Finite Group Databasebeta

← Group #68593

Character table — Group #68593

Order 384.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51
size111122222222222244444444444444444888888888888242424244848
order122234444666121212124888812121212242424242424242488882424242424242424448844
χ1111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111111111111111-1-1-1-1-1-1
χ3111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1
χ4111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111
χ511111111111111111-1-1-1-11111-1-1-1-1-1-1-1-111-1-11111-1-1-1-111-1-11-1
χ611111111111111111-1-1-1-11111-1-1-1-1-1-1-1-111-1-11111-1-1-1-1-1-111-11
χ711111111111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-111-1-1-1-1111111-1-1-11
χ811111111111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-111-1-1-1-11111-1-1111-1
χ9222222-22-22222222-20000-2-2-2-2000000000000000000002-20000
χ10222222-22-22222222-20000-2-2-2-200000000000000000000-220000
χ1122222-22-22222-2-2-2-2-222-2-2-2-2222222-2-2-2-2000000000000000000
χ1222222-22-22222-2-2-2-2-2-2-222-2-222-2-2-2-22222000000000000000000
χ1322222-2-2-2-2222-2-2-2-22000022-2-200000000000000000000002i−2i00
χ1422222-2-2-2-2222-2-2-2-22000022-2-20000000000000000000000−2i2i00
χ152222-12222-1-1-1-1-1-1-122222-1-1-1-1-1-1-1-1-1-1-1-12222-1-1-1-1-1-1-1-1000000
χ162222-12222-1-1-1-1-1-1-122222-1-1-1-1-1-1-1-1-1-1-1-1-2-2-2-211111111000000
χ172222-12222-1-1-1-1-1-1-12-2-2-2-2-1-1-1-11111111122-2-2-1-1-1-11111000000
χ182222-12222-1-1-1-1-1-1-12-2-2-2-2-1-1-1-111111111-2-2221111-1-1-1-1000000
χ192222-1-22-22-1-1-11111-222-2-211-1-1-1-1-1-11111000033−3−333−3−3000000
χ202222-1-22-22-1-1-11111-222-2-211-1-1-1-1-1-111110000−3−333−3−333000000
χ212222-1-22-22-1-1-11111-2-2-22211-1-11111-1-1-1-1000033−3−3−3−333000000
χ222222-1-22-22-1-1-11111-2-2-22211-1-11111-1-1-1-10000−3−33333−3−3000000
χ2322-2-22020-22-2-2000002-200002-222-2-200002−22−22−22−22−22−2000000
χ2422-2-22020-22-2-2000002-200002-222-2-20000−22−22−22−22−22−22000000
χ2522-2-22020-22-2-200000-2200002-2-2-22200002−2−222−22−2−22−22000000
χ2622-2-22020-22-2-200000-2200002-2-2-2220000−222−2−22−222−22−2000000
χ2722-2-2-1020-2-1113−33−302-2003−3-11-1-11133−3−32−22−2ζ5−ζ7−ζ5+ζ7ζ13−ζ23−ζ13+ζ23ζ5−ζ7−ζ5+ζ7ζ13−ζ23−ζ13+ζ23000000
χ2822-2-2-1020-2-1113−33−302-2003−3-11-1-11133−3−3−22−22−ζ5+ζ7ζ5−ζ7−ζ13+ζ23ζ13−ζ23−ζ5+ζ7ζ5−ζ7−ζ13+ζ23ζ13−ζ23000000
χ2922-2-2-1020-2-1113−33−30-22003−3-1111-1-1−3−3332−2−22ζ5−ζ7−ζ5+ζ7ζ13−ζ23−ζ13+ζ23−ζ5+ζ7ζ5−ζ7−ζ13+ζ23ζ13−ζ23000000
χ3022-2-2-1020-2-1113−33−30-22003−3-1111-1-1−3−333−222−2−ζ5+ζ7ζ5−ζ7−ζ13+ζ23ζ13−ζ23ζ5−ζ7−ζ5+ζ7ζ13−ζ23−ζ13+ζ23000000
χ3122-2-2-1020-2-111−33−3302-200−33-11-1-111−3−3332−22−2ζ13−ζ23−ζ13+ζ23ζ5−ζ7−ζ5+ζ7ζ13−ζ23−ζ13+ζ23ζ5−ζ7−ζ5+ζ7000000
χ3222-2-2-1020-2-111−33−3302-200−33-11-1-111−3−333−22−22−ζ13+ζ23ζ13−ζ23−ζ5+ζ7ζ5−ζ7−ζ13+ζ23ζ13−ζ23−ζ5+ζ7ζ5−ζ7000000
χ3322-2-2-1020-2-111−33−330-2200−33-1111-1-133−3−32−2−22ζ13−ζ23−ζ13+ζ23ζ5−ζ7−ζ5+ζ7−ζ13+ζ23ζ13−ζ23−ζ5+ζ7ζ5−ζ7000000
χ3422-2-2-1020-2-111−33−330-2200−33-1111-1-133−3−3−222−2−ζ13+ζ23ζ13−ζ23−ζ5+ζ7ζ5−ζ7ζ13−ζ23−ζ13+ζ23ζ5−ζ7−ζ5+ζ7000000
χ354444-24-44-4-2-2-2-2-2-2-2-40000222200000000000000000000000000
χ364444-2-4-4-4-4-2-2-2222240000-2-22200000000000000000000000000
χ3744-4-440-4044-4-400000000000-4400000000000000000000000000
χ3844-4-4-20-404-22223−2323−2300000−23232-200000000000000000000000000
χ3944-4-4-20-404-222−2323−23230000023−232-200000000000000000000000000
χ404-44-440000-44-40000000−2i22i200000000−2i22i2−2i22i2000000000000000000
χ414-44-440000-44-400000002i2−2i2000000002i2−2i22i2−2i2000000000000000000
χ424-44-4-200002-2223−23−2323000−2i22i20000i6−i6i6−i6i2−i2i2−i2000000000000000000
χ434-44-4-200002-2223−23−23230002i2−2i20000−i6i6−i6i6−i2i2−i2i2000000000000000000
χ444-44-4-200002-22−232323−23000−2i22i20000−i6i6−i6i6i2−i2i2−i2000000000000000000
χ454-44-4-200002-22−232323−230002i2−2i20000i6−i6i6−i6−i2i2−i2i2000000000000000000
χ464-4-44440-40-4-4444-4-400000000000000000000000000000000000
χ474-4-444-4040-4-44-4-44400000000000000000000000000000000000
χ484-4-44-240-4022-2-2-222000000000i6−i6−i6i6i6−i6−i6i6000000000000000000
χ494-4-44-240-4022-2-2-222000000000−i6i6i6−i6−i6i6i6−i6000000000000000000
χ504-4-44-2-404022-222-2-2000000000i6−i6−i6i6−i6i6i6−i6000000000000000000
χ514-4-44-2-404022-222-2-2000000000−i6i6i6−i6i6−i6−i6i6000000000000000000

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