Finite Group Databasebeta

← Group #72068

Character table — Group #72068

Order 384.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60
size111111112222222222224444444444444444888888888888121212121212121224242424
order12222222344446666666888812121212242424242424242444441212121212121212444488884444
χ1111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1
χ3111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1
χ4111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111
χ511111111111111111111-1-1-1-11111-1-1-1-1-1-1-1-111-1-11111-1-1-1-11111-1-1-1-111-1-1
χ611111111111111111111-1-1-1-11111-1-1-1-1-1-1-1-111-1-11111-1-1-1-1-1-1-1-11111-1-111
χ711111111111111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-111-1-1-1-111111111-1-1-1-1-1-111
χ811111111111111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-111-1-1-1-11111-1-1-1-1111111-1-1
χ9222222222-2-2-2-222222220000-2-2-2-20000000000000000000022-2-200000000
χ10222222222-2-2-2-222222220000-2-2-2-200000000000000000000-2-22200000000
χ1122222222-12222-1-1-1-1-1-1-12222-1-1-1-1-1-1-1-1-1-1-1-12222-1-1-1-1-1-1-1-1000000000000
χ1222222222-12222-1-1-1-1-1-1-12222-1-1-1-1-1-1-1-1-1-1-1-1-2-2-2-211111111000000000000
χ1322222222-12222-1-1-1-1-1-1-1-2-2-2-2-1-1-1-11111111122-2-2-1-1-1-11111000000000000
χ1422222222-12222-1-1-1-1-1-1-1-2-2-2-2-1-1-1-111111111-2-2221111-1-1-1-1000000000000
χ152222-2-2-2-220000222-2-2-2-222−2−200002222−2−2−2−2000000000000002-222−2−20000
χ162222-2-2-2-220000222-2-2-2-222−2−200002222−2−2−2−200000000000000-22−2−2220000
χ172222-2-2-2-220000222-2-2-2-2−2−2220000−2−2−2−22222000000000000002-2−2−2220000
χ182222-2-2-2-220000222-2-2-2-2−2−2220000−2−2−2−2222200000000000000-2222−2−20000
χ1922-2-2-222-2222-2-22-2-22-2-22000022-2-20000000000000000000000000000002i−2i
χ2022-2-2-222-2222-2-22-2-22-2-22000022-2-2000000000000000000000000000000−2i2i
χ2122-2-2-222-22-2-2222-2-22-2-220000-2-22200000000002-2000022-2-2000000000000
χ2222-2-2-222-22-2-2222-2-22-2-220000-2-2220000000000-220000-2-222000000000000
χ2322-2-2-222-2-1-2-222-111-111-1000011-1-1−i3−i3i3i3−i3−i3i3i3002-2−i3−i3i3i3-1-111000000000000
χ2422-2-2-222-2-1-2-222-111-111-1000011-1-1−i3−i3i3i3−i3−i3i3i300-22i3i3−i3−i311-1-1000000000000
χ2522-2-2-222-2-1-2-222-111-111-1000011-1-1i3i3−i3−i3i3i3−i3−i3002-2i3i3−i3−i3-1-111000000000000
χ2622-2-2-222-2-1-2-222-111-111-1000011-1-1i3i3−i3−i3i3i3−i3−i300-22−i3−i3i3i311-1-1000000000000
χ272-22-2-22-2222-22-2-22-2-22-2200002-22-200000000000000000000000000002i−2i00
χ282-22-2-22-2222-22-2-22-2-22-2200002-22-20000000000000000000000000000−2i2i00
χ292-22-2-22-222-22-22-22-2-22-220000-22-22000000002-2002-22-20000000000000000
χ302-22-2-22-222-22-22-22-2-22-220000-22-2200000000-2200-22-220000000000000000
χ312-22-2-22-22-1-22-221-111-11-100001-11-1−i3i3−i3i3−i3i3−i3i32-200-11-11−i3i3−i3i3000000000000
χ322-22-2-22-22-1-22-221-111-11-100001-11-1−i3i3−i3i3−i3i3−i3i3-22001-11-1i3−i3i3−i3000000000000
χ332-22-2-22-22-1-22-221-111-11-100001-11-1i3−i3i3−i3i3−i3i3−i32-200-11-11i3−i3i3−i3000000000000
χ342-22-2-22-22-1-22-221-111-11-100001-11-1i3−i3i3−i3i3−i3i3−i3-22001-11-1−i3i3−i3i3000000000000
χ352-2-2222-2-222-2-22-2-22-2-2222-22-22-2-222-2-222-2-22000000000000000000000000
χ362-2-2222-2-222-2-22-2-22-2-222-22-222-2-22-222-2-222-2000000000000000000000000
χ372-2-2222-2-22-222-2-2-22-2-2220000-222-20000000000000000000000002i−2i2i−2i0000
χ382-2-2222-2-22-222-2-2-22-2-2220000-222-2000000000000000000000000−2i2i−2i2i0000
χ392-2-2222-2-2-12-2-2211-111-1-12-22-2-111-1-111-1-111-10000−i3i3i3−i3−i3i3i3−i3000000000000
χ402-2-2222-2-2-12-2-2211-111-1-12-22-2-111-1-111-1-111-10000i3−i3−i3i3i3−i3−i3i3000000000000
χ412-2-2222-2-2-12-2-2211-111-1-1-22-22-111-11-1-111-1-110000−i3i3i3−i3i3−i3−i3i3000000000000
χ422-2-2222-2-2-12-2-2211-111-1-1-22-22-111-11-1-111-1-110000i3−i3−i3i3−i3i3i3−i3000000000000
χ432-2-22-2-22220000-2-2222-2-22−2−2200002−2−22−222−20000000000002i−2i00−i2i2i2−i20000
χ442-2-22-2-22220000-2-2222-2-22−2−2200002−2−22−222−2000000000000−2i2i00i2−i2−i2i20000
χ452-2-22-2-22220000-2-2222-2-2−222−20000−222−22−2−220000000000002i−2i00i2−i2−i2i20000
χ462-2-22-2-22220000-2-2222-2-2−222−20000−222−22−2−22000000000000−2i2i00−i2i2i2−i20000
χ4744444444-2-4-4-4-4-2-2-2-2-2-2-20000222200000000000000000000000000000000
χ484444-4-4-4-4-20000-2-2-222222222−22−220000−2−2−2−22222000000000000000000000000
χ494444-4-4-4-4-20000-2-2-22222−22−22222200002222−2−2−2−2000000000000000000000000
χ5044-4-44-4-44400004-4-4-444-40000000000000000000000000000000000000000
χ5144-4-44-4-44-20000-2222-2-2200000000i6i6−i6−i6−i6−i6i6i6000000000000000000000000
χ5244-4-44-4-44-20000-2222-2-2200000000−i6−i6i6i6i6i6−i6−i6000000000000000000000000
χ5344-4-4-444-4-244-4-4-222-222-20000-2-22200000000000000000000000000000000
χ544-44-44-44-440000-44-44-44-40000000000000000000000000000000000000000
χ554-44-44-44-4-200002-22-22-2200000000i6−i6i6−i6−i6i6−i6i6000000000000000000000000
χ564-44-44-44-4-200002-22-22-2200000000−i6i6−i6i6i6−i6i6−i6000000000000000000000000
χ574-44-4-44-44-24-44-42-222-22-20000-22-2200000000000000000000000000000000
χ584-4-4444-4-4-2-444-422-222-2-200002-2-2200000000000000000000000000000000
χ594-4-44-4-444-2000022-2-2-22222−22−22220000−222−22−2−22000000000000000000000000
χ604-4-44-4-444-2000022-2-2-222−222222−2200002−2−22−222−2000000000000000000000000

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