000000000001-1-11i3−i3−i3i300000000
χ442222-2-2-1-2-2-2-2-222-2-1-1-12211111111-1-1-222-20000-1-1i3i3−i3−i3−i3−i3i3i3000000000000001-1-11−i3i3i3−i300000000
χ4522-2-22-22-200002-22-22-2002-2002-2002-20000002i−2i0000002i−2i2i−2i2i−2i2i−2i000022-2-2000000000000000000
χ4622-2-22-22-200002-22-22-2002-2002-2002-20000002i−2i0000002i−2i2i−2i−2i2i−2i2i0000-2-222000000000000000000
χ4722-2-22-22-200002-22-22-2002-2002-2002-2000000−2i2i000000−2i2i−2i2i2i−2i2i−2i0000-2-222000000000000000000
χ4822-2-22-22-200002-22-22-2002-2002-2002-2000000−2i2i000000−2i2i−2i2i−2i2i−2i2i000022-2-2000000000000000000
χ4922-2-2-222-20000-222-22-200-22002-200-2200002i−2i00002i−2i2i−2i00002i−2i−2i2i22-2-20000000000000000000000
χ5022-2-2-222-20000-222-22-200-22002-200-2200002i−2i00002i−2i2i−2i0000−2i2i2i−2i-2-2220000000000000000000000
χ5122-2-2-222-20000-222-22-200-22002-200-220000−2i2i0000−2i2i−2i2i00002i−2i−2i2i-2-2220000000000000000000000
χ5222-2-2-222-20000-222-22-200-22002-200-220000−2i2i0000−2i2i−2i2i0000−2i2i2i−2i22-2-20000000000000000000000
χ53444444-2-444-4-4-4-4-4-2-2-24-4-2-22222-2-222000000002-200000000000000000000000000000000000000
χ54444444-2-4-4-444-4-4-4-2-2-2-44-2-2-2-222222200000000-2200000000000000000000000000000000000000
χ554444-4-4-2444-4-4-4-44-2-2-2-442222-2-2-2-22200000000-2200000000000000000000000000000000000000
χ564444-4-4-24-4-444-4-44-2-2-24-422-2-2-2-22222000000002-200000000000000000000000000000000000000
χ5744-4-44-4440000-44-4-44-4004-400-4400-44000000000000000000000000000000000000000000000000
χ5844-4-44-4-240000-44-42-2200-22002-2002-2000000000023−23−23230000000000000000000000000000000000
χ5944-4-44-4-240000-44-42-2200-22002-2002-20000000000−232323−230000000000000000000000000000000000
χ6044-4-44-4-2-400004-442-2200-2200-2200-220000004i−4i000000−2i2i−2i2i000000000000000000000000000000
χ6144-4-44-4-2-400004-442-2200-2200-2200-22000000−4i4i0000002i−2i2i−2i000000000000000000000000000000
χ6244-4-4-444400004-4-4-44-400-4400-44004-4000000000000000000000000000000000000000000000000
χ6344-4-4-44-2400004-4-42-22002-2002-200-220000000000000023−23−2323000000000000000000000000000000
χ6444-4-4-44-2400004-4-42-22002-2002-200-2200000000000000−232323−23000000000000000000000000000000
χ6544-4-4-44-2-40000-4442-22002-200-22002-200004i−4i0000−2i2i−2i2i0000000000000000000000000000000000
χ6644-4-4-44-2-40000-4442-22002-200-22002-20000−4i4i00002i−2i2i−2i0000000000000000000000000000000000
χ674-44-400404-400000-4-44000000004-40000000000000000000000002i−2i2i−2i2i−2i2i−2i000000000000000000
χ684-44-400404-400000-4-44000000004-4000000000000000000000000−2i2i−2i2i−2i2i−2i2i000000000000000000
χ694-44-40040-4400000-4-4400000000-440000000000000000000000002i−2i2i−2i−2i2i−2i2i000000000000000000
χ704-44-40040-4400000-4-4400000000-44000000000000000000000000−2i2i−2i2i2i−2i2i−2i000000000000000000
χ714-4-440040004-40004-4-400004-400000000000000000000000000002i−2i−2i2i2i−2i−2i2i000000000000000000
χ724-4-440040004-40004-4-400004-40000000000000000000000000000−2i2i2i−2i−2i2i2i−2i000000000000000000
χ734-4-44004000-440004-4-40000-4400000000000000000000000000002i−2i−2i2i−2i2i2i−2i000000000000000000
χ744-4-44004000-440004-4-40000-440000000000000000000000000000−2i2i2i−2i2i−2i−2i2i000000000000000000
χ758-88-800-408-80000044-400000000-4400000000000000000000000000000000000000000000000000
χ768-88-800-40-880000044-4000000004-400000000000000000000000000000000000000000000000000
χ778-8-8800-40008-8000-4440000-44000000000000000000000000000000000000000000000000000000
χ788-8-8800-4000-88000-44400004-4000000000000000000000000000000000000000000000000000000

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