Finite Group Databasebeta

← Group #10698801

Character table — Group #10698801

Order 768.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69
size11112222222222224444444444444888888888888881616161616161616161616162424242424242424242424244848
order12222234444446664446612121212121212128888121224242424242424244488121212122424242444448888888888
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
χ511111111111111111111111111111-1-1-1-111-1-1-1-1-1-1-1-111-1-11111-1-1-1-111111111-1-1-1-1-1-1
χ611111111111111111111111111111-1-1-1-111-1-1-1-1-1-1-1-111-1-11111-1-1-1-1-1-1-1-1-1-1-1-1111111
χ711111111111111111111111111111-1-1-1-111-1-1-1-1-1-1-1-1-1-111-1-1-1-111111111-1-1-1-1-1-1-1-111
χ811111111111111111111111111111-1-1-1-111-1-1-1-1-1-1-1-1-1-111-1-1-1-11111-1-1-1-111111111-1-1
χ922222222-2-2222222-2-2-222-2-2222-2-220000-2-20000000000000000000022-2-20000000000
χ1022222222-2-2222222-2-2-222-2-2222-2-220000-2-200000000000000000000-2-2220000000000
χ112222222-222-2-2-22222-2-222-2-2-2-2-222-200002-2000000000000000000000000000000002i−2i
χ122222222-222-2-2-22222-2-222-2-2-2-2-222-200002-200000000000000000000000000000000−2i2i
χ132222222-2-2-2-2-2-2222-2222222-2-2-2-2-2-20000-2200000000002i−2i00002i2i−2i−2i00000000000000
χ142222222-2-2-2-2-2-2222-2222222-2-2-2-2-2-20000-220000000000−2i2i0000−2i−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
χ19222222-1-2-2-2-2-2-2-1-1-1-222-1-1-1-111111100001-13333−3−3−3−3002i−2i−i3−i3i3i3−i−iii00000000000000
χ20222222-1-2-2-2-2-2-2-1-1-1-222-1-1-1-111111100001-13333−3−3−3−300−2i2ii3i3−i3−i3ii−i−i00000000000000
χ21222222-1-2-2-2-2-2-2-1-1-1-222-1-1-1-111111100001-1−3−3−3−33333002i−2ii3i3−i3−i3−i−iii00000000000000
χ22222222-1-2-2-2-2-2-2-1-1-1-222-1-1-1-111111100001-1−3−3−3−3333300−2i2i−i3−i3i3i3ii−i−i00000000000000
χ232222-2-222222-2-2222-2-22-2-2-2-22-2-222222-2-2-2222-2-222-2-200000000000000000000000000
χ242222-2-222222-2-2222-2-22-2-2-2-22-2-2222-2-222-22-2-222-2-22200000000000000000000000000
χ252222-2-222-2-22-2-222222-2-2-2222-2-2-2-2200002-200000000000000000000000000002i2i−2i−2i00
χ262222-2-222-2-22-2-222222-2-2-2222-2-2-2-2200002-20000000000000000000000000000−2i−2i2i2i00
χ272222-2-22-222-222222-22-2-2-222-22222-20000-2-200000000000000000000000022-2-2000000
χ282222-2-22-222-222222-22-2-2-222-22222-20000-2-2000000000000000000000000-2-222000000
χ292222-2-22-2-2-2-2222222-22-2-2-2-2-222-2-2-2000022000000002-2002-22-2000000000000000000
χ302222-2-22-2-2-2-2222222-22-2-2-2-2-222-2-2-200002200000000-2200-22-22000000000000000000
χ312222-2-2-12222-2-2-1-1-1-2-221111-111-1-1-122-2-21-1-1-111-1-1110000−i3i3i3−i3−i3i3−i3i300000000000000
χ322222-2-2-12222-2-2-1-1-1-2-221111-111-1-1-122-2-21-1-1-111-1-1110000i3−i3−i3i3i3−i3i3−i300000000000000
χ332222-2-2-12222-2-2-1-1-1-2-221111-111-1-1-1-2-2221-111-1-111-1-10000−i3i3i3−i3i3−i3i3−i300000000000000
χ342222-2-2-12222-2-2-1-1-1-2-221111-111-1-1-1-2-2221-111-1-111-1-10000i3−i3−i3i3−i3i3−i3i300000000000000
χ352222-2-2-1-2-2-2-222-1-1-12-2211111-1-11110000-1-133−3−3−3−3332-200-11-113−3−3300000000000000
χ362222-2-2-1-2-2-2-222-1-1-12-2211111-1-11110000-1-133−3−3−3−333-22001-11-1−333−300000000000000
χ372222-2-2-1-2-2-2-222-1-1-12-2211111-1-11110000-1-1−3−33333−3−32-200-11-11−333−300000000000000
χ382222-2-2-1-2-2-2-222-1-1-12-2211111-1-11110000-1-1−3−33333−3−3-22001-11-13−3−3300000000000000
χ392-2-222-22200-22-2-2-220002-20022-200-2−i2i2−i2i200−i2i2−i2i2−i2i2−i2i2000000000000002-20000−i2i2−i2i200
χ402-2-222-22200-22-2-2-220002-20022-200-2−i2i2−i2i200−i2i2−i2i2−i2i2−i2i200000000000000-220000i2−i2i2−i200
χ412-2-222-22200-22-2-2-220002-20022-200-2i2−i2i2−i200i2−i2i2−i2i2−i2i2−i2000000000000002-20000i2−i2i2−i200
χ422-2-222-22200-22-2-2-220002-20022-200-2i2−i2i2−i200i2−i2i2−i2i2−i2i2−i200000000000000-220000−i2i2−i2i200
χ432-2-22-222200-2-22-2-22000-22002-2200-2−i2i2i2−i200−i2i2i2−i2−i2i2i2−i20000000000002i−2i0000002−2−2200
χ442-2-22-222200-2-22-2-22000-22002-2200-2−i2i2i2−i200−i2i2i2−i2−i2i2i2−i2000000000000−2i2i000000−222−200
χ452-2-22-222200-2-22-2-22000-22002-2200-2i2−i2−i2i200i2−i2−i2i2i2−i2−i2i20000000000002i−2i000000−222−200
χ462-2-22-222200-2-22-2-22000-22002-2200-2i2−i2−i2i200i2−i2−i2i2i2−i2−i2i2000000000000−2i2i0000002−2−2200
χ47444444-24-4-4444-2-2-2-4-4-4-2-222-2-2-222-20000220000000000000000000000000000000000
χ48444444-2-444-4-4-4-2-2-24-4-4-2-222222-2-220000-220000000000000000000000000000000000
χ494444-4-4-24-4-44-4-4-2-2-244-422-2-2-22222-20000-220000000000000000000000000000000000
χ504444-4-4-2-444-444-2-2-2-44-422-2-22-2-2-2-220000220000000000000000000000000000000000
χ5144-4-400404-40004-4-400000000004-400000000000000000000000000000000022−22000000
χ5244-4-400404-40004-4-400000000004-4000000000000000000000000000000000−2222000000
χ5344-4-40040-440004-4-40000000000-44000000000000000000000000000000022−2200000000
χ5444-4-40040-440004-4-40000000000-440000000000000000000000000000000−222200000000
χ554-4-444-44-4004-44-4-440004-400-4-440040000000000000000000000000000000000000000
χ564-4-444-4-2400-44-422-2000-2200-2-22002−2i22i2−2i22i200i2−i2i2−i2i2−i2i2−i200000000000000000000000000
χ574-4-444-4-2400-44-422-2000-2200-2-220022i2−2i22i2−2i200−i2i2−i2i2−i2i2−i2i200000000000000000000000000
χ584-4-444-4-2-4004-4422-2000-220022-200-2000000i6−i6i6−i6−i6i6−i6i600000000000000000000000000
χ594-4-444-4-2-4004-4422-2000-220022-200-2000000−i6i6−i6i6i6−i6i6−i600000000000000000000000000
χ604-4-44-444-40044-4-4-44000-4400-44-40040000000000000000000000000000000000000000
χ614-4-44-44-2400-4-4422-20002-200-22-2002−2i22i22i2−2i200i2−i2−i2i2i2−i2−i2i200000000000000000000000000
χ624-4-44-44-2400-4-4422-20002-200-22-20022i2−2i2−2i22i200−i2i2i2−i2−i2i2i2−i200000000000000000000000000
χ634-4-44-44-2-40044-422-20002-2002-2200-2000000i6−i6−i6i6−i6i6i6−i600000000000000000000000000
χ644-4-44-44-2-40044-422-20002-2002-2200-2000000−i6i6i6−i6i6−i6−i6i600000000000000000000000000
χ6588-8-800-408-8000-4440000000000-4400000000000000000000000000000000000000000
χ6688-8-800-40-88000-44400000000004-400000000000000000000000000000000000000000
χ678-88-8008000000-88-800000000000000000000000000000000000000000000000000000
χ688-88-800-40000004-4400000−4i34i30000000000000000000000000000000000000000000000
χ698-88-800-40000004-44000004i3−4i30000000000000000000000000000000000000000000000

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