Finite Group Databasebeta

← Group #72044

Character table — Group #72044

Order 384.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60
size111111112222222222224444444444444444888888888888121212121212121224242424
order122222223444466666668888121212122424242424242424222266666666444488882244
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
χ15222-22-2-2-2222-2-222-2-2-2-22000022-2-20000000000000000000000000000002i−2i
χ16222-22-2-2-2222-2-222-2-2-2-22000022-2-2000000000000000000000000000000−2i2i
χ17222-22-2-2-22-2-22222-2-2-2-220000-2-22200000000002-2000022-2-2000000000000
χ18222-22-2-2-22-2-22222-2-2-2-220000-2-2220000000000-220000-2-222000000000000
χ19222-22-2-2-2-1-2-222-1-11111-1000011-1-1−i3−i3−i3−i3i3i3i3i3002-2−i3−i3i3i3-1-111000000000000
χ20222-22-2-2-2-1-2-222-1-11111-1000011-1-1−i3−i3−i3−i3i3i3i3i300-22i3i3−i3−i311-1-1000000000000
χ21222-22-2-2-2-1-2-222-1-11111-1000011-1-1i3i3i3i3−i3−i3−i3−i3002-2i3i3−i3−i3-1-111000000000000
χ22222-22-2-2-2-1-2-222-1-11111-1000011-1-1i3i3i3i3−i3−i3−i3−i300-22−i3−i3i3i311-1-1000000000000
χ2322-2-2-22-22200002-222-2-2-222−2−2000022−2−222−2−2000000000000002-222−2−20000
χ2422-2-2-22-22200002-222-2-2-222−2−2000022−2−222−2−200000000000000-22−2−2220000
χ2522-2-2-22-22200002-222-2-2-2−2−2220000−2−222−2−222000000000000002-2−2−2220000
χ2622-2-2-22-22200002-222-2-2-2−2−2220000−2−222−2−22200000000000000-2222−2−20000
χ272-22-2-2-22220000-222-22-2-22−22−200002−22−22−22−20000000000002-2002−22−20000
χ282-22-2-2-22220000-222-22-2-22−22−200002−22−22−22−2000000000000-2200−22−220000
χ292-22-2-2-22220000-222-22-2-2−22−220000−22−22−22−220000000000002-200−22−220000
χ302-22-2-2-22220000-222-22-2-2−22−220000−22−22−22−22000000000000-22002−22−20000
χ312-2-222-2-2222-22-2-2-22-2-2222-2-222-2-222-2-222-2-22000000000000000000000000
χ322-2-222-2-2222-22-2-2-22-2-222-222-22-2-22-222-2-222-2000000000000000000000000
χ332-2-222-2-222-22-22-2-22-2-2220000-222-20000000000000000000000002-2-220000
χ342-2-222-2-222-22-22-2-22-2-2220000-222-2000000000000000000000000-222-20000
χ352-2-222-2-22-12-22-211-111-1-12-2-22-111-1-111-1-111-10000−i3i3−i3i3−i3i3−i3i3000000000000
χ362-2-222-2-22-12-22-211-111-1-12-2-22-111-1-111-1-111-10000i3−i3i3−i3i3−i3i3−i3000000000000
χ372-2-222-2-22-12-22-211-111-1-1-222-2-111-11-1-111-1-110000−i3i3−i3i3i3−i3i3−i3000000000000
χ382-2-222-2-22-12-22-211-111-1-1-222-2-111-11-1-111-1-110000i3−i3i3−i3−i3i3−i3i3000000000000
χ392-2-2-2222-222-2-22-2-2-222-2200002-22-200000000000000000000000000002-200
χ402-2-2-2222-222-2-22-2-2-222-2200002-22-20000000000000000000000000000-2200
χ412-2-2-2222-22-222-2-2-2-222-220000-22-22000000002-2002-2-220000000000000000
χ422-2-2-2222-22-222-2-2-2-222-220000-22-2200000000-2200-222-20000000000000000
χ432-2-2-2222-2-1-222-2111-1-11-100001-11-1−i3i3i3−i3i3−i3−i3i32-200-111-1−i3i3i3−i3000000000000
χ442-2-2-2222-2-1-222-2111-1-11-100001-11-1−i3i3i3−i3i3−i3−i3i3-22001-1-11i3−i3−i3i3000000000000
χ452-2-2-2222-2-1-222-2111-1-11-100001-11-1i3−i3−i3i3−i3i3i3−i32-200-111-1i3−i3−i3i3000000000000
χ462-2-2-2222-2-1-222-2111-1-11-100001-11-1i3−i3−i3i3−i3i3i3−i3-22001-1-11−i3i3i3−i3000000000000
χ4744444444-2-4-4-4-4-2-2-2-2-2-2-20000222200000000000000000000000000000000
χ48444-44-4-4-4-244-4-4-2-22222-20000-2-22200000000000000000000000000000000
χ4944-44-4-44-4400004-4-4-444-40000000000000000000000000000000000000000
χ5044-44-4-44-4-20000-2222-2-2200000000i6i6−i6−i6−i6−i6i6i6000000000000000000000000
χ5144-44-4-44-4-20000-2222-2-2200000000−i6−i6i6i6i6i6−i6−i6000000000000000000000000
χ5244-4-4-44-44-20000-22-2-22222222−22−220000−2−222−2−222000000000000000000000000
χ5344-4-4-44-44-20000-22-2-2222−22−222222000022−2−222−2−2000000000000000000000000
χ544-444-44-4-440000-44-44-44-40000000000000000000000000000000000000000
χ554-444-44-4-4-200002-22-22-2200000000i6−i6i6−i6−i6i6−i6i6000000000000000000000000
χ564-444-44-4-4-200002-22-22-2200000000−i6i6−i6i6i6−i6i6−i6000000000000000000000000
χ574-44-4-4-444-200002-2-22-22222−2222−220000−22−22−22−22000000000000000000000000
χ584-44-4-4-444-200002-2-22-222−2222−222200002−22−22−22−2000000000000000000000000
χ594-4-444-4-44-2-44-4422-222-2-200002-2-2200000000000000000000000000000000
χ604-4-4-4444-4-24-4-44222-2-22-20000-22-2200000000000000000000000000000000

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