Finite Group Databasebeta

← Group #10697545

Character table — Group #10697545

Order 768.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69
size11112222222222224444444444444888888888888881616161616161616161616162424242424242424242424244848
order12222234444446664446612121212121212128888121224242424242424242224666666121222444444888888
χ1111111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ31111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1
χ41111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-111
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
χ711111111111111111111111111111-1-1-1-111-1-1-1-1-1-1-1-1-1-111-1-1-1-111111111-1-1-1-1-1-1-1-111
χ811111111111111111111111111111-1-1-1-111-1-1-1-1-1-1-1-1-1-111-1-1-1-11111-1-1-1-111111111-1-1
χ92222222222-2-22222-2-2-222-2-22222-2-20000-2-20000000000000000000022-2-20000000000
χ102222222222-2-22222-2-2-222-2-22222-2-20000-2-200000000000000000000-2-2220000000000
χ112222222-2-2-222-2222-22-222-2-2-2-2-2-22200002-2000000002-20022-2-2000000000000000000
χ122222222-2-2-222-2222-22-222-2-2-2-2-2-22200002-200000000-2200-2-222000000000000000000
χ132222222-2-2-2-2-2-22222-222222-2-2-2-2-2-20000-2200000000000000000000000022-2-2000000
χ142222222-2-2-2-2-2-22222-222222-2-2-2-2-2-20000-22000000000000000000000000-2-222000000
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
χ19222222-1-2-2-222-2-1-1-1-22-2-1-1111111-1-10000-11−i3−i3−i3−i3i3i3i3i32-200-1-111−i3i3−i3i300000000000000
χ20222222-1-2-2-222-2-1-1-1-22-2-1-1111111-1-10000-11−i3−i3−i3−i3i3i3i3i3-220011-1-1i3−i3i3−i300000000000000
χ21222222-1-2-2-222-2-1-1-1-22-2-1-1111111-1-10000-11i3i3i3i3−i3−i3−i3−i32-200-1-111i3−i3i3−i300000000000000
χ22222222-1-2-2-222-2-1-1-1-22-2-1-1111111-1-10000-11i3i3i3i3−i3−i3−i3−i3-220011-1-1−i3i3−i3i300000000000000
χ232222-2-2222-222-2222-2-22-2-2-2-222-2-22222-2-2-2222-2-222-2-200000000000000000000000000
χ242222-2-2222-222-2222-2-22-2-2-2-222-2-222-2-222-22-2-222-2-22200000000000000000000000000
χ252222-2-2222-2-2-2-222222-2-2-22222-2-2-2-200002-200000000000000000000000000002i2i−2i−2i00
χ262222-2-2222-2-2-2-222222-2-2-22222-2-2-2-200002-20000000000000000000000000000−2i−2i2i2i00
χ272222-2-22-2-222222222-2-2-2-222-2-222220000-2-200000000002-2000022-2-200000000000000
χ282222-2-22-2-222222222-2-2-2-222-2-222220000-2-20000000000-220000-2-22200000000000000
χ292222-2-22-2-22-2-22222-222-2-2-2-2-2-222-2-2000022000000000000000000000000000000002-2
χ302222-2-22-2-22-2-22222-222-2-2-2-2-2-222-2-200002200000000000000000000000000000000-22
χ312222-2-2-122-222-2-1-1-1-2-221111-1-111-1-122-2-21-1-1-111-1-1110000−i3i3−i3i3−i3i3i3−i300000000000000
χ322222-2-2-122-222-2-1-1-1-2-221111-1-111-1-122-2-21-1-1-111-1-1110000i3−i3i3−i3i3−i3−i3i300000000000000
χ332222-2-2-122-222-2-1-1-1-2-221111-1-111-1-1-2-2221-111-1-111-1-10000−i3i3−i3i3i3−i3−i3i300000000000000
χ342222-2-2-122-222-2-1-1-1-2-221111-1-111-1-1-2-2221-111-1-111-1-10000i3−i3i3−i3−i3i3i3−i300000000000000
χ352222-2-2-1-2-22222-1-1-12-2-211-1-111-1-1-1-1000011−i3−i3i3i3i3i3−i3−i3002-2−i3i3i3−i3-1-11100000000000000
χ362222-2-2-1-2-22222-1-1-12-2-211-1-111-1-1-1-1000011−i3−i3i3i3i3i3−i3−i300-22i3−i3−i3i311-1-100000000000000
χ372222-2-2-1-2-22222-1-1-12-2-211-1-111-1-1-1-1000011i3i3−i3−i3−i3−i3i3i3002-2i3−i3−i3i3-1-11100000000000000
χ382222-2-2-1-2-22222-1-1-12-2-211-1-111-1-1-1-1000011i3i3−i3−i3−i3−i3i3i300-22−i3i3i3−i311-1-100000000000000
χ392-22-22-222-2200-2-2-220002-2002-22-2002−22−2002−22−22−22−2000000000000002i−2i0000−i2i2−i2i200
χ402-22-22-222-2200-2-2-220002-2002-22-2002−22−2002−22−22−22−200000000000000−2i2i0000i2−i2i2−i200
χ412-22-22-222-2200-2-2-220002-2002-22-200−22−2200−22−22−22−22000000000000002i−2i0000i2−i2i2−i200
χ422-22-22-222-2200-2-2-220002-2002-22-200−22−2200−22−22−22−2200000000000000−2i2i0000−i2i2−i2i200
χ432-22-2-2222-2-2002-2-22000-22002-2-22002−2−22002−2−222−2−220000000000002-20000002−2−2200
χ442-22-2-2222-2-2002-2-22000-22002-2-22002−2−22002−2−222−2−22000000000000-22000000−222−200
χ452-22-2-2222-2-2002-2-22000-22002-2-2200−222−200−222−2−222−20000000000002-2000000−222−200
χ462-22-2-2222-2-2002-2-22000-22002-2-2200−222−200−222−2−222−2000000000000-220000002−2−2200
χ47444444-2444-4-44-2-2-2-4-4-4-2-222-2-2-2-2220000220000000000000000000000000000000000
χ48444444-2-4-4-4-4-4-4-2-2-24-44-2-2-2-222222200002-20000000000000000000000000000000000
χ494444-4-4-244-4-4-4-4-2-2-244-422-2-2-2-222220000-220000000000000000000000000000000000
χ504444-4-4-2-4-44-4-44-2-2-2-444222222-2-2220000-2-20000000000000000000000000000000000
χ514-44-44-44-44-4004-4-440004-400-44-44000000000000000000000000000000000000000000
χ524-44-44-4-24-4400-422-2000-2200-22-220022−2222−2200−22−22−22−2200000000000000000000000000
χ534-44-44-4-24-4400-422-2000-2200-22-2200−2222−2222002−22−22−22−200000000000000000000000000
χ544-44-44-4-2-44-400422-2000-22002-22-200000000i6−i6i6−i6−i6i6−i6i600000000000000000000000000
χ554-44-44-4-2-44-400422-2000-22002-22-200000000−i6i6−i6i6i6−i6i6−i600000000000000000000000000
χ564-44-4-444-44400-4-4-44000-4400-444-4000000000000000000000000000000000000000000
χ574-44-4-44-24-4-400422-20002-200-222-20022−22−222200−222−2−222−200000000000000000000000000
χ584-44-4-44-24-4-400422-20002-200-222-200−222222−22002−2−222−2−2200000000000000000000000000
χ594-44-4-44-2-44400-422-20002-2002-2-2200000000i6−i6−i6i6−i6i6i6−i600000000000000000000000000
χ604-44-4-44-2-44400-422-20002-2002-2-2200000000−i6i6i6−i6i6−i6−i6i600000000000000000000000000
χ614-4-440040004-404-4-4000000000004-40000000000000000000000000000002-22-2000000
χ624-4-440040004-404-4-4000000000004-4000000000000000000000000000000-22-22000000
χ634-4-44004000-4404-4-400000000000-440000000000000000000000000000002-2-22000000
χ644-4-44004000-4404-4-400000000000-44000000000000000000000000000000-222-2000000
χ6588-8-8008000000-88-800000000000000000000000000000000000000000000000000000
χ6688-8-800-40000004-4400000−4i34i30000000000000000000000000000000000000000000000
χ6788-8-800-40000004-44000004i3−4i30000000000000000000000000000000000000000000000
χ688-8-8800-40008-80-44400000000000-440000000000000000000000000000000000000000
χ698-8-8800-4000-880-444000000000004-40000000000000000000000000000000000000000

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