Finite Group Databasebeta

← Group #10692898

Character table — Group #10692898

Order 768.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63
size11112222222244444444444888888881212121216161616161616161616161616161616242424242424242424244848
order1222223446664444466121212128888121212124444226666882424242424242424444444888888
χ1111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-111-1-1-1-11111-1-1
χ31111111111111111111111111111111-1-1-1-11111111111111111-1-1-1-1-1-1-1-1-1-1-1-1
χ41111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-11111-1-1-1-111
χ511111111111111111111111-1-1-1-111111111111111-1-1-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1
χ611111111111111111111111-1-1-1-111111111-1-1-1-1-1-111-1-1-1-1111111-1-1-1-1-1-1-1-111
χ711111111111111111111111-1-1-1-11111-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111
χ811111111111111111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-111-1-1-1-11111-1-111111111-1-1
χ91111111-1-1111-111-1-111-1-1-1-1ii−i−i11-1-111-1-11-111-1-1i−iii−i−iii−i−i1-111-1-1ii−i−ii−i
χ101111111-1-1111-111-1-111-1-1-1-1ii−i−i11-1-111-1-1-11-1-111−iiii−i−i−i−iii1-1-1-111ii−i−i−ii
χ111111111-1-1111-111-1-111-1-1-1-1ii−i−i11-1-1-1-1111-111-1-1i−iii−i−iii−i−i-11-1-111−i−iii−ii
χ121111111-1-1111-111-1-111-1-1-1-1ii−i−i11-1-1-1-111-11-1-111−iiii−i−i−i−iii-1111-1-1−i−iiii−i
χ131111111-1-1111-111-1-111-1-1-1-1−i−iii11-1-111-1-11-111-1-1−ii−i−iii−i−iii1-111-1-1−i−iii−ii
χ141111111-1-1111-111-1-111-1-1-1-1−i−iii11-1-111-1-1-11-1-111i−i−i−iiiii−i−i1-1-1-111−i−iiii−i
χ151111111-1-1111-111-1-111-1-1-1-1−i−iii11-1-1-1-1111-111-1-1−ii−i−iii−i−iii-11-1-111ii−i−ii−i
χ161111111-1-1111-111-1-111-1-1-1-1−i−iii11-1-1-1-111-11-1-111i−i−i−iiiii−i−i-1111-1-1ii−i−i−ii
χ172222222222222-2-2-2-22222-2-20000-2-22-222220000000000000000-2-20000000000
χ182222222222222-2-2-2-22222-2-20000-2-22-2-2-2-2-20000000000000000220000000000
χ192222222-2-2222-2-2-22222-2-2220000-2-2-2222-2-20000000000000000-220000000000
χ202222222-2-2222-2-2-22222-2-2220000-2-2-22-2-22200000000000000002-20000000000
χ21222222-122-1-1-122222-1-1-1-1-1-12222-1-1-1-1000022-1-1-1-122-1-1-1-1-1-1-1-1000000000000
χ22222222-122-1-1-122222-1-1-1-1-1-12222-1-1-1-10000-2-21111-2-2-1-1-1-11111000000000000
χ23222222-122-1-1-122222-1-1-1-1-1-1-2-2-2-2-1-1-1-1000022-1-1-1-1-2-211111111000000000000
χ24222222-122-1-1-122222-1-1-1-1-1-1-2-2-2-2-1-1-1-10000-2-21111221111-1-1-1-1000000000000
χ25222222-1-2-2-1-1-1-222-2-2-1-111112i2i−2i−2i-1-11100002-2-1-1112i−2i−i−iii−i−iii000000000000
χ26222222-1-2-2-1-1-1-222-2-2-1-111112i2i−2i−2i-1-1110000-2211-1-1−2i2i−i−iiiii−i−i000000000000
χ27222222-1-2-2-1-1-1-222-2-2-1-11111−2i−2i2i2i-1-11100002-2-1-111−2i2iii−i−iii−i−i000000000000
χ28222222-1-2-2-1-1-1-222-2-2-1-11111−2i−2i2i2i-1-1110000-2211-1-12i−2iii−i−i−i−iii000000000000
χ292222-2-2222222-22-22-2-2-222222-22-22-2-2-20000000000002-22-20000000000000000
χ302222-2-2222222-22-22-2-2-22222-22-222-2-2-2000000000000-22-220000000000000000
χ312222-2-2222222-2-22-22-2-222-2-20000-22-22000000000000000000000000002-22-200
χ322222-2-2222222-2-22-22-2-222-2-20000-22-2200000000000000000000000000-22-2200
χ332222-2-22-2-222222-2-22-2-2-2-2-2-22i−2i−2i2i2-2220000000000002i−2i−2i2i0000000000000000
χ342222-2-22-2-222222-2-22-2-2-2-2-2-2−2i2i2i−2i2-222000000000000−2i2i2i−2i0000000000000000
χ352222-2-22-2-22222-222-2-2-2-2-2220000-222-2000000000000000000000000002i−2i−2i2i00
χ362222-2-22-2-22222-222-2-2-2-2-2220000-222-200000000000000000000000000−2i2i2i−2i00
χ372222-2-2-122-1-1-1-22-22-211-1-1-1-12-22-2-1111000000−i3i3−i3i300-11-11−i3i3−i3i3000000000000
χ382222-2-2-122-1-1-1-22-22-211-1-1-1-12-22-2-1111000000i3−i3i3−i300-11-11i3−i3i3−i3000000000000
χ392222-2-2-122-1-1-1-22-22-211-1-1-1-1-22-22-1111000000−i3i3−i3i3001-11-1i3−i3i3−i3000000000000
χ402222-2-2-122-1-1-1-22-22-211-1-1-1-1-22-22-1111000000i3−i3i3−i3001-11-1−i3i3−i3i3000000000000
χ412222-2-2-1-2-2-1-1-122-2-221111112i−2i−2i2i-11-1-1000000−i3i3i3−i300−iii−i3−3−33000000000000
χ422222-2-2-1-2-2-1-1-122-2-221111112i−2i−2i2i-11-1-1000000i3−i3−i3i300−iii−i−333−3000000000000
χ432222-2-2-1-2-2-1-1-122-2-22111111−2i2i2i−2i-11-1-1000000−i3i3i3−i300i−i−ii−333−3000000000000
χ442222-2-2-1-2-2-1-1-122-2-22111111−2i2i2i−2i-11-1-1000000i3−i3−i3i300i−i−ii3−3−33000000000000
χ45444444-244-2-2-24-4-4-4-4-2-2-2-222000022-2200000000000000000000000000000000
χ46444444-2-4-4-2-2-2-4-4-444-2-222-2-20000222-200000000000000000000000000000000
χ474444-4-4-244-2-2-2-4-44-4422-2-22200002-22-200000000000000000000000000000000
χ484444-4-4-2-4-4-2-2-24-444-42222-2-200002-2-2200000000000000000000000000000000
χ4944-4-40044-44-4-400000004-4000000000000000000000000000000002i−2i2i−2i000000
χ5044-4-40044-44-4-400000004-400000000000000000000000000000000−2i2i−2i2i000000
χ5144-4-4004-444-4-40000000-44000000000000000000000000000000002i−2i−2i2i000000
χ5244-4-4004-444-4-40000000-4400000000000000000000000000000000−2i2i2i−2i000000
χ534-44-44-4400-44-4000004-4000000000000004i−4i0000000000000000000000000000
χ544-44-44-4400-44-4000004-400000000000000−4i4i0000000000000000000000000000
χ554-44-4-44400-44-400000-440000000000004-4000000000000000000000000000000
χ564-44-4-44400-44-400000-44000000000000-44000000000000000000000000000000
χ5788-8-800-48-8-4440000000-44000000000000000000000000000000000000000000
χ5888-8-800-4-88-44400000004-4000000000000000000000000000000000000000000
χ598-88-88-8-4004-4400000-4400000000000000000000000000000000000000000000
χ608-88-8-88-4004-44000004-400000000000000000000000000000000000000000000
χ618-8-8800800-8-88000000000000000000000000000000000000000000000000000
χ628-8-8800-40044-4000000000−4i34i30000000000000000000000000000000000000000
χ638-8-8800-40044-40000000004i3−4i30000000000000000000000000000000000000000

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