Finite Group Databasebeta

← Group #68592

Character table — Group #68592

Order 384.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51
size111122222222222244444444444444444888888888888242424244848
order122234444666121212124888812121212242424242424242488882424242424242424448824
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
χ232-2-222020-22-2-2000002-200002-222-2-20000−i2i2−i2i2−i2i2−i2i2−i2i2−i2i2000000
χ242-2-222020-22-2-2000002-200002-222-2-20000i2−i2i2−i2i2−i2i2−i2i2−i2i2−i2000000
χ252-2-222020-22-2-200000-2200002-2-2-2220000−i2i2i2−i2−i2i2−i2i2i2−i2i2−i2000000
χ262-2-222020-22-2-200000-2200002-2-2-2220000i2−i2−i2i2i2−i2i2−i2−i2i2−i2i2000000
χ272-2-22-1020-2-1113−33−302-2003−3-11-1-11133−3−3−i2i2−i2i2ζ5+ζ7−ζ5−ζ7ζ13+ζ23−ζ13−ζ23ζ5+ζ7−ζ5−ζ7ζ13+ζ23−ζ13−ζ23000000
χ282-2-22-1020-2-1113−33−302-2003−3-11-1-11133−3−3i2−i2i2−i2−ζ5−ζ7ζ5+ζ7−ζ13−ζ23ζ13+ζ23−ζ5−ζ7ζ5+ζ7−ζ13−ζ23ζ13+ζ23000000
χ292-2-22-1020-2-1113−33−30-22003−3-1111-1-1−3−333−i2i2i2−i2ζ5+ζ7−ζ5−ζ7ζ13+ζ23−ζ13−ζ23−ζ5−ζ7ζ5+ζ7−ζ13−ζ23ζ13+ζ23000000
χ302-2-22-1020-2-1113−33−30-22003−3-1111-1-1−3−333i2−i2−i2i2−ζ5−ζ7ζ5+ζ7−ζ13−ζ23ζ13+ζ23ζ5+ζ7−ζ5−ζ7ζ13+ζ23−ζ13−ζ23000000
χ312-2-22-1020-2-111−33−3302-200−33-11-1-111−3−333−i2i2−i2i2ζ13+ζ23−ζ13−ζ23ζ5+ζ7−ζ5−ζ7ζ13+ζ23−ζ13−ζ23ζ5+ζ7−ζ5−ζ7000000
χ322-2-22-1020-2-111−33−3302-200−33-11-1-111−3−333i2−i2i2−i2−ζ13−ζ23ζ13+ζ23−ζ5−ζ7ζ5+ζ7−ζ13−ζ23ζ13+ζ23−ζ5−ζ7ζ5+ζ7000000
χ332-2-22-1020-2-111−33−330-2200−33-1111-1-133−3−3−i2i2i2−i2ζ13+ζ23−ζ13−ζ23ζ5+ζ7−ζ5−ζ7−ζ13−ζ23ζ13+ζ23−ζ5−ζ7ζ5+ζ7000000
χ342-2-22-1020-2-111−33−330-2200−33-1111-1-133−3−3i2−i2−i2i2−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
χ3744-4-440000-44-40000000−2i22i200000000−2i22i2−2i22i2000000000000000000
χ3844-4-440000-44-400000002i2−2i2000000002i2−2i22i2−2i2000000000000000000
χ3944-4-4-200002-2223−23−2323000−2i22i20000i6−i6i6−i6i2−i2i2−i2000000000000000000
χ4044-4-4-200002-2223−23−23230002i2−2i20000−i6i6−i6i6−i2i2−i2i2000000000000000000
χ4144-4-4-200002-22−232323−23000−2i22i20000−i6i6−i6i6i2−i2i2−i2000000000000000000
χ4244-4-4-200002-22−232323−230002i2−2i20000i6−i6i6−i6−i2i2−i2i2000000000000000000
χ434-44-4440-40-4-4444-4-400000000000000000000000000000000000
χ444-44-44-4040-4-44-4-44400000000000000000000000000000000000
χ454-44-4-240-4022-2-2-222000000000i6−i6−i6i6i6−i6−i6i6000000000000000000
χ464-44-4-240-4022-2-2-222000000000−i6i6i6−i6−i6i6i6−i6000000000000000000
χ474-44-4-2-404022-222-2-2000000000i6−i6−i6i6−i6i6i6−i6000000000000000000
χ484-44-4-2-404022-222-2-2000000000−i6i6i6−i6i6−i6−i6i6000000000000000000
χ494-4-4440-4044-4-400000000000-4400000000000000000000000000
χ504-4-44-20-404-22223−2323−2300000−23232-200000000000000000000000000
χ514-4-44-20-404-222−2323−23230000023−232-200000000000000000000000000

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