Finite Group Databasebeta

← Group #10696971

Character table — Group #10696971

Order 768.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72
size1111222222222222224444444444448888888888888812121212121212121616161616161616161616162424242448484848
order12222234444444466644661212121212121212888812122424242424242424888888884488121212122424242488882244
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
χ5111111111111111111111111111111-1-1-1-111-1-1-1-1-1-1-1-11111111111-1-11111-1-1-1-1-1-1-1-111-1-1
χ6111111111111111111111111111111-1-1-1-111-1-1-1-1-1-1-1-111111111-1-111-1-1-1-11111-1-1-1-1-1-111
χ7111111111111111111111111111111-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-11111-1-1-1-11111-1-111
χ8111111111111111111111111111111-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-11111111111-1-1
χ922222222-2-2222-2-2222-2-222-2-2-2-2222222-2-2-2-22222-2-2-2-20000000000000000000000000000
χ1022222222-2-2222-2-2222-2-222-2-2-2-22222-2-222-2-2-2-2-2-222220000000000000000000000000000
χ112222222-222-2-2-2-2-22222-22222-2-2-2-2-2-200002-20000000000000000002i−2i00002i2i−2i−2i00000000
χ122222222-222-2-2-2-2-22222-22222-2-2-2-2-2-200002-2000000000000000000−2i2i0000−2i−2i2i2i00000000
χ132222222-2-2-2-2-2-222222-2222-2-222-2-2-2-20000-2200000000000000002-20022-2-2000000000000
χ142222222-2-2-2-2-2-222222-2222-2-222-2-2-2-20000-220000000000000000-2200-2-222000000000000
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
χ19222222-12-2-2222-2-2-1-1-1-2-2-1-11111-1-1-1-122-2-211-1-1-1-11111000000000000−i3i3−i3i3−i3i3−i3i300000000
χ20222222-12-2-2222-2-2-1-1-1-2-2-1-11111-1-1-1-122-2-211-1-1-1-11111000000000000i3−i3i3−i3i3−i3i3−i300000000
χ21222222-12-2-2222-2-2-1-1-1-2-2-1-11111-1-1-1-1-2-222111111-1-1-1-1000000000000−i3i3−i3i3i3−i3i3−i300000000
χ22222222-12-2-2222-2-2-1-1-1-2-2-1-11111-1-1-1-1-2-222111111-1-1-1-1000000000000i3−i3i3−i3−i3i3−i3i300000000
χ23222222-1-222-2-2-2-2-2-1-1-12-2-1-1-1-11111110000-1133−3−333−3−300000000002i−2i−i3i3i3−i3−i−iii00000000
χ24222222-1-222-2-2-2-2-2-1-1-12-2-1-1-1-11111110000-1133−3−333−3−30000000000−2i2ii3−i3−i3i3ii−i−i00000000
χ25222222-1-222-2-2-2-2-2-1-1-12-2-1-1-1-11111110000-11−3−333−3−33300000000002i−2ii3−i3−i3i3−i−iii00000000
χ26222222-1-222-2-2-2-2-2-1-1-12-2-1-1-1-11111110000-11−3−333−3−3330000000000−2i2i−i3i3i3−i3ii−i−i00000000
χ27222222-1-2-2-2-2-2-222-1-1-1-22-1-111-1-1111100001-133−3−3−3−333000000002-200-1-1113−3−3300000000
χ28222222-1-2-2-2-2-2-222-1-1-1-22-1-111-1-1111100001-133−3−3−3−33300000000-220011-1-1−333−300000000
χ29222222-1-2-2-2-2-2-222-1-1-1-22-1-111-1-1111100001-1−3−33333−3−3000000002-200-1-111−333−300000000
χ30222222-1-2-2-2-2-2-222-1-1-1-22-1-111-1-1111100001-1−3−33333−3−300000000-220011-1-13−3−3300000000
χ312222-2-22222-2-22-2-2222-22-2-222-2-22-2-220000-22000000002222-2-2-2-200000000000000000000
χ322222-2-22222-2-22-2-2222-22-2-222-2-22-2-220000-2200000000-2-2-2-2222200000000000000000000
χ332222-2-222-2-2-2-22222222-2-2-2-2-2222-2-2200002-2000000000000000000000000000022-2-20000
χ342222-2-222-2-2-2-22222222-2-2-2-2-2222-2-2200002-20000000000000000000000000000-2-2220000
χ352222-2-22-22222-222222-2-2-2-22222-222-20000-2-200000000000000000000000000000000002-2
χ362222-2-22-22222-222222-2-2-2-22222-222-20000-2-20000000000000000000000000000000000-22
χ372222-2-22-2-2-222-2-2-222222-2-2-2-2-2-2-222-2000022000000000000000000000000000000002-200
χ382222-2-22-2-2-222-2-2-222222-2-2-2-2-2-2-222-200002200000000000000000000000000000000-2200
χ3922-2-22-222002-2-200-2-22002-2000022-2-2002i−2i0000002i−2i2i−2i22−2−222−2−2000000000000−i2i2−i2i20000
χ4022-2-22-222002-2-200-2-22002-2000022-2-2002i−2i0000002i−2i2i−2i−2−222−2−222000000000000i2−i2i2−i20000
χ4122-2-22-222002-2-200-2-22002-2000022-2-200−2i2i000000−2i2i−2i2i22−2−222−2−2000000000000i2−i2i2−i20000
χ4222-2-22-222002-2-200-2-22002-2000022-2-200−2i2i000000−2i2i−2i2i−2−222−2−222000000000000−i2i2−i2i20000
χ4322-2-2-222200-22-200-2-2200-2200002-22-22i−2i00002i−2i2i−2i000022−2−2−2−222000000000000−i2i2i2−i20000
χ4422-2-2-222200-22-200-2-2200-2200002-22-22i−2i00002i−2i2i−2i0000−2−22222−2−2000000000000i2−i2−i2i20000
χ4522-2-2-222200-22-200-2-2200-2200002-22-2−2i2i0000−2i2i−2i2i000022−2−2−2−222000000000000i2−i2−i2i20000
χ4622-2-2-222200-22-200-2-2200-2200002-22-2−2i2i0000−2i2i−2i2i0000−2−22222−2−2000000000000−i2i2i2−i20000
χ474444-4-4-2444-4-44-4-4-2-2-2-4422-2-222-222-200002-2000000000000000000000000000000000000
χ484444-4-4-24-4-4-4-4444-2-2-24-42222-2-2-222-20000-22000000000000000000000000000000000000
χ494444-4-4-2-44444-444-2-2-2-4-422-2-2-2-22-2-22000022000000000000000000000000000000000000
χ504444-4-4-2-4-4-444-4-4-4-2-2-2442222222-2-220000-2-2000000000000000000000000000000000000
χ5144-4-44-44-400-44400-4-44004-40000-4-444000000000000000000000000000000000000000000
χ5244-4-44-4-24004-4-40022-200-220000-2-222004i−4i000000−2i2i−2i2i0000000000000000000000000000
χ5344-4-44-4-24004-4-40022-200-220000-2-22200−4i4i0000002i−2i2i−2i0000000000000000000000000000
χ5444-4-44-4-2-400-4440022-200-22000022-2-20000000000−2i32i32i3−2i30000000000000000000000000000
χ5544-4-44-4-2-400-4440022-200-22000022-2-200000000002i3−2i3−2i32i30000000000000000000000000000
χ5644-4-4-444-4004-4400-4-4400-440000-44-44000000000000000000000000000000000000000000
χ5744-4-4-44-2400-44-40022-2002-20000-22-224i−4i0000−2i2i−2i2i00000000000000000000000000000000
χ5844-4-4-44-2400-44-40022-2002-20000-22-22−4i4i00002i−2i2i−2i00000000000000000000000000000000
χ5944-4-4-44-2-4004-440022-2002-200002-22-2000000−2i32i32i3−2i300000000000000000000000000000000
χ6044-4-4-44-2-4004-440022-2002-200002-22-20000002i3−2i3−2i32i300000000000000000000000000000000
χ614-44-40040000004-44-4-40000004-40000000000000000002i−2i2i−2i2i−2i2i−2i00000000000000000000
χ624-44-40040000004-44-4-40000004-4000000000000000000−2i2i−2i2i−2i2i−2i2i00000000000000000000
χ634-44-4004000000-444-4-4000000-440000000000000000002i−2i2i−2i−2i2i−2i2i00000000000000000000
χ644-44-4004000000-444-4-4000000-44000000000000000000−2i2i−2i2i2i−2i2i−2i00000000000000000000
χ654-4-4400404-400000-44-400004-4000000000000000000000000−2i22i22i2−2i200000000000000000000
χ664-4-4400404-400000-44-400004-40000000000000000000000002i2−2i2−2i22i200000000000000000000
χ674-4-440040-4400000-44-40000-4400000000000000000000−2i22i22i2−2i2000000000000000000000000
χ684-4-440040-4400000-44-40000-44000000000000000000002i2−2i2−2i22i2000000000000000000000000
χ698-88-800-40000008-8-444000000-440000000000000000000000000000000000000000000000
χ708-88-800-4000000-88-4440000004-40000000000000000000000000000000000000000000000
χ718-8-8800-408-8000004-440000-44000000000000000000000000000000000000000000000000
χ728-8-8800-40-88000004-4400004-4000000000000000000000000000000000000000000000000

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