Finite Group Databasebeta

← Group #10692763

Character table — Group #10692763

Order 768.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66
size1111222222222244444444448888888812121212121212121616161616161616161616161616161624242424242424244848
order1222223444466644446612121212244412121212888888884468812121212121212242424248888888824
χ1111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111-1-11-1-1111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1
χ311111111111111111111111111111111-1-1-1-1-1-1-1-11111111111111111-1-1-1-1-1-1-1-1-1-1
χ411111111111111111111111111111111-1-1-1-1-1-1-1-1-1-11-1-1111-1-1-1-1-1-1-1-1-1-1-1-1111111
χ5111111111111111111111111-1-1-1-111111111-1-1-1-111-1-1-1-1-1-11111-1-1-1-111-1-11111-1-1
χ6111111111111111111111111-1-1-1-111111111-1-1-1-1-1-1-111-1-1-1-1-1-1-1111111-1-1-1-1-1-111
χ7111111111111111111111111-1-1-1-11111-1-1-1-1111111-1-1-1-1-1-11111-1-1-1-1-1-111-1-1-1-111
χ8111111111111111111111111-1-1-1-11111-1-1-1-11111-1-1-111-1-1-1-1-1-1-11111-1-1111111-1-1
χ91111-1-11-1-1-1-111111-11-1-1-1-1-1-111-1-1111-1ii−i−iii−i−ii−i1i−i1-1-1ii−i−iii−i−ii−ii−i11-1-11-1
χ101111-1-11-1-1-1-111111-11-1-1-1-1-1-111-1-1111-1ii−i−iii−i−i−ii1−ii1-1-1−i−iii−i−iiii−ii−i-1-111-11
χ111111-1-11-1-1-1-111111-11-1-1-1-1-1-111-1-1111-1−i−iii−i−iiii−i1i−i1-1-1ii−i−iii−i−i−ii−ii-1-111-11
χ121111-1-11-1-1-1-111111-11-1-1-1-1-1-111-1-1111-1−i−iii−i−iii−ii1−ii1-1-1−i−iii−i−iii−ii−ii11-1-11-1
χ131111-1-11-1-1-1-111111-11-1-1-1-1-1-1-1-111111-1ii−i−i−i−iiii−i-1−ii-111ii−i−i−i−iiii−i−ii11-1-1-11
χ141111-1-11-1-1-1-111111-11-1-1-1-1-1-1-1-111111-1ii−i−i−i−iii−ii-1i−i-111−i−iiiii−i−ii−i−ii-1-1111-1
χ151111-1-11-1-1-1-111111-11-1-1-1-1-1-1-1-111111-1−i−iiiii−i−ii−i-1−ii-111ii−i−i−i−iii−iii−i-1-1111-1
χ161111-1-11-1-1-1-111111-11-1-1-1-1-1-1-1-111111-1−i−iiiii−i−i−ii-1i−i-111−i−iiiii−i−i−iii−i11-1-1-11
χ17222222222-2-2222-2-2-2222-2-2222-2-222-2-2-20000000000200-22-2000000000000000000
χ18222222222-2-2222-2-2-2222-2-222-222-22-2-2-20000000000-2002-22000000000000000000
χ192222222-2-2222222-2-2-22222-2-20000-22-2-200002222000000000000000000-2-2000000
χ202222222-2-2222222-2-2-22222-2-20000-22-2-20000-2-2-2-200000000000000000022000000
χ212222222-2-2-2-2222-222-222-2-2-2-20000-2-2222i2i−2i−2i00000000000000000000−2i2i00000000
χ222222222-2-2-2-2222-222-222-2-2-2-20000-2-222−2i−2i2i2i000000000000000000002i−2i00000000
χ23222222-12222-1-1-12222-1-1-1-1-1-12222-1-1-1-10000000022-122-1-1-1-1-1-1-1-1-1-1-10000000000
χ24222222-12222-1-1-12222-1-1-1-1-1-12222-1-1-1-100000000-2-2-1-2-2-1-1-1111111110000000000
χ25222222-12222-1-1-12222-1-1-1-1-1-1-2-2-2-2-1-1-1-100000000221-2-2111-1-1-1-111110000000000
χ26222222-12222-1-1-12222-1-1-1-1-1-1-2-2-2-2-1-1-1-100000000-2-21221111111-1-1-1-10000000000
χ27222222-122-2-2-1-1-1-2-2-22-1-111-1-12-2-22-11110000000000-1001-11−i3i3−i3i3−i3i3−i3i30000000000
χ28222222-122-2-2-1-1-1-2-2-22-1-111-1-12-2-22-11110000000000-1001-11i3−i3i3−i3i3−i3i3−i30000000000
χ29222222-122-2-2-1-1-1-2-2-22-1-111-1-1-222-2-11110000000000100-11-1−i3i3−i3i3i3−i3i3−i30000000000
χ30222222-122-2-2-1-1-1-2-2-22-1-111-1-1-222-2-11110000000000100-11-1i3−i3i3−i3−i3i3−i3i30000000000
χ312222-2-222222222-22-2-2-2-222220000-2-22-2222200000000000000000000-2-200000000
χ322222-2-222222222-22-2-2-2-222220000-2-22-2-2-2-2-2000000000000000000002200000000
χ332222-2-2222-2-22222-22-2-2-2-2-2220000-22-2200002i2i−2i−2i000000000000000000−2i2i000000
χ342222-2-2222-2-22222-22-2-2-2-2-2220000-22-220000−2i−2i2i2i0000000000000000002i−2i000000
χ352222-2-22-2-222222-2-222-2-222-2-22-22-22-2-220000000000200-2-22000000000000000000
χ362222-2-22-2-222222-2-222-2-222-2-2-22-222-2-220000000000-20022-2000000000000000000
χ372222-2-2-1-2-222-1-1-1-2-22211-1-1112-22-2-111-10000000000-10011-13−3−333−3−330000000000
χ382222-2-2-1-2-222-1-1-1-2-22211-1-1112-22-2-111-10000000000-10011-1−333−3−333−30000000000
χ392222-2-2-1-2-222-1-1-1-2-22211-1-111-22-22-111-10000000000100-1-113−3−33−333−30000000000
χ402222-2-2-1-2-222-1-1-1-2-22211-1-111-22-22-111-10000000000100-1-11−333−33−3−330000000000
χ412222-2-2-1-2-2-2-2-1-1-122-2211111122-2-2-1-1-11000000002i−2i-12i−2i-111−i−iii−i−iii0000000000
χ422222-2-2-1-2-2-2-2-1-1-122-2211111122-2-2-1-1-1100000000−2i2i-1−2i2i-111ii−i−iii−i−i0000000000
χ432222-2-2-1-2-2-2-2-1-1-122-22111111-2-222-1-1-11000000002i−2i1−2i2i1-1-1−i−iiiii−i−i0000000000
χ442222-2-2-1-2-2-2-2-1-1-122-22111111-2-222-1-1-1100000000−2i2i12i−2i1-1-1ii−i−i−i−iii0000000000
χ45444444-2-4-444-2-2-24-4-4-4-2-2-2-22200002-2220000000000000000000000000000000000
χ46444444-2-4-4-4-4-2-2-2-444-4-2-22222000022-2-20000000000000000000000000000000000
χ474444-4-4-24444-2-2-2-44-4-422-2-2-2-2000022-220000000000000000000000000000000000
χ484444-4-4-244-4-4-2-2-24-44-42222-2-200002-22-20000000000000000000000000000000000
χ4944-4-4004004i−4i4-4-40000004i−4i000000000000000000000000000000000000002-22i−2i00
χ5044-4-4004004i−4i4-4-40000004i−4i00000000000000000000000000000000000000-22−2i2i00
χ5144-4-400400−4i4i4-4-4000000−4i4i000000000000000000000000000000000000002-2−2i2i00
χ5244-4-400400−4i4i4-4-4000000−4i4i00000000000000000000000000000000000000-222i−2i00
χ534-44-40044i−4i00-44-4000000004i−4i000000002+2i−2−2i2−2i−2+2i000000000000000000000000000000
χ544-44-40044i−4i00-44-4000000004i−4i00000000−2−2i2+2i−2+2i2−2i000000000000000000000000000000
χ554-44-4004−4i4i00-44-400000000−4i4i000000002−2i−2+2i2+2i−2−2i000000000000000000000000000000
χ564-44-4004−4i4i00-44-400000000−4i4i00000000−2+2i2−2i−2−2i2+2i000000000000000000000000000000
χ574-4-444-440000-4-4400004-40000000000000000−2i22i2−2i22i200000000000000000000000000
χ584-4-444-440000-4-4400004-400000000000000002i2−2i22i2−2i200000000000000000000000000
χ594-4-44-4440000-4-440000-44000000000000000022−22−222200000000000000000000000000
χ604-4-44-4440000-4-440000-440000000000000000−222222−2200000000000000000000000000
χ6188-8-800-4008i−8i-444000000−4i4i00000000000000000000000000000000000000000000
χ6288-8-800-400−8i8i-4440000004i−4i00000000000000000000000000000000000000000000
χ638-88-800-48i−8i004-4400000000−4i4i000000000000000000000000000000000000000000
χ648-88-800-4−8i8i004-44000000004i−4i000000000000000000000000000000000000000000
χ658-8-888-8-4000044-40000-440000000000000000000000000000000000000000000000
χ668-8-88-88-4000044-400004-40000000000000000000000000000000000000000000000

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