Finite Group Databasebeta

← Group #10692817

Character table — Group #10692817

Order 768.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72
size11112222222222444444444444448888888888888888881212121212121212161616161616161616162424242448484848
order1222223444466644446612121212121212122244888812122424242424242424444444442466661212121244448888
χ1111111111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-1
χ311111111111111111111111111111111-1-1-1-111-1-1-1-1-1-1-1-111111111-1-111-1-111-1-11111-1-1-1-1
χ411111111111111111111111111111111-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-111-1-1-1-1-1-11111
χ51111111111111111111111111111-1-1-1-1111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-111-1-1
χ61111111111111111111111111111-1-1-1-111111111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-111-1-111
χ71111111111111111111111111111-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-11111-1-1-1-111-1-111-1-11111-1-1-1-111
χ81111111111111111111111111111-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1111111-1-111-1-111-1-11111-1-1
χ91111-1-11-1-1-1-111111-11-1-1-1-1-1-1-1-1111-11-111-1-1111111-1-1-1-1ii−i−iii−i−i1-11-1111-1-1-1i−ii−ii−ii−i
χ101111-1-11-1-1-1-111111-11-1-1-1-1-1-1-1-1111-11-111-1-1111111-1-1-1-1−i−iii−i−iii1-11-1111-1-1-1−ii−ii−ii−ii
χ111111-1-11-1-1-1-111111-11-1-1-1-1-1-1-1-1111-11-1-1-11111-1-1-1-11111ii−i−iii−i−i-111-1-1-11-111i−ii−i−ii−ii
χ121111-1-11-1-1-1-111111-11-1-1-1-1-1-1-1-1111-11-1-1-11111-1-1-1-11111−i−iii−i−iii-111-1-1-11-111−ii−iii−ii−i
χ131111-1-11-1-1-1-111111-11-1-1-1-1-1-1-1-111-11-1111-1-1111111-1-1-1-1ii−i−i−i−iii-11-11-1-1-1111i−i−iii−i−ii
χ141111-1-11-1-1-1-111111-11-1-1-1-1-1-1-1-111-11-1111-1-1111111-1-1-1-1−i−iiiii−i−i-11-11-1-1-1111−iii−i−iii−i
χ151111-1-11-1-1-1-111111-11-1-1-1-1-1-1-1-111-11-11-1-11111-1-1-1-11111ii−i−i−i−iii1-1-1111-11-1-1i−i−ii−iii−i
χ161111-1-11-1-1-1-111111-11-1-1-1-1-1-1-1-111-11-11-1-11111-1-1-1-11111−i−iiiii−i−i1-1-1111-11-1-1−iii−ii−i−ii
χ17222222222-2-22222-2-2-22222-2-2-2-2-2-2000000002-20000000000002222000000000000-2-20000
χ18222222222-2-22222-2-2-22222-2-2-2-2-2-2000000002-2000000000000-2-2-2-2000000000000220000
χ192222222-2-222222-22-2-222-2-222-2-2-2-200000000-2200000000222200000000000000-2-2000000
χ202222222-2-222222-22-2-222-2-222-2-2-2-200000000-2200000000-2-2-2-20000000000000022000000
χ212222222-2-2-2-2222-2-22222-2-2-2-2222222-2-20000-2-20000000000000000002200-2-20000000000
χ222222222-2-2-2-2222-2-22222-2-2-2-22222-2-2220000-2-2000000000000000000-2-200220000000000
χ23222222-12222-1-1-12222-1-1-1-1-1-1-1-1-1-122222222-1-1-1-1-1-1-1-1-1-10000000022-1-1-1-1-1-1-1-100000000
χ24222222-12222-1-1-12222-1-1-1-1-1-1-1-1-1-12222-2-2-2-2-1-11111111100000000-2-2-1-111-1-11100000000
χ25222222-12222-1-1-12222-1-1-1-1-1-1-1-1-1-1-2-2-2-22222-1-1-1-1-1-1-1-1-1-100000000-2-21111111100000000
χ26222222-12222-1-1-12222-1-1-1-1-1-1-1-1-1-1-2-2-2-2-2-2-2-2-1-111111111000000002211-1-111-1-100000000
χ27222222-1-2-2-2-2-1-1-1-2-222-1-11111-1-1-1-122-2-2000011−i3−i3i3i3−i3−i3i3i30000000000-1-1−i3i311−i3i300000000
χ28222222-1-2-2-2-2-1-1-1-2-222-1-11111-1-1-1-122-2-2000011i3i3−i3−i3i3i3−i3−i30000000000-1-1i3−i311i3−i300000000
χ29222222-1-2-2-2-2-1-1-1-2-222-1-11111-1-1-1-1-2-222000011−i3−i3i3i3−i3−i3i3i3000000000011i3−i3-1-1i3−i300000000
χ30222222-1-2-2-2-2-1-1-1-2-222-1-11111-1-1-1-1-2-222000011i3i3−i3−i3i3i3−i3−i3000000000011−i3i3-1-1−i3i300000000
χ312222-2-222222222-2-2-22-2-22222-2-2222-2-220000-2-20000000000000000002-200-220000000000
χ322222-2-222222222-2-2-22-2-22222-2-222-222-20000-2-2000000000000000000-22002-20000000000
χ332222-2-2222-2-2222-222-2-2-222-2-222-2-200000000-22000000002i2i−2i−2i00000000000000−2i2i000000
χ342222-2-2222-2-2222-222-2-2-222-2-222-2-200000000-2200000000−2i−2i2i2i000000000000002i−2i000000
χ352222-2-22-2-2222222-22-2-2-2-2-22222-2-2000000002-20000000000002i2i−2i−2i000000000000−2i2i0000
χ362222-2-22-2-2222222-22-2-2-2-2-22222-2-2000000002-2000000000000−2i−2i2i2i0000000000002i−2i0000
χ372222-2-2-12222-1-1-1-2-2-2211-1-1-1-111-1-12-2-22000011−i3−i3i3i3i3i3−i3−i30000000000-11−i3i31-1i3−i300000000
χ382222-2-2-12222-1-1-1-2-2-2211-1-1-1-111-1-12-2-22000011i3i3−i3−i3−i3−i3i3i30000000000-11i3−i31-1−i3i300000000
χ392222-2-2-12222-1-1-1-2-2-2211-1-1-1-111-1-1-222-2000011−i3−i3i3i3i3i3−i3−i300000000001-1i3−i3-11−i3i300000000
χ402222-2-2-12222-1-1-1-2-2-2211-1-1-1-111-1-1-222-2000011i3i3−i3−i3−i3−i3i3i300000000001-1−i3i3-11i3−i300000000
χ412222-2-2-1-2-2-2-2-1-1-122-2211111111-1-12-22-222-2-2-1-1-1-1-1-11111000000002-2-11-1-1-111100000000
χ422222-2-2-1-2-2-2-2-1-1-122-2211111111-1-12-22-2-2-222-1-11111-1-1-1-100000000-22-1111-11-1-100000000
χ432222-2-2-1-2-2-2-2-1-1-122-2211111111-1-1-22-2222-2-2-1-1-1-1-1-1111100000000-221-1111-1-1-100000000
χ442222-2-2-1-2-2-2-2-1-1-122-2211111111-1-1-22-22-2-222-1-11111-1-1-1-1000000002-21-1-1-11-11100000000
χ45444444-244-4-4-2-2-24-4-4-4-2-2-2-222222200000000-220000000000000000000000000000000000
χ46444444-2-4-444-2-2-2-44-4-4-2-222-2-22222000000002-20000000000000000000000000000000000
χ474444-4-4-244-4-4-2-2-2-444-422-2-222-2-222000000002-20000000000000000000000000000000000
χ484444-4-4-2-4-444-2-2-24-44-42222-2-2-2-22200000000-220000000000000000000000000000000000
χ4944-4-4004004i−4i4-4-4000000004i−4i00000000000000000000002+2i−2−2i2−2i−2+2i0000000000000000000000
χ5044-4-4004004i−4i4-4-4000000004i−4i0000000000000000000000−2−2i2+2i−2+2i2−2i0000000000000000000000
χ5144-4-400400−4i4i4-4-400000000−4i4i00000000000000000000002−2i−2+2i2+2i−2−2i0000000000000000000000
χ5244-4-400400−4i4i4-4-400000000−4i4i0000000000000000000000−2+2i2−2i−2−2i2+2i0000000000000000000000
χ534-44-40044i−4i00-44-40000004i−4i00000000000000000000000000002+2i−2−2i2−2i−2+2i000000000000000000
χ544-44-40044i−4i00-44-40000004i−4i0000000000000000000000000000−2−2i2+2i−2+2i2−2i000000000000000000
χ554-44-4004−4i4i00-44-4000000−4i4i00000000000000000000000000002−2i−2+2i2+2i−2−2i000000000000000000
χ564-44-4004−4i4i00-44-4000000−4i4i0000000000000000000000000000−2+2i2−2i−2−2i2+2i000000000000000000
χ574-4-444-440000-4-4400004-40000000000002-22-2002-22-22-22-200000000000000000000000000
χ584-4-444-440000-4-4400004-4000000000000-22-2200-22-22-22-2200000000000000000000000000
χ594-4-444-4-2000022-20000-220000−2i32i3−2i32i300002-22-200−1−i31+i3−1+i31−i3−1−i31+i3−1+i31−i300000000000000000000000000
χ604-4-444-4-2000022-20000-220000−2i32i3−2i32i30000-22-22001+i3−1−i31−i3−1+i31+i3−1−i31−i3−1+i300000000000000000000000000
χ614-4-444-4-2000022-20000-2200002i3−2i32i3−2i300002-22-200−1+i31−i3−1−i31+i3−1+i31−i3−1−i31+i300000000000000000000000000
χ624-4-444-4-2000022-20000-2200002i3−2i32i3−2i30000-22-22001−i3−1+i31+i3−1−i31−i3−1+i31+i3−1−i300000000000000000000000000
χ634-4-44-4440000-4-440000-440000000000002-2-22002-22-2-22-2200000000000000000000000000
χ644-4-44-4440000-4-440000-44000000000000-222-200-22-222-22-200000000000000000000000000
χ654-4-44-44-2000022-200002-20000−2i32i32i3−2i300002-2-2200−1+i31−i3−1−i31+i31−i3−1+i31+i3−1−i300000000000000000000000000
χ664-4-44-44-2000022-200002-20000−2i32i32i3−2i30000-222-2001−i3−1+i31+i3−1−i3−1+i31−i3−1−i31+i300000000000000000000000000
χ674-4-44-44-2000022-200002-200002i3−2i3−2i32i300002-2-2200−1−i31+i3−1+i31−i31+i3−1−i31−i3−1+i300000000000000000000000000
χ684-4-44-44-2000022-200002-200002i3−2i3−2i32i30000-222-2001+i3−1−i31−i3−1+i3−1−i31+i3−1+i31−i300000000000000000000000000
χ6988-8-800-4008i−8i-44400000000−4i4i000000000000000000000000000000000000000000000000
χ7088-8-800-400−8i8i-444000000004i−4i000000000000000000000000000000000000000000000000
χ718-88-800-48i−8i004-44000000−4i4i00000000000000000000000000000000000000000000000000
χ728-88-800-4−8i8i004-440000004i−4i00000000000000000000000000000000000000000000000000

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