Finite Group Databasebeta

← Group #10692804

Character table — Group #10692804

Order 768.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66
size1111222222222244444444448888888812121212121212121616161616161616161616161616161624242424242424244848
order122222344446664444661212121222441212121244444444668888121224242424242424244444888844
χ1111111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111111111111-1-1-1-111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1
χ311111111111111111111111111111111-1-1-1-1-1-1-1-11111111111111111-1-1-1-1-1-1-1-1-1-1
χ411111111111111111111111111111111-1-1-1-1-1-1-1-111-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1111111
χ5111111111111111111111111-1-1-1-111111111-1-1-1-1-1-111-1-1-1-11111-1-1-1-111-1-11111-1-1
χ6111111111111111111111111-1-1-1-111111111-1-1-1-1-1-1-1-111-1-1-1-1-1-1111111-1-1-1-1-1-111
χ7111111111111111111111111-1-1-1-11111-1-1-1-11111-1-111-1-1-1-11111-1-1-1-1-1-111-1-1-1-111
χ8111111111111111111111111-1-1-1-11111-1-1-1-11111-1-1-1-111-1-1-1-1-1-11111-1-1111111-1-1
χ91111-1-11-1-1-1-1111-1111-1-1-1-1-1-11-11-1111-1ii−i−iii−i−i1-1i−ii−i1-1ii−i−iii−i−ii−ii−i11-1-11-1
χ101111-1-11-1-1-1-1111-1111-1-1-1-1-1-11-11-1111-1ii−i−iii−i−i1-1−ii−ii1-1−i−iii−i−iiii−ii−i-1-111-11
χ111111-1-11-1-1-1-1111-1111-1-1-1-1-1-11-11-1111-1−i−iii−i−iii1-1i−ii−i1-1ii−i−iii−i−i−ii−ii-1-111-11
χ121111-1-11-1-1-1-1111-1111-1-1-1-1-1-11-11-1111-1−i−iii−i−iii1-1−ii−ii1-1−i−iii−i−iii−ii−ii11-1-11-1
χ131111-1-11-1-1-1-1111-1111-1-1-1-1-1-1-11-11111-1ii−i−i−i−iii-11i−i−ii-11ii−i−i−i−iiii−i−ii11-1-1-11
χ141111-1-11-1-1-1-1111-1111-1-1-1-1-1-1-11-11111-1ii−i−i−i−iii-11−iii−i-11−i−iiiii−i−ii−i−ii-1-1111-1
χ151111-1-11-1-1-1-1111-1111-1-1-1-1-1-1-11-11111-1−i−iiiii−i−i-11i−i−ii-11ii−i−i−i−iii−iii−i-1-1111-1
χ161111-1-11-1-1-1-1111-1111-1-1-1-1-1-1-11-11111-1−i−iiiii−i−i-11−iii−i-11−i−iiiii−i−i−iii−i11-1-1-11
χ17222222222-2-2222-22-2-22222-2-200002-2-2-200002222000000000000000000-2-2000000
χ18222222222-2-2222-22-2-22222-2-200002-2-2-20000-2-2-2-200000000000000000022000000
χ192222222-2-222222-2-22-222-2-2220000-22-2-2222200000000000000000000-2-200000000
χ202222222-2-222222-2-22-222-2-2220000-22-2-2-2-2-2-2000000000000000000002200000000
χ212222222-2-2-2-22222-2-2222-2-2-2-222-2-2-2-22200000000220000-2-2000000000000000000
χ222222222-2-2-2-22222-2-2222-2-2-2-2-2-222-2-22200000000-2-2000022000000000000000000
χ23222222-12222-1-1-12222-1-1-1-1-1-12222-1-1-1-100000000-1-12222-1-1-1-1-1-1-1-1-1-10000000000
χ24222222-12222-1-1-12222-1-1-1-1-1-12222-1-1-1-100000000-1-1-2-2-2-2-1-1111111110000000000
χ25222222-12222-1-1-12222-1-1-1-1-1-1-2-2-2-2-1-1-1-1000000001122-2-211-1-1-1-111110000000000
χ26222222-12222-1-1-12222-1-1-1-1-1-1-2-2-2-2-1-1-1-10000000011-2-222111111-1-1-1-10000000000
χ27222222-1-2-2-2-2-1-1-12-2-22-1-1111122-2-211-1-100000000-1-10000113−33−33−33−30000000000
χ28222222-1-2-2-2-2-1-1-12-2-22-1-1111122-2-211-1-100000000-1-1000011−33−33−33−330000000000
χ29222222-1-2-2-2-2-1-1-12-2-22-1-11111-2-22211-1-100000000110000-1-13−33−3−33−330000000000
χ30222222-1-2-2-2-2-1-1-12-2-22-1-11111-2-22211-1-100000000110000-1-1−33−333−33−30000000000
χ312222-2-222222222-2-2-22-2-222222-2-22-2-22-2000000002-20000-22000000000000000000
χ322222-2-222222222-2-2-22-2-22222-222-2-2-22-200000000-2200002-2000000000000000000
χ332222-2-2222-2-22222-22-2-2-222-2-20000-22-222i2i−2i−2i00000000000000000000−2i2i00000000
χ342222-2-2222-2-22222-22-2-2-222-2-20000-22-22−2i−2i2i2i000000000000000000002i−2i00000000
χ352222-2-22-2-22222222-2-2-2-2-2-22200002-2-2200002i2i−2i−2i000000000000000000−2i2i000000
χ362222-2-22-2-22222222-2-2-2-2-2-22200002-2-220000−2i−2i2i2i0000000000000000002i−2i000000
χ372222-2-2-12222-1-1-1-2-2-2211-1-1-1-12-2-2211-1100000000-1100001-1−i3i3i3−i3−i3i3i3−i30000000000
χ382222-2-2-12222-1-1-1-2-2-2211-1-1-1-12-2-2211-1100000000-1100001-1i3−i3−i3i3i3−i3−i3i30000000000
χ392222-2-2-12222-1-1-1-2-2-2211-1-1-1-1-222-211-11000000001-10000-11−i3i3i3−i3i3−i3−i3i30000000000
χ402222-2-2-12222-1-1-1-2-2-2211-1-1-1-1-222-211-11000000001-10000-11i3−i3−i3i3−i3i3i3−i30000000000
χ412222-2-2-1-2-2-2-2-1-1-1-22221111112-22-2-1-1-1100000000-112i−2i2i−2i-11−i−iii−i−iii0000000000
χ422222-2-2-1-2-2-2-2-1-1-1-22221111112-22-2-1-1-1100000000-11−2i2i−2i2i-11ii−i−iii−i−i0000000000
χ432222-2-2-1-2-2-2-2-1-1-1-2222111111-22-22-1-1-11000000001-12i−2i−2i2i1-1−i−iiiii−i−i0000000000
χ442222-2-2-1-2-2-2-2-1-1-1-2222111111-22-22-1-1-11000000001-1−2i2i2i−2i1-1ii−i−i−i−iii0000000000
χ45444444-244-4-4-2-2-2-44-4-4-2-2-2-2220000-22220000000000000000000000000000000000
χ46444444-2-4-444-2-2-2-4-44-4-2-222-2-200002-2220000000000000000000000000000000000
χ474444-4-4-244-4-4-2-2-24-44-422-2-22200002-22-20000000000000000000000000000000000
χ484444-4-4-2-4-444-2-2-244-4-42222-2-20000-222-20000000000000000000000000000000000
χ4944-4-44-440000-4-4400004-400000000000000000000000000000000000000002i−2i2i−2i00
χ5044-4-44-440000-4-4400004-40000000000000000000000000000000000000000−2i2i−2i2i00
χ5144-4-4-4440000-4-440000-4400000000000000000000000000000000000000002i−2i−2i2i00
χ5244-4-4-4440000-4-440000-440000000000000000000000000000000000000000−2i2i2i−2i00
χ534-44-4004004i−4i4-4-4000000004i−4i000000002+2i−2−2i2−2i−2+2i000000000000000000000000000000
χ544-44-4004004i−4i4-4-4000000004i−4i00000000−2−2i2+2i−2+2i2−2i000000000000000000000000000000
χ554-44-400400−4i4i4-4-400000000−4i4i000000002−2i−2+2i2+2i−2−2i000000000000000000000000000000
χ564-44-400400−4i4i4-4-400000000−4i4i00000000−2+2i2−2i−2−2i2+2i000000000000000000000000000000
χ574-4-440044i−4i00-44-40000004i−4i000000000000002+2i−2−2i2−2i−2+2i00000000000000000000000000
χ584-4-440044i−4i00-44-40000004i−4i00000000000000−2−2i2+2i−2+2i2−2i00000000000000000000000000
χ594-4-44004−4i4i00-44-4000000−4i4i000000000000002−2i−2+2i2+2i−2−2i00000000000000000000000000
χ604-4-44004−4i4i00-44-4000000−4i4i00000000000000−2+2i2−2i−2−2i2+2i00000000000000000000000000
χ6188-8-88-8-4000044-40000-440000000000000000000000000000000000000000000000
χ6288-8-8-88-4000044-400004-40000000000000000000000000000000000000000000000
χ638-88-800-4008i−8i-44400000000−4i4i000000000000000000000000000000000000000000
χ648-88-800-400−8i8i-444000000004i−4i000000000000000000000000000000000000000000
χ658-8-8800-48i−8i004-44000000−4i4i00000000000000000000000000000000000000000000
χ668-8-8800-4−8i8i004-440000004i−4i00000000000000000000000000000000000000000000

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