Finite Group Databasebeta

← Group #10692721

Character table — Group #10692721

Order 768.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60
size111122222244444444444488888888161616161616161616161616161616162424242424242424242424244848
order12222236664444446612121212444412121212448812121212121212122424242422224444888888
χ1111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ3111111111111111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-111111111-1-1-1-1-1-1
χ4111111111111111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1111111
χ51111111111111111111111-1-1-1-1111111-1-11111-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1
χ61111111111111111111111-1-1-1-1111111-1-11111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-111
χ71111111111111111111111-1-1-1-11111-1-111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-111
χ81111111111111111111111-1-1-1-11111-1-111-1-1-1-1-1-1-1-11111-1-1-1-111111111-1-1
χ91111-1-11111-111-11-1-1-1-1-1-1-1ii−i−i111-11-1i−i11-1-1ii−i−iii−i−i11-1-1ii−i−i11-1-1i−i
χ101111-1-11111-111-11-1-1-1-1-1-1-1ii−i−i111-11-1i−i11-1-1ii−i−iii−i−i-1-111−i−iii-1-111−ii
χ111111-1-11111-111-11-1-1-1-1-1-1-1ii−i−i111-1-11−ii-1-111ii−i−i−i−iii11-1-1ii−i−i-1-111−ii
χ121111-1-11111-111-11-1-1-1-1-1-1-1ii−i−i111-1-11−ii-1-111ii−i−i−i−iii-1-111−i−iii11-1-1i−i
χ131111-1-11111-111-11-1-1-1-1-1-1-1−i−iii111-11-1−ii11-1-1−i−iii−i−iii11-1-1−i−iii11-1-1−ii
χ141111-1-11111-111-11-1-1-1-1-1-1-1−i−iii111-11-1−ii11-1-1−i−iii−i−iii-1-111ii−i−i-1-111i−i
χ151111-1-11111-111-11-1-1-1-1-1-1-1−i−iii111-1-11i−i-1-111−i−iiiii−i−i11-1-1−i−iii-1-111i−i
χ161111-1-11111-111-11-1-1-1-1-1-1-1−i−iii111-1-11i−i-1-111−i−iiiii−i−i-1-111ii−i−i11-1-1−ii
χ1722222222222-2-2-22-22222-2-200002-2-2-200000000000000002-22-20000000000
χ1822222222222-2-2-22-22222-2-200002-2-2-20000000000000000-22-220000000000
χ192222222222-22-22-2-222-2-2222-22-2-22-2-2000000002-22-2000000000000000000
χ202222222222-22-22-2-222-2-222-22-22-22-2-200000000-22-22000000000000000000
χ212222222222-2-22-2-2222-2-2-2-20000-2-222000000000000000000002-22-2000000
χ222222222222-2-22-2-2222-2-2-2-20000-2-22200000000000000000000-22-22000000
χ23222222-1-1-1-1222222-1-1-1-1-1-12222-1-1-1-12222-1-1-1-1-1-1-1-1-1-1-1-100000000000000
χ24222222-1-1-1-1222222-1-1-1-1-1-12222-1-1-1-1-2-2-2-21111-1-1-1-1111100000000000000
χ25222222-1-1-1-1222222-1-1-1-1-1-1-2-2-2-2-1-1-1-122-2-2-1-1-1-11111111100000000000000
χ26222222-1-1-1-1222222-1-1-1-1-1-1-2-2-2-2-1-1-1-1-2-22211111111-1-1-1-100000000000000
χ27222222-1-1-1-1-22-22-2-2-1-111-1-12-22-21-1110000−i3i3−i3i3-11-11−i3i3−i3i300000000000000
χ28222222-1-1-1-1-22-22-2-2-1-111-1-12-22-21-1110000i3−i3i3−i3-11-11i3−i3i3−i300000000000000
χ29222222-1-1-1-1-22-22-2-2-1-111-1-1-22-221-1110000−i3i3−i3i31-11-1i3−i3i3−i300000000000000
χ30222222-1-1-1-1-22-22-2-2-1-111-1-1-22-221-1110000i3−i3i3−i31-11-1−i3i3−i3i300000000000000
χ312222-2-2222222-2-2-22-2-222-2-22i−2i−2i2i-22-22000000002i−2i−2i2i000000000000000000
χ322222-2-2222222-2-2-22-2-222-2-2−2i2i2i−2i-22-2200000000−2i2i2i−2i000000000000000000
χ332222-2-222222-222-2-2-2-222220000-2-22-2000000000000000000002i−2i−2i2i000000
χ342222-2-222222-222-2-2-2-222220000-2-22-200000000000000000000−2i2i2i−2i000000
χ352222-2-22222-2-2-2222-2-2-2-22200002-2-2200000000000000002-2-220000000000
χ362222-2-22222-2-2-2222-2-2-2-22200002-2-220000000000000000-222-20000000000
χ372222-2-2-1-1-1-122-2-2-2211-1-1112i−2i−2i2i1-11-10000−i3i3i3−i3−iii−i3−3−3300000000000000
χ382222-2-2-1-1-1-122-2-2-2211-1-1112i−2i−2i2i1-11-10000i3−i3−i3i3−iii−i−333−300000000000000
χ392222-2-2-1-1-1-122-2-2-2211-1-111−2i2i2i−2i1-11-10000−i3i3i3−i3i−i−ii−333−300000000000000
χ402222-2-2-1-1-1-122-2-2-2211-1-111−2i2i2i−2i1-11-10000i3−i3−i3i3i−i−ii3−3−3300000000000000
χ412222-2-2-1-1-1-1-222-22-21111112i2i−2i−2i-1-1-112-22i−2i-1-111−i−iii−i−iii00000000000000
χ422222-2-2-1-1-1-1-222-22-21111112i2i−2i−2i-1-1-11-22−2i2i11-1-1−i−iiiii−i−i00000000000000
χ432222-2-2-1-1-1-1-222-22-2111111−2i−2i2i2i-1-1-112-2−2i2i-1-111ii−i−iii−i−i00000000000000
χ442222-2-2-1-1-1-1-222-22-2111111−2i−2i2i2i-1-1-11-222i−2i11-1-1ii−i−i−i−iii00000000000000
χ45444444-2-2-2-24-4-4-44-4-2-2-2-2220000-2222000000000000000000000000000000
χ46444444-2-2-2-2-4-44-4-44-2-22222000022-2-2000000000000000000000000000000
χ474444-4-4-2-2-2-24-444-4-422-2-2-2-2000022-22000000000000000000000000000000
χ484444-4-4-2-2-2-2-4-4-44442222-2-20000-222-2000000000000000000000000000000
χ4944-4-44-444-4-40000004-40000000000000000000000000000000000002i−2i2i−2i00
χ5044-4-44-444-4-40000004-4000000000000000000000000000000000000−2i2i−2i2i00
χ5144-4-4-4444-4-4000000-440000000000000000000000000000000000002i−2i−2i2i00
χ5244-4-4-4444-4-4000000-44000000000000000000000000000000000000−2i2i2i−2i00
χ5388-8-88-8-4-444000000-44000000000000000000000000000000000000000000
χ5488-8-8-88-4-4440000004-4000000000000000000000000000000000000000000
χ558-88-8008-88-800000000000000000000000000000000000000000000000000
χ568-88-800-44-440000000043−430000000000000000000000000000000000000000
χ578-88-800-44-4400000000−43430000000000000000000000000000000000000000
χ588-8-88008-8-8800000000000000000000000000000000000000000000000000
χ598-8-8800-444-4000000000043−4300000000000000000000000000000000000000
χ608-8-8800-444-40000000000−434300000000000000000000000000000000000000

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