Finite Group Databasebeta

← Group #10693205

Character table — Group #10693205

Order 768.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63
size11112222222244444444444888888881212121216161616161616161616161616161616242424242424242424244848
order122222344666224446612121212668888121288884488121212122424242424242424244444448888
χ1111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1-1-111-1-1
χ31111111111111111111111111111111-1-1-1-11111111111111111-1-1-1-1-1-1-1-1-1-1-1-1
χ41111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-11111-1-111
χ51111111111111111111111111-1-1-1-111111111-1-11111-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1
χ61111111111111111111111111-1-1-1-1111111-1-111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-11111
χ71111111111111111111111111-1-1-1-111-1-1-1-111-1-11111-1-1-1-1-1-1-1-11111-1-1-1-1-1-111
χ81111111111111111111111111-1-1-1-111-1-1-1-1-1-111-1-1-1-1-1-1-1-1111111111111-1-1-1-1
χ91111-1-11-1-11111-111-1-1-111-1-11-1ii−i−i1-1ii−i−ii−i1-1ii−i−iii−i−i11-1-111-1-111-1-1i−ii−i
χ101111-1-11-1-11111-111-1-1-111-1-11-1ii−i−i1-1ii−i−i−ii-11−i−iiiii−i−i-1-11111-1-1-1-111i−i−ii
χ111111-1-11-1-11111-111-1-1-111-1-11-1ii−i−i1-1−i−iiii−i1-1ii−i−iii−i−i11-1-1-1-111-1-111−ii−ii
χ121111-1-11-1-11111-111-1-1-111-1-11-1ii−i−i1-1−i−iii−ii-11−i−iiiii−i−i-1-111-1-11111-1-1−iii−i
χ131111-1-11-1-11111-111-1-1-111-1-11-1−i−iii1-1ii−i−ii−i-11ii−i−i−i−iii-1-111-1-11111-1-1i−i−ii
χ141111-1-11-1-11111-111-1-1-111-1-11-1−i−iii1-1ii−i−i−ii1-1−i−iii−i−iii11-1-1-1-111-1-111i−ii−i
χ151111-1-11-1-11111-111-1-1-111-1-11-1−i−iii1-1−i−iiii−i-11ii−i−i−i−iii-1-11111-1-1-1-111−iii−i
χ161111-1-11-1-11111-111-1-1-111-1-11-1−i−iii1-1−i−iii−ii1-1−i−iii−i−iii11-1-111-1-111-1-1−ii−ii
χ17222222222222-2-22-2-222-2-222-2-200002-22222000000000000000000000000-2-200
χ18222222222222-2-22-2-222-2-222-2-200002-2-2-2-2-20000000000000000000000002200
χ192222222-2-222222-2-2-222-2-2-2-2222i−2i2i−2i-2-20000000000002i−2i2i−2i0000000000000000
χ202222222-2-222222-2-2-222-2-2-2-222−2i2i−2i2i-2-2000000000000−2i2i−2i2i0000000000000000
χ212222222-2-2222-2-2-2222222-2-2-2-20000-22000000000000000000002-22-200000000
χ222222222-2-2222-2-2-2222222-2-2-2-20000-2200000000000000000000-22-2200000000
χ23222222-122-1-1-122222-1-1-1-1-1-1-1-12222-1-100002222-1-1-1-1-1-1-1-1-1-1-1-1000000000000
χ24222222-122-1-1-122222-1-1-1-1-1-1-1-12222-1-10000-2-2-2-21111-1-1-1-11111000000000000
χ25222222-122-1-1-122222-1-1-1-1-1-1-1-1-2-2-2-2-1-1000022-2-2-1-1-1-111111111000000000000
χ26222222-122-1-1-122222-1-1-1-1-1-1-1-1-2-2-2-2-1-10000-2-22211111111-1-1-1-1000000000000
χ27222222-1-2-2-1-1-122-2-2-2-1-11111-1-12i−2i2i−2i1100000000−i3i3−i3i3−ii−ii3−33−3000000000000
χ28222222-1-2-2-1-1-122-2-2-2-1-11111-1-12i−2i2i−2i1100000000i3−i3i3−i3−ii−ii−33−33000000000000
χ29222222-1-2-2-1-1-122-2-2-2-1-11111-1-1−2i2i−2i2i1100000000−i3i3−i3i3i−ii−i−33−33000000000000
χ30222222-1-2-2-1-1-122-2-2-2-1-11111-1-1−2i2i−2i2i1100000000i3−i3i3−i3i−ii−i3−33−3000000000000
χ312222-2-22222222-2-2-22-2-2-2-2222-22-2-22-220000000000002-2-220000000000000000
χ322222-2-22222222-2-2-22-2-2-2-2222-2-222-2-22000000000000-222-20000000000000000
χ332222-2-2222222-22-22-2-2-22222-220000-2-2000000000000000000002-2-2200000000
χ342222-2-2222222-22-22-2-2-22222-220000-2-200000000000000000000-222-200000000
χ352222-2-22-2-2222-222-22-2-2-2-2-2-2-220000222i2i−2i−2i000000000000000000000000−2i2i00
χ362222-2-22-2-2222-222-22-2-2-2-2-2-2-22000022−2i−2i2i2i0000000000000000000000002i−2i00
χ372222-2-2-122-1-1-12-2-2-221111-1-1-112-2-221-1000000003−3−33-111-1−333−3000000000000
χ382222-2-2-122-1-1-12-2-2-221111-1-1-112-2-221-100000000−333−3-111-13−3−33000000000000
χ392222-2-2-122-1-1-12-2-2-221111-1-1-11-222-21-1000000003−3−331-1-113−3−33000000000000
χ402222-2-2-122-1-1-12-2-2-221111-1-1-11-222-21-100000000−333−31-1-11−333−3000000000000
χ412222-2-2-1-2-2-1-1-12-222-211-1-111-112i2i−2i−2i-1100002i−2i2-2−i−iii−i−iii-1-111000000000000
χ422222-2-2-1-2-2-1-1-12-222-211-1-111-112i2i−2i−2i-110000−2i2i-22ii−i−i−i−iii11-1-1000000000000
χ432222-2-2-1-2-2-1-1-12-222-211-1-111-11−2i−2i2i2i-1100002i−2i-22−i−iiiii−i−i11-1-1000000000000
χ442222-2-2-1-2-2-1-1-12-222-211-1-111-11−2i−2i2i2i-110000−2i2i2-2ii−i−iii−i−i-1-111000000000000
χ45444444-244-2-2-2-4-44-4-4-2-222-2-2220000-2200000000000000000000000000000000
χ46444444-2-4-4-2-2-2-4-4-444-2-2-2-2222200002-200000000000000000000000000000000
χ474444-4-4-244-2-2-2-44-44-422-2-2-2-22-200002200000000000000000000000000000000
χ484444-4-4-2-4-4-2-2-2-444-442222222-20000-2-200000000000000000000000000000000
χ4944-4-44-44004-4-4000004-400000000000022−2222−220000000000000000000000000000
χ5044-4-44-44004-4-4000004-4000000000000−2222−22220000000000000000000000000000
χ5144-4-4-444004-4-400000-44000000000000−2i22i22i2−2i20000000000000000000000000000
χ5244-4-4-444004-4-400000-440000000000002i2−2i2−2i22i20000000000000000000000000000
χ534-4-440044-4-4-440000000004-4000000000000000000000000000000002-22-20000
χ544-4-440044-4-4-440000000004-400000000000000000000000000000000-22-220000
χ554-4-44004-44-4-44000000000-44000000000000000000000000000000002-2-220000
χ564-4-44004-44-4-44000000000-4400000000000000000000000000000000-222-20000
χ5788-8-88-8-400-44400000-4400000000000000000000000000000000000000000000
χ5888-8-8-88-400-444000004-400000000000000000000000000000000000000000000
χ598-88-800800-88-8000000000000000000000000000000000000000000000000000
χ608-88-800-4004-44000000043−43000000000000000000000000000000000000000000
χ618-88-800-4004-440000000−4343000000000000000000000000000000000000000000
χ628-8-8800-48-844-4000000000-440000000000000000000000000000000000000000
χ638-8-8800-4-8844-40000000004-40000000000000000000000000000000000000000

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