Finite Group Databasebeta

← Group #67488

Character table — Group #67488

Order 384.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57
size1111222222222222222244444444444444488888888888812121212121212124848
order122234444666888812121212266881212242424242424242488882424242424242424161616161616161644
χ1111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1
χ311111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1
χ411111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111
χ51111111-1-1111-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1ii−i−iiiii−i−i−i−iiiii−i−i−i−i1-1
χ61111111-1-1111-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1ii−i−iiiii−i−i−i−i−i−i−i−iiiii-11
χ71111111-1-1111-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1−i−iii−i−i−i−iiiiiiiii−i−i−i−i-11
χ81111111-1-1111-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1−i−iii−i−i−i−iiiii−i−i−i−iiiii1-1
χ9222222222222-2-2-2-22222222-2-222-2-2-2-2-2-2-2-20000000000000000000000
χ102222222-2-22222222-2-2-2-2-2-2-2-2-222-2-2-2-222220000000000000000000000
χ1122222-2-22222200002222-2-2-200-2-20000000000000000000022−2−222−2−200
χ1222222-2-22222200002222-2-2-200-2-200000000000000000000−2−222−2−22200
χ1322222-2-2-2-22220000-2-2-2-222200-2-200000000000000000000−i2−i2i2i2i2i2−i2−i200
χ1422222-2-2-2-22220000-2-2-2-222200-2-200000000000000000000i2i2−i2−i2−i2−i2i2i200
χ152222-12222-1-1-12222-1-1-1-12-1-122-1-1-1-1-1-1-1-1-1-12222-1-1-1-1-1-1-1-10000000000
χ162222-12222-1-1-12222-1-1-1-12-1-122-1-1-1-1-1-1-1-1-1-1-2-2-2-2111111110000000000
χ172222-12222-1-1-1-2-2-2-2-1-1-1-12-1-1-2-2-1-1111111110000−i3−i3i3i3−i3−i3i3i30000000000
χ182222-12222-1-1-1-2-2-2-2-1-1-1-12-1-1-2-2-1-1111111110000i3i3−i3−i3i3i3−i3−i30000000000
χ192222-122-2-2-1-1-122221111-211-2-2-1-11111-1-1-1-1000033−3−3−3−3330000000000
χ202222-122-2-2-1-1-122221111-211-2-2-1-11111-1-1-1-10000−3−33333−3−30000000000
χ212222-122-2-2-1-1-1-2-2-2-21111-21122-1-1-1-1-1-111112i2i−2i−2i−i−i−i−iiiii0000000000
χ222222-122-2-2-1-1-1-2-2-2-21111-21122-1-1-1-1-1-11111−2i−2i2i2iiiii−i−i−i−i0000000000
χ232-22-22002i−2i2-2-2−i2−i2i2i22i2i−2i−2i0002−20022−2−2−i2−i2i2i2000000000000ζ11−ζ25−ζ41+ζ43−ζ11+ζ25+ζ41−ζ43−ζ13−ζ29−ζ31−ζ47ζ13+ζ29+ζ31+ζ47−ζ13−ζ29+ζ31+ζ47ζ13+ζ29−ζ31−ζ47ζ11+ζ25+ζ41+ζ43−ζ11−ζ25−ζ41−ζ4300
χ242-22-22002i−2i2-2-2−i2−i2i2i22i2i−2i−2i0002−20022−2−2−i2−i2i2i2000000000000−ζ11+ζ25+ζ41−ζ43ζ11−ζ25−ζ41+ζ43ζ13+ζ29+ζ31+ζ47−ζ13−ζ29−ζ31−ζ47ζ13+ζ29−ζ31−ζ47−ζ13−ζ29+ζ31+ζ47−ζ11−ζ25−ζ41−ζ43ζ11+ζ25+ζ41+ζ4300
χ252-22-22002i−2i2-2-2i2i2−i2−i22i2i−2i−2i000−2200−2−222i2i2−i2−i2000000000000−ζ13−ζ29−ζ31−ζ47ζ13+ζ29+ζ31+ζ47−ζ11+ζ25+ζ41−ζ43ζ11−ζ25−ζ41+ζ43ζ11+ζ25+ζ41+ζ43−ζ11−ζ25−ζ41−ζ43ζ13+ζ29−ζ31−ζ47−ζ13−ζ29+ζ31+ζ4700
χ262-22-22002i−2i2-2-2i2i2−i2−i22i2i−2i−2i000−2200−2−222i2i2−i2−i2000000000000ζ13+ζ29+ζ31+ζ47−ζ13−ζ29−ζ31−ζ47ζ11−ζ25−ζ41+ζ43−ζ11+ζ25+ζ41−ζ43−ζ11−ζ25−ζ41−ζ43ζ11+ζ25+ζ41+ζ43−ζ13−ζ29+ζ31+ζ47ζ13+ζ29−ζ31−ζ4700
χ272-22-2200−2i2i2-2-2−i2−i2i2i2−2i−2i2i2i000−2200−2−222−i2−i2i2i2000000000000ζ11+ζ25+ζ41+ζ43−ζ11−ζ25−ζ41−ζ43ζ13+ζ29−ζ31−ζ47−ζ13−ζ29+ζ31+ζ47−ζ13−ζ29−ζ31−ζ47ζ13+ζ29+ζ31+ζ47−ζ11+ζ25+ζ41−ζ43ζ11−ζ25−ζ41+ζ4300
χ282-22-2200−2i2i2-2-2−i2−i2i2i2−2i−2i2i2i000−2200−2−222−i2−i2i2i2000000000000−ζ11−ζ25−ζ41−ζ43ζ11+ζ25+ζ41+ζ43−ζ13−ζ29+ζ31+ζ47ζ13+ζ29−ζ31−ζ47ζ13+ζ29+ζ31+ζ47−ζ13−ζ29−ζ31−ζ47ζ11−ζ25−ζ41+ζ43−ζ11+ζ25+ζ41−ζ4300
χ292-22-2200−2i2i2-2-2i2i2−i2−i2−2i−2i2i2i0002−20022−2−2i2i2−i2−i2000000000000−ζ13−ζ29+ζ31+ζ47ζ13+ζ29−ζ31−ζ47ζ11+ζ25+ζ41+ζ43−ζ11−ζ25−ζ41−ζ43ζ11−ζ25−ζ41+ζ43−ζ11+ζ25+ζ41−ζ43−ζ13−ζ29−ζ31−ζ47ζ13+ζ29+ζ31+ζ4700
χ302-22-2200−2i2i2-2-2i2i2−i2−i2−2i−2i2i2i0002−20022−2−2i2i2−i2−i2000000000000ζ13+ζ29−ζ31−ζ47−ζ13−ζ29+ζ31+ζ47−ζ11−ζ25−ζ41−ζ43ζ11+ζ25+ζ41+ζ43−ζ11+ζ25+ζ41−ζ43ζ11−ζ25−ζ41+ζ43ζ13+ζ29+ζ31+ζ47−ζ13−ζ29−ζ31−ζ4700
χ312-2-2222-200-2-222i−2i2i−2i0000000002-200002i−2i2i−2i1+i−1−i1−i−1+i1+i−1−i1+i−1−i1−i−1+i1−i−1+i0000000000
χ322-2-2222-200-2-222i−2i2i−2i0000000002-200002i−2i2i−2i−1−i1+i−1+i1−i−1−i1+i−1−i1+i−1+i1−i−1+i1−i0000000000
χ332-2-2222-200-2-22−2i2i−2i2i0000000002-20000−2i2i−2i2i1−i−1+i1+i−1−i1−i−1+i1−i−1+i1+i−1−i1+i−1−i0000000000
χ342-2-2222-200-2-22−2i2i−2i2i0000000002-20000−2i2i−2i2i−1+i1−i−1−i1+i−1+i1−i−1+i1−i−1−i1+i−1−i1+i0000000000
χ352-2-22-12-20011-12i−2i2i−2i−i3i3−i3i30−i3i300-113−33−3−ii−ii1+i−1−i1−i−1+i−ζ8+ζ28ζ8−ζ28−ζ40+ζ44ζ40−ζ44−ζ8−ζ28ζ8+ζ28−ζ40−ζ44ζ40+ζ440000000000
χ362-2-22-12-20011-12i−2i2i−2i−i3i3−i3i30−i3i300-113−33−3−ii−ii−1−i1+i−1+i1−iζ8−ζ28−ζ8+ζ28ζ40−ζ44−ζ40+ζ44ζ8+ζ28−ζ8−ζ28ζ40+ζ44−ζ40−ζ440000000000
χ372-2-22-12-20011-12i−2i2i−2ii3−i3i3−i30i3−i300-11−33−33−ii−ii1+i−1−i1−i−1+i−ζ40+ζ44ζ40−ζ44−ζ8+ζ28ζ8−ζ28−ζ40−ζ44ζ40+ζ44−ζ8−ζ28ζ8+ζ280000000000
χ382-2-22-12-20011-12i−2i2i−2ii3−i3i3−i30i3−i300-11−33−33−ii−ii−1−i1+i−1+i1−iζ40−ζ44−ζ40+ζ44ζ8−ζ28−ζ8+ζ28ζ40+ζ44−ζ40−ζ44ζ8+ζ28−ζ8−ζ280000000000
χ392-2-22-12-20011-1−2i2i−2i2i−i3i3−i3i30−i3i300-11−33−33i−ii−i1−i−1+i1+i−1−i−ζ8−ζ28ζ8+ζ28−ζ40−ζ44ζ40+ζ44−ζ8+ζ28ζ8−ζ28−ζ40+ζ44ζ40−ζ440000000000
χ402-2-22-12-20011-1−2i2i−2i2i−i3i3−i3i30−i3i300-11−33−33i−ii−i−1+i1−i−1−i1+iζ8+ζ28−ζ8−ζ28ζ40+ζ44−ζ40−ζ44ζ8−ζ28−ζ8+ζ28ζ40−ζ44−ζ40+ζ440000000000
χ412-2-22-12-20011-1−2i2i−2i2ii3−i3i3−i30i3−i300-113−33−3i−ii−i1−i−1+i1+i−1−i−ζ40−ζ44ζ40+ζ44−ζ8−ζ28ζ8+ζ28−ζ40+ζ44ζ40−ζ44−ζ8+ζ28ζ8−ζ280000000000
χ422-2-22-12-20011-1−2i2i−2i2ii3−i3i3−i30i3−i300-113−33−3i−ii−i−1+i1−i−1−i1+iζ40+ζ44−ζ40−ζ44ζ8+ζ28−ζ8−ζ28ζ40−ζ44−ζ40+ζ44ζ8−ζ28−ζ8+ζ280000000000
χ434444-2-4-444-2-2-20000-2-2-2-2-4220022000000000000000000000000000000
χ444444-2-4-4-4-4-2-2-2000022224-2-20022000000000000000000000000000000
χ4544-4-440000-44-422−22−222200000000000000022−22−22220000000000000000000000
χ4644-4-440000-44-4−222222−22000000000000000−222222−220000000000000000000000
χ4744-4-4-200002-2222−22−222223−23−232300000006−6−66−222−20000000000000000000000
χ4844-4-4-200002-2222−22−2222−232323−230000000−666−6−222−20000000000000000000000
χ4944-4-4-200002-22−222222−2223−23−23230000000−666−62−2−220000000000000000000000
χ5044-4-4-200002-22−222222−22−232323−2300000006−6−662−2−220000000000000000000000
χ514-44-4-2004i−4i-222−2i2−2i22i22i2−2i−2i2i2i00022−2200−2−222i2i2−i2−i20000000000000000000000
χ524-44-4-2004i−4i-2222i22i2−2i2−2i2−2i−2i2i2i000−22220022−2−2−i2−i2i2i20000000000000000000000
χ534-44-4-200−4i4i-222−2i2−2i22i22i22i2i−2i−2i000−22220022−2−2i2i2−i2−i20000000000000000000000
χ544-44-4-200−4i4i-2222i22i2−2i2−2i22i2i−2i−2i00022−2200−2−222−i2−i2i2i20000000000000000000000
χ554-4-444-4400-4-440000000000000-44000000000000000000000000000000
χ564-4-44-2-440022-20000−2i32i3−2i32i302i3−2i3002-2000000000000000000000000000000
χ574-4-44-2-440022-200002i3−2i32i3−2i30−2i32i3002-2000000000000000000000000000000

Here ζ is a primitive root of unity of order 48 (ζ48 = 1); i = ζ12.