Finite Group Databasebeta

← Group #10697296

Character table — Group #10697296

Order 768.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69
size11112222222222224444444444444888888888888881616161616161616161616162424242424242424242424244848
order12222234444446664446612121212121212128888121224242424242424244444121212121212121244448888888824
χ1111111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ31111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-111
χ41111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1
χ511111111111111111111111111111-1-1-1-111-1-1-1-1-1-1-1-111-1-11111-1-1-1-111111111-1-1-1-1-1-1
χ611111111111111111111111111111-1-1-1-111-1-1-1-1-1-1-1-111-1-11111-1-1-1-1-1-1-1-1-1-1-1-1111111
χ711111111111111111111111111111-1-1-1-111-1-1-1-1-1-1-1-1-1-111-1-1-1-111111111-1-1-1-11111-1-1
χ811111111111111111111111111111-1-1-1-111-1-1-1-1-1-1-1-1-1-111-1-1-1-11111-1-1-1-11111-1-1-1-111
χ922222222-2-2-2-222222-2-222-2-2-2-222-2-200002-2000000000000000000000000000022-2-200
χ1022222222-2-2-2-222222-2-222-2-2-2-222-2-200002-20000000000000000000000000000-2-22200
χ112222222-22222-2222-2-2-2222222-2-2-2-20000-2-200000000000000000000000022-2-2000000
χ122222222-22222-2222-2-2-2222222-2-2-2-20000-2-2000000000000000000000000-2-222000000
χ132222222-2-2-2-2-2-2222-22222-2-2-2-2-2-22222-2-2-222222-2-2-2-200000000000000000000000000
χ142222222-2-2-2-2-2-2222-22222-2-2-2-2-2-222-2-222-22-2-2-2-2222200000000000000000000000000
χ15222222-1222222-1-1-1222-1-1-1-1-1-1-1-1-1-12222-1-1-1-1-1-1-1-1-1-12222-1-1-1-1-1-1-1-100000000000000
χ16222222-1222222-1-1-1222-1-1-1-1-1-1-1-1-1-12222-1-1-1-1-1-1-1-1-1-1-2-2-2-21111111100000000000000
χ17222222-1222222-1-1-1222-1-1-1-1-1-1-1-1-1-1-2-2-2-2-1-11111111122-2-2-1-1-1-1111100000000000000
χ18222222-1222222-1-1-1222-1-1-1-1-1-1-1-1-1-1-2-2-2-2-1-111111111-2-2221111-1-1-1-100000000000000
χ19222222-1-2-2-2-2-2-2-1-1-1-222-1-1111111-1-122-2-21-1-1-1-1-111110000−i3i3−i3i3−i3−i3i3i300000000000000
χ20222222-1-2-2-2-2-2-2-1-1-1-222-1-1111111-1-122-2-21-1-1-1-1-111110000i3−i3i3−i3i3i3−i3−i300000000000000
χ21222222-1-2-2-2-2-2-2-1-1-1-222-1-1111111-1-1-2-2221-11111-1-1-1-10000−i3i3−i3i3i3i3−i3−i300000000000000
χ22222222-1-2-2-2-2-2-2-1-1-1-222-1-1111111-1-1-2-2221-11111-1-1-1-10000i3−i3i3−i3−i3−i3i3i300000000000000
χ232222-2-22222-2-22222-2-22-2-222-2-222220000-2-2000000002-20022-2-2000000000000000000
χ242222-2-22222-2-22222-2-22-2-222-2-222220000-2-200000000-2200-2-222000000000000000000
χ252222-2-222-2-2222222-22-2-2-2-2-22222-2-20000-22000000000000000000000000000000002-2
χ262222-2-222-2-2222222-22-2-2-2-2-22222-2-20000-2200000000000000000000000000000000-22
χ272222-2-22-222-2-2-222222-2-2-222-2-2-2-2-2-2000022000000000000000000002i2i−2i−2i0000000000
χ282222-2-22-222-2-2-222222-2-2-222-2-2-2-2-2-200002200000000000000000000−2i−2i2i2i0000000000
χ292222-2-22-2-2-222-22222-22-2-2-2-222-2-22200002-200000000002-200002-22-200000000000000
χ302222-2-22-2-2-222-22222-22-2-2-2-222-2-22200002-20000000000-220000-22-2200000000000000
χ312222-2-2-1222-2-22-1-1-1-2-2211-1-111-1-1-1-1000011−i3−i3i3i3−i3−i3i3i32-200-1-111−i3i3i3−i300000000000000
χ322222-2-2-1222-2-22-1-1-1-2-2211-1-111-1-1-1-1000011−i3−i3i3i3−i3−i3i3i3-220011-1-1i3−i3−i3i300000000000000
χ332222-2-2-1222-2-22-1-1-1-2-2211-1-111-1-1-1-1000011i3i3−i3−i3i3i3−i3−i32-200-1-111i3−i3−i3i300000000000000
χ342222-2-2-1222-2-22-1-1-1-2-2211-1-111-1-1-1-1000011i3i3−i3−i3i3i3−i3−i3-220011-1-1−i3i3i3−i300000000000000
χ352222-2-2-1-2-2-222-2-1-1-12-221111-1-111-1-10000-11−i3−i3i3i3i3i3−i3−i3002-2−i3i3i3−i3-11-1100000000000000
χ362222-2-2-1-2-2-222-2-1-1-12-221111-1-111-1-10000-11−i3−i3i3i3i3i3−i3−i300-22i3−i3−i3i31-11-100000000000000
χ372222-2-2-1-2-2-222-2-1-1-12-221111-1-111-1-10000-11i3i3−i3−i3−i3−i3i3i3002-2i3−i3−i3i3-11-1100000000000000
χ382222-2-2-1-2-2-222-2-1-1-12-221111-1-111-1-10000-11i3i3−i3−i3−i3−i3i3i300-22−i3i3i3−i31-11-100000000000000
χ392-22-2-22202-22-202-2-20002-22-22-200002−22−2002−22−22−22−20000000000000000002i−2i−i2i2−i2i200
χ402-22-2-22202-22-202-2-20002-22-22-200002−22−2002−22−22−22−2000000000000000000−2i2ii2−i2i2−i200
χ412-22-2-22202-22-202-2-20002-22-22-20000−22−2200−22−22−22−220000000000000000002i−2ii2−i2i2−i200
χ422-22-2-22202-22-202-2-20002-22-22-20000−22−2200−22−22−22−22000000000000000000−2i2i−i2i2−i2i200
χ432-22-2-2220-22-2202-2-20002-2-22-2200002−2−22002−22−2−22−2200000000000000002i−2i00−i2i2i2−i200
χ442-22-2-2220-22-2202-2-20002-2-22-2200002−2−22002−22−2−22−220000000000000000−2i2i00i2−i2−i2i200
χ452-22-2-2220-22-2202-2-20002-2-22-220000−222−200−22−222−22−200000000000000002i−2i00i2−i2−i2i200
χ462-22-2-2220-22-2202-2-20002-2-22-220000−222−200−22−222−22−20000000000000000−2i2i00−i2i2i2−i200
χ47444444-24-4-4-4-44-2-2-24-4-4-2-22222-2-2220000-220000000000000000000000000000000000
χ48444444-2-44444-4-2-2-2-4-4-4-2-2-2-2-2-222220000220000000000000000000000000000000000
χ494444-4-4-24-4-4444-2-2-2-44-42222-2-2-2-22200002-20000000000000000000000000000000000
χ504444-4-4-2-444-4-4-4-2-2-244-422-2-22222220000-2-20000000000000000000000000000000000
χ5144-4-400440000-4-44-40000000004-400000000000000000000000000002-22-20000000000
χ5244-4-400440000-4-44-40000000004-40000000000000000000000000000-22-220000000000
χ5344-4-4004-400004-44-4000000000-4400000000000000000000000000002i−2i−2i2i0000000000
χ5444-4-4004-400004-44-4000000000-440000000000000000000000000000−2i2i2i−2i0000000000
χ554-44-44-4404-4-4404-4-4000-444-4-4400000000000000000000000000000000000000000000
χ564-44-44-440-444-404-4-4000-44-444-400000000000000000000000000000000000000000000
χ574-44-44-4-204-4-440-2220002-2-222-20000000000i6−i6−i6i6i6−i6−i6i600000000000000000000000000
χ584-44-44-4-204-4-440-2220002-2-222-20000000000−i6i6i6−i6−i6i6i6−i600000000000000000000000000
χ594-44-44-4-20-444-40-2220002-22-2-220000000000i6−i6−i6i6−i6i6i6−i600000000000000000000000000
χ604-44-44-4-20-444-40-2220002-22-2-220000000000−i6i6i6−i6i6−i6−i6i600000000000000000000000000
χ614-44-4-44-204-44-40-222000-22-22-22000022−2222−2200−22−22−22−2200000000000000000000000000
χ624-44-4-44-204-44-40-222000-22-22-220000−2222−2222002−22−22−22−200000000000000000000000000
χ634-44-4-44-20-44-440-222000-222-22-2000022−22−222200−22−222−22−200000000000000000000000000
χ644-44-4-44-20-44-440-222000-222-22-20000−222222−22002−22−2−22−2200000000000000000000000000
χ6588-8-800-480000-84-44000000000-44000000000000000000000000000000000000000000
χ6688-8-800-4-8000084-440000000004-4000000000000000000000000000000000000000000
χ678-8-88008000000-8-8800000000000000000000000000000000000000000000000000000
χ688-8-8800-400000044-400000000000−4i34i30000000000000000000000000000000000000000
χ698-8-8800-400000044-4000000000004i3−4i30000000000000000000000000000000000000000

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