Finite Group Databasebeta

← Group #10692070

Character table — Group #10692070

Order 768.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69
size11112222222222224444444444444888888888888881616161616161616161616162424242424242424242424244848
order122222344444466644466121212121212121224446612121212121212124488121212122424242444448888888888
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
χ511111111111111111111111111111-1-1-1-1-1-11-1-1-1-11-1-111-1-11111-1-1-1-11111-1-11111-1-1-1-1
χ611111111111111111111111111111-1-1-1-1-1-11-1-1-1-11-1-111-1-11111-1-1-1-1-1-1-1-111-1-1-1-11111
χ711111111111111111111111111111-1-1-1-1-1-11-1-1-1-11-1-1-1-111-1-1-1-11111111111-1-1-1-111-1-1
χ811111111111111111111111111111-1-1-1-1-1-11-1-1-1-11-1-1-1-111-1-1-1-11111-1-1-1-1-1-11111-1-111
χ91111-1-111-11-1-1-11111-11-1-1111-1-1-1-1111-1-111-111-1-11-1-11-11-111-1-111-1-1ii−i−ii−iii−i−ii−ii−i
χ101111-1-111-11-1-1-11111-11-1-1111-1-1-1-1111-1-111-111-1-11-1-11-11-111-1-111-1-1−i−iii−ii−i−iii−ii−ii
χ111111-1-111-11-1-1-11111-11-1-1111-1-1-1-1111-1-111-111-1-11-1-1-11-11-1-111-1-111ii−i−i−ii−i−iii−iii−i
χ121111-1-111-11-1-1-11111-11-1-1111-1-1-1-1111-1-111-111-1-11-1-1-11-11-1-111-1-111−i−iiii−iii−i−ii−i−ii
χ131111-1-111-11-1-1-11111-11-1-1111-1-1-1-11-1-111-1-1-1-1-1111111-1-1111-1-1-1-111ii−i−i−iiii−i−i−ii−ii
χ141111-1-111-11-1-1-11111-11-1-1111-1-1-1-11-1-111-1-1-1-1-1111111-1-1111-1-1-1-111−i−iiii−i−i−iiii−ii−i
χ151111-1-111-11-1-1-11111-11-1-1111-1-1-1-11-1-111-1-1-1-1-111111-111-1-1-11111-1-1ii−i−ii−i−i−iiii−i−ii
χ161111-1-111-11-1-1-11111-11-1-1111-1-1-1-11-1-111-1-1-1-1-111111-111-1-1-11111-1-1−i−iii−iiii−i−i−iii−i
χ172222222222-22-2222-2-2-2222-2-222-2-222-22-222-2-2-222-2-2-200000000000000000000000000
χ182222222222-22-2222-2-2-2222-2-222-2-22-22-22-2-2-222-2-2-22200000000000000000000000000
χ192222222-2-2-22-22222-2-2222-2-2-2-2-222-2000000-200002000000000000000000002-22-20000
χ202222222-2-2-22-22222-2-2222-2-2-2-2-222-2000000-20000200000000000000000000-22-220000
χ212222222-2-2-2-2-2-222222-222-222-2-2-2-2-200000020000-20000000000000000002i−2i0000−2i2i00
χ222222222-2-2-2-2-2-222222-222-222-2-2-2-2-200000020000-2000000000000000000−2i2i00002i−2i00
χ23222222-1222222-1-1-1222-1-1-1-1-1-1-1-1-1-12222-1-1-1-1-1-1-1-1-1-12222-1-1-1-1-1-1-1-100000000000000
χ24222222-1222222-1-1-1222-1-1-1-1-1-1-1-1-1-12222-1-1-1-1-1-1-1-1-1-1-2-2-2-21111111100000000000000
χ25222222-1222222-1-1-1222-1-1-1-1-1-1-1-1-1-1-2-2-2-211-11111-11122-2-2-1-1-1-1111100000000000000
χ26222222-1222222-1-1-1222-1-1-1-1-1-1-1-1-1-1-2-2-2-211-11111-111-2-2221111-1-1-1-100000000000000
χ27222222-1222-22-2-1-1-1-2-2-2-1-1-111-1-111-12-22-2-1-1111-1-11110000−i3i3−i3i3−i3i3−i3i300000000000000
χ28222222-1222-22-2-1-1-1-2-2-2-1-1-111-1-111-12-22-2-1-1111-1-11110000i3−i3i3−i3i3−i3i3−i300000000000000
χ29222222-1222-22-2-1-1-1-2-2-2-1-1-111-1-111-1-22-22111-1-1111-1-10000−i3i3−i3i3i3−i3i3−i300000000000000
χ30222222-1222-22-2-1-1-1-2-2-2-1-1-111-1-111-1-22-22111-1-1111-1-10000i3−i3i3−i3−i3i3−i3i300000000000000
χ312222-2-222-222-22222-22-2-2-22-2-2-2-22222-2-22222-2-2-2-2-22200000000000000000000000000
χ322222-2-222-222-22222-22-2-2-22-2-2-2-2222-222-2-2-222222-2-2-200000000000000000000000000
χ332222-2-22-22-22222222-2-2-2-2-2222222-2000000-20000-2000000000000000000220000-2-200
χ342222-2-22-22-22222222-2-2-2-2-2222222-2000000-20000-2000000000000000000-2-200002200
χ352222-2-22-22-2-22-2222-222-2-2-2-2-222-2-2-2000000200002000000000000000000002i−2i−2i2i0000
χ362222-2-22-22-2-22-2222-222-2-2-2-2-222-2-2-200000020000200000000000000000000−2i2i2i−2i0000
χ372222-2-2-12-222-22-1-1-1-22-211-11111-1-1-12-2-22-1-1-111111-1-10000−i3i3i3−i3−i3i3i3−i300000000000000
χ382222-2-2-12-222-22-1-1-1-22-211-11111-1-1-12-2-22-1-1-111111-1-10000i3−i3−i3i3i3−i3−i3i300000000000000
χ392222-2-2-12-222-22-1-1-1-22-211-11111-1-1-1-222-211-1-1-1-1-11110000−i3i3i3−i3i3−i3−i3i300000000000000
χ402222-2-2-12-222-22-1-1-1-22-211-11111-1-1-1-222-211-1-1-1-1-11110000i3−i3−i3i3−i3i3i3−i300000000000000
χ412222-2-2-12-22-2-2-2-1-1-12-2211-1-1-11111-122-2-2-1-11-1-111-1112-22-2-1-111-1-11100000000000000
χ422222-2-2-12-22-2-2-2-1-1-12-2211-1-1-11111-122-2-2-1-11-1-111-111-22-2211-1-111-1-100000000000000
χ432222-2-2-12-22-2-2-2-1-1-12-2211-1-1-11111-1-2-22211111-1-1-1-1-12-2-22-1-11111-1-100000000000000
χ442222-2-2-12-22-2-2-2-1-1-12-2211-1-1-11111-1-2-22211111-1-1-1-1-1-222-211-1-1-1-11100000000000000
χ45444444-2-4-4-44-44-2-2-2-4-44-2-222222-2-2200000020000-20000000000000000000000000000
χ46444444-2-4-4-4-4-4-4-2-2-244-4-2-22-2-222222000000-2000020000000000000000000000000000
χ474444-4-4-2-44-4444-2-2-24-4-4222-2-2-2-2-2-220000002000020000000000000000000000000000
χ484444-4-4-2-44-4-44-4-2-2-2-44422222-2-2222000000-20000-20000000000000000000000000000
χ4944-4-44-444-4-40404-4-40004-44004-400-40000000000000000000000000000000000000000
χ5044-4-44-44-4440-404-4-40004-4-400-440040000000000000000000000000000000000000000
χ5144-4-44-4-24-4-4040-222000-22-200-220020000−2i32i3000−2i32i300000000000000000000000000000
χ5244-4-44-4-24-4-4040-222000-22-200-2200200002i3−2i30002i3−2i300000000000000000000000000000
χ5344-4-44-4-2-4440-40-222000-222002-200-2000000023−2300023−2300000000000000000000000000
χ5444-4-44-4-2-4440-40-222000-222002-200-20000000−2323000−232300000000000000000000000000
χ5544-4-4-44444-40-404-4-4000-44400-4400-40000000000000000000000000000000000000000
χ5644-4-4-444-4-440404-4-4000-44-4004-40040000000000000000000000000000000000000000
χ5744-4-4-44-244-40-40-2220002-2-2002-20020000−2i32i30002i3−2i300000000000000000000000000000
χ5844-4-4-44-244-40-40-2220002-2-2002-200200002i3−2i3000−2i32i300000000000000000000000000000
χ5944-4-4-44-2-4-44040-2220002-2200-2200-2000000023−23000−232300000000000000000000000000
χ6044-4-4-44-2-4-44040-2220002-2200-2200-20000000−232300023−2300000000000000000000000000
χ614-4-4400400040-4-4-4400000000004-40000000000000000000000000002i−2i2i−2i0000000000
χ624-4-4400400040-4-4-4400000000004-4000000000000000000000000000−2i2i−2i2i0000000000
χ634-4-44004000-404-4-440000000000-440000000000000000000000000002-2-220000000000
χ644-4-44004000-404-4-440000000000-44000000000000000000000000000-222-20000000000
χ658-88-8008000000-88-800000000000000000000000000000000000000000000000000000
χ668-88-800-40000004-44000000−4i34i3000000000000000000000000000000000000000000000
χ678-88-800-40000004-440000004i3−4i3000000000000000000000000000000000000000000000
χ688-8-8800-400080-844-40000000000-4400000000000000000000000000000000000000000
χ698-8-8800-4000-80844-400000000004-400000000000000000000000000000000000000000

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