Finite Group Databasebeta

← Group #68751

Character table — Group #68751

Order 384.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54
size11112222222222222244444444444444448888888888882424242424242424
order1244222344466612121212444466121212121212121212124488121212122424242444888888
χ1111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1
χ31111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1
χ41111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111
χ5111111111111111111-1-1-1-11111-1-1-1-1-1-1-1-111-1-11111-1-1-1-111-1-111-1-1
χ6111111111111111111-1-1-1-11111-1-1-1-1-1-1-1-111-1-11111-1-1-1-1-1-111-1-111
χ7111111111111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-111-1-1-1-1111111-1-1-1-111
χ8111111111111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-111-1-1-1-11111-1-11111-1-1
χ92222222-1222-1-1-1-1-1-1-12222-1-1-1-1-1-1-1-1-1-1-1-12222-1-1-1-1-1-1-1-100000000
χ102222222-1222-1-1-1-1-1-1-12222-1-1-1-1-1-1-1-1-1-1-1-1-2-2-2-21111111100000000
χ112222222-1222-1-1-1-1-1-1-1-2-2-2-2-1-1-1-11111111122-2-2-1-1-1-1111100000000
χ122222222-1222-1-1-1-1-1-1-1-2-2-2-2-1-1-1-111111111-2-2221111-1-1-1-100000000
χ1322222-2-222-2-222222220000-2-2-2-2000000000000000000002i−2i000000
χ1422222-2-222-2-222222220000-2-2-2-200000000000000000000−2i2i000000
χ152222-22-22-2-222-2-2-2-2220000-222-20000000000000000000000002-200
χ162222-22-22-2-222-2-2-2-2220000-222-2000000000000000000000000-2200
χ172222-2-222-22-22-2-2-2-22200002-2-22000000002i−2i002i2i−2i−2i000000000000
χ182222-2-222-22-22-2-2-2-22200002-2-2200000000−2i2i00−2i−2i2i2i000000000000
χ192222-2-22-1-22-2-11111-1-10000-111-13333−3−3−3−32i−2i00−i−iii−i3−i3i3i300000000
χ202222-2-22-1-22-2-11111-1-10000-111-13333−3−3−3−3−2i2i00ii−i−ii3i3−i3−i300000000
χ212222-2-22-1-22-2-11111-1-10000-111-1−3−3−3−333332i−2i00−i−iiii3i3−i3−i300000000
χ222222-2-22-1-22-2-11111-1-10000-111-1−3−3−3−33333−2i2i00ii−i−i−i3−i3i3i300000000
χ2322-2-22222-2-2-2222-2-2-2-2000022-2-2000000000000000000000000002i−2i
χ2422-2-22222-2-2-2222-2-2-2-2000022-2-200000000000000000000000000−2i2i
χ2522-2-22-2-22-222222-2-2-2-20000-2-22200000000002i−2i00002i−2i2i−2i00000000
χ2622-2-22-2-22-222222-2-2-2-20000-2-2220000000000−2i2i0000−2i2i−2i2i00000000
χ2722-2-22-2-2-1-222-1-1-11111000011-1-133−3−333−3−3002i−2i−i3i3−i3i3−ii−ii00000000
χ2822-2-22-2-2-1-222-1-1-11111000011-1-133−3−333−3−300−2i2ii3−i3i3−i3i−ii−i00000000
χ2922-2-22-2-2-1-222-1-1-11111000011-1-1−3−333−3−333002i−2ii3−i3i3−i3−ii−ii00000000
χ3022-2-22-2-2-1-222-1-1-11111000011-1-1−3−333−3−33300−2i2i−i3i3−i3i3i−ii−i00000000
χ3122-2-2-22-2222-22-2-222-2-222-2-2-22-2222-2-2-2-22200000000000000000000
χ3222-2-2-22-2222-22-2-222-2-2-2-222-22-22-2-22222-2-200000000000000000000
χ3322-2-2-22-2-122-2-111-1-11122-2-21-11-1-1-11111-1-100003−3−33−333−300000000
χ3422-2-2-22-2-122-2-111-1-11122-2-21-11-1-1-11111-1-10000−333−33−3−3300000000
χ3522-2-2-22-2-122-2-111-1-111-2-2221-11-111-1-1-1-11100003−3−333−3−3300000000
χ3622-2-2-22-2-122-2-111-1-111-2-2221-11-111-1-1-1-1110000−333−3−333−300000000
χ3722-2-2-2-2222-222-2-222-2-200002-22-200000000000000000000002i−2i0000
χ3822-2-2-2-2222-222-2-222-2-200002-22-20000000000000000000000−2i2i0000
χ3944444-4-4-24-4-4-2-2-2-2-2-2-2000022220000000000000000000000000000
χ404444-44-4-2-4-44-22222-2-200002-2-220000000000000000000000000000
χ4144-4-4444-2-4-4-4-2-2-222220000-2-2220000000000000000000000000000
χ4244-4-4-4-44-24-44-222-2-2220000-22-220000000000000000000000000000
χ434-44i−4i0004000-400004i−4i2-22i−2i00002-22i−2i2i−2i2-200000000000000000000
χ444-44i−4i0004000-400004i−4i-22−2i2i0000-22−2i2i−2i2i-2200000000000000000000
χ454-44i−4i000-20002−2i32i323−23−2i2i2-22i−2i0000−1+31−3ζ2+ζ7−ζ10+ζ11−ζ2−ζ7+ζ10−ζ11−ζ2+ζ7+ζ10+ζ11ζ2−ζ7−ζ10−ζ11−1−31+300000000000000000000
χ464-44i−4i000-20002−2i32i323−23−2i2i-22−2i2i00001−3−1+3−ζ2−ζ7+ζ10−ζ11ζ2+ζ7−ζ10+ζ11ζ2−ζ7−ζ10−ζ11−ζ2+ζ7+ζ10+ζ111+3−1−300000000000000000000
χ474-44i−4i000-200022i3−2i3−2323−2i2i2-22i−2i0000−1−31+3−ζ2+ζ7+ζ10+ζ11ζ2−ζ7−ζ10−ζ11ζ2+ζ7−ζ10+ζ11−ζ2−ζ7+ζ10−ζ11−1+31−300000000000000000000
χ484-44i−4i000-200022i3−2i3−2323−2i2i-22−2i2i00001+3−1−3ζ2−ζ7−ζ10−ζ11−ζ2+ζ7+ζ10+ζ11−ζ2−ζ7+ζ10−ζ11ζ2+ζ7−ζ10+ζ111−3−1+300000000000000000000
χ494-4−4i4i0004000-40000−4i4i2-2−2i2i00002-2−2i2i−2i2i2-200000000000000000000
χ504-4−4i4i0004000-40000−4i4i-222i−2i0000-222i−2i2i−2i-2200000000000000000000
χ514-4−4i4i000-20002−2i32i3−23232i−2i2-2−2i2i0000−1−31+3ζ2−ζ7−ζ10−ζ11−ζ2+ζ7+ζ10+ζ11−ζ2−ζ7+ζ10−ζ11ζ2+ζ7−ζ10+ζ11−1+31−300000000000000000000
χ524-4−4i4i000-20002−2i32i3−23232i−2i-222i−2i00001+3−1−3−ζ2+ζ7+ζ10+ζ11ζ2−ζ7−ζ10−ζ11ζ2+ζ7−ζ10+ζ11−ζ2−ζ7+ζ10−ζ111−3−1+300000000000000000000
χ534-4−4i4i000-200022i3−2i323−232i−2i2-2−2i2i0000−1+31−3−ζ2−ζ7+ζ10−ζ11ζ2+ζ7−ζ10+ζ11ζ2−ζ7−ζ10−ζ11−ζ2+ζ7+ζ10+ζ11−1−31+300000000000000000000
χ544-4−4i4i000-200022i3−2i323−232i−2i-222i−2i00001−3−1+3ζ2+ζ7−ζ10+ζ11−ζ2−ζ7+ζ10−ζ11−ζ2+ζ7+ζ10+ζ11ζ2−ζ7−ζ10−ζ111+3−1−300000000000000000000

Here ζ is a primitive root of unity of order 12 (ζ12 = 1); i = ζ3.