Finite Group Databasebeta

← Group #10826847

Character table — Group #10826847

Order 768.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78
size111122222222222222444444444444888888888888888888121212121212121212121212161616161616161616162424242424244848
order1222223444444446662266121212121212121222244444666666121212124444444444446881212122424242422244488
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-1
χ311111111111111111111111111111111-1-1-111-11111111111111111111111-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-1
χ411111111111111111111111111111111-1-1-111-11111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111
χ5111111111111111111111111111111-1-1111-1-1111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-11-1-1111-1-1-1-1111111-1-1
χ6111111111111111111111111111111-1-1111-1-1111-1-1-1-1-1-1-1-1-1-1-1-1111111111-1-1111-1-1-1-1-1-1-1-1-1-111
χ7111111111111111111111111111111-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-111-1-1-1111111-1-1-1-111
χ8111111111111111111111111111111-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-111111111-111-1-1-11111-1-11111-1-1
χ91111111-1-1-1-11111111-1-11111-1-1-1-111111-1-1-1-11-1-11111-1-1-1-111111111-1-1-1-111-1-1-1111-1-1-1-11-1-111-1
χ101111111-1-1-1-11111111-1-11111-1-1-1-111111-1-1-1-11-1-11111-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-1111-1-111-111-1-11
χ111111111-1-1-1-11111111-1-11111-1-1-1-11111-111-1-1-1-1-11111-1-1-1-111111111-1-1-1-1-1-1111-1-1-111-1-1-111-1-11
χ121111111-1-1-1-11111111-1-11111-1-1-1-11111-111-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1111-1-1-111111-1-111-1
χ131111111-1-1-1-11111111-1-11111-1-1-1-111-1-11-1-1111-1-1-1-1-1-111111111-1-1-1-111111-11-1-11-1-111-1-11-1-11-11
χ141111111-1-1-1-11111111-1-11111-1-1-1-111-1-11-1-1111-1-1-1-1-1-11111-1-1-1-11111-1-1-1-11-11-1-11-1-11111-111-11-1
χ151111111-1-1-1-11111111-1-11111-1-1-1-111-1-1-11111-1-1-1-1-1-1-111111111-1-1-1-11111-11-111-111-1-1-1-1-111-11-1
χ161111111-1-1-1-11111111-1-11111-1-1-1-111-1-1-11111-1-1-1-1-1-1-11111-1-1-1-11111-1-1-1-1-11-111-111-1-1111-1-11-11
χ1722222222222-2-2-2-2222-2-222-2-22222-2-200000000-2-20000000022-2-20000000000000000002-2000000
χ1822222222222-2-2-2-2222-2-222-2-22222-2-200000000-2-200000000-2-222000000000000000000-22000000
χ192222222-2-2-2-2-2-2-2-22222222-2-2-2-2-2-2-2-200000000220000000022-2-2000000000000000000-22000000
χ202222222-2-2-2-2-2-2-2-22222222-2-2-2-2-2-2-2-2000000002200000000-2-2220000000000000000002-2000000
χ21222222-122222222-1-1-122-1-1-1-1-1-1-1-1-1-122222222-1-1-1-1-1-1-1-1-1-1000000000000-122-1-1-1-1-1-1-100000000
χ22222222-122222222-1-1-122-1-1-1-1-1-1-1-1-1-122-2-2-222-2-1-1-1-1-1-1-1-1-1-10000000000001-2-2111111100000000
χ23222222-122222222-1-1-122-1-1-1-1-1-1-1-1-1-1-2-2222-2-22-1-111111111000000000000-1-2-2-1-1-1111100000000
χ24222222-122222222-1-1-122-1-1-1-1-1-1-1-1-1-1-2-2-2-2-2-2-2-2-1-111111111000000000000122111-1-1-1-100000000
χ25222222-1-2-2-2-22222-1-1-1-2-2-1-1-1-11111-1-1222-2-2-2-2211-1-1-1-11111000000000000-12-211-1-1-11100000000
χ26222222-1-2-2-2-22222-1-1-1-2-2-1-1-1-11111-1-122-222-2-2-211-1-1-1-111110000000000001-22-1-1111-1-100000000
χ27222222-1-2-2-2-22222-1-1-1-2-2-1-1-1-11111-1-1-2-22-2-2222111111-1-1-1-1000000000000-1-2211-111-1-100000000
χ28222222-1-2-2-2-22222-1-1-1-2-2-1-1-1-11111-1-1-2-2-22222-2111111-1-1-1-100000000000012-2-1-11-1-11100000000
χ292222-2-2222-2-222-2-22222-2-2-2-2-222-2-2220022-200-22-2000000000000000000002002-2-2000000000000
χ302222-2-2222-2-222-2-22222-2-2-2-2-222-2-22200-2-220022-200000000000000000000-200-222000000000000
χ312222-2-2222-2-2-2-222222-22-2-22222-2-2-2-200000000-220000000000000000000000000000000022-2-200
χ322222-2-2222-2-2-2-222222-22-2-22222-2-2-2-200000000-2200000000000000000000000000000000-2-22200
χ332222-2-22-2-22222-2-2222-22-2-2-2-2-2-22222002-2200-2-2200000000000000000000200-22-2000000000000
χ342222-2-22-2-22222-2-2222-22-2-2-2-2-2-2222200-22-2002-2200000000000000000000-2002-22000000000000
χ352222-2-22-2-222-2-2222222-2-2-222-2-222-2-2000000002-2000000000000000000000000000000002-22-200
χ362222-2-22-2-222-2-2222222-2-2-222-2-222-2-2000000002-200000000000000000000000000000000-22-2200
χ372222-2-2-122-2-222-2-2-1-1-12-21111-1-111-1-10022-200-2-11−i3−i3i3i3−i3−i3i3i3000000000000-100-111−i3i3−i3i300000000
χ382222-2-2-122-2-222-2-2-1-1-12-21111-1-111-1-10022-200-2-11i3i3−i3−i3i3i3−i3−i3000000000000-100-111i3−i3i3−i300000000
χ392222-2-2-122-2-222-2-2-1-1-12-21111-1-111-1-100-2-22002-11−i3−i3i3i3−i3−i3i3i30000000000001001-1-1i3−i3i3−i300000000
χ402222-2-2-122-2-222-2-2-1-1-12-21111-1-111-1-100-2-22002-11i3i3−i3−i3i3i3−i3−i30000000000001001-1-1−i3i3−i3i300000000
χ412222-2-2-1-2-22222-2-2-1-1-1-22111111-1-1-1-1002-2200-21-1−i3−i3i3i3i3i3−i3−i3000000000000-1001-11−i3i3i3−i300000000
χ422222-2-2-1-2-22222-2-2-1-1-1-22111111-1-1-1-1002-2200-21-1i3i3−i3−i3−i3−i3i3i3000000000000-1001-11i3−i3−i3i300000000
χ432222-2-2-1-2-22222-2-2-1-1-1-22111111-1-1-1-100-22-20021-1−i3−i3i3i3i3i3−i3−i3000000000000100-11-1i3−i3−i3i300000000
χ442222-2-2-1-2-22222-2-2-1-1-1-22111111-1-1-1-100-22-20021-1i3i3−i3−i3−i3−i3i3i3000000000000100-11-1−i3i3i3−i300000000
χ452-2-22-22200002-22-2-2-22002-22-200002-2000002-200000002-22-22-22-2000022-2-2000000000000000000
χ462-2-22-22200002-22-2-2-22002-22-200002-2000002-200000002-22-2-22-220000-2-222000000000000000000
χ472-2-22-22200002-22-2-2-22002-22-200002-200000-220000000-22-222-22-20000-2-222000000000000000000
χ482-2-22-22200002-22-2-2-22002-22-200002-200000-220000000-22-22-22-22000022-2-2000000000000000000
χ492-2-22-2220000-22-22-2-22002-2-220000-222-2000000002-22-200002-2-2222-2-20000000000000000000000
χ502-2-22-2220000-22-22-2-22002-2-220000-222-2000000002-22-20000-222-2-2-2220000000000000000000000
χ512-2-22-2220000-22-22-2-22002-2-220000-22-2200000000-22-2200002-2-22-2-2220000000000000000000000
χ522-2-22-2220000-22-22-2-22002-2-220000-22-2200000000-22-220000-222-222-2-20000000000000000000000
χ53444444-24444-4-4-4-4-2-2-2-4-4-2-222-2-2-2-222000000002200000000000000000000000000000000000000
χ54444444-2-4-4-4-4-4-4-4-4-2-2-244-2-22222222200000000-2-200000000000000000000000000000000000000
χ554444-4-4-244-4-4-4-444-2-2-2-4422-2-2-2-22222000000002-200000000000000000000000000000000000000
χ564444-4-4-2-4-444-4-444-2-2-24-422-2-222-2-22200000000-2200000000000000000000000000000000000000
χ5744-4-4004004i−4i00004-4-4000000004i−4i0000000000000000000000002i−2i2i−2i2-22-2000000000000000000
χ5844-4-4004004i−4i00004-4-4000000004i−4i000000000000000000000000−2i2i−2i2i-22-22000000000000000000
χ5944-4-400400−4i4i00004-4-400000000−4i4i0000000000000000000000002i−2i2i−2i-22-22000000000000000000
χ6044-4-400400−4i4i00004-4-400000000−4i4i000000000000000000000000−2i2i−2i2i2-22-2000000000000000000
χ614-44-40044i−4i000000-44-40000004i−4i000000000000000000000000002i−2i−2i2i2-2-22000000000000000000
χ624-44-40044i−4i000000-44-40000004i−4i00000000000000000000000000−2i2i2i−2i-222-2000000000000000000
χ634-44-4004−4i4i000000-44-4000000−4i4i000000000000000000000000002i−2i−2i2i-222-2000000000000000000
χ644-44-4004−4i4i000000-44-4000000−4i4i00000000000000000000000000−2i2i2i−2i2-2-22000000000000000000
χ654-4-444-4400004-4-44-4-4400-44-4400004-4000000000000000000000000000000000000000000000000
χ664-4-444-440000-444-4-4-4400-444-40000-44000000000000000000000000000000000000000000000000
χ674-4-444-4-200004-4-4422-2002-22-20000-2200000000000000−2i32i32i3−2i3000000000000000000000000000000
χ684-4-444-4-200004-4-4422-2002-22-20000-22000000000000002i3−2i3−2i32i3000000000000000000000000000000
χ694-4-444-4-20000-444-422-2002-2-2200002-20000000000−2i32i32i3−2i30000000000000000000000000000000000
χ704-4-444-4-20000-444-422-2002-2-2200002-200000000002i3−2i3−2i32i30000000000000000000000000000000000
χ714-4-44-44-200004-44-422-200-22-220000-22000004-40000000-22-22000000000000000000000000000000
χ724-4-44-44-200004-44-422-200-22-220000-2200000-4400000002-22-2000000000000000000000000000000
χ734-4-44-44-20000-44-4422-200-222-200002-24-400000000-22-220000000000000000000000000000000000
χ744-4-44-44-20000-44-4422-200-222-200002-2-44000000002-22-20000000000000000000000000000000000
χ7588-8-800-4008i−8i0000-44400000000−4i4i00000000000000000000000000000000000000000000000000
χ7688-8-800-400−8i8i0000-444000000004i−4i00000000000000000000000000000000000000000000000000
χ778-88-800-48i−8i0000004-44000000−4i4i0000000000000000000000000000000000000000000000000000
χ788-88-800-4−8i8i0000004-440000004i−4i0000000000000000000000000000000000000000000000000000

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