Finite Group Databasebeta

← Group #68580

Character table — Group #68580

Order 384.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57
size1111222222222222222244444444444444488888888888812121212121212124848
order122234444666888812121212488121212122424242424242424888824242424242424242244888824
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
χ5111111111111-1-1-1-111111-1-11111-1-1-1-1-1-1-1-111-1-11111-1-1-1-11111-1-1-1-11-1
χ6111111111111-1-1-1-111111-1-11111-1-1-1-1-1-1-1-111-1-11111-1-1-1-1-1-1-1-11111-11
χ7111111111111-1-1-1-111111-1-11111-1-1-1-1-1-1-1-1-1-111-1-1-1-111111111-1-1-1-1-11
χ8111111111111-1-1-1-111111-1-11111-1-1-1-1-1-1-1-1-1-111-1-1-1-11111-1-1-1-111111-1
χ9222222-22-222200002222-200-2-2-2-20000000000000000000022-2-2000000
χ10222222-22-222200002222-200-2-2-2-200000000000000000000-2-222000000
χ1122222-22-222222222-2-2-2-2-2-2-2-2-2222222-2-2-2-20000000000000000000000
χ1222222-22-22222-2-2-2-2-2-2-2-2-222-2-222-2-2-2-222220000000000000000000000
χ1322222-2-2-2-22220000-2-2-2-220022-2-20000000000000000000000002i2i−2i−2i00
χ1422222-2-2-2-22220000-2-2-2-220022-2-2000000000000000000000000−2i−2i2i2i00
χ152222-12222-1-1-12222-1-1-1-1222-1-1-1-1-1-1-1-1-1-1-1-12222-1-1-1-1-1-1-1-10000000000
χ162222-12222-1-1-12222-1-1-1-1222-1-1-1-1-1-1-1-1-1-1-1-1-2-2-2-2111111110000000000
χ172222-12222-1-1-1-2-2-2-2-1-1-1-12-2-2-1-1-1-11111111122-2-2-1-1-1-111110000000000
χ182222-12222-1-1-1-2-2-2-2-1-1-1-12-2-2-1-1-1-111111111-2-2221111-1-1-1-10000000000
χ192222-1-22-22-1-1-122221111-2-2-211-1-1-1-1-1-11111000033−3−333−3−30000000000
χ202222-1-22-22-1-1-122221111-2-2-211-1-1-1-1-1-111110000−3−333−3−3330000000000
χ212222-1-22-22-1-1-1-2-2-2-21111-22211-1-11111-1-1-1-1000033−3−3−3−3330000000000
χ222222-1-22-22-1-1-1-2-2-2-21111-22211-1-11111-1-1-1-10000−3−33333−3−30000000000
χ232-22-22020-22-2-22i2i−2i−2i0000000002-22i2i−2i−2i00002−2−i2i22−22−2−i2i2−i2i20000000000
χ242-22-22020-22-2-22i2i−2i−2i0000000002-22i2i−2i−2i0000−22i2−i2−22−22i2−i2i2−i20000000000
χ252-22-22020-22-2-2−2i−2i2i2i0000000002-2−2i−2i2i2i00002−2i2−i22−22−2i2−i2i2−i20000000000
χ262-22-22020-22-2-2−2i−2i2i2i0000000002-2−2i−2i2i2i0000−22−i2i2−22−22−i2i2−i2i20000000000
χ272-22-2-1020-2-1112i2i−2i−2i3−33−30003−3-11−i−iii−i3−i3i3i32−2−i2i2ζ5−ζ7−ζ5+ζ7ζ13−ζ23−ζ13+ζ23ζ13+ζ23−ζ13−ζ23ζ5+ζ7−ζ5−ζ70000000000
χ282-22-2-1020-2-1112i2i−2i−2i3−33−30003−3-11−i−iii−i3−i3i3i3−22i2−i2−ζ5+ζ7ζ5−ζ7−ζ13+ζ23ζ13−ζ23−ζ13−ζ23ζ13+ζ23−ζ5−ζ7ζ5+ζ70000000000
χ292-22-2-1020-2-1112i2i−2i−2i−33−33000−33-11−i−iiii3i3−i3−i32−2−i2i2ζ13−ζ23−ζ13+ζ23ζ5−ζ7−ζ5+ζ7ζ5+ζ7−ζ5−ζ7ζ13+ζ23−ζ13−ζ230000000000
χ302-22-2-1020-2-1112i2i−2i−2i−33−33000−33-11−i−iiii3i3−i3−i3−22i2−i2−ζ13+ζ23ζ13−ζ23−ζ5+ζ7ζ5−ζ7−ζ5−ζ7ζ5+ζ7−ζ13−ζ23ζ13+ζ230000000000
χ312-22-2-1020-2-111−2i−2i2i2i3−33−30003−3-11ii−i−ii3i3−i3−i32−2i2−i2ζ5−ζ7−ζ5+ζ7ζ13−ζ23−ζ13+ζ23−ζ13−ζ23ζ13+ζ23−ζ5−ζ7ζ5+ζ70000000000
χ322-22-2-1020-2-111−2i−2i2i2i3−33−30003−3-11ii−i−ii3i3−i3−i3−22−i2i2−ζ5+ζ7ζ5−ζ7−ζ13+ζ23ζ13−ζ23ζ13+ζ23−ζ13−ζ23ζ5+ζ7−ζ5−ζ70000000000
χ332-22-2-1020-2-111−2i−2i2i2i−33−33000−33-11ii−i−i−i3−i3i3i32−2i2−i2ζ13−ζ23−ζ13+ζ23ζ5−ζ7−ζ5+ζ7−ζ5−ζ7ζ5+ζ7−ζ13−ζ23ζ13+ζ230000000000
χ342-22-2-1020-2-111−2i−2i2i2i−33−33000−33-11ii−i−i−i3−i3i3i3−22−i2i2−ζ13+ζ23ζ13−ζ23−ζ5+ζ7ζ5−ζ7ζ5+ζ7−ζ5−ζ7ζ13+ζ23−ζ13−ζ230000000000
χ352-2-22220-20-22-22−22−222-2-202−200002−22−22−22−2000000000000002i−2i−i2i2−i2i200
χ362-2-22220-20-22-22−22−222-2-202−200002−22−22−22−200000000000000−2i2ii2−i2i2−i200
χ372-2-22220-20-22-2−22−2222-2-20−220000−22−22−22−22000000000000002i−2ii2−i2i2−i200
χ382-2-22220-20-22-2−22−2222-2-20−220000−22−22−22−2200000000000000−2i2i−i2i2−i2i200
χ392-2-222-2020-22-22−22−2-2-2220−2200002−22−2−22−220000000000002-2002−2−2200
χ402-2-222-2020-22-22−22−2-2-2220−2200002−22−2−22−22000000000000-2200−222−200
χ412-2-222-2020-22-2−22−22-2-22202−20000−22−222−22−20000000000002-200−222−200
χ422-2-222-2020-22-2−22−22-2-22202−20000−22−222−22−2000000000000-22002−2−2200
χ434444-24-44-4-2-2-20000-2-2-2-2-4002222000000000000000000000000000000
χ444444-2-4-4-4-4-2-2-200002222400-2-222000000000000000000000000000000
χ4544-4-440000-4-44−2i22i22i2−2i200000000000−2i22i22i2−2i200000000000000000000000000
χ4644-4-440000-4-442i2−2i2−2i22i2000000000002i2−2i2−2i22i200000000000000000000000000
χ4744-4-4-2000022-2−2i22i22i2−2i223−23−23230000000i2−i2−i2i2i6−i6−i6i60000000000000000000000
χ4844-4-4-2000022-2−2i22i22i2−2i2−232323−230000000i2−i2−i2i2−i6i6i6−i60000000000000000000000
χ4944-4-4-2000022-22i2−2i2−2i22i223−23−23230000000−i2i2i2−i2−i6i6i6−i60000000000000000000000
χ5044-4-4-2000022-22i2−2i2−2i22i2−232323−230000000−i2i2i2−i2i6−i6−i6i60000000000000000000000
χ514-44-440-4044-4-40000000000000-44000000000000000000000000000000
χ524-44-4-20-404-222000023−2323−23000−23232-2000000000000000000000000000000
χ534-44-4-20-404-2220000−2323−232300023−232-2000000000000000000000000000000
χ544-4-44-240-402-2222−2222−22-2-222022−220000−22−22−22−220000000000000000000000
χ554-4-44-240-402-22−2222−2222-2-2220−222200002−22−22−22−20000000000000000000000
χ564-4-44-2-40402-2222−2222−2222-2-20−22220000−22−222−22−20000000000000000000000
χ574-4-44-2-40402-22−2222−222222-2-2022−2200002−22−2−22−220000000000000000000000

Here ζ is a primitive root of unity of order 24 (ζ24 = 1); i = ζ6.