Finite Group Databasebeta

← Group #10692077

Character table — Group #10692077

Order 768.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69
size11112222222222224444444444444888888888888881616161616161616161616162424242424242424242424244848
order12222234444446664446612121212121212122444661212121212121212226666882424242444448888888888
χ1111111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ31111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-111
χ41111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1
χ511111111111111111111111111111-1-1-1-1-1-111-1-1-1-1-1-1111111-1-1-1-1-1-11111-1-11111-1-1-1-1
χ611111111111111111111111111111-1-1-1-1-1-111-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1-1-111-1-1-1-11111
χ711111111111111111111111111111-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-111-1-1
χ811111111111111111111111111111-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-1-1-1-11111-1-111
χ91111-1-111-11-1-1-111111-1-1-1111-1-1-1-1111-1-1111-111-1-1-1-11-111-1-11-111-1-1ii−i−ii−iii−i−ii−ii−i
χ101111-1-111-11-1-1-111111-1-1-1111-1-1-1-1111-1-1111-111-1-1-1-11-111-1-11-111-1-1−i−iii−ii−i−iii−ii−ii
χ111111-1-111-11-1-1-111111-1-1-1111-1-1-1-1111-1-1111-111-1-1-1-1-11-1-111-11-1-111ii−i−i−ii−i−iii−iii−i
χ121111-1-111-11-1-1-111111-1-1-1111-1-1-1-1111-1-1111-111-1-1-1-1-11-1-111-11-1-111−i−iiii−iii−i−ii−i−ii
χ131111-1-111-11-1-1-111111-1-1-1111-1-1-1-11-1-111-1-11-1-1-111111-111-1-1-11-1-111ii−i−i−iiii−i−i−ii−ii
χ141111-1-111-11-1-1-111111-1-1-1111-1-1-1-11-1-111-1-11-1-1-111111-111-1-1-11-1-111−i−iiii−i−i−iiii−ii−i
χ151111-1-111-11-1-1-111111-1-1-1111-1-1-1-11-1-111-1-11-1-1-11111-11-1-1111-111-1-1ii−i−ii−i−i−iiii−i−ii
χ161111-1-111-11-1-1-111111-1-1-1111-1-1-1-11-1-111-1-11-1-1-11111-11-1-1111-111-1-1−i−iii−iiii−i−i−iii−i
χ172222222222-22-2222-2-2-2222-2-222-2-222-22-222-2-2-2-222-2-200000000000000000000000000
χ182222222222-22-2222-2-2-2222-2-222-2-22-22-22-2-2-2-222-2-22200000000000000000000000000
χ192222222-2-2-22-222222-2-222-2-2-2-2-222-20000002-20000000000000000000000002-22-20000
χ202222222-2-2-22-222222-2-222-2-2-2-2-222-20000002-2000000000000000000000000-22-220000
χ212222222-2-2-2-2-2-2222-22222-222-2-2-2-2-2000000-2200000000000000000000002i−2i0000−2i2i00
χ222222222-2-2-2-2-2-2222-22222-222-2-2-2-2-2000000-220000000000000000000000−2i2i00002i−2i00
χ23222222-1222222-1-1-1222-1-1-1-1-1-1-1-1-1-12222-1-1-1-1-1-1-1-1-1-122-1-1-1-122-1-1-1-100000000000000
χ24222222-1222222-1-1-1222-1-1-1-1-1-1-1-1-1-12222-1-1-1-1-1-1-1-1-1-1-2-21111-2-2111100000000000000
χ25222222-1222222-1-1-1222-1-1-1-1-1-1-1-1-1-1-2-2-2-211-1-111111122-1-1-1-1-2-2111100000000000000
χ26222222-1222222-1-1-1222-1-1-1-1-1-1-1-1-1-1-2-2-2-211-1-1111111-2-2111122-1-1-1-100000000000000
χ27222222-1222-22-2-1-1-1-2-2-2-1-1-111-1-111-12-22-2-1-11111-1-11100−i3i3−i3i300−i3i3−i3i300000000000000
χ28222222-1222-22-2-1-1-1-2-2-2-1-1-111-1-111-12-22-2-1-11111-1-11100i3−i3i3−i300i3−i3i3−i300000000000000
χ29222222-1222-22-2-1-1-1-2-2-2-1-1-111-1-111-1-22-221111-1-111-1-100−i3i3−i3i300i3−i3i3−i300000000000000
χ30222222-1222-22-2-1-1-1-2-2-2-1-1-111-1-111-1-22-221111-1-111-1-100i3−i3i3−i300−i3i3−i3i300000000000000
χ312222-2-222-222-22222-2-22-2-22-2-2-2-22222-2-2222-22-2-2-2-22200000000000000000000000000
χ322222-2-222-222-22222-2-22-2-22-2-2-2-2222-222-2-2-2-222222-2-200000000000000000000000000
χ332222-2-22-22-2222222-22-2-2-2-2222222-2000000-2-20000000000000000000000220000-2-200
χ342222-2-22-22-2222222-22-2-2-2-2222222-2000000-2-20000000000000000000000-2-200002200
χ352222-2-22-22-2-22-22222-22-2-2-2-2-222-2-2-2000000220000000000000000000000002i−2i−2i2i0000
χ362222-2-22-22-2-22-22222-22-2-2-2-2-222-2-2-200000022000000000000000000000000−2i2i2i−2i0000
χ372222-2-2-12-222-22-1-1-1-2-2211-11111-1-1-12-2-22-1-11-11111-1-100−i3i3i3−i300−i3i3i3−i300000000000000
χ382222-2-2-12-222-22-1-1-1-2-2211-11111-1-1-12-2-22-1-11-11111-1-100i3−i3−i3i300i3−i3−i3i300000000000000
χ392222-2-2-12-222-22-1-1-1-2-2211-11111-1-1-1-222-2111-1-1-1-1-11100−i3i3i3−i300i3−i3−i3i300000000000000
χ402222-2-2-12-222-22-1-1-1-2-2211-11111-1-1-1-222-2111-1-1-1-1-11100i3−i3−i3i300−i3i3i3−i300000000000000
χ412222-2-2-12-22-2-2-2-1-1-122-211-1-1-11111-122-2-2-1-1-11-1-111112-2-1-1112-2-1-11100000000000000
χ422222-2-2-12-22-2-2-2-1-1-122-211-1-1-11111-122-2-2-1-1-11-1-11111-2211-1-1-2211-1-100000000000000
χ432222-2-2-12-22-2-2-2-1-1-122-211-1-1-11111-1-2-22211-1111-1-1-1-12-2-1-111-2211-1-100000000000000
χ442222-2-2-12-22-2-2-2-1-1-122-211-1-1-11111-1-2-22211-1111-1-1-1-1-2211-1-12-2-1-11100000000000000
χ45444444-2-4-4-44-44-2-2-24-4-4-2-222222-2-22000000-2200000000000000000000000000000000
χ46444444-2-4-4-4-4-4-4-2-2-2-444-2-22-2-2222220000002-200000000000000000000000000000000
χ474444-4-4-2-44-4444-2-2-2-44-4222-2-2-2-2-2-220000002200000000000000000000000000000000
χ484444-4-4-2-44-4-44-4-2-2-24-4422222-2-2222000000-2-200000000000000000000000000000000
χ4944-4-400400040-44-4-400000000004-40000000000000000000000000002i−2i2i−2i0000000000
χ5044-4-400400040-44-4-400000000004-4000000000000000000000000000−2i2i−2i2i0000000000
χ5144-4-4004000-4044-4-40000000000-440000000000000000000000000002-2-220000000000
χ5244-4-4004000-4044-4-40000000000-44000000000000000000000000000-222-20000000000
χ534-44-44-4444-40-40-44-40004-44004-400-40000000000000000000000000000000000000000
χ544-44-44-44-4-44040-44-40004-4-400-440040000000000000000000000000000000000000000
χ554-44-44-4-244-40-402-22000-22-200-220020000000023−230023−2300000000000000000000000000
χ564-44-44-4-244-40-402-22000-22-200-2200200000000−232300−232300000000000000000000000000
χ574-44-44-4-2-4-440402-22000-222002-200-20000−2i32i30000−2i32i30000000000000000000000000000
χ584-44-44-4-2-4-440402-22000-222002-200-200002i3−2i300002i3−2i30000000000000000000000000000
χ594-44-4-4444-4-4040-44-4000-44400-4400-40000000000000000000000000000000000000000
χ604-44-4-444-4440-40-44-4000-44-4004-40040000000000000000000000000000000000000000
χ614-44-4-44-24-4-40402-220002-2-2002-20020000000023−2300−232300000000000000000000000000
χ624-44-4-44-24-4-40402-220002-2-2002-200200000000−23230023−2300000000000000000000000000
χ634-44-4-44-2-4440-402-220002-2200-2200-20000−2i32i300002i3−2i30000000000000000000000000000
χ644-44-4-44-2-4440-402-220002-2200-2200-200002i3−2i30000−2i32i30000000000000000000000000000
χ6588-8-800-400080-8-4440000000000-4400000000000000000000000000000000000000000
χ6688-8-800-4000-808-44400000000004-400000000000000000000000000000000000000000
χ678-8-88008000000-8-8800000000000000000000000000000000000000000000000000000
χ688-8-8800-400000044-4000000−4i34i3000000000000000000000000000000000000000000000
χ698-8-8800-400000044-40000004i3−4i3000000000000000000000000000000000000000000000

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