Finite Group Databasebeta

← Group #10698752

Character table — Group #10698752

Order 768.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69
size11112222222222224444444444444888888888888881616161616161616161616162424242424242424242424244848
order1222223444444666444661212121212121212888812122424242424242424226666882424242422448888888888
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
χ511111111111111111111111111111-1-1-1-111-1-1-1-1-1-1-1-1111111-1-1-1-1-1-111111111-1-1-1-1-1-1
χ611111111111111111111111111111-1-1-1-111-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111
χ711111111111111111111111111111-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-111
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
χ112222222-2-222-2-2222-22-222-2-2-2-2-222-200002-2000000000000000000000000000000002i−2i
χ122222222-2-222-2-2222-22-222-2-2-2-2-222-200002-200000000000000000000000000000000−2i2i
χ132222222-2-2-2-2-2-22222-2222-2-2-222-2-2-20000-22000000000000002i−2i2i2i−2i−2i00000000000000
χ142222222-2-2-2-2-2-22222-2222-2-2-222-2-2-20000-2200000000000000−2i2i−2i−2i2i2i00000000000000
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
χ19222222-1-2-2-2-2-2-2-1-1-12-22-1-1111-1-111100001-13333−3−3−3−300−i3−i3i3i32i−2i−i−iii00000000000000
χ20222222-1-2-2-2-2-2-2-1-1-12-22-1-1111-1-111100001-13333−3−3−3−300i3i3−i3−i3−2i2iii−i−i00000000000000
χ21222222-1-2-2-2-2-2-2-1-1-12-22-1-1111-1-111100001-1−3−3−3−3333300−i3−i3i3i3−2i2iii−i−i00000000000000
χ22222222-1-2-2-2-2-2-2-1-1-12-22-1-1111-1-111100001-1−3−3−3−3333300i3i3−i3−i32i−2i−i−iii00000000000000
χ232222-2-222-2222-2222-2-22-2-22-2-2-2-222222-2-2-2222-2-222-2-200000000000000000000000000
χ242222-2-222-2222-2222-2-22-2-22-2-2-2-2222-2-222-22-2-222-2-22200000000000000000000000000
χ252222-2-222-2-2-22-222222-2-2-22-2-222-2-2200002-200000000000000000000000000002i2i−2i−2i00
χ262222-2-222-2-2-22-222222-2-2-22-2-222-2-2200002-20000000000000000000000000000−2i−2i2i2i00
χ272222-2-22-2222-222222-2-2-2-2-2222222-20000-2-200000000000000000000000022-2-2000000
χ282222-2-22-2222-222222-2-2-2-2-2222222-20000-2-2000000000000000000000000-2-222000000
χ292222-2-22-22-2-2-22222-222-2-2-222-2-2-2-2-2000022000000002-22-22-200000000000000000000
χ302222-2-22-22-2-2-22222-222-2-2-222-2-2-2-2-200002200000000-22-22-2200000000000000000000
χ312222-2-2-12-2222-2-1-1-1-2-2211-11111-1-1-122-2-21-1-1-111-1-11100−i3i3i3−i300−i3i3−i3i300000000000000
χ322222-2-2-12-2222-2-1-1-1-2-2211-11111-1-1-122-2-21-1-1-111-1-11100i3−i3−i3i300i3−i3i3−i300000000000000
χ332222-2-2-12-2222-2-1-1-1-2-2211-11111-1-1-1-2-2221-111-1-111-1-100−i3i3i3−i300i3−i3i3−i300000000000000
χ342222-2-2-12-2222-2-1-1-1-2-2211-11111-1-1-1-2-2221-111-1-111-1-100i3−i3−i3i300−i3i3−i3i300000000000000
χ352222-2-2-1-22-2-2-22-1-1-1-222111-1-1111110000-1-133−3−3−3−3332-2-11-11003−3−3300000000000000
χ362222-2-2-1-22-2-2-22-1-1-1-222111-1-1111110000-1-133−3−3−3−333-221-11-100−333−300000000000000
χ372222-2-2-1-22-2-2-22-1-1-1-222111-1-1111110000-1-1−3−33333−3−32-2-11-1100−333−300000000000000
χ382222-2-2-1-22-2-2-22-1-1-1-222111-1-1111110000-1-1−3−33333−3−3-221-11-1003−3−3300000000000000
χ3922-2-22-22-22002-22-2-20002-2-22-2000022−22−2002−22−22−22−2000000000000002i−2i0000−i2i2−i2i200
χ4022-2-22-22-22002-22-2-20002-2-22-2000022−22−2002−22−22−22−200000000000000−2i2i0000i2−i2i2−i200
χ4122-2-22-22-22002-22-2-20002-2-22-200002−22−2200−22−22−22−22000000000000002i−2i0000i2−i2i2−i200
χ4222-2-22-22-22002-22-2-20002-2-22-200002−22−2200−22−22−22−2200000000000000−2i2i0000−i2i2−i2i200
χ4322-2-2-222-2-200222-2-2000-22-2-22000022−2−22002−2−222−2−220000000000002-20000002−2−2200
χ4422-2-2-222-2-200222-2-2000-22-2-22000022−2−22002−2−222−2−22000000000000-22000000−222−200
χ4522-2-2-222-2-200222-2-2000-22-2-2200002−222−200−222−2−222−20000000000002-2000000−222−200
χ4622-2-2-222-2-200222-2-2000-22-2-2200002−222−200−222−2−222−2000000000000-220000002−2−2200
χ47444444-244-4-444-2-2-2-4-4-4-2-2-2-2-22222-20000220000000000000000000000000000000000
χ48444444-2-4-444-4-4-2-2-2-44-4-2-222222-2-220000-220000000000000000000000000000000000
χ494444-4-4-24-4-4-44-4-2-2-244-422-222-2-222-20000-220000000000000000000000000000000000
χ504444-4-4-2-4444-44-2-2-24-4-4222-2-2-2-2-2-220000220000000000000000000000000000000000
χ5144-4-44-444-400-444-4-40004-44-440000-40000000000000000000000000000000000000000
χ5244-4-44-4-24-400-44-222000-22-22-2000020000006−66−6−66−6600000000000000000000000000
χ5344-4-44-4-24-400-44-222000-22-22-200002000000−66−666−66−600000000000000000000000000
χ5444-4-44-4-2-44004-4-222000-222-220000-222−2222−2200−22−22−22−2200000000000000000000000000
χ5544-4-44-4-2-44004-4-222000-222-220000-2−2222−2222002−22−22−22−200000000000000000000000000
χ5644-4-4-4444400-4-44-4-4000-4444-40000-40000000000000000000000000000000000000000
χ5744-4-4-44-24400-4-4-2220002-2-2-22000020000006−6−66−666−600000000000000000000000000
χ5844-4-4-44-24400-4-4-2220002-2-2-2200002000000−666−66−6−6600000000000000000000000000
χ5944-4-4-44-2-4-40044-2220002-222-20000-222−22−222200−222−2−222−200000000000000000000000000
χ6044-4-4-44-2-4-40044-2220002-222-20000-2−222222−22002−2−222−2−2200000000000000000000000000
χ614-4-44004004-400-44-400000000004-400000000000000000000000000000000022−22000000
χ624-4-44004004-400-44-400000000004-4000000000000000000000000000000000−2222000000
χ634-4-4400400-4400-44-40000000000-44000000000000000000000000000000022−2200000000
χ644-4-4400400-4400-44-40000000000-440000000000000000000000000000000−222200000000
χ658-88-8008000000-8-8800000000000000000000000000000000000000000000000000000
χ668-88-800-400000044-400000000−4i34i30000000000000000000000000000000000000000000
χ678-88-800-400000044-4000000004i3−4i30000000000000000000000000000000000000000000
χ688-8-8800-4008-8004-440000000000-4400000000000000000000000000000000000000000
χ698-8-8800-400-88004-4400000000004-400000000000000000000000000000000000000000

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