Finite Group Databasebeta

← Group #72065

Character table — Group #72065

Order 384.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66
size111111112222222222224444444444444444444466668888888888121212121212121212122424
order12222222344446666666444488881212121224242424242424244444441212121212121212444444888844
χ1111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-1-1-1
χ3111111111111111111111111-1-1-1-11111-1-1-1-1-1-1-1-11111-1-11111-1-1-1-1111111-1-1-1-1-1-1
χ4111111111111111111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1111111
χ511111111111111111111-1-1-1-111111111111111111111-1-1-1-1-1-1-1-1-1-111-1-1-1-11111-1-1
χ611111111111111111111-1-1-1-11111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-111
χ711111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1111111-1-1-1-1111111-1-1-1-1-1-1-1-111
χ811111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-11111-1-111111111-1-1
χ9111-1-11-1-111-11-111-1-1-1-1111-1-111-1-11-1-111111-1-1-1-1ii−i−i1-111-1-111-1-1i−iii−i−iii−i−ii−i
χ10111-1-11-1-111-11-111-1-1-1-1111-1-111-1-11-1-111111-1-1-1-1−i−iii1-111-1-111-1-1−ii−i−iii−i−iii−ii
χ11111-1-11-1-111-11-111-1-1-1-1111-1-1-1-1111-1-11-1-1-1-11111ii−i−i-1111-1-1-1-111i−iii−i−i−i−iii−ii
χ12111-1-11-1-111-11-111-1-1-1-1111-1-1-1-1111-1-11-1-1-1-11111−i−iii-1111-1-1-1-111−ii−i−iiiii−i−ii−i
χ13111-1-11-1-111-11-111-1-1-1-11-1-11111-1-11-1-111111-1-1-1-1ii−i−i-11-1-111-1-111i−i−i−iiiii−i−i−ii
χ14111-1-11-1-111-11-111-1-1-1-11-1-11111-1-11-1-111111-1-1-1-1−i−iii-11-1-111-1-111−iiii−i−i−i−iiii−i
χ15111-1-11-1-111-11-111-1-1-1-11-1-111-1-1111-1-11-1-1-1-11111ii−i−i1-1-1-11111-1-1i−i−i−iii−i−iiii−i
χ16111-1-11-1-111-11-111-1-1-1-11-1-111-1-1111-1-11-1-1-1-11111−i−iii1-1-1-11111-1-1−iiii−i−iii−i−i−ii
χ17222222222-2-2-2-2222222200000000-2-2-2-20000000022220000000000-2-20000000000
χ18222222222-2-2-2-2222222200000000-2-2-2-200000000-2-2-2-20000000000220000000000
χ1922222222-12222-1-1-1-1-1-1-122222222-1-1-1-1-1-1-1-1-1-1-1-1000022-1-1-1-1-1-1-1-1000000000000
χ2022222222-12222-1-1-1-1-1-1-12222-2-2-2-2-1-1-1-1111111110000-2-2-1-1-1-11111000000000000
χ2122222222-12222-1-1-1-1-1-1-1-2-2-2-22222-1-1-1-1-1-1-1-1-1-1-1-10000-2-211111111000000000000
χ2222222222-12222-1-1-1-1-1-1-1-2-2-2-2-2-2-2-2-1-1-1-1111111110000221111-1-1-1-1000000000000
χ23222-2-22-2-22-22-2222-2-2-2-2200000000-222-2000000002i2i−2i−2i0000000000−2i2i0000000000
χ24222-2-22-2-22-22-2222-2-2-2-2200000000-222-200000000−2i−2i2i2i00000000002i−2i0000000000
χ25222-2-22-2-2-12-22-2-1-11111-122-2-222-2-2-111-1-1-1-1-1111100002-2-1-111-1-111000000000000
χ26222-2-22-2-2-12-22-2-1-11111-122-2-2-2-222-111-11111-1-1-1-10000-22-1-11111-1-1000000000000
χ27222-2-22-2-2-12-22-2-1-11111-1-2-22222-2-2-111-1-1-1-1-111110000-2211-1-111-1-1000000000000
χ28222-2-22-2-2-12-22-2-1-11111-1-2-222-2-222-111-11111-1-1-1-100002-211-1-1-1-111000000000000
χ2922-222-2-2-2200002-222-2-2-200002−22−2000022−2−222−2−22-22-200000000000000002−22−200
χ3022-222-2-2-2200002-222-2-2-200002−22−2000022−2−222−2−2-22-220000000000000000−22−2200
χ3122-222-2-2-2200002-222-2-2-20000−22−220000−2−222−2−2222-22-20000000000000000−22−2200
χ3222-222-2-2-2200002-222-2-2-20000−22−220000−2−222−2−222-22-2200000000000000002−22−200
χ3322-2-2-2-222200002-2-2-222-200002−2−22000022−2−2−2−2222i−2i−2i2i0000000000000000i2−i2−i2i200
χ3422-2-2-2-222200002-2-2-222-200002−2−22000022−2−2−2−222−2i2i2i−2i0000000000000000−i2i2i2−i200
χ3522-2-2-2-222200002-2-2-222-20000−222−20000−2−22222−2−22i−2i−2i2i0000000000000000−i2i2i2−i200
χ3622-2-2-2-222200002-2-2-222-20000−222−20000−2−22222−2−2−2i2i2i−2i0000000000000000i2−i2−i2i200
χ372-2-22-222-2222-2-2-2-22-22-220000000022-2-20000000000000000000000002i−2i2i−2i000000
χ382-2-22-222-2222-2-2-2-22-22-220000000022-2-2000000000000000000000000−2i2i−2i2i000000
χ392-2-22-222-22-2-222-2-22-22-222-22-20000-2-222000000000000002-22-20000000000000000
χ402-2-22-222-22-2-222-2-22-22-22-22-220000-2-22200000000000000-22-220000000000000000
χ412-2-22-222-2-1-2-22211-11-11-12-22-2000011-1-1−i3i3−i3i3−i3i3−i3i3000000-11-11−i3i3−i3i3000000000000
χ422-2-22-222-2-1-2-22211-11-11-12-22-2000011-1-1i3−i3i3−i3i3−i3i3−i3000000-11-11i3−i3i3−i3000000000000
χ432-2-22-222-2-1-2-22211-11-11-1-22-22000011-1-1−i3i3−i3i3−i3i3−i3i30000001-11-1i3−i3i3−i3000000000000
χ442-2-22-222-2-1-2-22211-11-11-1-22-22000011-1-1i3−i3i3−i3i3−i3i3−i30000001-11-1−i3i3−i3i3000000000000
χ452-2-2-222-2222-2-22-2-2-22-222000000002-22-20000000000000000000000002-2-22000000
χ462-2-2-222-2222-2-22-2-2-22-222000000002-22-2000000000000000000000000-222-2000000
χ472-2-2-222-222-222-2-2-2-22-2222-2-220000-22-22000000000000002-2-220000000000000000
χ482-2-2-222-222-222-2-2-2-22-222-222-20000-22-2200000000000000-222-20000000000000000
χ492-2-2-222-22-1-222-2111-11-1-12-2-2200001-11-1−i3i3−i3i3i3−i3i3−i3000000-111-1−i3i3i3−i3000000000000
χ502-2-2-222-22-1-222-2111-11-1-12-2-2200001-11-1i3−i3i3−i3−i3i3−i3i3000000-111-1i3−i3−i3i3000000000000
χ512-2-2-222-22-1-222-2111-11-1-1-222-200001-11-1−i3i3−i3i3i3−i3i3−i30000001-1-11i3−i3−i3i3000000000000
χ522-2-2-222-22-1-222-2111-11-1-1-222-200001-11-1i3−i3i3−i3−i3i3−i3i30000001-1-11−i3i3i3−i3000000000000
χ5344444444-2-4-4-4-4-2-2-2-2-2-2-20000000022220000000000000000000000000000000000
χ54444-4-44-4-4-2-44-44-2-22222-2000000002-2-220000000000000000000000000000000000
χ5544-444-4-4-4-20000-22-2-2222000022−2222−220000−2−222−2−22200000000000000000000000000
χ5644-444-4-4-4-20000-22-2-22220000−2222−2222000022−2−222−2−200000000000000000000000000
χ5744-4-4-4-444-20000-2222-2-22000022−22−22220000−2−22222−2−200000000000000000000000000
χ5844-4-4-4-444-20000-2222-2-220000−222222−22000022−2−2−2−22200000000000000000000000000
χ594-444-4-4-4440000-444-4-44-40000000000000000000000000000000000000000000000
χ604-444-4-4-44-200002-2-222-22000000000000i6−i6−i6i6i6−i6−i6i600000000000000000000000000
χ614-444-4-4-44-200002-2-222-22000000000000−i6i6i6−i6−i6i6i6−i600000000000000000000000000
χ624-44-44-44-440000-44-444-4-40000000000000000000000000000000000000000000000
χ634-44-44-44-4-200002-22-2-222000000000000i6−i6−i6i6−i6i6i6−i600000000000000000000000000
χ644-44-44-44-4-200002-22-2-222000000000000−i6i6i6−i6i6−i6−i6i600000000000000000000000000
χ654-4-44-444-4-244-4-422-22-22-200000000-2-2220000000000000000000000000000000000
χ664-4-4-444-44-24-4-44222-22-2-200000000-22-220000000000000000000000000000000000

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