Finite Group Databasebeta

← Group #10846237

Character table — Group #10846237

Order 768.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75
size111122222222222244444444444444444888888888888121212121616161616161616161616162424242424242424242424242424
order122222344444466644466888812121212121212128812122424242424242424888824668812122424242422444444888888
χ1111111111111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-111-1-111-1-1-1-1-1-111
χ3111111111111111111111111111111111111111111111-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ4111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1111111-1-1
χ5111111111111111111111-1-1-1-111111111-1-111-1-1-1-1-1-1-1-111111111-1-111-1-1-1-1-1-111-1-111-1-1-1-111
χ6111111111111111111111-1-1-1-111111111-1-111-1-1-1-1-1-1-1-11111-1-1-1-111-1-11111-1-1-1-1-1-1-1-1111111
χ7111111111111111111111-1-1-1-111111111-1-111-1-1-1-1-1-1-1-1-1-1-1-11111-1-111-1-1-1-111-1-111-1-11111-1-1
χ8111111111111111111111-1-1-1-111111111-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1111111111111-1-1-1-1-1-1
χ91111111-1-11111111-1-1-1111111-1-1-1-11111-1-1-1-11111-1-1-1-111-1-11-1111-1-1-111-1-11-1111-1-1-111-1-11-1
χ101111111-1-11111111-1-1-1111111-1-1-1-11111-1-1-1-11111-1-1-1-111-1-1-11-1-1-1111-1-1111-1-1-11-111-1-1111-1
χ111111111-1-11111111-1-1-1111111-1-1-1-11111-1-1-1-11111-1-1-1-1-1-1111-1111-1-1-111-1-1-11-1-1-1111-1-111-11
χ121111111-1-11111111-1-1-1111111-1-1-1-11111-1-1-1-11111-1-1-1-1-1-111-11-1-1-1111-1-111-1111-11-1-111-1-1-11
χ131111111-1-11111111-1-1-111-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1111111-1-11-111-11-1-1-1-111-1111-11-1-1-1-1111-1
χ141111111-1-11111111-1-1-111-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1111111-1-1-11-1-11-11111-1-1-11-1-1-111111-1-11-1
χ151111111-1-11111111-1-1-111-1-1-1-1-1-1-1-1111111-1-1-1-1-1-11111-1-1111-111-11-1-1-1-1111-1-1-11-11111-1-1-11
χ161111111-1-11111111-1-1-111-1-1-1-1-1-1-1-1111111-1-1-1-1-1-11111-1-111-11-1-11-11111-1-11-1111-1-1-1-1-111-11
χ17222222222-2-2-2-22222-2-2222i2i−2i−2i22-2-2-2-2-2-22i−2i2-22i2i−2i−2i2i2i−2i−2i000000000000000000000000000000
χ18222222222-2-2-2-22222-2-222−2i−2i2i2i22-2-2-2-2-2-2−2i2i2-2−2i−2i2i2i−2i−2i2i2i000000000000000000000000000000
χ192222222-2-2-2-2-2-2222-222222i2i−2i−2i-2-222-2-2-2-2−2i2i-222i2i−2i−2i−2i−2i2i2i000000000000000000000000000000
χ202222222-2-2-2-2-2-2222-22222−2i−2i2i2i-2-222-2-2-2-22i−2i-22−2i−2i2i2i2i2i−2i−2i000000000000000000000000000000
χ21222222-1222222-1-1-1222-1-12222-1-1-1-1-1-1-1-122-1-1-1-1-1-1-1-1-1-1000022-1-122-1-1-1-1-1-100000000000000
χ22222222-1222222-1-1-1222-1-12222-1-1-1-1-1-1-1-122-1-1-1-1-1-1-1-1-1-10000-2-211-2-211111100000000000000
χ23222222-1222222-1-1-1222-1-1-2-2-2-2-1-1-1-1-1-1-1-1-2-2-1-111111111000022-1-1-2-2-1-1111100000000000000
χ24222222-1222222-1-1-1222-1-1-2-2-2-2-1-1-1-1-1-1-1-1-2-2-1-1111111110000-2-2112211-1-1-1-100000000000000
χ25222222-122-2-2-2-2-1-1-12-2-2-1-12i2i−2i−2i-1-11111112i−2i-11−i−iii−i−iii000000−i3i300−i3i33−33−300000000000000
χ26222222-122-2-2-2-2-1-1-12-2-2-1-12i2i−2i−2i-1-11111112i−2i-11−i−iii−i−iii000000i3−i300i3−i3−33−3300000000000000
χ27222222-122-2-2-2-2-1-1-12-2-2-1-1−2i−2i2i2i-1-1111111−2i2i-11ii−i−iii−i−i000000−i3i300−i3i3−33−3300000000000000
χ28222222-122-2-2-2-2-1-1-12-2-2-1-1−2i−2i2i2i-1-1111111−2i2i-11ii−i−iii−i−i000000i3−i300i3−i33−33−300000000000000
χ29222222-1-2-22222-1-1-1-2-2-2-1-122221111-1-1-1-1-2-211-1-1-1-1111100002-2-1-12-211-1-11100000000000000
χ30222222-1-2-22222-1-1-1-2-2-2-1-122221111-1-1-1-1-2-211-1-1-1-111110000-2211-22-1-111-1-100000000000000
χ31222222-1-2-22222-1-1-1-2-2-2-1-1-2-2-2-21111-1-1-1-122111111-1-1-1-100002-2-1-1-221111-1-100000000000000
χ32222222-1-2-22222-1-1-1-2-2-2-1-1-2-2-2-21111-1-1-1-122111111-1-1-1-10000-22112-2-1-1-1-11100000000000000
χ33222222-1-2-2-2-2-2-2-1-1-1-222-1-12i2i−2i−2i11-1-11111−2i2i1-1−i−iiiii−i−i000000−i3i300i3−i33−3−3300000000000000
χ34222222-1-2-2-2-2-2-2-1-1-1-222-1-12i2i−2i−2i11-1-11111−2i2i1-1−i−iiiii−i−i000000i3−i300−i3i3−333−300000000000000
χ35222222-1-2-2-2-2-2-2-1-1-1-222-1-1−2i−2i2i2i11-1-111112i−2i1-1ii−i−i−i−iii000000−i3i300i3−i3−333−300000000000000
χ36222222-1-2-2-2-2-2-2-1-1-1-222-1-1−2i−2i2i2i11-1-111112i−2i1-1ii−i−i−i−iii000000i3−i300−i3i33−3−3300000000000000
χ372222-2-22222-2-22222-22-2-2-200002222-222-200-2-2000000002222000000000000000000000000-2-2
χ382222-2-22222-2-22222-22-2-2-200002222-222-200-2-200000000-2-2-2-200000000000000000000000022
χ392222-2-2222-222-2222-2-22-2-2000022-2-22-2-2200-220000000000000000000000002-200-2200000000
χ402222-2-2222-222-2222-2-22-2-2000022-2-22-2-2200-22000000000000000000000000-22002-200000000
χ412222-2-22-2-22-2-222222-22-2-20000-2-2-2-2-222-200220000000022-2-2000000000000000000000000-22
χ422222-2-22-2-22-2-222222-22-2-20000-2-2-2-2-222-2002200000000-2-2220000000000000000000000002-2
χ432222-2-22-2-2-222-222222-2-2-20000-2-2222-2-22002-20000000000000000000000002200-2-200000000
χ442222-2-22-2-2-222-222222-2-2-20000-2-2222-2-22002-2000000000000000000000000-2-2002200000000
χ452-2-222-220022-2-2-2-220002-22i−2i2i−2i000022-2-200002i−2i2i−2i00000000000000000000002i−2i00002-20000
χ462-2-222-220022-2-2-2-220002-22i−2i2i−2i000022-2-200002i−2i2i−2i0000000000000000000000−2i2i0000-220000
χ472-2-222-220022-2-2-2-220002-2−2i2i−2i2i000022-2-20000−2i2i−2i2i00000000000000000000002i−2i0000-220000
χ482-2-222-220022-2-2-2-220002-2−2i2i−2i2i000022-2-20000−2i2i−2i2i0000000000000000000000−2i2i00002-20000
χ492-2-222-2200-2-222-2-220002-22-2-220000-2-22200002-2-22000000000000000000000000002-2002-200
χ502-2-222-2200-2-222-2-220002-22-2-220000-2-22200002-2-2200000000000000000000000000-2200-2200
χ512-2-222-2200-2-222-2-220002-2-222-20000-2-2220000-222-2000000000000000000000000002-200-2200
χ522-2-222-2200-2-222-2-220002-2-222-20000-2-2220000-222-200000000000000000000000000-22002-200
χ534444-4-4-2444-4-44-2-2-2-44-4220000-2-2-2-22-2-22002200000000000000000000000000000000000000
χ544444-4-4-244-444-4-2-2-2-4-44220000-2-222-222-2002-200000000000000000000000000000000000000
χ554444-4-4-2-4-44-4-44-2-2-24-4422000022222-2-2200-2-200000000000000000000000000000000000000
χ564444-4-4-2-4-4-444-4-2-2-244-422000022-2-2-222-200-2200000000000000000000000000000000000000
χ574-44-40044i−4i00004-4-40000000004i−4i00000000000000000022−22−2i22i200000000000000000000000000
χ584-44-40044i−4i00004-4-40000000004i−4i000000000000000000−22222i2−2i200000000000000000000000000
χ594-44-4004−4i4i00004-4-4000000000−4i4i00000000000000000022−222i2−2i200000000000000000000000000
χ604-44-4004−4i4i00004-4-4000000000−4i4i000000000000000000−2222−2i22i200000000000000000000000000
χ614-4-444-4-20044-4-422-2000-224i−4i4i−4i0000-2-2220000−2i2i−2i2i0000000000000000000000000000000000
χ624-4-444-4-20044-4-422-2000-22−4i4i−4i4i0000-2-22200002i−2i2i−2i0000000000000000000000000000000000
χ634-4-444-4-200-4-44422-2000-224-4-44000022-2-20000-222-20000000000000000000000000000000000
χ644-4-444-4-200-4-44422-2000-22-444-4000022-2-200002-2-220000000000000000000000000000000000
χ654-4-44-444004-44-4-4-44000-4400000000-44-44000000000000000000000000000000000000000000
χ664-4-44-44400-44-44-4-44000-44000000004-44-4000000000000000000000000000000000000000000
χ674-4-44-44-2004-44-422-20002-2000000002-22-200000000−2i32i3−2i32i3000000000000000000000000000000
χ684-4-44-44-2004-44-422-20002-2000000002-22-2000000002i3−2i32i3−2i3000000000000000000000000000000
χ694-4-44-44-200-44-4422-20002-200000000-22-220000000023−23−2323000000000000000000000000000000
χ704-4-44-44-200-44-4422-20002-200000000-22-2200000000−232323−23000000000000000000000000000000
χ7188-8-8008000000-88-800000000000000000000000000000000000000000000000000000000000
χ7288-8-800-40000004-440000000000043−430000000000000000000000000000000000000000000000
χ7388-8-800-40000004-4400000000000−43430000000000000000000000000000000000000000000000
χ748-88-800-48i−8i0000-444000000000−4i4i000000000000000000000000000000000000000000000000
χ758-88-800-4−8i8i0000-4440000000004i−4i000000000000000000000000000000000000000000000000

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