Finite Group Databasebeta

← Group #10697313

Character table — Group #10697313

Order 768.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69
size11112222222222224444444444444888888888888881616161616161616161616162424242424242424242424244848
order1222223444444666444661212121212121212888812122424242424242424224466661212121244448888888844
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
χ511111111111111111111111111111-1-1-1-111-1-1-1-1-1-1-1-11-11-111-1-111-1-111111111-1-1-1-1-1-1
χ611111111111111111111111111111-1-1-1-111-1-1-1-1-1-1-1-11-11-111-1-111-1-1-1-1-1-1-1-1-1-1111111
χ711111111111111111111111111111-1-1-1-111-1-1-1-1-1-1-1-1-11-11-1-111-1-1111111-1-1-1-11111-1-1
χ811111111111111111111111111111-1-1-1-111-1-1-1-1-1-1-1-1-11-11-1-111-1-111-1-1-1-11111-1-1-1-111
χ9222222222-2-222222-2-2-222-2-2-22222-20000-2-200000000000000000000000022-2-2000000
χ10222222222-2-222222-2-2-222-2-2-22222-20000-2-2000000000000000000000000-2-222000000
χ112222222-2-222-2-2222-22-222222-2-2-2-2222-2-2-2-22222-2-2-2-200000000000000000000000000
χ122222222-2-222-2-2222-22-222222-2-2-2-22-2-222-2-2-2-2-2-2222200000000000000000000000000
χ132222222-2-2-2-2-2-22222-2222-2-2-2-2-2-2-2-2000022000000000000000000000000000022-2-200
χ142222222-2-2-2-2-2-22222-2222-2-2-2-2-2-2-2-20000220000000000000000000000000000-2-22200
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
χ17222222-1222222-1-1-1222-1-1-1-1-1-1-1-1-1-1-2-2-2-2-1-1111111112-22-2-1-111-1-11100000000000000
χ18222222-1222222-1-1-1222-1-1-1-1-1-1-1-1-1-1-2-2-2-2-1-111111111-22-2211-1-111-1-100000000000000
χ19222222-1-2-222-2-2-1-1-1-22-2-1-1-1-1-11111-122-2-211-1-1-1-111110000−i3i3−i3i3−i3i3−i3i300000000000000
χ20222222-1-2-222-2-2-1-1-1-22-2-1-1-1-1-11111-122-2-211-1-1-1-111110000i3−i3i3−i3i3−i3i3−i300000000000000
χ21222222-1-2-222-2-2-1-1-1-22-2-1-1-1-1-11111-1-2-222111111-1-1-1-10000−i3i3i3−i3−i3i3i3−i300000000000000
χ22222222-1-2-222-2-2-1-1-1-22-2-1-1-1-1-11111-1-2-222111111-1-1-1-10000i3−i3−i3i3i3−i3−i3i300000000000000
χ232222-2-222222-2-2222-2-22-2-22-2-222-2-2200002-20000000020-202200-2-20000000000000000
χ242222-2-222222-2-2222-2-22-2-22-2-222-2-2200002-200000000-2020-2-200220000000000000000
χ252222-2-2222-2-2-2-222222-2-2-2-22222-2-2-20000-22000000000000000000002i2i−2i−2i0000000000
χ262222-2-2222-2-2-2-222222-2-2-2-22222-2-2-20000-2200000000000000000000−2i−2i2i2i0000000000
χ272222-2-22-2-222222222-2-2-2-22-2-2-2-22220000-2200000000020-2002200-2-200000000000000
χ282222-2-22-2-222222222-2-2-2-22-2-2-2-22220000-22000000000-20200-2-2002200000000000000
χ292222-2-22-2-2-2-222222-222-2-2-222-2-222-200002-2000000000000000000000000000000002-2
χ302222-2-22-2-2-2-222222-222-2-2-222-2-222-200002-200000000000000000000000000000000-22
χ312222-2-2-12222-2-2-1-1-1-2-2211-111-1-111-10000-11−i3−i3i3i3−i3−i3i3i320-20-1-1−i3i311i3−i300000000000000
χ322222-2-2-12222-2-2-1-1-1-2-2211-111-1-111-10000-11−i3−i3i3i3−i3−i3i3i3-202011i3−i3-1-1−i3i300000000000000
χ332222-2-2-12222-2-2-1-1-1-2-2211-111-1-111-10000-11i3i3−i3−i3i3i3−i3−i320-20-1-1i3−i311−i3i300000000000000
χ342222-2-2-12222-2-2-1-1-1-2-2211-111-1-111-10000-11i3i3−i3−i3i3i3−i3−i3-202011−i3i3-1-1i3−i300000000000000
χ352222-2-2-1-2-22222-1-1-12-2-211-11111-1-1-100001-1−i3−i3i3i3i3i3−i3−i3020-2−i3i3-1-1i3−i31100000000000000
χ362222-2-2-1-2-22222-1-1-12-2-211-11111-1-1-100001-1−i3−i3i3i3i3i3−i3−i30-202i3−i311−i3i3-1-100000000000000
χ372222-2-2-1-2-22222-1-1-12-2-211-11111-1-1-100001-1i3i3−i3−i3−i3−i3i3i3020-2i3−i3-1-1−i3i31100000000000000
χ382222-2-2-1-2-22222-1-1-12-2-211-11111-1-1-100001-1i3i3−i3−i3−i3−i3i3i30-202−i3i311i3−i3-1-100000000000000
χ392-22-22-222-2002-2-2-220002-20002-22-202−22−2002−22−22−22−20000000000000000002i−2i−i2i2−i2i200
χ402-22-22-222-2002-2-2-220002-20002-22-202−22−2002−22−22−22−2000000000000000000−2i2ii2−i2i2−i200
χ412-22-22-222-2002-2-2-220002-20002-22-20−22−2200−22−22−22−220000000000000000002i−2ii2−i2i2−i200
χ422-22-22-222-2002-2-2-220002-20002-22-20−22−2200−22−22−22−22000000000000000000−2i2i−i2i2−i2i200
χ432-22-22-22-2200-22-2-220002-2000-22-2202−2−22002−22−2−22−2200000000000000002i−2i00−i2i2i2−i200
χ442-22-22-22-2200-22-2-220002-2000-22-2202−2−22002−22−2−22−220000000000000000−2i2i00i2−i2−i2i200
χ452-22-22-22-2200-22-2-220002-2000-22-220−222−200−22−222−22−200000000000000002i−2i00i2−i2−i2i200
χ462-22-22-22-2200-22-2-220002-2000-22-220−222−200−22−222−22−20000000000000000−2i2i00−i2i2i2−i200
χ47444444-244-4-444-2-2-2-4-4-4-2-2222-2-2-2-220000220000000000000000000000000000000000
χ48444444-2-4-4-4-4-4-4-2-2-24-44-2-2222222220000-2-20000000000000000000000000000000000
χ494444-4-4-244-4-4-4-4-2-2-244-4222-2-2-2-222200002-20000000000000000000000000000000000
χ504444-4-4-2-4-4-4-444-2-2-2-444222-2-222-2-220000-220000000000000000000000000000000000
χ514-44-44-4-24-4004-422-2000-22000-22-22022−2222−2200−22−22−22−2200000000000000000000000000
χ524-44-44-4-24-4004-422-2000-22000-22-220−2222−2222002−22−22−22−200000000000000000000000000
χ534-44-44-4-2-4400-4422-2000-220002-22-2022−22−222200−22−222−22−200000000000000000000000000
χ544-44-44-4-2-4400-4422-2000-220002-22-20−222222−22002−22−2−22−2200000000000000000000000000
χ554-44-4-4444-400-44-4-44000-440004-4-4400000000000000000000000000000000000000000
χ564-44-4-444-44004-4-4-44000-44000-444-400000000000000000000000000000000000000000
χ574-44-4-44-24-400-4422-20002-2000-222-20000000i6−i6−i6i6i6−i6−i6i600000000000000000000000000
χ584-44-4-44-24-400-4422-20002-2000-222-20000000−i6i6i6−i6−i6i6i6−i600000000000000000000000000
χ594-44-4-44-2-44004-422-20002-20002-2-220000000i6−i6−i6i6−i6i6i6−i600000000000000000000000000
χ604-44-4-44-2-44004-422-20002-20002-2-220000000−i6i6i6−i6i6−i6−i6i600000000000000000000000000
χ614-4-44004004-4004-4-4000004000000-4000000000000000000000000002i−2i2i−2i0000000000
χ624-4-44004004-4004-4-4000004000000-400000000000000000000000000−2i2i−2i2i0000000000
χ634-4-4400400-44004-4-400000-40000004000000000000000000000000002-2-220000000000
χ644-4-4400400-44004-4-400000-4000000400000000000000000000000000-222-20000000000
χ6588-8-8008000000-88-800000000000000000000000000000000000000000000000000000
χ6688-8-800-40000004-4400000043−43000000000000000000000000000000000000000000000
χ6788-8-800-40000004-44000000−4343000000000000000000000000000000000000000000000
χ688-8-8800-4008-800-44400000-400000040000000000000000000000000000000000000000
χ698-8-8800-400-8800-444000004000000-40000000000000000000000000000000000000000

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