Finite Group Databasebeta

← Group #10698765

Character table — Group #10698765

Order 768.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69
size11112222222222224444444444444888888888888881616161616161616161616162424242424242424242424244848
order1222223444444666444661212121212121212888812122424242424242424226666882424242444448888888888
χ1111111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ31111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1
χ41111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111
χ511111111111111111111111111111-1-1-1-111-1-1-1-1-1-1-1-1111111-1-1-1-1-1-11111-1-1-1-11111-1-1
χ611111111111111111111111111111-1-1-1-111-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1-1-11111-1-1-1-111
χ711111111111111111111111111111-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-111
χ811111111111111111111111111111-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-1-111111111-1-1
χ9222222222-2-222222-2-2-222222-2-2-2-220000-2-20000000000000000000022-2-20000000000
χ10222222222-2-222222-2-2-222222-2-2-2-220000-2-200000000000000000000-2-2220000000000
χ112222222-2-222-2-22222-2-222-2-2-222-2-2-200002-2000000000000002i−2i2i2i−2i−2i00000000000000
χ122222222-2-222-2-22222-2-222-2-2-222-2-2-200002-200000000000000−2i2i−2i−2i2i2i00000000000000
χ132222222-2-2-2-2-2-2222-22222-2-2-2-2-222-20000-22000000000000000000000000000000002i−2i
χ142222222-2-2-2-2-2-2222-22222-2-2-2-2-222-20000-2200000000000000000000000000000000−2i2i
χ15222222-1222222-1-1-1222-1-1-1-1-1-1-1-1-1-12222-1-1-1-1-1-1-1-1-1-122-1-1-1-122-1-1-1-100000000000000
χ16222222-1222222-1-1-1222-1-1-1-1-1-1-1-1-1-12222-1-1-1-1-1-1-1-1-1-1-2-21111-2-2111100000000000000
χ17222222-1222222-1-1-1222-1-1-1-1-1-1-1-1-1-1-2-2-2-2-1-11111111122-1-1-1-1-2-2111100000000000000
χ18222222-1222222-1-1-1222-1-1-1-1-1-1-1-1-1-1-2-2-2-2-1-111111111-2-2111122-1-1-1-100000000000000
χ19222222-1-2-222-2-2-1-1-12-2-2-1-1111-1-11110000-113333−3−3−3−300−i3−i3i3i32i−2i−i−iii00000000000000
χ20222222-1-2-222-2-2-1-1-12-2-2-1-1111-1-11110000-113333−3−3−3−300i3i3−i3−i3−2i2iii−i−i00000000000000
χ21222222-1-2-222-2-2-1-1-12-2-2-1-1111-1-11110000-11−3−3−3−3333300−i3−i3i3i3−2i2iii−i−i00000000000000
χ22222222-1-2-222-2-2-1-1-12-2-2-1-1111-1-11110000-11−3−3−3−3333300i3i3−i3−i32i−2i−i−iii00000000000000
χ232222-2-222-2222-2222-2-22-2-222-22222-20000-2-200000000000000000000000022-2-2000000
χ242222-2-222-2222-2222-2-22-2-222-22222-20000-2-2000000000000000000000000-2-222000000
χ252222-2-222-2-2-22-222222-2-2-222-2-2-2-2-2-22i2i−2i−2i222i2i−2i−2i2i2i−2i−2i00000000000000000000000000
χ262222-2-222-2-2-22-222222-2-2-222-2-2-2-2-2-2−2i−2i2i2i22−2i−2i2i2i−2i−2i2i2i00000000000000000000000000
χ272222-2-22-2222-22222-22-2-2-2-2-2222-2-220000-22000000000000000000000000000022-2-200
χ282222-2-22-2222-22222-22-2-2-2-2-2222-2-220000-220000000000000000000000000000-2-22200
χ292222-2-22-22-2-2-222222-22-2-2-2-22-2-222200002-2000000002-22-22-200000000000000000000
χ302222-2-22-22-2-2-222222-22-2-2-2-22-2-222200002-200000000-22-22-2200000000000000000000
χ312222-2-2-12-2-2-22-2-1-1-122-211-1-11111112i2i−2i−2i-1-1−i−iii−i−iii00−i3i3i3−i3003−33−300000000000000
χ322222-2-2-12-2-2-22-2-1-1-122-211-1-11111112i2i−2i−2i-1-1−i−iii−i−iii00i3−i3−i3i300−33−3300000000000000
χ332222-2-2-12-2-2-22-2-1-1-122-211-1-1111111−2i−2i2i2i-1-1ii−i−iii−i−i00−i3i3i3−i300−33−3300000000000000
χ342222-2-2-12-2-2-22-2-1-1-122-211-1-1111111−2i−2i2i2i-1-1ii−i−iii−i−i00i3−i3−i3i3003−33−300000000000000
χ352222-2-2-1-22-2-2-22-1-1-12-221111-111-1-1-10000-11−i3−i3i3i3i3i3−i3−i32-2-11-1100−i3i3i3−i300000000000000
χ362222-2-2-1-22-2-2-22-1-1-12-221111-111-1-1-10000-11−i3−i3i3i3i3i3−i3−i3-221-11-100i3−i3−i3i300000000000000
χ372222-2-2-1-22-2-2-22-1-1-12-221111-111-1-1-10000-11i3i3−i3−i3−i3−i3i3i32-2-11-1100i3−i3−i3i300000000000000
χ382222-2-2-1-22-2-2-22-1-1-12-221111-111-1-1-10000-11i3i3−i3−i3−i3−i3i3i3-221-11-100−i3i3i3−i300000000000000
χ392-22-22-22-22002-22-2-20002-22-220000-2−i2i2−i2i200−i2i2−i2i2−i2i2−i2i2000000000000002i−2i2−22−2000000
χ402-22-22-22-22002-22-2-20002-22-220000-2−i2i2−i2i200−i2i2−i2i2−i2i2−i2i200000000000000−2i2i−22−22000000
χ412-22-22-22-22002-22-2-20002-22-220000-2i2−i2i2−i200i2−i2i2−i2i2−i2i2−i2000000000000002i−2i−22−22000000
χ422-22-22-22-22002-22-2-20002-22-220000-2i2−i2i2−i200i2−i2i2−i2i2−i2i2−i200000000000000−2i2i2−22−2000000
χ432-22-2-222-2-200222-2-2000-222-2-2000022−2−22002−2−222−2−220000000000002-2002−2−22000000
χ442-22-2-222-2-200222-2-2000-222-2-2000022−2−22002−2−222−2−22000000000000-2200−222−2000000
χ452-22-2-222-2-200222-2-2000-222-2-200002−222−200−222−2−222−20000000000002-200−222−2000000
χ462-22-2-222-2-200222-2-2000-222-2-200002−222−200−222−2−222−2000000000000-22002−2−22000000
χ47444444-244-4-444-2-2-2-4-4-4-2-2-2-2-22222-20000220000000000000000000000000000000000
χ48444444-2-4-4-4-4-4-4-2-2-2-444-2-222222-2-2200002-20000000000000000000000000000000000
χ494444-4-4-24-4444-4-2-2-2-4-4422-2-22-2-2-2-220000220000000000000000000000000000000000
χ504444-4-4-2-4444-44-2-2-2-44-42222-2-2-222-200002-20000000000000000000000000000000000
χ5144-4-4004004-400-44-4000000004-4000000000000000000000000000000000000000−2i22i200
χ5244-4-4004004-400-44-4000000004-40000000000000000000000000000000000000002i2−2i200
χ5344-4-400400-4400-44-400000000-440000000000000000000000000000000000000−2i22i20000
χ5444-4-400400-4400-44-400000000-4400000000000000000000000000000000000002i2−2i20000
χ554-44-44-444-400-444-4-40004-4-44-4000040000000000000000000000000000000000000000
χ564-44-44-4-24-400-44-222000-222-220000-2000000i6−i6i6−i6−i6i6−i6i600000000000000000000000000
χ574-44-44-4-24-400-44-222000-222-220000-2000000−i6i6−i6i6i6−i6i6−i600000000000000000000000000
χ584-44-44-4-2-44004-4-222000-22-22-200002−2i22i2−2i22i200i2−i2i2−i2i2−i2i2−i200000000000000000000000000
χ594-44-44-4-2-44004-4-222000-22-22-2000022i2−2i22i2−2i200−i2i2−i2i2−i2i2−i2i200000000000000000000000000
χ604-44-4-4444400-4-44-4-4000-44-4440000-40000000000000000000000000000000000000000
χ614-44-4-44-24400-4-4-2220002-22-2-2000020000006−6−66−666−600000000000000000000000000
χ624-44-4-44-24400-4-4-2220002-22-2-200002000000−666−66−6−6600000000000000000000000000
χ634-44-4-44-2-4-40044-2220002-2-2220000-222−22−222200−222−2−222−200000000000000000000000000
χ644-44-4-44-2-4-40044-2220002-2-2220000-2−222222−22002−2−222−2−2200000000000000000000000000
χ6588-8-800-4008-8004-4400000000-440000000000000000000000000000000000000000000
χ6688-8-800-400-88004-44000000004-40000000000000000000000000000000000000000000
χ678-8-88008000000-8-8800000000000000000000000000000000000000000000000000000
χ688-8-8800-400000044-40000000000−4i34i300000000000000000000000000000000000000000
χ698-8-8800-400000044-400000000004i3−4i300000000000000000000000000000000000000000

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