Finite Group Databasebeta

← Group #10849641

Character table — Group #10849641

Order 768.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90
size1111222222222222224444444444444444444444448888888888888888888888888888888812121212121212122424242448484848
order12222234444444466644444466121212121212121212121212121212122224444444666666121212121212121212121212121212124444444488884488
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ31111111111111111111111111111111111111111111-1-11-1-1-1-1-1-111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-1
χ41111111111111111111111111111111111111111111-1-11-1-1-1-1-1-111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111
χ511111111111111111111-1-1-1-11111111111-1-1-1-1-1-1-1-1-111-111-1-1-1-1-1-1111111-1-11111-1-1-1-1-1-1-1-111111111-1-1-1-111-1-1
χ611111111111111111111-1-1-1-11111111111-1-1-1-1-1-1-1-1-111-111-1-1-1-1-1-1111111-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-111
χ711111111111111111111-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-111-1-1-1-1-1-11111111111111111-1-1-1-1-1-111
χ811111111111111111111-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-111-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1111111-1-1
χ911111111-1-1-1-1111111-1-11111111111-1-1-1-111111111-111-1-1-111-1-1-1-11111-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1-1-111-1-11-11-1
χ1011111111-1-1-1-1111111-1-11111111111-1-1-1-111111111-111-1-1-111-1-1-1-11111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-11111-1-111-11-11
χ1111111111-1-1-1-1111111-1-11111111111-1-1-1-111111111-1-1-1-111-1-111-1-1-1-1-1-1-1-1-1-11111-1-1-1-111111111-1-1-1-111-1-1-11-11
χ1211111111-1-1-1-1111111-1-11111111111-1-1-1-111111111-1-1-1-111-1-111-1-1-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1-1-11111-1-1111-11-1
χ1311111111-1-1-1-1111111-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-111111111-1-111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1111-1-11
χ1411111111-1-1-1-1111111-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-111111111-1-111-1-1-1-1-1-1-1-11111-1-1-1-1111111-1-1-111-1
χ1511111111-1-1-1-1111111-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-11-1-111111-1-111-1-1-1-1-1-11111111111-1-1-1-11111-1-1-1-1-1-111-111-1
χ1611111111-1-1-1-1111111-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-11-1-111111-1-111-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-1111111-1-11-1-11
χ172222222-222-2-2-2-2-22222-2000022-2-2-2-222-2-20000000002-202-200000022-2-22-20022-2-2000000000000000000000000
χ182222222-222-2-2-2-2-22222-2000022-2-2-2-222-2-2000000000-220-22000000-2-2222-200-2-222000000000000000000000000
χ192222222-2-2-222-2-2-2222-22000022-2-2-2-2-2-2220000000002-20-2200000022-2-2-2200-2-222000000000000000000000000
χ202222222-2-2-222-2-2-2222-22000022-2-2-2-2-2-222000000000-2202-2000000-2-222-220022-2-2000000000000000000000000
χ21222222-122222222-1-1-1222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-12222222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-10000000000000000
χ22222222-122222222-1-1-1222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-12-2-22-2-2-2-2-2-2-1-11111-1-1-1-11111111111110000000000000000
χ23222222-122222222-1-1-122-2-2-2-2-1-1-1-1-1-1-1-1-1-111111111-222-222-2-2-2-211-1-1-1-1-1-111-1-1-1-1111111110000000000000000
χ24222222-122222222-1-1-122-2-2-2-2-1-1-1-1-1-1-1-1-1-111111111-2-2-2-2-2-22222111111-1-1111111-1-1-1-1-1-1-1-10000000000000000
χ25222222-12-2-2-2-2222-1-1-1-2-22222-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-222-2-2-222-2-211-1-1-1-111111111-1-1-1-111110000000000000000
χ26222222-12-2-2-2-2222-1-1-1-2-22222-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-2-2-2-222-2-2221111111111-1-1-1-11111-1-1-1-10000000000000000
χ27222222-12-2-2-2-2222-1-1-1-2-2-2-2-2-2-1-1-1-1-1-11111111111112222-2-2-2-222-1-1-1-1-1-111-1-111111111-1-1-1-10000000000000000
χ28222222-12-2-2-2-2222-1-1-1-2-2-2-2-2-2-1-1-1-1-1-11111111111112-2-222222-2-2-1-1111111-1-1-1-1-1-1-1-1-1-111110000000000000000
χ29222222-1-222-2-2-2-2-2-1-1-12-20000-1-11111-1-111−i3−i3−i3−i3i3i3i3i302-202-20000−i3i3-1-111-11−i3i3-1-111−i3−i3i3i3−i3−i3i3i30000000000000000
χ30222222-1-222-2-2-2-2-2-1-1-12-20000-1-11111-1-111−i3−i3−i3−i3i3i3i3i30-220-220000−i3i311-1-1-11−i3i311-1-1i3i3−i3−i3i3i3−i3−i30000000000000000
χ31222222-1-222-2-2-2-2-2-1-1-12-20000-1-11111-1-111i3i3i3i3−i3−i3−i3−i302-202-20000i3−i3-1-111-11i3−i3-1-111i3i3−i3−i3i3i3−i3−i30000000000000000
χ32222222-1-222-2-2-2-2-2-1-1-12-20000-1-11111-1-111i3i3i3i3−i3−i3−i3−i30-220-220000i3−i311-1-1-11i3−i311-1-1−i3−i3i3i3−i3−i3i3i30000000000000000
χ33222222-1-2-2-222-2-2-2-1-1-1-220000-1-1111111-1-1−i3−i3−i3−i3i3i3i3i302-20-220000i3−i3-1-1111-1i3−i311-1-1−i3−i3i3i3i3i3−i3−i30000000000000000
χ34222222-1-2-2-222-2-2-2-1-1-1-220000-1-1111111-1-1−i3−i3−i3−i3i3i3i3i30-2202-20000i3−i311-1-11-1i3−i3-1-111i3i3−i3−i3−i3−i3i3i30000000000000000
χ35222222-1-2-2-222-2-2-2-1-1-1-220000-1-1111111-1-1i3i3i3i3−i3−i3−i3−i302-20-220000−i3i3-1-1111-1−i3i311-1-1i3i3−i3−i3−i3−i3i3i30000000000000000
χ36222222-1-2-2-222-2-2-2-1-1-1-220000-1-1111111-1-1i3i3i3i3−i3−i3−i3−i30-2202-20000−i3i311-1-11-1−i3i3-1-111−i3−i3i3i3i3i3−i3−i30000000000000000
χ372222-2-22222-2-2-2-22222-2222-2-2-2-222-2-222-2-222-2-222-2-2200-2000000220000-22-2-20000000000000000000000000000
χ382222-2-22222-2-2-2-22222-22-2-222-2-222-2-222-2-2-2-222-2-222-2002000000-2-20000-22220000000000000000000000000000
χ392222-2-222-2-222-2-222222-222-2-2-2-222-2-2-2-22222-2-222-2-2-2002000000-2-200002-2220000000000000000000000000000
χ402222-2-222-2-222-2-222222-2-2-222-2-222-2-2-2-222-2-222-2-222200-20000002200002-2-2-20000000000000000000000000000
χ412222-2-22-2222222-2222-2-20000-2-2-2-2222222000000000000002-22-2000000-2-20000002-22-22-22-20000000000000000
χ422222-2-22-2222222-2222-2-20000-2-2-2-222222200000000000000-22-22000000-2-2000000-22-22-22-220000000000000000
χ432222-2-22-2-2-2-2-222-2222220000-2-2-2-222-2-2-2-2000000000000002-2-22000000220000002-22-2-22-220000000000000000
χ442222-2-22-2-2-2-2-222-2222220000-2-2-2-222-2-2-2-200000000000000-222-200000022000000-22-222-22-20000000000000000
χ452222-2-2-1222-2-2-2-22-1-1-1-2222-2-211-1-111-1-111-1-111-1-111200-2000000-1-1−i3i3−i3i31-111−i3i3−i3i3−i3i3i3−i3−i3i3i3−i30000000000000000
χ462222-2-2-1222-2-2-2-22-1-1-1-2222-2-211-1-111-1-111-1-111-1-111200-2000000-1-1i3−i3i3−i31-111i3−i3i3−i3i3−i3−i3i3i3−i3−i3i30000000000000000
χ472222-2-2-1222-2-2-2-22-1-1-1-22-2-22211-1-111-1-11111-1-111-1-1-200200000011−i3i3−i3i31-1-1-1−i3i3−i3i3i3−i3−i3i3i3−i3−i3i30000000000000000
χ482222-2-2-1222-2-2-2-22-1-1-1-22-2-22211-1-111-1-11111-1-111-1-1-200200000011i3−i3i3−i31-1-1-1i3−i3i3−i3−i3i3i3−i3−i3i3i3−i30000000000000000
χ492222-2-2-12-2-222-2-22-1-1-12-222-2-211-1-11111-1-1-1-111-1-111-200200000011−i3i3−i3i3-11-1-1i3−i3i3−i3−i3i3i3−i3i3−i3−i3i30000000000000000
χ502222-2-2-12-2-222-2-22-1-1-12-222-2-211-1-11111-1-1-1-111-1-111-200200000011i3−i3i3−i3-11-1-1−i3i3−i3i3i3−i3−i3i3−i3i3i3−i30000000000000000
χ512222-2-2-12-2-222-2-22-1-1-12-2-2-22211-1-11111-1-111-1-111-1-1200-2000000-1-1−i3i3−i3i3-1111i3−i3i3−i3i3−i3−i3i3−i3i3i3−i30000000000000000
χ522222-2-2-12-2-222-2-22-1-1-12-2-2-22211-1-11111-1-111-1-111-1-1200-2000000-1-1i3−i3i3−i3-1111−i3i3−i3i3−i3i3i3−i3i3−i3−i3i30000000000000000
χ532222-2-2-1-2222222-2-1-1-1-2-200001111-1-1-1-1-1-1−i3−i3i3i3i3i3−i3−i30000002-22-2−i3i3−i3i3i3−i311i3−i3−i3i3i3−i3-11-11-11-110000000000000000
χ542222-2-2-1-2222222-2-1-1-1-2-200001111-1-1-1-1-1-1−i3−i3i3i3i3i3−i3−i3000000-22-22−i3i3i3−i3−i3i311i3−i3i3−i3−i3i31-11-11-11-10000000000000000
χ552222-2-2-1-2222222-2-1-1-1-2-200001111-1-1-1-1-1-1i3i3−i3−i3−i3−i3i3i30000002-22-2i3−i3i3−i3−i3i311−i3i3i3−i3−i3i3-11-11-11-110000000000000000
χ562222-2-2-1-2222222-2-1-1-1-2-200001111-1-1-1-1-1-1i3i3−i3−i3−i3−i3i3i3000000-22-22i3−i3−i3i3i3−i311−i3i3−i3i3i3−i31-11-11-11-10000000000000000
χ572222-2-2-1-2-2-2-2-222-2-1-1-12200001111-1-11111−i3−i3i3i3i3i3−i3−i30000002-2-22i3−i3−i3i3i3−i3-1-1−i3i3i3−i3−i3i3-11-111-11-10000000000000000
χ582222-2-2-1-2-2-2-2-222-2-1-1-12200001111-1-11111−i3−i3i3i3i3i3−i3−i3000000-222-2i3−i3i3−i3−i3i3-1-1−i3i3−i3i3i3−i31-11-1-11-110000000000000000
χ592222-2-2-1-2-2-2-2-222-2-1-1-12200001111-1-11111i3i3−i3−i3−i3−i3i3i30000002-2-22−i3i3i3−i3−i3i3-1-1i3−i3−i3i3i3−i3-11-111-11-10000000000000000
χ602222-2-2-1-2-2-2-2-222-2-1-1-12200001111-1-11111i3i3−i3−i3−i3−i3i3i3000000-222-2−i3i3−i3i3i3−i3-1-1i3−i3i3−i3−i3i31-11-1-11-110000000000000000
χ6122-2-22-22-200002-222-2-2002i−2i2i−2i2-22-22-200002i−2i2i−2i2i−2i2i−2i0000000000000000000000000000000000002i2i−2i−2i002-20000
χ6222-2-22-22-200002-222-2-2002i−2i2i−2i2-22-22-200002i−2i2i−2i2i−2i2i−2i000000000000000000000000000000000000−2i−2i2i2i00-220000
χ6322-2-22-22-200002-222-2-200−2i2i−2i2i2-22-22-20000−2i2i−2i2i−2i2i−2i2i0000000000000000000000000000000000002i2i−2i−2i00-220000
χ6422-2-22-22-200002-222-2-200−2i2i−2i2i2-22-22-20000−2i2i−2i2i−2i2i−2i2i000000000000000000000000000000000000−2i−2i2i2i002-20000
χ6522-2-2-222-20000-2222-2-2002i−2i−2i2i-222-2-2200002i−2i−2i2i2i−2i−2i2i000000000000000000000000000000002i2i−2i−2i00002-2000000
χ6622-2-2-222-20000-2222-2-2002i−2i−2i2i-222-2-2200002i−2i−2i2i2i−2i−2i2i00000000000000000000000000000000−2i−2i2i2i0000-22000000
χ6722-2-2-222-20000-2222-2-200−2i2i2i−2i-222-2-220000−2i2i2i−2i−2i2i2i−2i000000000000000000000000000000002i2i−2i−2i0000-22000000
χ6822-2-2-222-20000-2222-2-200−2i2i2i−2i-222-2-220000−2i2i2i−2i−2i2i2i−2i00000000000000000000000000000000−2i−2i2i2i00002-2000000
χ6944-4-44-4440000-44-44-4-40000004-4-44-44000000000000000000000000000000000000000000000000000000000000
χ7044-4-44-4-240000-44-4-222000000-222-22-2000023−2323−23−2323−2323000000000000000000000000000000000000000000000000
χ7144-4-44-4-240000-44-4-222000000-222-22-20000−2323−232323−2323−23000000000000000000000000000000000000000000000000
χ7244-4-44-4-2-400004-44-222004i−4i4i−4i-22-22-220000−2i2i−2i2i−2i2i−2i2i000000000000000000000000000000000000000000000000
χ7344-4-44-4-2-400004-44-22200−4i4i−4i4i-22-22-2200002i−2i2i−2i2i−2i2i−2i000000000000000000000000000000000000000000000000
χ7444-4-4-444400004-4-44-4-4000000-44-444-4000000000000000000000000000000000000000000000000000000000000
χ7544-4-4-44-2400004-4-4-2220000002-22-2-22000023−23−2323−232323−23000000000000000000000000000000000000000000000000
χ7644-4-4-44-2400004-4-4-2220000002-22-2-220000−232323−2323−23−2323000000000000000000000000000000000000000000000000
χ7744-4-4-44-2-40000-444-222004i−4i−4i4i2-2-222-20000−2i2i2i−2i−2i2i2i−2i000000000000000000000000000000000000000000000000
χ7844-4-4-44-2-40000-444-22200−4i4i4i−4i2-2-222-200002i−2i−2i2i2i−2i−2i2i000000000000000000000000000000000000000000000000
χ794-44-40040004i−4i000-44-4000000000000004i−4i00000000000000000000000000000000000000002-22-22i−2i2i−2i00000000
χ804-44-40040004i−4i000-44-4000000000000004i−4i0000000000000000000000000000000000000000-22-22−2i2i−2i2i00000000
χ814-44-4004000−4i4i000-44-400000000000000−4i4i00000000000000000000000000000000000000002-22-2−2i2i−2i2i00000000
χ824-44-4004000−4i4i000-44-400000000000000−4i4i0000000000000000000000000000000000000000-22-222i−2i2i−2i00000000
χ834-4-4400404i−4i00000-4-440000000000004i−4i0000000000000000000000000000000000000000002i−2i−2i2i2-2-2200000000
χ844-4-4400404i−4i00000-4-440000000000004i−4i000000000000000000000000000000000000000000−2i2i2i−2i-222-200000000
χ854-4-440040−4i4i00000-4-44000000000000−4i4i0000000000000000000000000000000000000000002i−2i−2i2i-222-200000000
χ864-4-440040−4i4i00000-4-44000000000000−4i4i000000000000000000000000000000000000000000−2i2i2i−2i2-2-2200000000
χ878-88-800-40008i−8i0004-4400000000000000−4i4i00000000000000000000000000000000000000000000000000000000
χ888-88-800-4000−8i8i0004-44000000000000004i−4i00000000000000000000000000000000000000000000000000000000
χ898-8-8800-408i−8i0000044-4000000000000−4i4i0000000000000000000000000000000000000000000000000000000000
χ908-8-8800-40−8i8i0000044-40000000000004i−4i0000000000000000000000000000000000000000000000000000000000

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