Finite Group Databasebeta

← Group #68813

Character table — Group #68813

Order 384.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66
size111111112222222222224444444444444444444466668888888888121212121212121212122424
order12222222344446666666444488881212121224242424242424244444441212121212121212224444888844
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
χ91-1-11-111-1111-1-11-1-1-111-111-1-1ii−i−i11-1-1iiii−i−i−i−i11-1-1i−i11-1-1ii−i−i1-111-1-1ii−i−ii−i
χ101-1-11-111-1111-1-11-1-1-111-111-1-1ii−i−i11-1-1iiii−i−i−i−i-1-111i−i11-1-1ii−i−i-11-1-111−i−iii−ii
χ111-1-11-111-1111-1-11-1-1-111-111-1-1−i−iii11-1-1−i−i−i−iiiii11-1-1−ii11-1-1−i−iii1-111-1-1−i−iii−ii
χ121-1-11-111-1111-1-11-1-1-111-111-1-1−i−iii11-1-1−i−i−i−iiiii-1-111−ii11-1-1−i−iii-11-1-111ii−i−ii−i
χ131-1-11-111-1111-1-11-1-1-111-1-1-111ii−i−i11-1-1iiii−i−i−i−i11-1-1−ii-1-111−i−iii1-1-1-111ii−i−i−ii
χ141-1-11-111-1111-1-11-1-1-111-1-1-111ii−i−i11-1-1iiii−i−i−i−i-1-111−ii-1-111−i−iii-1111-1-1−i−iiii−i
χ151-1-11-111-1111-1-11-1-1-111-1-1-111−i−iii11-1-1−i−i−i−iiiii11-1-1i−i-1-111ii−i−i1-1-1-111−i−iiii−i
χ161-1-11-111-1111-1-11-1-1-111-1-1-111−i−iii11-1-1−i−i−i−iiiii-1-111i−i-1-111ii−i−i-1111-1-1ii−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
χ2322-2-222-2-222-22-2-22-2-22-22000000002-2-220000000000000000000000002i−2i2i−2i000000
χ2422-2-222-2-222-22-2-22-2-22-22000000002-2-22000000000000000000000000−2i2i−2i2i000000
χ2522-2-222-2-22-22-22-22-2-22-222i−2i2i−2i0000-222-2000000000000002i−2i2i−2i0000000000000000
χ2622-2-222-2-22-22-22-22-2-22-22−2i2i−2i2i0000-222-200000000000000−2i2i−2i2i0000000000000000
χ2722-2-222-2-2-1-22-221-111-11-12i−2i2i−2i00001-1-1133−3−333−3−3000000−ii−ii−i3i3−i3i3000000000000
χ2822-2-222-2-2-1-22-221-111-11-12i−2i2i−2i00001-1-11−3−333−3−333000000−ii−iii3−i3i3−i3000000000000
χ2922-2-222-2-2-1-22-221-111-11-1−2i2i−2i2i00001-1-1133−3−333−3−3000000i−ii−ii3−i3i3−i3000000000000
χ3022-2-222-2-2-1-22-221-111-11-1−2i2i−2i2i00001-1-11−3−333−3−333000000i−ii−i−i3i3−i3i3000000000000
χ3122-2-2-2-22220000222-2-2-2-200002−22−200002−22−22−22−22i−2i2i−2i0000000000000000−i2i2−i2i200
χ3222-2-2-2-22220000222-2-2-2-200002−22−200002−22−22−22−2−2i2i−2i2i0000000000000000i2−i2i2−i200
χ3322-2-2-2-22220000222-2-2-2-20000−22−220000−22−22−22−222i−2i2i−2i0000000000000000i2−i2i2−i200
χ3422-2-2-2-22220000222-2-2-2-20000−22−220000−22−22−22−22−2i2i−2i2i0000000000000000−i2i2−i2i200
χ352-22-22-22-2200002-2-22-2-220000−i2i2i2−i20000−i2i2−i2i2i2−i2i2−i22i−2i−2i2i0000000000000000−222−200
χ362-22-22-22-2200002-2-22-2-220000−i2i2i2−i20000−i2i2−i2i2i2−i2i2−i2−2i2i2i−2i00000000000000002−2−2200
χ372-22-22-22-2200002-2-22-2-220000i2−i2−i2i20000i2−i2i2−i2−i2i2−i2i22i−2i−2i2i00000000000000002−2−2200
χ382-22-22-22-2200002-2-22-2-220000i2−i2−i2i20000i2−i2i2−i2−i2i2−i2i2−2i2i2i−2i0000000000000000−222−200
χ392-22-2-22-2222-2-22-2-2222-2-2000000002-22-20000000000000000000000002i−2i−2i2i000000
χ402-22-2-22-2222-2-22-2-2222-2-2000000002-22-2000000000000000000000000−2i2i2i−2i000000
χ412-22-2-22-222-222-2-2-2222-2-22i−2i−2i2i0000-22-22000000000000002i−2i−2i2i0000000000000000
χ422-22-2-22-222-222-2-2-2222-2-2−2i2i2i−2i0000-22-2200000000000000−2i2i2i−2i0000000000000000
χ432-22-2-22-22-1-222-211-1-1-1112i−2i−2i2i00001-11-1−i3−i3i3i3i3i3−i3−i3000000−iii−i−333−3000000000000
χ442-22-2-22-22-1-222-211-1-1-1112i−2i−2i2i00001-11-1i3i3−i3−i3−i3−i3i3i3000000−iii−i3−3−33000000000000
χ452-22-2-22-22-1-222-211-1-1-111−2i2i2i−2i00001-11-1−i3−i3i3i3i3i3−i3−i3000000i−i−ii3−3−33000000000000
χ462-22-2-22-22-1-222-211-1-1-111−2i2i2i−2i00001-11-1i3i3−i3−i3−i3−i3i3i3000000i−i−ii−333−3000000000000
χ472-2-22-222-22-2-2222-2-2-222-200000000-2-2220000000022-2-20000000000-220000000000
χ482-2-22-222-22-2-2222-2-2-222-200000000-2-22200000000-2-22200000000002-20000000000
χ492-2-22-222-2-122-2-2-1111-1-1122-2-22i2i−2i−2i-1-111−i−i−i−iiiii00002i−2i-1-111−i−iii000000000000
χ502-2-22-222-2-122-2-2-1111-1-1122-2-2−2i−2i2i2i-1-111iiii−i−i−i−i0000−2i2i-1-111ii−i−i000000000000
χ512-2-22-222-2-122-2-2-1111-1-11-2-2222i2i−2i−2i-1-111−i−i−i−iiiii0000−2i2i11-1-1ii−i−i000000000000
χ522-2-22-222-2-122-2-2-1111-1-11-2-222−2i−2i2i2i-1-111iiii−i−i−i−i00002i−2i11-1-1−i−iii000000000000
χ5344444444-2-4-4-4-4-2-2-2-2-2-2-20000000022220000000000000000000000000000000000
χ544444-4-4-4-440000-44-44-44-40000000000000000000000000000000000000000000000
χ554444-4-4-4-4-200002-22-22-220000000000006−6−666−6−6600000000000000000000000000
χ564444-4-4-4-4-200002-22-22-22000000000000−666−6−666−600000000000000000000000000
χ5744-4-444-4-4-24-44-42-222-22-200000000-222-20000000000000000000000000000000000
χ5844-4-4-4-444-20000-2-2-22222000022−2222−220000−22−22−22−2200000000000000000000000000
χ5944-4-4-4-444-20000-2-2-222220000−2222−222200002−22−22−22−200000000000000000000000000
χ604-44-44-44-4-20000-222-222-20000−2i22i22i2−2i20000i2−i2i2−i2−i2i2−i2i200000000000000000000000000
χ614-44-44-44-4-20000-222-222-200002i2−2i2−2i22i20000−i2i2−i2i2i2−i2i2−i200000000000000000000000000
χ624-44-4-44-44-24-4-4422-2-2-22200000000-22-220000000000000000000000000000000000
χ634-4-444-4-4440000-4-44-4-4440000000000000000000000000000000000000000000000
χ644-4-444-4-44-2000022-222-2-2000000000000i6−i6−i6i6−i6i6i6−i600000000000000000000000000
χ654-4-444-4-44-2000022-222-2-2000000000000−i6i6i6−i6i6−i6−i6i600000000000000000000000000
χ664-4-44-444-4-2-4-444-2222-2-220000000022-2-20000000000000000000000000000000000

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