Finite Group Databasebeta

← Group #10692448

Character table — Group #10692448

Order 768.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63
size11112222222244444444444888888881212121216161616161616161616161616161616242424242424242424244848
order1222223446664444466121212122444121212128888446881212121212121224242424444488888888
χ1111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111-1-11-1-1111-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1
χ31111111111111111111111111111111-1-1-1-11111111111111111-1-1-1-1-1-1-1-1-1-1-1-1
χ41111111111111111111111111111111-1-1-1-1-1-11-1-1111-1-1-1-1-1-1-1-11111-1-1-1-1-1-111
χ511111111111111111111111-1-1-1-11111111111-1-1-1-1-1-11111-1-1-1-11111-1-111-1-1-1-1
χ611111111111111111111111-1-1-1-111111111-1-1-111-1-1-1-1-1-1-11111-1-1-1-1-1-111-1-111
χ711111111111111111111111-1-1-1-11111-1-1-1-111-1-1-1-1-1-11111-1-1-1-1-1-1-1-111-1-11111
χ811111111111111111111111-1-1-1-11111-1-1-1-1-1-1-111-1-1-1-1-1-1-11111111111-1-111-1-1
χ91111-1-11-1-111111-11-1-1-1-1-11111-1-11-11-1ii−i−i1-111-11-1-111-1-111-1-1ii−i−ii−ii−ii−ii−i
χ101111-1-11-1-111111-11-1-1-1-1-11111-1-11-11-1ii−i−i-111-111-1-1-1-111-1-111−i−iiii−ii−ii−i−ii
χ111111-1-11-1-111111-11-1-1-1-1-11111-1-11-11-1−i−iii1-111-11-1-111-1-111-1-1−i−iii−ii−ii−ii−ii
χ121111-1-11-1-111111-11-1-1-1-1-11111-1-11-11-1−i−iii-111-111-1-1-1-111-1-111ii−i−i−ii−ii−iii−i
χ131111-1-11-1-111111-11-1-1-1-1-111-1-1111-11-1ii−i−i1-1-1-11-11111-1-1-1-111ii−i−i−iii−i−ii−ii
χ141111-1-11-1-111111-11-1-1-1-1-111-1-1111-11-1ii−i−i-11-11-1-111-1-11111-1-1−i−iii−iii−i−iii−i
χ151111-1-11-1-111111-11-1-1-1-1-111-1-1111-11-1−i−iii1-1-1-11-11111-1-1-1-111−i−iiii−i−iii−ii−i
χ161111-1-11-1-111111-11-1-1-1-1-111-1-1111-11-1−i−iii-11-11-1-111-1-11111-1-1ii−i−ii−i−iii−i−ii
χ172222222222222-2-2-2-22222-2-200002-2-2-222220000000000000000000000-2-20000
χ182222222222222-2-2-2-22222-2-200002-2-2-2-2-2-2-20000000000000000000000220000
χ192222222-2-2222-222-2-222-2-2-2-20000-2-2220000000000000000000000002i−2i00−2i2i00
χ202222222-2-2222-222-2-222-2-2-2-20000-2-222000000000000000000000000−2i2i002i−2i00
χ212222222-2-2222-2-2-22222-2-2222-2-22-22-2-2000000200-2-2200000000000000000000
χ222222222-2-2222-2-2-22222-2-222-222-2-22-2-2000000-20022-200000000000000000000
χ23222222-122-1-1-122222-1-1-1-1-1-12222-1-1-1-1000022-122-1-1-1-1-1-1-1-1-1-1-1000000000000
χ24222222-122-1-1-122222-1-1-1-1-1-12222-1-1-1-10000-2-2-1-2-2-1-1-111111111000000000000
χ25222222-122-1-1-122222-1-1-1-1-1-1-2-2-2-2-1-1-1-10000221-2-2111-1-1-1-11111000000000000
χ26222222-122-1-1-122222-1-1-1-1-1-1-2-2-2-2-1-1-1-10000-2-21221111111-1-1-1-1000000000000
χ27222222-1-2-2-1-1-1-2-2-222-1-111-1-12-2-221-111000000-10011-1−i3i3−i3i3−i3i3−i3i3000000000000
χ28222222-1-2-2-1-1-1-2-2-222-1-111-1-12-2-221-111000000-10011-1i3−i3i3−i3i3−i3i3−i3000000000000
χ29222222-1-2-2-1-1-1-2-2-222-1-111-1-1-222-21-111000000100-1-11−i3i3−i3i3i3−i3i3−i3000000000000
χ30222222-1-2-2-1-1-1-2-2-222-1-111-1-1-222-21-111000000100-1-11i3−i3i3−i3−i3i3−i3i3000000000000
χ312222-2-2222222-22-2-22-2-222-2-20000-222-20000000000000000000000002200-2-200
χ322222-2-2222222-22-2-22-2-222-2-20000-222-2000000000000000000000000-2-2002200
χ332222-2-2222222-2-222-2-2-222222-22-2-2-2-22000000200-22-200000000000000000000
χ342222-2-2222222-2-222-2-2-22222-22-22-2-2-22000000-2002-2200000000000000000000
χ352222-2-22-2-22222-22-22-2-2-2-2-2-2000022-222i2i−2i−2i0000000000000000000000−2i2i0000
χ362222-2-22-2-22222-22-22-2-2-2-2-2-2000022-22−2i−2i2i2i00000000000000000000002i−2i0000
χ372222-2-2-122-1-1-1-2-222-211-1-1-1-12-22-2111-1000000-1001-11−i3i3i3−i3−i3i3i3−i3000000000000
χ382222-2-2-122-1-1-1-2-222-211-1-1-1-12-22-2111-1000000-1001-11i3−i3−i3i3i3−i3−i3i3000000000000
χ392222-2-2-122-1-1-1-2-222-211-1-1-1-1-22-22111-1000000100-11-1−i3i3i3−i3i3−i3−i3i3000000000000
χ402222-2-2-122-1-1-1-2-222-211-1-1-1-1-22-22111-1000000100-11-1i3−i3−i3i3−i3i3i3−i3000000000000
χ412222-2-2-1-2-2-1-1-122-22-21111-1-122-2-2-11-1100002-2-12-2-111-1-111-1-111000000000000
χ422222-2-2-1-2-2-1-1-122-22-21111-1-122-2-2-11-110000-22-1-22-11111-1-111-1-1000000000000
χ432222-2-2-1-2-2-1-1-122-22-21111-1-1-2-222-11-1100002-21-221-1-1-1-11111-1-1000000000000
χ442222-2-2-1-2-2-1-1-122-22-21111-1-1-2-222-11-110000-2212-21-1-111-1-1-1-111000000000000
χ45444444-244-2-2-24-4-4-4-4-2-2-2-2220000-222200000000000000000000000000000000
χ46444444-2-4-4-2-2-2-444-4-4-2-22222000022-2-200000000000000000000000000000000
χ474444-4-4-244-2-2-2-44-4-4422-2-22200002-2-2200000000000000000000000000000000
χ484444-4-4-2-4-4-2-2-24-44-442222220000-2-22-200000000000000000000000000000000
χ4944-4-40044-44-4-400000004-40000000000000000000000000000002-22-200000000
χ5044-4-40044-44-4-400000004-4000000000000000000000000000000-22-2200000000
χ5144-4-4004-444-4-40000000-440000000000000000000000000000002i−2i−2i2i00000000
χ5244-4-4004-444-4-40000000-44000000000000000000000000000000−2i2i2i−2i00000000
χ534-4-444-4400-4-44000004-4000000000000−2i22i2−2i22i20000000000000000000000000000
χ544-4-444-4400-4-44000004-40000000000002i2−2i22i2−2i20000000000000000000000000000
χ554-4-44-44400-4-4400000-4400000000000022−22−22220000000000000000000000000000
χ564-4-44-44400-4-4400000-44000000000000−222222−220000000000000000000000000000
χ5788-8-800-48-8-4440000000-44000000000000000000000000000000000000000000
χ5888-8-800-4-88-44400000004-4000000000000000000000000000000000000000000
χ598-88-800800-88-8000000000000000000000000000000000000000000000000000
χ608-88-800-4004-44000000000−4i34i30000000000000000000000000000000000000000
χ618-88-800-4004-440000000004i3−4i30000000000000000000000000000000000000000
χ628-8-888-8-40044-400000-4400000000000000000000000000000000000000000000
χ638-8-88-88-40044-4000004-400000000000000000000000000000000000000000000

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