Finite Group Databasebeta

← Group #10692471

Character table — Group #10692471

Order 768.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63
size11112222222244444444444888888881212121216161616161616161616161616161616242424242424242424244848
order12222234466644444661212121244441212121244444488121212121212121224242424224444888888
χ1111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-1111111-1-1-1-1-1-1
χ31111111111111111111111111111111-1-1-1-11111111111111111-1-1-1-1-1-1-1-1-1-1-1-1
χ41111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1111111
χ511111111111111111111111-1-1-1-11111111111-1-11111-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1
χ611111111111111111111111-1-1-1-111111111-1-111-1-1-1-1-1-1-1-11111-1-1-1-111-1-1-1-111
χ711111111111111111111111-1-1-1-11111-1-1-1-111-1-11111-1-1-1-1-1-1-1-11111-1-1-1-1-1-111
χ811111111111111111111111-1-1-1-11111-1-1-1-1-1-111-1-1-1-1-1-1-1-111111111-1-11111-1-1
χ91111-1-11-1-111111-1-11-1-1-1-1-1-1i−ii−i111-1ii−i−i1-1i−i11-1-1ii−i−iii−i−i1-11-1i−iii−i−i1-1
χ101111-1-11-1-111111-1-11-1-1-1-1-1-1i−ii−i111-1ii−i−i-11−ii-1-111ii−i−i−i−iii1-11-1i−i−i−iii-11
χ111111-1-11-1-111111-1-11-1-1-1-1-1-1i−ii−i111-1−i−iii1-1i−i11-1-1ii−i−iii−i−i-11-11−ii−i−iii-11
χ121111-1-11-1-111111-1-11-1-1-1-1-1-1i−ii−i111-1−i−iii-11−ii-1-111ii−i−i−i−iii-11-11−iiii−i−i1-1
χ131111-1-11-1-111111-1-11-1-1-1-1-1-1−ii−ii111-1ii−i−i1-1−ii11-1-1−i−iii−i−iii-11-11i−iii−i−i-11
χ141111-1-11-1-111111-1-11-1-1-1-1-1-1−ii−ii111-1ii−i−i-11i−i-1-111−i−iiiii−i−i-11-11i−i−i−iii1-1
χ151111-1-11-1-111111-1-11-1-1-1-1-1-1−ii−ii111-1−i−iii1-1−ii11-1-1−i−iii−i−iii1-11-1−ii−i−iii1-1
χ161111-1-11-1-111111-1-11-1-1-1-1-1-1−ii−ii111-1−i−iii-11i−i-1-111−i−iiiii−i−i1-11-1−iiii−i−i-11
χ172222222222222-2-2-2-22222-2-200002-2-2-2222200000000000000000000-2-2000000
χ182222222222222-2-2-2-22222-2-200002-2-2-2-2-2-2-20000000000000000000022000000
χ192222222-2-2222-22-22-222-2-22222-2-2-22-2-20000000000002-22-20000000000000000
χ202222222-2-2222-22-22-222-2-222-2-222-22-2-2000000000000-22-220000000000000000
χ212222222-2-2222-2-22-2222-2-2-2-20000-2-2220000000000000000000022-2-200000000
χ222222222-2-2222-2-22-2222-2-2-2-20000-2-22200000000000000000000-2-22200000000
χ23222222-122-1-1-122222-1-1-1-1-1-12222-1-1-1-100002222-1-1-1-1-1-1-1-1-1-1-1-1000000000000
χ24222222-122-1-1-122222-1-1-1-1-1-12222-1-1-1-10000-2-2-2-21111-1-1-1-11111000000000000
χ25222222-122-1-1-122222-1-1-1-1-1-1-2-2-2-2-1-1-1-1000022-2-2-1-1-1-111111111000000000000
χ26222222-122-1-1-122222-1-1-1-1-1-1-2-2-2-2-1-1-1-10000-2-22211111111-1-1-1-1000000000000
χ27222222-1-2-2-1-1-1-22-22-2-1-111-1-122-2-21-11100000000−i3i3−i3i3-11-11−i3i3−i3i3000000000000
χ28222222-1-2-2-1-1-1-22-22-2-1-111-1-122-2-21-11100000000i3−i3i3−i3-11-11i3−i3i3−i3000000000000
χ29222222-1-2-2-1-1-1-22-22-2-1-111-1-1-2-2221-11100000000−i3i3−i3i31-11-1i3−i3i3−i3000000000000
χ30222222-1-2-2-1-1-1-22-22-2-1-111-1-1-2-2221-11100000000i3−i3i3−i31-11-1−i3i3−i3i3000000000000
χ312222-2-2222222-222-2-2-2-222-2-22i−2i−2i2i-22-220000000000002i−2i−2i2i0000000000000000
χ322222-2-2222222-222-2-2-2-222-2-2−2i2i2i−2i-22-22000000000000−2i2i2i−2i0000000000000000
χ332222-2-2222222-2-2-222-2-222220000-2-22-2000000000000000000002-2-2200000000
χ342222-2-2222222-2-2-222-2-222220000-2-22-200000000000000000000-222-200000000
χ352222-2-22-2-22222-222-2-2-2-2-22200002-2-222i2i−2i−2i00000000000000000000−2i2i000000
χ362222-2-22-2-22222-222-2-2-2-2-22200002-2-22−2i−2i2i2i000000000000000000002i−2i000000
χ372222-2-2-122-1-1-1-222-2-211-1-1112i−2i−2i2i1-11-100000000−i3i3i3−i3−iii−i3−3−33000000000000
χ382222-2-2-122-1-1-1-222-2-211-1-1112i−2i−2i2i1-11-100000000i3−i3−i3i3−iii−i−333−3000000000000
χ392222-2-2-122-1-1-1-222-2-211-1-111−2i2i2i−2i1-11-100000000−i3i3i3−i3i−i−ii−333−3000000000000
χ402222-2-2-122-1-1-1-222-2-211-1-111−2i2i2i−2i1-11-100000000i3−i3−i3i3i−i−ii3−3−33000000000000
χ412222-2-2-1-2-2-1-1-122-2-221111112i−2i2i−2i-1-1-1100002-22i−2i-1-111−i−iii−i−iii000000000000
χ422222-2-2-1-2-2-1-1-122-2-221111112i−2i2i−2i-1-1-110000-22−2i2i11-1-1−i−iiiii−i−i000000000000
χ432222-2-2-1-2-2-1-1-122-2-22111111−2i2i−2i2i-1-1-1100002-2−2i2i-1-111ii−i−iii−i−i000000000000
χ442222-2-2-1-2-2-1-1-122-2-22111111−2i2i−2i2i-1-1-110000-222i−2i11-1-1ii−i−i−i−iii000000000000
χ45444444-244-2-2-24-4-4-4-4-2-2-2-2220000-222200000000000000000000000000000000
χ46444444-2-4-4-2-2-2-4-44-44-2-22222000022-2-200000000000000000000000000000000
χ474444-4-4-244-2-2-2-4-4-44422-2-2-2-2000022-2200000000000000000000000000000000
χ484444-4-4-2-4-4-2-2-24-444-42222-2-20000-222-200000000000000000000000000000000
χ4944-4-44-44004-4-4000004-4000000000000000000000000000000000000002-22-200
χ5044-4-44-44004-4-4000004-400000000000000000000000000000000000000-22-2200
χ5144-4-4-444004-4-400000-44000000000000000000000000000000000000002i−2i−2i2i00
χ5244-4-4-444004-4-400000-4400000000000000000000000000000000000000−2i2i2i−2i00
χ534-44-40044i−4i-44-400000004i−4i00000000002+2i−2−2i2−2i−2+2i0000000000000000000000000000
χ544-44-40044i−4i-44-400000004i−4i0000000000−2−2i2+2i−2+2i2−2i0000000000000000000000000000
χ554-44-4004−4i4i-44-40000000−4i4i00000000002−2i−2+2i2+2i−2−2i0000000000000000000000000000
χ564-44-4004−4i4i-44-40000000−4i4i0000000000−2+2i2−2i−2−2i2+2i0000000000000000000000000000
χ5788-8-88-8-400-44400000-4400000000000000000000000000000000000000000000
χ5888-8-8-88-400-444000004-400000000000000000000000000000000000000000000
χ598-88-800-48i−8i4-440000000−4i4i000000000000000000000000000000000000000000
χ608-88-800-4−8i8i4-4400000004i−4i000000000000000000000000000000000000000000
χ618-8-8800800-8-88000000000000000000000000000000000000000000000000000
χ628-8-8800-40044-400000000043−430000000000000000000000000000000000000000
χ638-8-8800-40044-4000000000−43430000000000000000000000000000000000000000

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