Finite Group Databasebeta

← Group #10699223

Character table — Group #10699223

Order 768.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69
size11112222222222224444444444444888888888888881616161616161616161616162424242424242424242424244848
order12222234444446664446612121212121212128888121224242424242424244488121212122424242444448888888844
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
χ511111111111111111111111111111-1-1-1-111-1-1-1-1-1-1-1-111-1-11111-1-1-1-11111-1-11111-1-1-1-1
χ611111111111111111111111111111-1-1-1-111-1-1-1-1-1-1-1-111-1-11111-1-1-1-1-1-1-1-111-1-1-1-11111
χ711111111111111111111111111111-1-1-1-111-1-1-1-1-1-1-1-1-1-111-1-1-1-11111111111-1-1-1-111-1-1
χ811111111111111111111111111111-1-1-1-111-1-1-1-1-1-1-1-1-1-111-1-1-1-11111-1-1-1-1-1-11111-1-111
χ922222222222-2-2222-2-2-222-2-2-2-2222222-2-2-2-22222-2-2-2-200000000000000000000000000
χ1022222222222-2-2222-2-2-222-2-2-2-22222-2-222-2-2-2-2-2-2222200000000000000000000000000
χ112222222-2-2-2-2222222-2-22222-2-2-2-2-2-200002-2000000002-20022-2-2000000000000000000
χ122222222-2-2-2-2222222-2-22222-2-2-2-2-2-200002-200000000-2200-2-222000000000000000000
χ132222222-2-2-2-2-2-2222-22222-2-222-2-2-2-20000-2200000000002i−2i00002i2i−2i−2i00000000000000
χ142222222-2-2-2-2-2-2222-22222-2-222-2-2-2-20000-220000000000−2i2i0000−2i−2i2i2i00000000000000
χ15222222-1222222-1-1-1222-1-1-1-1-1-1-1-1-1-12222-1-1-1-1-1-1-1-1-1-12222-1-1-1-1-1-1-1-100000000000000
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
χ19222222-12222-2-2-1-1-1-2-2-2-1-11111-1-1-1-122-2-211-1-1-1-111110000−i3i3−i3i3−i3i3−i3i300000000000000
χ20222222-12222-2-2-1-1-1-2-2-2-1-11111-1-1-1-122-2-211-1-1-1-111110000i3−i3i3−i3i3−i3i3−i300000000000000
χ21222222-12222-2-2-1-1-1-2-2-2-1-11111-1-1-1-1-2-222111111-1-1-1-10000−i3i3−i3i3i3−i3i3−i300000000000000
χ22222222-12222-2-2-1-1-1-2-2-2-1-11111-1-1-1-1-2-222111111-1-1-1-10000i3−i3i3−i3−i3i3−i3i300000000000000
χ23222222-1-2-2-2-222-1-1-12-2-2-1-1-1-11111110000-1133−3−333−3−32-200-1-1113−3−3300000000000000
χ24222222-1-2-2-2-222-1-1-12-2-2-1-1-1-11111110000-1133−3−333−3−3-220011-1-1−333−300000000000000
χ25222222-1-2-2-2-222-1-1-12-2-2-1-1-1-11111110000-11−3−333−3−3332-200-1-111−333−300000000000000
χ26222222-1-2-2-2-222-1-1-12-2-2-1-1-1-11111110000-11−3−333−3−333-220011-1-13−3−3300000000000000
χ27222222-1-2-2-2-2-2-2-1-1-1-222-1-111-1-1111100001-133−3−3−3−333002i−2i−i3i3i3−i3−i−iii00000000000000
χ28222222-1-2-2-2-2-2-2-1-1-1-222-1-111-1-1111100001-133−3−3−3−33300−2i2ii3−i3−i3i3ii−i−i00000000000000
χ29222222-1-2-2-2-2-2-2-1-1-1-222-1-111-1-1111100001-1−3−33333−3−3002i−2ii3−i3−i3i3−i−iii00000000000000
χ30222222-1-2-2-2-2-2-2-1-1-1-222-1-111-1-1111100001-1−3−33333−3−300−2i2i−i3i3i3−i3ii−i−i00000000000000
χ312222-2-222-2-2222222-22-2-2-222-2-22-2-220000-22000000000000000000000000000000002-2
χ322222-2-222-2-2222222-22-2-2-222-2-22-2-220000-2200000000000000000000000000000000-22
χ332222-2-222-2-22-2-22222-22-2-2-2-2222-2-2200002-2000000000000000000002i2i−2i−2i0000000000
χ342222-2-222-2-22-2-22222-22-2-2-2-2222-2-2200002-200000000000000000000−2i−2i2i2i0000000000
χ352222-2-22-222-222222-2-22-2-22222-222-20000-2-2000000000000000000000000220000-2-200
χ362222-2-22-222-222222-2-22-2-22222-222-20000-2-2000000000000000000000000-2-200002200
χ372222-2-22-222-2-2-222222-2-2-2-2-2-2-2-222-2000022000000000000000000000000002i2i−2i−2i0000
χ382222-2-22-222-2-2-222222-2-2-2-2-2-2-2-222-200002200000000000000000000000000−2i−2i2i2i0000
χ3922-2-22-22-22-2200-2-220002-20000-22-22002-20000002-22-20000000000000000−i2i2−i2i2−i2i2−i2i200
χ4022-2-22-22-22-2200-2-220002-20000-22-22002-20000002-22-20000000000000000i2−i2i2−i2i2−i2i2−i200
χ4122-2-22-22-22-2200-2-220002-20000-22-2200-22000000-22-220000000000000000−i2i2i2−i2i2−i2−i2i200
χ4222-2-22-22-22-2200-2-220002-20000-22-2200-22000000-22-220000000000000000i2−i2−i2i2−i2i2i2−i200
χ4322-2-2-22222-2-200-2-22000-22000022-2-22i−2i00002i−2i2i−2i00000000000000000000−i2i22−2−22i2−i200
χ4422-2-2-22222-2-200-2-22000-22000022-2-22i−2i00002i−2i2i−2i00000000000000000000i2−i2−222−2−i2i200
χ4522-2-2-22222-2-200-2-22000-22000022-2-2−2i2i0000−2i2i−2i2i00000000000000000000−i2i2−222−2i2−i200
χ4622-2-2-22222-2-200-2-22000-22000022-2-2−2i2i0000−2i2i−2i2i00000000000000000000i2−i22−2−22−i2i200
χ474444-4-4-24-4-4444-2-2-2-44-422-2-222-222-200002-20000000000000000000000000000000000
χ484444-4-4-24-4-44-4-4-2-2-24-442222-2-2-222-20000-220000000000000000000000000000000000
χ494444-4-4-2-444-444-2-2-2-4-4422-2-2-2-22-2-220000220000000000000000000000000000000000
χ504444-4-4-2-444-4-4-4-2-2-244-42222222-2-220000-2-20000000000000000000000000000000000
χ5144-4-44-444-44-400-4-440004-400004-44-40000000000000000000000000000000000000000
χ5244-4-44-4-24-44-40022-2000-220000-22-22000000000023−23−232300000000000000000000000000
χ5344-4-44-4-24-44-40022-2000-220000-22-220000000000−232323−2300000000000000000000000000
χ5444-4-44-4-2-44-440022-2000-2200002-22-2004-4000000-22-2200000000000000000000000000
χ5544-4-44-4-2-44-440022-2000-2200002-22-200-440000002-22-200000000000000000000000000
χ5644-4-4-444-4-44400-4-44000-440000-4-4440000000000000000000000000000000000000000
χ5744-4-4-44-244-4-40022-20002-20000-2-2224i−4i0000−2i2i−2i2i000000000000000000000000000000
χ5844-4-4-44-244-4-40022-20002-20000-2-222−4i4i00002i−2i2i−2i000000000000000000000000000000
χ5944-4-4-44-2-4-4440022-20002-2000022-2-2000000−2i32i32i3−2i3000000000000000000000000000000
χ6044-4-4-44-2-4-4440022-20002-2000022-2-20000002i3−2i3−2i32i3000000000000000000000000000000
χ614-44-400400004-44-4-4000004-4000000000000000000000000000000002-22-20000000000
χ624-44-400400004-44-4-4000004-400000000000000000000000000000000-22-220000000000
χ634-44-40040000-444-4-400000-44000000000000000000000000000000002i−2i−2i2i0000000000
χ644-44-40040000-444-4-400000-4400000000000000000000000000000000−2i2i2i−2i0000000000
χ658-88-800-400008-8-44400000-440000000000000000000000000000000000000000000000
χ668-88-800-40000-88-444000004-40000000000000000000000000000000000000000000000
χ678-8-88008000000-88-800000000000000000000000000000000000000000000000000000
χ688-8-8800-40000004-440000000−4i34i300000000000000000000000000000000000000000000
χ698-8-8800-40000004-4400000004i3−4i300000000000000000000000000000000000000000000

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