Finite Group Databasebeta

← Group #68907

Character table — Group #68907

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
χ911-1-11-11-111-1-111-1-1-111-1ii−i−iii−i−i11-1-1iiii−i−i−i−iii−i−i1-1ii−i−i11-1-1i−i11-1-111-1-1i−i
χ1011-1-11-11-111-1-111-1-1-111-1ii−i−iii−i−i11-1-1iiii−i−i−i−i−i−iii1-1ii−i−i11-1-1−ii-1-111-1-111−ii
χ1111-1-11-11-111-1-111-1-1-111-1ii−i−i−i−iii11-1-1−i−i−i−iiiiiii−i−i-11ii−i−i-1-111i−i11-1-1-1-111−ii
χ1211-1-11-11-111-1-111-1-1-111-1ii−i−i−i−iii11-1-1−i−i−i−iiiii−i−iii-11ii−i−i-1-111−ii-1-11111-1-1i−i
χ1311-1-11-11-111-1-111-1-1-111-1−i−iiiii−i−i11-1-1iiii−i−i−i−iii−i−i-11−i−iii-1-111i−i-1-11111-1-1−ii
χ1411-1-11-11-111-1-111-1-1-111-1−i−iiiii−i−i11-1-1iiii−i−i−i−i−i−iii-11−i−iii-1-111−ii11-1-1-1-111i−i
χ1511-1-11-11-111-1-111-1-1-111-1−i−iii−i−iii11-1-1−i−i−i−iiiiiii−i−i1-1−i−iii11-1-1i−i-1-111-1-111i−i
χ1611-1-11-11-111-1-111-1-1-111-1−i−iii−i−iii11-1-1−i−i−i−iiiii−i−iii1-1−i−iii11-1-1−ii11-1-111-1-1−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
χ2322-2-22-22-22-222-22-2-2-222-200000000-2-222000000002i2i−2i−2i0000000000−2i2i0000000000
χ2422-2-22-22-22-222-22-2-2-222-200000000-2-22200000000−2i−2i2i2i00000000002i−2i0000000000
χ2522-2-22-22-2-12-2-22-1111-1-112i2i−2i−2i2i2i−2i−2i-1-111−i−i−i−iiiii00002-2−i−iii-1-111000000000000
χ2622-2-22-22-2-12-2-22-1111-1-112i2i−2i−2i−2i−2i2i2i-1-111iiii−i−i−i−i0000-22−i−iii11-1-1000000000000
χ2722-2-22-22-2-12-2-22-1111-1-11−2i−2i2i2i2i2i−2i−2i-1-111−i−i−i−iiiii0000-22ii−i−i11-1-1000000000000
χ2822-2-22-22-2-12-2-22-1111-1-11−2i−2i2i2i−2i−2i2i2i-1-111iiii−i−i−i−i00002-2ii−i−i-1-111000000000000
χ292-222-2-22-2222-2-2-222-22-2-2000000002-22-20000000000000000000000002-22-2000000
χ302-222-2-22-2222-2-2-222-22-2-2000000002-22-2000000000000000000000000-22-22000000
χ312-222-2-22-22-2-222-222-22-2-22i−2i2i−2i0000-22-22000000000000002i−2i2i−2i0000000000000000
χ322-222-2-22-22-2-222-222-22-2-2−2i2i−2i2i0000-22-2200000000000000−2i2i−2i2i0000000000000000
χ332-222-2-22-2-1-2-2221-1-11-1112i−2i2i−2i00001-11-1−i3−i3i3i3−i3−i3i3i3000000−ii−ii3−33−3000000000000
χ342-222-2-22-2-1-2-2221-1-11-1112i−2i2i−2i00001-11-1i3i3−i3−i3i3i3−i3−i3000000−ii−ii−33−33000000000000
χ352-222-2-22-2-1-2-2221-1-11-111−2i2i−2i2i00001-11-1−i3−i3i3i3−i3−i3i3i3000000i−ii−i−33−33000000000000
χ362-222-2-22-2-1-2-2221-1-11-111−2i2i−2i2i00001-11-1i3i3−i3−i3i3i3−i3−i3000000i−ii−i3−33−3000000000000
χ372-22-222-2-220000-22-2-2-22200002−22−200002−22−22−22−22i−2i2i−2i0000000000000000−i2i2−i2i200
χ382-22-222-2-220000-22-2-2-22200002−22−200002−22−22−22−2−2i2i−2i2i0000000000000000i2−i2i2−i200
χ392-22-222-2-220000-22-2-2-2220000−22−220000−22−22−22−222i−2i2i−2i0000000000000000i2−i2i2−i200
χ402-22-222-2-220000-22-2-2-2220000−22−220000−22−22−22−22−2i2i−2i2i0000000000000000−i2i2−i2i200
χ412-2-222-2-2220000-2-222-22-20000−i2i2i2−i20000−i2i2−i2i2i2−i2i2−i22-2-220000000000000000−i2i2i2−i200
χ422-2-222-2-2220000-2-222-22-20000−i2i2i2−i20000−i2i2−i2i2i2−i2i2−i2-222-20000000000000000i2−i2−i2i200
χ432-2-222-2-2220000-2-222-22-20000i2−i2−i2i20000i2−i2i2−i2−i2i2−i2i22-2-220000000000000000i2−i2−i2i200
χ442-2-222-2-2220000-2-222-22-20000i2−i2−i2i20000i2−i2i2−i2−i2i2−i2i2-222-20000000000000000−i2i2i2−i200
χ452-2-2-2-222222-22-2-2-2-222-22000000002-2-220000000000000000000000002-2-22000000
χ462-2-2-2-222222-22-2-2-2-222-22000000002-2-22000000000000000000000000-222-2000000
χ472-2-2-2-22222-22-22-2-2-222-222-2-220000-222-2000000000000002-2-220000000000000000
χ482-2-2-2-22222-22-22-2-2-222-22-222-20000-222-200000000000000-222-20000000000000000
χ492-2-2-2-2222-1-22-22111-1-11-12-2-2200001-1-1133−3−3−3−333000000-111-1−333−3000000000000
χ502-2-2-2-2222-1-22-22111-1-11-12-2-2200001-1-11−3−33333−3−3000000-111-13−3−33000000000000
χ512-2-2-2-2222-1-22-22111-1-11-1-222-200001-1-1133−3−3−3−3330000001-1-113−3−33000000000000
χ522-2-2-2-2222-1-22-22111-1-11-1-222-200001-1-11−3−33333−3−30000001-1-11−333−3000000000000
χ5344444444-2-4-4-4-4-2-2-2-2-2-2-20000000022220000000000000000000000000000000000
χ54444-4-4-4-444000044-44-4-4-40000000000000000000000000000000000000000000000
χ55444-4-4-4-44-20000-2-22-2222000000000000i6−i6−i6i6i6−i6−i6i600000000000000000000000000
χ56444-4-4-4-44-20000-2-22-2222000000000000−i6i6i6−i6−i6i6i6−i600000000000000000000000000
χ5744-44-44-4-4400004-44-4-4-440000000000000000000000000000000000000000000000
χ5844-44-44-4-4-20000-22-2222-20000000000006−6−66−666−600000000000000000000000000
χ5944-44-44-4-4-20000-22-2222-2000000000000−666−66−6−6600000000000000000000000000
χ6044-4-44-44-4-2-444-4-2222-2-220000000022-2-20000000000000000000000000000000000
χ614-444-4-44-4-244-4-42-2-22-22200000000-22-220000000000000000000000000000000000
χ624-44-444-4-4-200002-2222-2-2000022−2222−220000−22−22−22−2200000000000000000000000000
χ634-44-444-4-4-200002-2222-2-20000−2222−222200002−22−22−22−200000000000000000000000000
χ644-4-444-4-44-2000022-2-22-220000−2i22i22i2−2i20000i2−i2i2−i2−i2i2−i2i200000000000000000000000000
χ654-4-444-4-44-2000022-2-22-2200002i2−2i2−2i22i20000−i2i2−i2i2i2−i2i2−i200000000000000000000000000
χ664-4-4-4-4444-24-44-4222-2-22-200000000-222-20000000000000000000000000000000000

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