Finite Group Databasebeta

← Group #10697657

Character table — Group #10697657

Order 768.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72
size1111222222222222224444444444448888888888888812121212121212121616161616161616161616162424242448484848
order1222223444444446664466121212121212121288881212242424242424242488888888224466661212121222448888
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
χ5111111111111111111111111111111-1-1-1-111-1-1-1-1-1-1-1-1111111111-11-111-1-111-1-1-1-1-1-111-1-1
χ6111111111111111111111111111111-1-1-1-111-1-1-1-1-1-1-1-111111111-11-11-1-111-1-111-1-1-1-1-1-111
χ7111111111111111111111111111111-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11-11-111-1-111-1-11111-1-111
χ8111111111111111111111111111111-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11-11-1-111-1-111111111-1-1
χ9222222222-2-2-2-222222-2-222-2-2-22222-20000-2-2000000000000000000000000000022-2-20000
χ10222222222-2-2-2-222222-2-222-2-2-22222-20000-2-20000000000000000000000000000-2-2220000
χ112222222-2-22222-2-2222-2-222222-2-2-2-2222-2-2-2-22222-2-2-2-20000000000000000000000000000
χ122222222-2-22222-2-2222-2-222222-2-2-2-22-2-222-2-2-2-2-2-222220000000000000000000000000000
χ132222222-2-2-2-2-2-2-2-22222222-2-2-2-2-2-2-2-2000022000000002i2i2i2i−2i−2i−2i−2i00000000000000000000
χ142222222-2-2-2-2-2-2-2-22222222-2-2-2-2-2-2-2-200002200000000−2i−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
χ17222222-122222222-1-1-122-1-1-1-1-1-1-1-1-1-1-2-2-2-2-1-111111111000000002-22-2-1-111-1-11100000000
χ18222222-122222222-1-1-122-1-1-1-1-1-1-1-1-1-1-2-2-2-2-1-11111111100000000-22-2211-1-111-1-100000000
χ19222222-1-2-22222-2-2-1-1-1-2-2-1-1-1-1-11111-122-2-211-1-1-1-11111000000000000−i3i3−i3i3−i3i3−i3i300000000
χ20222222-1-2-22222-2-2-1-1-1-2-2-1-1-1-1-11111-122-2-211-1-1-1-11111000000000000i3−i3i3−i3i3−i3i3−i300000000
χ21222222-1-2-22222-2-2-1-1-1-2-2-1-1-1-1-11111-1-2-222111111-1-1-1-1000000000000−i3i3i3−i3−i3i3i3−i300000000
χ22222222-1-2-22222-2-2-1-1-1-2-2-1-1-1-1-11111-1-2-222111111-1-1-1-1000000000000i3−i3−i3i3i3−i3−i3i300000000
χ232222-2-222-222-2-22-22222-2-2-22-2-222-2-2200002-20000000000000000020-2002200-2-200000000
χ242222-2-222-222-2-22-22222-2-2-22-2-222-2-2200002-200000000000000000-20200-2-2002200000000
χ252222-2-222-2-2-2222-2222-22-2-2-22222-2-2-20000-22000000000000000000000000000000002-200
χ262222-2-222-2-2-2222-2222-22-2-2-22222-2-2-20000-2200000000000000000000000000000000-2200
χ272222-2-22-2222-2-2-22222-22-2-22-2-2-2-22220000-22000000000000000020-202200-2-20000000000
χ282222-2-22-2222-2-2-22222-22-2-22-2-2-2-22220000-220000000000000000-2020-2-200220000000000
χ292222-2-22-22-2-222-222222-2-2-2-222-2-222-200002-200000000000000000000000000000000002-2
χ302222-2-22-22-2-222-222222-2-2-2-222-2-222-200002-20000000000000000000000000000000000-22
χ312222-2-2-12-222-2-22-2-1-1-12-211-111-1-111-10000-11−i3−i3i3i3−i3−i3i3i300000000020-2−i3i3-1-1i3−i31100000000
χ322222-2-2-12-222-2-22-2-1-1-12-211-111-1-111-10000-11−i3−i3i3i3−i3−i3i3i3000000000-202i3−i311−i3i3-1-100000000
χ332222-2-2-12-222-2-22-2-1-1-12-211-111-1-111-10000-11i3i3−i3−i3i3i3−i3−i300000000020-2i3−i3-1-1−i3i31100000000
χ342222-2-2-12-222-2-22-2-1-1-12-211-111-1-111-10000-11i3i3−i3−i3i3i3−i3−i3000000000-202−i3i311i3−i3-1-100000000
χ352222-2-2-1-2222-2-2-22-1-1-1-2211-11111-1-1-100001-1−i3−i3i3i3i3i3−i3−i30000000020-20-1-1−i3i311i3−i300000000
χ362222-2-2-1-2222-2-2-22-1-1-1-2211-11111-1-1-100001-1−i3−i3i3i3i3i3−i3−i300000000-202011i3−i3-1-1−i3i300000000
χ372222-2-2-1-2222-2-2-22-1-1-1-2211-11111-1-1-100001-1i3i3−i3−i3−i3−i3i3i30000000020-20-1-1i3−i311−i3i300000000
χ382222-2-2-1-2222-2-2-22-1-1-1-2211-11111-1-1-100001-1i3i3−i3−i3−i3−i3i3i300000000-202011−i3i3-1-1i3−i300000000
χ392-22-22-22220000-2-2-2-22002-20002-22-202−22−2002−22−22−22−2−i2−i2i2i2−i2−i2i2i2000000000000002i−2i0000
χ402-22-22-22220000-2-2-2-22002-20002-22-202−22−2002−22−22−22−2i2i2−i2−i2i2i2−i2−i200000000000000−2i2i0000
χ412-22-22-22220000-2-2-2-22002-20002-22-20−22−2200−22−22−22−22−i2−i2i2i2−i2−i2i2i200000000000000−2i2i0000
χ422-22-22-22220000-2-2-2-22002-20002-22-20−22−2200−22−22−22−22i2i2−i2−i2i2i2−i2−i2000000000000002i−2i0000
χ432-22-22-22-2-2000022-2-22002-2000-22-2202−2−22002−22−2−22−2222−2−2−2−2220000000000002-2000000
χ442-22-22-22-2-2000022-2-22002-2000-22-2202−2−22002−22−2−22−22−2−22222−2−2000000000000-22000000
χ452-22-22-22-2-2000022-2-22002-2000-22-220−222−200−22−222−22−222−2−2−2−222000000000000-22000000
χ462-22-22-22-2-2000022-2-22002-2000-22-220−222−200−22−222−22−2−2−22222−2−20000000000002-2000000
χ47444444-244-4-4-4-444-2-2-2-4-4-2-2222-2-2-2-22000022000000000000000000000000000000000000
χ48444444-2-4-4-4-4-4-4-4-4-2-2-244-2-2222222220000-2-2000000000000000000000000000000000000
χ494444-4-4-24-4-4-4444-4-2-2-2-44222-2-2-2-222200002-2000000000000000000000000000000000000
χ504444-4-4-2-44-4-444-44-2-2-24-4222-2-222-2-220000-22000000000000000000000000000000000000
χ5144-4-400400004i−4i004-4-4000004i−4i00000000000000000002ζ7+2ζ23−2ζ7−2ζ232ζ7+2ζ23−2ζ7−2ζ23−2ζ5−2ζ132ζ5+2ζ13−2ζ5−2ζ132ζ5+2ζ1300000000000000000000
χ5244-4-400400004i−4i004-4-4000004i−4i0000000000000000000−2ζ7−2ζ232ζ7+2ζ23−2ζ7−2ζ232ζ7+2ζ232ζ5+2ζ13−2ζ5−2ζ132ζ5+2ζ13−2ζ5−2ζ1300000000000000000000
χ5344-4-40040000−4i4i004-4-400000−4i4i0000000000000000000−2ζ5−2ζ132ζ5+2ζ13−2ζ5−2ζ132ζ5+2ζ132ζ7+2ζ23−2ζ7−2ζ232ζ7+2ζ23−2ζ7−2ζ2300000000000000000000
χ5444-4-40040000−4i4i004-4-400000−4i4i00000000000000000002ζ5+2ζ13−2ζ5−2ζ132ζ5+2ζ13−2ζ5−2ζ13−2ζ7−2ζ232ζ7+2ζ23−2ζ7−2ζ232ζ7+2ζ2300000000000000000000
χ554-44-44-4-2440000-4-422-200-22000-22-22022−2222−2200−22−22−22−220000000000000000000000000000
χ564-44-44-4-2440000-4-422-200-22000-22-220−2222−2222002−22−22−22−20000000000000000000000000000
χ574-44-44-4-2-4-400004422-200-220002-22-2022−22−222200−22−222−22−20000000000000000000000000000
χ584-44-44-4-2-4-400004422-200-220002-22-20−222222−22002−22−2−22−220000000000000000000000000000
χ594-44-4-4444-40000-44-4-4400-440004-4-440000000000000000000000000000000000000000000
χ604-44-4-444-4400004-4-4-4400-44000-444-40000000000000000000000000000000000000000000
χ614-44-4-44-24-40000-4422-2002-2000-222-20000000i6−i6−i6i6i6−i6−i6i60000000000000000000000000000
χ624-44-4-44-24-40000-4422-2002-2000-222-20000000−i6i6i6−i6−i6i6i6−i60000000000000000000000000000
χ634-44-4-44-2-4400004-422-2002-20002-2-220000000i6−i6−i6i6−i6i6i6−i60000000000000000000000000000
χ644-44-4-44-2-4400004-422-2002-20002-2-220000000−i6i6i6−i6i6−i6−i6i60000000000000000000000000000
χ654-4-44004004-40000-44-400004000000-4000000000000002i−2i−2i2i2i−2i−2i2i00000000000000000000
χ664-4-44004004-40000-44-400004000000-400000000000000−2i2i2i−2i−2i2i2i−2i00000000000000000000
χ674-4-4400400-440000-44-40000-40000004000000000000002-2-22-222-200000000000000000000
χ684-4-4400400-440000-44-40000-4000000400000000000000-222-22-2-2200000000000000000000
χ6988-8-800-400008i−8i00-44400000−4i4i00000000000000000000000000000000000000000000000
χ7088-8-800-40000−8i8i00-444000004i−4i00000000000000000000000000000000000000000000000
χ718-8-8800-4008-800004-440000-40000004000000000000000000000000000000000000000000
χ728-8-8800-400-8800004-4400004000000-4000000000000000000000000000000000000000000

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