Finite Group Databasebeta

← Group #10697931

Character table — Group #10697931

Order 768.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72
size1111222222222222224444444444448888888888888812121212121212121616161616161616161616162424242448484848
order12222234444444466644661212121212121212888812122424242424242424444444444488121212122424242488884444
χ1111111111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1
χ311111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-1
χ411111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111
χ5111111111111111111111111111111-1-1-1-111-1-1-1-1-1-1-1-11111111111-1-11111-1-1-1-1-1-1-1-1-111-1
χ6111111111111111111111111111111-1-1-1-111-1-1-1-1-1-1-1-111111111-1-111-1-1-1-11111-1-1-1-11-1-11
χ7111111111111111111111111111111-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-11111-1-1-1-111111-1-11
χ8111111111111111111111111111111-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-111111111-111-1
χ92222222222-2-22-2-2222-2-222-2-2222-2-220000-2-2000000002222-2-2-2-200000000000000000000
χ102222222222-2-22-2-2222-2-222-2-2222-2-220000-2-200000000-2-2-2-2222200000000000000000000
χ112222222-2-2-222-2-2-2222-2222-2-2-2-2-222-200002-20000000000000000000000000000000002-20
χ122222222-2-2-222-2-2-2222-2222-2-2-2-2-222-200002-2000000000000000000000000000000000-220
χ132222222-2-2-2-2-2-2222222-22222-2-2-2-2-2-20000-2200000000000000002-20022-2-2000000000000
χ142222222-2-2-2-2-2-2222222-22222-2-2-2-2-2-20000-220000000000000000-2200-2-222000000000000
χ15222222-122222222-1-1-122-1-1-1-1-1-1-1-1-1-12222-1-1-1-1-1-1-1-1-1-1000000002222-1-1-1-1-1-1-1-100000000
χ16222222-122222222-1-1-122-1-1-1-1-1-1-1-1-1-12222-1-1-1-1-1-1-1-1-1-100000000-2-2-2-21111111100000000
χ17222222-122222222-1-1-122-1-1-1-1-1-1-1-1-1-1-2-2-2-2-1-1111111110000000022-2-2-1-1-1-1111100000000
χ18222222-122222222-1-1-122-1-1-1-1-1-1-1-1-1-1-2-2-2-2-1-11111111100000000-2-2221111-1-1-1-100000000
χ19222222-1-2-2-2-2-2-222-1-1-12-2-1-1-1-111111100001-13333−3−3−3−3000000002-200-1-11133−3−300000000
χ20222222-1-2-2-2-2-2-222-1-1-12-2-1-1-1-111111100001-13333−3−3−3−300000000-220011-1-1−3−33300000000
χ21222222-1-2-2-2-2-2-222-1-1-12-2-1-1-1-111111100001-1−3−3−3−33333000000002-200-1-111−3−33300000000
χ22222222-1-2-2-2-2-2-222-1-1-12-2-1-1-1-111111100001-1−3−3−3−3333300000000-220011-1-133−3−300000000
χ232222-2-2222-222-222222-2-2-2-22222-222-20000-2-200000000000000000000000000000000200-2
χ242222-2-2222-222-222222-2-2-2-22222-222-20000-2-200000000000000000000000000000000-2002
χ252222-2-2222-2-2-2-2-2-222222-2-2-2-222-2-2-2-20000220000000000000000002i−2i00002i−2i2i−2i00000000
χ262222-2-2222-2-2-2-2-2-222222-2-2-2-222-2-2-2-2000022000000000000000000−2i2i0000−2i2i−2i2i00000000
χ272222-2-22-2-22222-2-22222-2-2-2-2-2-2-2222222-2-2-2222-2-222-2-20000000000000000000000000000
χ282222-2-22-2-22222-2-22222-2-2-2-2-2-2-22222-2-222-22-2-222-2-2220000000000000000000000000000
χ292222-2-22-2-22-2-2222222-22-2-222-2-22-2-2200002-2000000000000000000000000000022-2-20000
χ302222-2-22-2-22-2-2222222-22-2-222-2-22-2-2200002-20000000000000000000000000000-2-2220000
χ312222-2-2-122-2-2-2-2-2-2-1-1-1221111-1-111110000-1-133−3−3−3−33300000000002i−2i−i3i3−i3i3−ii−ii00000000
χ322222-2-2-122-2-2-2-2-2-2-1-1-1221111-1-111110000-1-133−3−3−3−3330000000000−2i2ii3−i3i3−i3i−ii−i00000000
χ332222-2-2-122-2-2-2-2-2-2-1-1-1221111-1-111110000-1-1−3−33333−3−300000000002i−2ii3−i3i3−i3−ii−ii00000000
χ342222-2-2-122-2-2-2-2-2-2-1-1-1221111-1-111110000-1-1−3−33333−3−30000000000−2i2i−i3i3−i3i3i−ii−i00000000
χ352222-2-2-1-2-22222-2-2-1-1-12-2111111-1-1-1-122-2-21-1-1-111-1-111000000000000−i3i3i3−i3−i3i3i3−i300000000
χ362222-2-2-1-2-22222-2-2-1-1-12-2111111-1-1-1-122-2-21-1-1-111-1-111000000000000i3−i3−i3i3i3−i3−i3i300000000
χ372222-2-2-1-2-22222-2-2-1-1-12-2111111-1-1-1-1-2-2221-111-1-111-1-1000000000000−i3i3i3−i3i3−i3−i3i300000000
χ382222-2-2-1-2-22222-2-2-1-1-12-2111111-1-1-1-1-2-2221-111-1-111-1-1000000000000i3−i3−i3i3−i3i3i3−i300000000
χ3922-2-22-222-2-200200-2-22002-2002-2-20022−22−2002−22−22−22−200002i2i−2i−2i000000000000−i2i2−i2i20000
χ4022-2-22-222-2-200200-2-22002-2002-2-20022−22−2002−22−22−22−20000−2i−2i2i2i000000000000i2−i2i2−i20000
χ4122-2-22-222-2-200200-2-22002-2002-2-2002−22−2200−22−22−22−2200002i2i−2i−2i000000000000i2−i2i2−i20000
χ4222-2-22-222-2-200200-2-22002-2002-2-2002−22−2200−22−22−22−220000−2i−2i2i2i000000000000−i2i2−i2i20000
χ4322-2-2-222-22-200200-2-2200-2200-22-20022−2−22002−2−222−2−222i2i−2i−2i0000000000000000−i2i2i2−i20000
χ4422-2-2-222-22-200200-2-2200-2200-22-20022−2−22002−2−222−2−22−2i−2i2i2i0000000000000000i2−i2−i2i20000
χ4522-2-2-222-22-200200-2-2200-2200-22-2002−222−200−222−2−222−22i2i−2i−2i0000000000000000i2−i2−i2i20000
χ4622-2-2-222-22-200200-2-2200-2200-22-2002−222−200−222−2−222−2−2i−2i2i2i0000000000000000−i2i2i2−i20000
χ47444444-2444-4-44-4-4-2-2-2-4-4-2-222-2-2-222-2000022000000000000000000000000000000000000
χ48444444-2-4-4-444-4-4-4-2-2-2-44-2-222222-2-220000-22000000000000000000000000000000000000
χ494444-4-4-244-444-444-2-2-2-4-422-2-2-2-22-2-22000022000000000000000000000000000000000000
χ504444-4-4-2-4-44-4-4444-2-2-2-4422-2-222-222-20000-22000000000000000000000000000000000000
χ5144-4-44-44-44400-400-4-44004-400-44400-4000000000000000000000000000000000000000000
χ5244-4-44-4-24-4-40040022-200-2200-22200-222−2222−2200−22−22−22−220000000000000000000000000000
χ5344-4-44-4-24-4-40040022-200-2200-22200-2−2222−2222002−22−22−22−20000000000000000000000000000
χ5444-4-44-4-2-44400-40022-200-22002-2-20020000006−66−6−66−660000000000000000000000000000
χ5544-4-44-4-2-44400-40022-200-22002-2-2002000000−66−666−66−60000000000000000000000000000
χ5644-4-4-4444-4400-400-4-4400-44004-4400-4000000000000000000000000000000000000000000
χ5744-4-4-44-24-4400-40022-2002-200-22-20020000006−6−66−666−60000000000000000000000000000
χ5844-4-4-44-24-4400-40022-2002-200-22-2002000000−666−66−6−660000000000000000000000000000
χ5944-4-4-44-2-44-40040022-2002-2002-2200-222−22−222200−222−2−222−20000000000000000000000000000
χ6044-4-4-44-2-44-40040022-2002-2002-2200-2−222222−22002−2−222−2−220000000000000000000000000000
χ614-44-40040000004-44-4-400004-4000000000000000000002-22-22-22-200000000000000000000
χ624-44-40040000004-44-4-400004-400000000000000000000-22-22-22-2200000000000000000000
χ634-44-4004000000-444-4-40000-44000000000000000000002-22-2-22-2200000000000000000000
χ644-44-4004000000-444-4-40000-4400000000000000000000-22-222-22-200000000000000000000
χ654-4-440040004-4000-44-40000000004-40000000000000002i−2i−2i2i2i−2i−2i2i00000000000000000000
χ664-4-440040004-4000-44-40000000004-4000000000000000−2i2i2i−2i−2i2i2i−2i00000000000000000000
χ674-4-44004000-44000-44-4000000000-440000000000000002i−2i−2i2i−2i2i2i−2i00000000000000000000
χ684-4-44004000-44000-44-4000000000-44000000000000000−2i2i2i−2i2i−2i−2i2i00000000000000000000
χ698-88-800-40000008-8-4440000-44000000000000000000000000000000000000000000000000
χ708-88-800-4000000-88-44400004-4000000000000000000000000000000000000000000000000
χ718-8-8800-40008-80004-44000000000-440000000000000000000000000000000000000000000
χ728-8-8800-4000-880004-440000000004-40000000000000000000000000000000000000000000

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