Finite Group Databasebeta

← Group #10848593

Character table — Group #10848593

Order 768.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78
size111122222222222222444444444444888888888888888888121212121212121212121212161616161616161616162424242424244848
order1222223444444446664466121212121212121244448888121224242424242424244444444444442266661212121222222488
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-1
χ31111111111111111111111111111111111-1-1-1-111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111-1-1
χ41111111111111111111111111111111111-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-11111-1-1-1-1-1-111
χ5111111111111111111111111111111-1-1-1-111111111111111111111111111-1-1-1-1-1-1-1-1-1-11-1-1-1-11-1-1
χ6111111111111111111111111111111-1-1-1-111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-111
χ7111111111111111111111111111111-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1111111-1-1-1-11-1-1-1-1111
χ8111111111111111111111111111111-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-111111111111111-1-1-1-1-11111-1-1-1
χ911111111-1-1-1-1111111-1-11111-1-1-1-11111-1-111-1-1-1-11111-1-1-1-111111111-1-1-1-11-111-1-111-1-1-111-1-1-11-1
χ1011111111-1-1-1-1111111-1-11111-1-1-1-11111-1-111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-111111-111-1-111-1-11-1-1111-11
χ1111111111-1-1-1-1111111-1-11111-1-1-1-11111-1-1-1-111-1-1-1-1-1-111111111-1-1-1-11111-11-1-11111-1-1-111-1-1-1-11
χ1211111111-1-1-1-1111111-1-11111-1-1-1-11111-1-1-1-111-1-1-1-1-1-11111-1-1-1-11111-1-1-1-1-11-1-11111-1-11-1-11111-1
χ1311111111-1-1-1-1111111-1-11111-1-1-1-111-1-11111-1-1-1-11111-1-1-1-111111111-1-1-1-1-11-1-111-1-111-1-1-111-1-11
χ1411111111-1-1-1-1111111-1-11111-1-1-1-111-1-11111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-11111-11-1-111-1-111111-1-111-1
χ1511111111-1-1-1-1111111-1-11111-1-1-1-111-1-111-1-111-1-1-1-1-1-111111111-1-1-1-111111-111-1-1-1-111-1-1-111-11-1
χ1611111111-1-1-1-1111111-1-11111-1-1-1-111-1-111-1-111-1-1-1-1-1-11111-1-1-1-11111-1-1-1-11-111-1-1-1-111111-1-11-11
χ172222222-222-2-2-2-2-22222-222-2-222-2-2-2-2000000002-200000000000000000000000000000002-22-2000
χ182222222-222-2-2-2-2-22222-222-2-222-2-2-2-2000000002-20000000000000000000000000000000-22-22000
χ192222222-2-2-222-2-2-2222-2222-2-2-2-222-2-200000000-2200000000000000000000000000000002-2-22000
χ202222222-2-2-222-2-2-2222-2222-2-2-2-222-2-200000000-220000000000000000000000000000000-222-2000
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
χ22222222-122222222-1-1-122-1-1-1-1-1-1-1-1-1-12222-2-2-2-2-1-111111111000000000000-2-21111-1-1-1-100000000
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
χ24222222-122222222-1-1-122-1-1-1-1-1-1-1-1-1-1-2-2-2-2-2-2-2-2-1-11111111100000000000022-1-1-1-1111100000000
χ25222222-12-2-2-2-2222-1-1-1-2-2-1-1-1-11111-1-122-2-222-2-211-1-1-1-111110000000000002-2-1-111-1-11100000000
χ26222222-12-2-2-2-2222-1-1-1-2-2-1-1-1-11111-1-122-2-2-2-222111111-1-1-1-1000000000000-2211-1-1-1-11100000000
χ27222222-12-2-2-2-2222-1-1-1-2-2-1-1-1-11111-1-1-2-22222-2-211-1-1-1-11111000000000000-2211-1-111-1-100000000
χ28222222-12-2-2-2-2222-1-1-1-2-2-1-1-1-11111-1-1-2-222-2-222111111-1-1-1-10000000000002-2-1-11111-1-100000000
χ292222-2-22222-2-2-2-22222-22-2-22222-2-2-2-200000000-220000000022-2-200000000000000000020000-200
χ302222-2-22222-2-2-2-22222-22-2-22222-2-2-2-200000000-2200000000-2-222000000000000000000-20000200
χ312222-2-222-2-222-2-222222-2-2-222-2-222-2-2000000002-20000000022-2-2000000000000000000-20000200
χ322222-2-222-2-222-2-222222-2-2-222-2-222-2-2000000002-200000000-2-22200000000000000000020000-200
χ332222-2-22-2222222-2222-2-2-2-2-2-22222222-22-20000-2-2000000000000000000000000002-22-200000000
χ342222-2-22-2222222-2222-2-2-2-2-2-2222222-22-220000-2-200000000000000000000000000-22-2200000000
χ352222-2-22-2-2-2-2-222-222222-2-2-2-2-2-2-2-2222-2-22000022000000000000000000000000002-2-2200000000
χ362222-2-22-2-2-2-2-222-222222-2-2-2-2-2-2-2-222-222-200002200000000000000000000000000-222-200000000
χ372222-2-2-1-2222222-2-1-1-1-2-21111-1-1-1-1-1-12-22-2000011−i3−i3i3i3−i3−i3i3i300000000000000−i3i3−i3i3-11-1100000000
χ382222-2-2-1-2222222-2-1-1-1-2-21111-1-1-1-1-1-12-22-2000011i3i3−i3−i3i3i3−i3−i300000000000000i3−i3i3−i3-11-1100000000
χ392222-2-2-1-2222222-2-1-1-1-2-21111-1-1-1-1-1-1-22-22000011−i3−i3i3i3−i3−i3i3i300000000000000i3−i3i3−i31-11-100000000
χ402222-2-2-1-2222222-2-1-1-1-2-21111-1-1-1-1-1-1-22-22000011i3i3−i3−i3i3i3−i3−i300000000000000−i3i3−i3i31-11-100000000
χ412222-2-2-1-2-2-2-2-222-2-1-1-12211111111-1-12-2-220000-1-1−i3−i3i3i3i3i3−i3−i300000000000000−i3i3i3−i3-111-100000000
χ422222-2-2-1-2-2-2-2-222-2-1-1-12211111111-1-12-2-220000-1-1i3i3−i3−i3−i3−i3i3i300000000000000i3−i3−i3i3-111-100000000
χ432222-2-2-1-2-2-2-2-222-2-1-1-12211111111-1-1-222-20000-1-1−i3−i3i3i3i3i3−i3−i300000000000000i3−i3−i3i31-1-1100000000
χ442222-2-2-1-2-2-2-2-222-2-1-1-12211111111-1-1-222-20000-1-1i3i3−i3−i3−i3−i3i3i300000000000000−i3i3i3−i31-1-1100000000
χ4522-2-22-22200002-2-22-2-2002-22-200002-20000002i−2i0000002i−2i2i−2i2i−2i2i−2i000022-2-2000000000000000000
χ4622-2-22-22200002-2-22-2-2002-22-200002-20000002i−2i0000002i−2i2i−2i−2i2i−2i2i0000-2-222000000000000000000
χ4722-2-22-22200002-2-22-2-2002-22-200002-2000000−2i2i000000−2i2i−2i2i2i−2i2i−2i0000-2-222000000000000000000
χ4822-2-22-22200002-2-22-2-2002-22-200002-2000000−2i2i000000−2i2i−2i2i−2i2i−2i2i000022-2-2000000000000000000
χ4922-2-2-22220000-22-22-2-200-222-20000-2200002i−2i00002i−2i2i−2i00002i−2i−2i2i22-2-20000000000000000000000
χ5022-2-2-22220000-22-22-2-200-222-20000-2200002i−2i00002i−2i2i−2i0000−2i2i2i−2i-2-2220000000000000000000000
χ5122-2-2-22220000-22-22-2-200-222-20000-220000−2i2i0000−2i2i−2i2i00002i−2i−2i2i-2-2220000000000000000000000
χ5222-2-2-22220000-22-22-2-200-222-20000-220000−2i2i0000−2i2i−2i2i0000−2i2i2i−2i22-2-20000000000000000000000
χ53444444-2-444-4-4-4-4-4-2-2-24-4-2-222-2-2222200000000-2200000000000000000000000000000000000000
χ54444444-2-4-4-444-4-4-4-2-2-2-44-2-22222-2-222000000002-200000000000000000000000000000000000000
χ554444-4-4-2444-4-4-4-44-2-2-2-4422-2-2-2-22222000000002-200000000000000000000000000000000000000
χ564444-4-4-24-4-444-4-44-2-2-24-422-2-222-2-22200000000-2200000000000000000000000000000000000000
χ5744-4-44-44-40000-4444-4-4004-4-440000-44000000000000000000000000000000000000000000000000
χ5844-4-44-4-2400004-4-4-22200-22-220000-220000004i−4i000000−2i2i−2i2i000000000000000000000000000000
χ5944-4-44-4-2400004-4-4-22200-22-220000-22000000−4i4i0000002i−2i2i−2i000000000000000000000000000000
χ6044-4-44-4-2-40000-444-22200-222-200002-2000000000023−23−23230000000000000000000000000000000000
χ6144-4-44-4-2-40000-444-22200-222-200002-20000000000−232323−230000000000000000000000000000000000
χ6244-4-4-444-400004-444-4-400-44-4400004-4000000000000000000000000000000000000000000000000
χ6344-4-4-44-240000-44-4-222002-2-2200002-200004i−4i0000−2i2i−2i2i0000000000000000000000000000000000
χ6444-4-4-44-240000-44-4-222002-2-2200002-20000−4i4i00002i−2i2i−2i0000000000000000000000000000000000
χ6544-4-4-44-2-400004-44-222002-22-20000-220000000000000023−23−2323000000000000000000000000000000
χ6644-4-4-44-2-400004-44-222002-22-20000-2200000000000000−232323−23000000000000000000000000000000
χ674-44-40040004-4000-44-4000000004-40000000000000000000000002-22-22-22-2000000000000000000
χ684-44-40040004-4000-44-4000000004-4000000000000000000000000-22-22-22-22000000000000000000
χ694-44-4004000-44000-44-400000000-440000000000000000000000002-22-2-22-22000000000000000000
χ704-44-4004000-44000-44-400000000-44000000000000000000000000-22-222-22-2000000000000000000
χ714-4-4400404-400000-4-440000004-4000000000000000000000000002-2-222-2-22000000000000000000
χ724-4-4400404-400000-4-440000004-400000000000000000000000000-222-2-222-2000000000000000000
χ734-4-440040-4400000-4-44000000-44000000000000000000000000002-2-22-222-2000000000000000000
χ744-4-440040-4400000-4-44000000-4400000000000000000000000000-222-22-2-22000000000000000000
χ758-88-800-40008-80004-4400000000-4400000000000000000000000000000000000000000000000000
χ768-88-800-4000-880004-44000000004-400000000000000000000000000000000000000000000000000
χ778-8-8800-408-80000044-4000000-440000000000000000000000000000000000000000000000000000
χ788-8-8800-40-880000044-40000004-40000000000000000000000000000000000000000000000000000

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