Finite Group Databasebeta

← Group #10691846

Character table — Group #10691846

Order 768.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72
size11112222222222444444444444448888888888888888881212121216161616161616161616242424242424242424244848
order122222344446664444661212121212121212224488881212242424242424242488884466121212121212888888888844
χ1111111111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111111111-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-1-1-1
χ311111111111111111111111111111111-1-1-1-111-1-1-1-1-1-1-1-11111-1-11111-1-1-1-1111111-1-1-1-1-1-1
χ411111111111111111111111111111111-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1111111
χ51111111111111111111111111111-1-1-1-1111111111111111111-1-1-1-1-1-1-1-1-1-111-1-1-1-11111-1-1
χ61111111111111111111111111111-1-1-1-111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-111
χ71111111111111111111111111111-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1111111-1-1-1-1111111-1-1-1-1-1-1-1-111
χ81111111111111111111111111111-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-11111-1-111111111-1-1
χ91111-1-1111-1-11111-11-1-1-11111-1-11111-1-111-1-1-1-11111-1-1-1-1ii−i−i1-111-1-111-1-1i−iii−i−iii−i−ii−i
χ101111-1-1111-1-11111-11-1-1-11111-1-11111-1-111-1-1-1-11111-1-1-1-1−i−iii1-111-1-111-1-1−ii−i−iii−i−iii−ii
χ111111-1-1111-1-11111-11-1-1-11111-1-11111-1-1-1-111-1-1-1-1-1-11111ii−i−i-1111-1-1-1-111i−iii−i−i−i−iii−ii
χ121111-1-1111-1-11111-11-1-1-11111-1-11111-1-1-1-111-1-1-1-1-1-11111−i−iii-1111-1-1-1-111−ii−i−iiiii−i−ii−i
χ131111-1-1111-1-11111-11-1-1-11111-1-111-1-11111-1-1-1-11111-1-1-1-1ii−i−i-11-1-111-1-111i−i−i−iiiii−i−i−ii
χ141111-1-1111-1-11111-11-1-1-11111-1-111-1-11111-1-1-1-11111-1-1-1-1−i−iii-11-1-111-1-111−iiii−i−i−i−iiii−i
χ151111-1-1111-1-11111-11-1-1-11111-1-111-1-111-1-111-1-1-1-1-1-11111ii−i−i1-1-1-11111-1-1i−i−i−iii−i−iiii−i
χ161111-1-1111-1-11111-11-1-1-11111-1-111-1-111-1-111-1-1-1-1-1-11111−i−iii1-1-1-11111-1-1−iiii−i−iii−i−i−ii
χ1722222222222222-2-2-2-222-2-22222-2-200000000-2-20000000022220000000000-2-20000000000
χ1822222222222222-2-2-2-222-2-22222-2-200000000-2-200000000-2-2-2-20000000000220000000000
χ192222222-2-2-2-222222-2-22222-2-2-2-2-2-2000000002-20000000000000000000000002i−2i2i−2i000000
χ202222222-2-2-2-222222-2-22222-2-2-2-2-2-2000000002-2000000000000000000000000−2i2i−2i2i000000
χ212222222-2-2-2-2222-2-22222-2-2-2-2-2-2222-22-20000-22000000000000002-22-20000000000000000
χ222222222-2-2-2-2222-2-22222-2-2-2-2-2-222-22-220000-2200000000000000-22-220000000000000000
χ23222222-12222-1-1-12222-1-1-1-1-1-1-1-1-1-122222222-1-1-1-1-1-1-1-1-1-1000022-1-1-1-1-1-1-1-1000000000000
χ24222222-12222-1-1-12222-1-1-1-1-1-1-1-1-1-12222-2-2-2-2-1-1111111110000-2-2-1-1-1-11111000000000000
χ25222222-12222-1-1-12222-1-1-1-1-1-1-1-1-1-1-2-2-2-22222-1-1-1-1-1-1-1-1-1-10000-2-211111111000000000000
χ26222222-12222-1-1-12222-1-1-1-1-1-1-1-1-1-1-2-2-2-2-2-2-2-2-1-1111111110000221111-1-1-1-1000000000000
χ27222222-1-2-2-2-2-1-1-1-2-222-1-1111111-1-12-22-200001-1−i3−i3i3i3−i3−i3i3i3000000-11-11−i3i3−i3i3000000000000
χ28222222-1-2-2-2-2-1-1-1-2-222-1-1111111-1-12-22-200001-1i3i3−i3−i3i3i3−i3−i3000000-11-11i3−i3i3−i3000000000000
χ29222222-1-2-2-2-2-1-1-1-2-222-1-1111111-1-1-22-2200001-1−i3−i3i3i3−i3−i3i3i30000001-11-1i3−i3i3−i3000000000000
χ30222222-1-2-2-2-2-1-1-1-2-222-1-1111111-1-1-22-2200001-1i3i3−i3−i3i3i3−i3−i30000001-11-1−i3i3−i3i3000000000000
χ312222-2-2222-2-2222-22-22-2-2-2-222-2-2-2-20000000022000000002i2i−2i−2i0000000000−2i2i0000000000
χ322222-2-2222-2-2222-22-22-2-2-2-222-2-2-2-2000000002200000000−2i−2i2i2i00000000002i−2i0000000000
χ332222-2-22-2-2222222-2-22-2-222-2-222-2-200000000-220000000000000000000000002-2-22000000
χ342222-2-22-2-2222222-2-22-2-222-2-222-2-200000000-22000000000000000000000000-222-2000000
χ352222-2-22-2-222222-222-2-2-2-2-2-2-222222-2-2200002-2000000000000002-2-220000000000000000
χ362222-2-22-2-222222-222-2-2-2-2-2-2-22222-222-200002-200000000000000-222-20000000000000000
χ372222-2-2-122-2-2-1-1-12-22-211-1-1-1-111-1-122-2-222-2-211-1-1-1-1111100002-2-1-111-1-111000000000000
χ382222-2-2-122-2-2-1-1-12-22-211-1-1-1-111-1-122-2-2-2-222111111-1-1-1-10000-22-1-11111-1-1000000000000
χ392222-2-2-122-2-2-1-1-12-22-211-1-1-1-111-1-1-2-22222-2-211-1-1-1-111110000-2211-1-111-1-1000000000000
χ402222-2-2-122-2-2-1-1-12-22-211-1-1-1-111-1-1-2-222-2-222111111-1-1-1-100002-211-1-1-1-111000000000000
χ412222-2-2-1-2-222-1-1-1-222-2111111-1-1-1-12-2-220000-11−i3−i3i3i3i3i3−i3−i3000000-111-1−i3i3i3−i3000000000000
χ422222-2-2-1-2-222-1-1-1-222-2111111-1-1-1-12-2-220000-11i3i3−i3−i3−i3−i3i3i3000000-111-1i3−i3−i3i3000000000000
χ432222-2-2-1-2-222-1-1-1-222-2111111-1-1-1-1-222-20000-11−i3−i3i3i3i3i3−i3−i30000001-1-11i3−i3−i3i3000000000000
χ442222-2-2-1-2-222-1-1-1-222-2111111-1-1-1-1-222-20000-11i3i3−i3−i3−i3−i3i3i30000001-1-11−i3i3i3−i3000000000000
χ452-22-22-222-2-22-22-200002-2002-22-2000000−i2i2−i2i200−i2i2−i2i2−i2i2−i2i22-22-20000000000000000−i2i2−i2i200
χ462-22-22-222-2-22-22-200002-2002-22-2000000−i2i2−i2i200−i2i2−i2i2−i2i2−i2i2-22-220000000000000000i2−i2i2−i200
χ472-22-22-222-2-22-22-200002-2002-22-2000000i2−i2i2−i200i2−i2i2−i2i2−i2i2−i22-22-20000000000000000i2−i2i2−i200
χ482-22-22-222-2-22-22-200002-2002-22-2000000i2−i2i2−i200i2−i2i2−i2i2−i2i2−i2-22-220000000000000000−i2i2−i2i200
χ492-22-2-2222-22-2-22-20000-22002-2-22000000−i2i2i2−i200−i2i2−i2i2i2−i2i2−i22i−2i−2i2i00000000000000002−2−2200
χ502-22-2-2222-22-2-22-20000-22002-2-22000000−i2i2i2−i200−i2i2−i2i2i2−i2i2−i2−2i2i2i−2i0000000000000000−222−200
χ512-22-2-2222-22-2-22-20000-22002-2-22000000i2−i2−i2i200i2−i2i2−i2−i2i2−i2i22i−2i−2i2i0000000000000000−222−200
χ522-22-2-2222-22-2-22-20000-22002-2-22000000i2−i2−i2i200i2−i2i2−i2−i2i2−i2i2−2i2i2i−2i00000000000000002−2−2200
χ53444444-24444-2-2-2-4-4-4-4-2-222-2-2-2-22200000000220000000000000000000000000000000000
χ54444444-2-4-4-4-4-2-2-244-4-4-2-2-2-222222200000000-220000000000000000000000000000000000
χ554444-4-4-244-4-4-2-2-2-44-442222-2-2222200000000-2-20000000000000000000000000000000000
χ564444-4-4-2-4-444-2-2-24-4-4422-2-222-2-222000000002-20000000000000000000000000000000000
χ574-44-44-44-444-4-44-400004-400-44-440000000000000000000000000000000000000000000000
χ584-44-44-4-24-4-442-220000-2200-22-22000000−2i22i2−2i22i200i2−i2i2−i2i2−i2i2−i200000000000000000000000000
χ594-44-44-4-24-4-442-220000-2200-22-220000002i2−2i22i2−2i200−i2i2−i2i2−i2i2−i2i200000000000000000000000000
χ604-44-44-4-2-444-42-220000-22002-22-20000000000006−6−666−6−6600000000000000000000000000
χ614-44-44-4-2-444-42-220000-22002-22-2000000000000−666−6−666−600000000000000000000000000
χ624-44-4-444-44-44-44-40000-4400-444-40000000000000000000000000000000000000000000000
χ634-44-4-44-24-44-42-2200002-200-222-2000000−2i22i22i2−2i200i2−i2i2−i2−i2i2−i2i200000000000000000000000000
χ644-44-4-44-24-44-42-2200002-200-222-20000002i2−2i2−2i22i200−i2i2−i2i2i2−i2i2−i200000000000000000000000000
χ654-44-4-44-2-44-442-2200002-2002-2-220000000000006−6−66−666−600000000000000000000000000
χ664-44-4-44-2-44-442-2200002-2002-2-22000000000000−666−66−6−6600000000000000000000000000
χ6788-8-800800008-8-80000000000000000000000000000000000000000000000000000000000
χ6888-8-800-40000-444000000−4i34i300000000000000000000000000000000000000000000000000
χ6988-8-800-40000-4440000004i3−4i300000000000000000000000000000000000000000000000000
χ708-8-880080000-8-880000000000000000000000000000000000000000000000000000000000
χ718-8-8800-4000044-4000000000000−4i34i300000000000000000000000000000000000000000000
χ728-8-8800-4000044-40000000000004i3−4i300000000000000000000000000000000000000000000

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