Finite Group Databasebeta

← Group #10697685

Character table — Group #10697685

Order 768.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72
size1111222222222222224444444444448888888888888812121212121212121616161616161616161616162424242448484848
order12222234444444466644661212121212121212444412121212121212121212888888884488121212122424242488884488
χ1111111111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1
χ311111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-1
χ411111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111
χ5111111111111111111111111111111-1-1-1-1-1-1-1-111-1-1-1-11111111111-1-11111-1-1-1-1-1-1-1-1-1-111
χ6111111111111111111111111111111-1-1-1-1-1-1-1-111-1-1-1-111111111-1-111-1-1-1-11111-1-1-1-111-1-1
χ7111111111111111111111111111111-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-111-1-11111-1-1-1-1111111-1-1
χ8111111111111111111111111111111-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-111111111-1-111
χ9222222222-22-2-22-2222-2-222222-2-2-2-2222-2-22222-2-2-2-2-2-20000000000000000000000000000
χ10222222222-22-2-22-2222-2-222222-2-2-2-22-2-222-2-2-2-2-2-222220000000000000000000000000000
χ112222222-2-22-222-22222-2-222-2-2-22222-200000000-2-200000000000000000000000022-2-20000
χ122222222-2-22-222-22222-2-222-2-2-22222-200000000-2-2000000000000000000000000-2-2220000
χ132222222-2-2-2-2-2-2-2-22222222-2-2-2-2-2-2-2-2000000002200002i2i2i2i−2i−2i−2i−2i00000000000000000000
χ142222222-2-2-2-2-2-2-2-22222222-2-2-2-2-2-2-2-200000000220000−2i−2i−2i−2i2i2i2i2i00000000000000000000
χ15222222-122222222-1-1-122-1-1-1-1-1-1-1-1-1-12222-1-1-1-1-1-1-1-1-1-1000000002222-1-1-1-1-1-1-1-100000000
χ16222222-122222222-1-1-122-1-1-1-1-1-1-1-1-1-12222-1-1-1-1-1-1-1-1-1-100000000-2-2-2-21111111100000000
χ17222222-122222222-1-1-122-1-1-1-1-1-1-1-1-1-1-2-2-2-21111-1-111110000000022-2-2-1-1-1-1111100000000
χ18222222-122222222-1-1-122-1-1-1-1-1-1-1-1-1-1-2-2-2-21111-1-1111100000000-2-2221111-1-1-1-100000000
χ19222222-122-22-2-22-2-1-1-1-2-2-1-1-1-1-11111-122-2-2-1-1-1-1111111000000000000−i3i3−i3i3−i3−i3i3i300000000
χ20222222-122-22-2-22-2-1-1-1-2-2-1-1-1-1-11111-122-2-2-1-1-1-1111111000000000000i3−i3i3−i3i3i3−i3−i300000000
χ21222222-122-22-2-22-2-1-1-1-2-2-1-1-1-1-11111-1-2-222111111-1-1-1-1000000000000−i3i3−i3i3i3i3−i3−i300000000
χ22222222-122-22-2-22-2-1-1-1-2-2-1-1-1-1-11111-1-2-222111111-1-1-1-1000000000000i3−i3i3−i3−i3−i3i3i300000000
χ232222-2-222-222-2-2-222222-2-2-22-2-222-2-22000000002-20000000000002-20022-2-2000000000000
χ242222-2-222-222-2-2-222222-2-2-22-2-222-2-22000000002-2000000000000-2200-2-222000000000000
χ252222-2-222-2-2222-2-2222-22-2-22-2-2-2-222200000000-22000000000000002-200002-22-200000000
χ262222-2-222-2-2222-2-2222-22-2-22-2-2-2-222200000000-2200000000000000-220000-22-2200000000
χ272222-2-22-222-2-2-222222-22-2-2-22222-2-2-200000000-2200000000000000000000000000002-200
χ282222-2-22-222-2-2-222222-22-2-2-22222-2-2-200000000-220000000000000000000000000000-2200
χ292222-2-22-22-2-2222-22222-2-2-2-222-2-222-2000000002-20000000000000000000000000000002-2
χ302222-2-22-22-2-2222-22222-2-2-2-222-2-222-2000000002-2000000000000000000000000000000-22
χ312222-2-2-12-222-2-2-22-1-1-12-211-111-1-111-10000−i3−i3i3i3-11−i3−i3i3i3000000002-200-1-111−i3i3i3−i300000000
χ322222-2-2-12-222-2-2-22-1-1-12-211-111-1-111-10000−i3−i3i3i3-11−i3−i3i3i300000000-220011-1-1i3−i3−i3i300000000
χ332222-2-2-12-222-2-2-22-1-1-12-211-111-1-111-10000i3i3−i3−i3-11i3i3−i3−i3000000002-200-1-111i3−i3−i3i300000000
χ342222-2-2-12-222-2-2-22-1-1-12-211-111-1-111-10000i3i3−i3−i3-11i3i3−i3−i300000000-220011-1-1−i3i3i3−i300000000
χ352222-2-2-12-2-2222-2-2-1-1-1-2211-11111-1-1-10000−i3−i3i3i31-1i3i3−i3−i300000000002-2−i3i3i3−i3-11-1100000000
χ362222-2-2-12-2-2222-2-2-1-1-1-2211-11111-1-1-10000−i3−i3i3i31-1i3i3−i3−i30000000000-22i3−i3−i3i31-11-100000000
χ372222-2-2-12-2-2222-2-2-1-1-1-2211-11111-1-1-10000i3i3−i3−i31-1−i3−i3i3i300000000002-2i3−i3−i3i3-11-1100000000
χ382222-2-2-12-2-2222-2-2-1-1-1-2211-11111-1-1-10000i3i3−i3−i31-1−i3−i3i3i30000000000-22−i3i3i3−i31-11-100000000
χ3922-2-22-22220-200-202-2-2002-222-20000-22-2002-22-200000022−2−222−2−20000000000002−22−20000
χ4022-2-22-22220-200-202-2-2002-222-20000-22-2002-22-2000000−2−222−2−222000000000000−22−220000
χ4122-2-22-22220-200-202-2-2002-222-20000-2-2200-22-2200000022−2−222−2−2000000000000−22−220000
χ4222-2-22-22220-200-202-2-2002-222-20000-2-2200-22-22000000−2−222−2−2220000000000002−22−20000
χ4322-2-22-22-2-20200202-2-2002-2-2-2200002002i−2i0000002i−2i2i−2i−i2−i2i2i2i2i2−i2−i20000000000002−2−220000
χ4422-2-22-22-2-20200202-2-2002-2-2-2200002002i−2i0000002i−2i2i−2ii2i2−i2−i2−i2−i2i2i2000000000000−222−20000
χ4522-2-22-22-2-20200202-2-2002-2-2-220000200−2i2i000000−2i2i−2i2i−i2−i2i2i2i2i2−i2−i2000000000000−222−20000
χ4622-2-22-22-2-20200202-2-2002-2-2-220000200−2i2i000000−2i2i−2i2ii2i2−i2−i2−i2−i2i2i20000000000002−2−220000
χ47444444-2-4-44-444-44-2-2-2-4-4-2-2222-2-2-2-22000000002200000000000000000000000000000000
χ48444444-2-4-4-4-4-4-4-4-4-2-2-244-2-22222222200000000-2-200000000000000000000000000000000
χ494444-4-4-2-444-4-4-444-2-2-2-44222-2-2-2-2222000000002-200000000000000000000000000000000
χ504444-4-4-2-44-4-4444-4-2-2-24-4222-2-222-2-2200000000-2200000000000000000000000000000000
χ5144-4-44-4-2440-400-40-22200-22-2-22000024-400-22-220000000000000000000000000000000000
χ5244-4-44-4-2440-400-40-22200-22-2-2200002-44002-22-20000000000000000000000000000000000
χ5344-4-44-4-2-4-4040040-22200-2222-20000-2004i−4i000000−2i2i−2i2i0000000000000000000000000000
χ5444-4-44-4-2-4-4040040-22200-2222-20000-200−4i4i0000002i−2i2i−2i0000000000000000000000000000
χ5544-4-4-4444-40-400404-4-400-444-440000-4000000000000000000000000000000000000000000
χ5644-4-4-444-440400-404-4-400-44-44-400004000000000000000000000000000000000000000000
χ5744-4-4-44-24-40-40040-222002-2-22-2000020000−2i32i32i3−2i30000000000000000000000000000000000
χ5844-4-4-44-24-40-40040-222002-2-22-20000200002i3−2i3−2i32i30000000000000000000000000000000000
χ5944-4-4-44-2-440400-40-222002-22-220000-2000000000023−23−23230000000000000000000000000000
χ6044-4-4-44-2-440400-40-222002-22-220000-20000000000−232323−230000000000000000000000000000
χ614-44-40040040000-4-44-400000004-4000000000000000002-22-22-22-200000000000000000000
χ624-44-40040040000-4-44-400000004-400000000000000000-22-22-22-2200000000000000000000
χ634-44-400400-400004-44-40000000-44000000000000000002i−2i2i−2i−2i2i−2i2i00000000000000000000
χ644-44-400400-400004-44-40000000-4400000000000000000−2i2i−2i2i2i−2i2i−2i00000000000000000000
χ654-4-4400400004i−4i00-4-440000000004i−4i0000000000000002ζ7+2ζ23−2ζ7−2ζ23−2ζ7−2ζ232ζ7+2ζ23−2ζ5−2ζ132ζ5+2ζ132ζ5+2ζ13−2ζ5−2ζ1300000000000000000000
χ664-4-4400400004i−4i00-4-440000000004i−4i000000000000000−2ζ7−2ζ232ζ7+2ζ232ζ7+2ζ23−2ζ7−2ζ232ζ5+2ζ13−2ζ5−2ζ13−2ζ5−2ζ132ζ5+2ζ1300000000000000000000
χ674-4-440040000−4i4i00-4-44000000000−4i4i000000000000000−2ζ5−2ζ132ζ5+2ζ132ζ5+2ζ13−2ζ5−2ζ132ζ7+2ζ23−2ζ7−2ζ23−2ζ7−2ζ232ζ7+2ζ2300000000000000000000
χ684-4-440040000−4i4i00-4-44000000000−4i4i0000000000000002ζ5+2ζ13−2ζ5−2ζ13−2ζ5−2ζ132ζ5+2ζ13−2ζ7−2ζ232ζ7+2ζ232ζ7+2ζ23−2ζ7−2ζ2300000000000000000000
χ698-88-800-40080000-84-440000000-44000000000000000000000000000000000000000000000
χ708-88-800-400-8000084-4400000004-4000000000000000000000000000000000000000000000
χ718-8-8800-400008i−8i0044-4000000000−4i4i0000000000000000000000000000000000000000000
χ728-8-8800-40000−8i8i0044-40000000004i−4i0000000000000000000000000000000000000000000

Here ζ is a primitive root of unity of order 24 (ζ24 = 1); i = ζ6.