Finite Group Databasebeta

← Group #10697222

Character table — Group #10697222

Order 768.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69
size11112222222222224444444444444888888888888881616161616161616161616162424242424242424242424244848
order12222234444446664446612121212121212124444121212121212121212124488121212122424242488888888888844
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
χ511111111111111111111111111111-1-1-1-1-1-1-1-111-1-1-1-111-1-11111-1-1-1-111111111-1-1-1-1-1-1
χ611111111111111111111111111111-1-1-1-1-1-1-1-111-1-1-1-111-1-11111-1-1-1-1-1-1-1-1-1-1-1-1111111
χ711111111111111111111111111111-1-1-1-1-1-1-1-111-1-1-1-1-1-111-1-1-1-111111111-1-1-1-11111-1-1
χ811111111111111111111111111111-1-1-1-1-1-1-1-111-1-1-1-1-1-111-1-1-1-11111-1-1-1-11111-1-1-1-111
χ9222222222-2-2-2-22222-2-2222222-2-2-2-200000000-2-2000000000000000000002i2i−2i−2i000000
χ10222222222-2-2-2-22222-2-2222222-2-2-2-200000000-2-200000000000000000000−2i−2i2i2i000000
χ112222222-2-22222222-2-2-222-2-2-2-2222222-2-2-2-2-2-2-2-2222200000000000000000000000000
χ122222222-2-22222222-2-2-222-2-2-2-22222-2-2222222-2-2-2-2-2-200000000000000000000000000
χ132222222-2-2-2-2-2-2222-22222-2-2-2-2-2-2-2-2000000002200000000000000000000000022-2-200
χ142222222-2-2-2-2-2-2222-22222-2-2-2-2-2-2-2-20000000022000000000000000000000000-2-22200
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
χ17222222-1222222-1-1-1222-1-1-1-1-1-1-1-1-1-1-2-2-2-21111-1-1111122-2-2-1-1-1-1111100000000000000
χ18222222-1222222-1-1-1222-1-1-1-1-1-1-1-1-1-1-2-2-2-21111-1-11111-2-2221111-1-1-1-100000000000000
χ19222222-1-2-22222-1-1-1-2-2-2-1-11111-1-1-1-122-2-2111111-1-1-1-10000−i3i3−i3i3−i3−i3i3i300000000000000
χ20222222-1-2-22222-1-1-1-2-2-2-1-11111-1-1-1-122-2-2111111-1-1-1-10000i3−i3i3−i3i3i3−i3−i300000000000000
χ21222222-1-2-22222-1-1-1-2-2-2-1-11111-1-1-1-1-2-222-1-1-1-11111110000−i3i3−i3i3i3i3−i3−i300000000000000
χ22222222-1-2-22222-1-1-1-2-2-2-1-11111-1-1-1-1-2-222-1-1-1-11111110000i3−i3i3−i3−i3−i3i3i300000000000000
χ232222-2-22222-22-2222-22-2-2-222-2-22-2-22000000002-200002-20022-2-2000000000000000000
χ242222-2-22222-22-2222-22-2-2-222-2-22-2-22000000002-20000-2200-2-222000000000000000000
χ252222-2-2222-22-22222-2-22-2-222-2-2-222-200000000-22000000000000000022-2-20000000000
χ262222-2-2222-22-22222-2-22-2-222-2-2-222-200000000-220000000000000000-2-2220000000000
χ272222-2-22-2-22-22-22222-22-2-2-2-2222-2-2200000000-220000002-200002-22-200000000000000
χ282222-2-22-2-22-22-22222-22-2-2-2-2222-2-2200000000-22000000-220000-22-2200000000000000
χ292222-2-22-2-2-22-2222222-2-2-2-2-222-222-2000000002-200000000000000000000000000002-2
χ302222-2-22-2-2-22-2222222-2-2-2-2-222-222-2000000002-20000000000000000000000000000-22
χ312222-2-2-1222-22-2-1-1-1-22-211-1-111-111-10000−i3−i3i3i3-11−i3−i3i3i32-200-1-111−i3i3i3−i300000000000000
χ322222-2-2-1222-22-2-1-1-1-22-211-1-111-111-10000−i3−i3i3i3-11−i3−i3i3i3-220011-1-1i3−i3−i3i300000000000000
χ332222-2-2-1222-22-2-1-1-1-22-211-1-111-111-10000i3i3−i3−i3-11i3i3−i3−i32-200-1-111i3−i3−i3i300000000000000
χ342222-2-2-1222-22-2-1-1-1-22-211-1-111-111-10000i3i3−i3−i3-11i3i3−i3−i3-220011-1-1−i3i3i3−i300000000000000
χ352222-2-2-1-2-22-22-2-1-1-12-221111-1-1-111-10000−i3−i3i3i31-1i3i3−i3−i3002-2i3−i3−i3i3-11-1100000000000000
χ362222-2-2-1-2-22-22-2-1-1-12-221111-1-1-111-10000−i3−i3i3i31-1i3i3−i3−i300-22−i3i3i3−i31-11-100000000000000
χ372222-2-2-1-2-22-22-2-1-1-12-221111-1-1-111-10000i3i3−i3−i31-1−i3−i3i3i3002-2−i3i3i3−i3-11-1100000000000000
χ382222-2-2-1-2-22-22-2-1-1-12-221111-1-1-111-10000i3i3−i3−i31-1−i3−i3i3i300-22i3−i3−i3i31-11-100000000000000
χ392-2-222-22002-2-222-2-20002-2000022-2-2002-22-22-20000000000000000000000−i2i2−i2i2−i2i2−i2i200
χ402-2-222-22002-2-222-2-20002-2000022-2-2002-22-22-20000000000000000000000i2−i2i2−i2i2−i2i2−i200
χ412-2-222-22002-2-222-2-20002-2000022-2-200-22-22-220000000000000000000000−i2i2−i2i2i2−i2i2−i200
χ422-2-222-22002-2-222-2-20002-2000022-2-200-22-22-220000000000000000000000i2−i2i2−i2−i2i2−i2i200
χ432-2-222-2200-222-22-2-20002-20000-2-2222i−2i000000002i−2i2i−2i00000000000000002−2−22−i2i2i2−i200
χ442-2-222-2200-222-22-2-20002-20000-2-2222i−2i000000002i−2i2i−2i0000000000000000−222−2i2−i2−i2i200
χ452-2-222-2200-222-22-2-20002-20000-2-222−2i2i00000000−2i2i−2i2i00000000000000002−2−22i2−i2−i2i200
χ462-2-222-2200-222-22-2-20002-20000-2-222−2i2i00000000−2i2i−2i2i0000000000000000−222−2−i2i2i2−i200
χ47444444-244-4-4-4-4-2-2-24-4-4-2-2-2-2-2-222220000000022000000000000000000000000000000
χ48444444-2-4-4-4-4-4-4-2-2-2-444-2-22222222200000000-2-2000000000000000000000000000000
χ494444-4-4-244-44-44-2-2-2-4-4422-2-2222-2-22000000002-2000000000000000000000000000000
χ504444-4-4-2-4-4-44-44-2-2-244-42222-2-22-2-2200000000-22000000000000000000000000000000
χ5144-4-40044-40000-44-4000004-4000000000000000000000000000000000022−220000000000
χ5244-4-40044-40000-44-4000004-40000000000000000000000000000000000−22220000000000
χ5344-4-4004-440000-44-400000-440000000000000000000000000000000022−22000000000000
χ5444-4-4004-440000-44-400000-4400000000000000000000000000000000−2222000000000000
χ554-4-444-4-2004-4-44-222000-220000-2-222004-4-22-2200000000000000000000000000000000
χ564-4-444-4-2004-4-44-222000-220000-2-22200-442-22-200000000000000000000000000000000
χ574-4-444-4-200-444-4-222000-22000022-2-24i−4i00000000−2i2i−2i2i00000000000000000000000000
χ584-4-444-4-200-444-4-222000-22000022-2-2−4i4i000000002i−2i2i−2i00000000000000000000000000
χ594-4-44-4440044-4-44-4-4000-4400004-44-40000000000000000000000000000000000000000
χ604-4-44-44400-4-4444-4-4000-440000-44-440000000000000000000000000000000000000000
χ614-4-44-44-20044-4-4-2220002-20000-22-220000−2i32i32i3−2i300000000000000000000000000000000
χ624-4-44-44-20044-4-4-2220002-20000-22-2200002i3−2i3−2i32i300000000000000000000000000000000
χ634-4-44-44-200-4-444-2220002-200002-22-2000000000023−23−232300000000000000000000000000
χ644-4-44-44-200-4-444-2220002-200002-22-20000000000−232323−2300000000000000000000000000
χ6588-8-800-48-800004-4400000-440000000000000000000000000000000000000000000000
χ6688-8-800-4-8800004-44000004-40000000000000000000000000000000000000000000000
χ678-88-8008000000-8-8800000000000000000000000000000000000000000000000000000
χ688-88-800-400000044-4000000043−4300000000000000000000000000000000000000000000
χ698-88-800-400000044-40000000−434300000000000000000000000000000000000000000000

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