Finite Group Databasebeta

← Group #68541

Character table — Group #68541

Order 384.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51
size111122222222222244444444444444444888888888888242424244848
order122234444666121212124888812121212242424242424242488882424242424242424248844
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
χ9222222-2-22222-2-2-2-2-222-2-2-2-2222222-2-2-2-2000000000000000000
χ10222222-2-22222-2-2-2-2-2-2-222-2-222-2-2-2-22222000000000000000000
χ1122222-222-22222222-20000-2-2-2-2000000000000000000002-20000
χ1222222-222-22222222-20000-2-2-2-200000000000000000000-220000
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
χ192222-12-2-22-1-1-11111-222-2-211-1-1-1-1-1-11111000033−3−333−3−3000000
χ202222-12-2-22-1-1-11111-222-2-211-1-1-1-1-1-111110000−3−333−3−333000000
χ212222-12-2-22-1-1-11111-2-2-22211-1-11111-1-1-1-1000033−3−3−3−333000000
χ222222-12-2-22-1-1-11111-2-2-22211-1-11111-1-1-1-10000−3−33333−3−3000000
χ232-2-222-20022-2-200000002-2002-2000022-2-22−22−22−22−22−22−2000000
χ242-2-222-20022-2-200000002-2002-2000022-2-2−22−22−22−22−22−22000000
χ252-2-222-20022-2-20000000-22002-20000-2-2222−2−222−22−2−22−22000000
χ262-2-222-20022-2-20000000-22002-20000-2-222−222−2−22−222−22−2000000
χ272-2-22-1-2002-11133−3−30002-23−3-1133−3−3-1-1112−22−2ζ5−ζ7−ζ5+ζ7ζ13−ζ23−ζ13+ζ23ζ13−ζ23−ζ13+ζ23ζ5−ζ7−ζ5+ζ7000000
χ282-2-22-1-2002-11133−3−30002-23−3-1133−3−3-1-111−22−22−ζ5+ζ7ζ5−ζ7−ζ13+ζ23ζ13−ζ23−ζ13+ζ23ζ13−ζ23−ζ5+ζ7ζ5−ζ7000000
χ292-2-22-1-2002-11133−3−3000-223−3-11−3−33311-1-12−2−22ζ5−ζ7−ζ5+ζ7ζ13−ζ23−ζ13+ζ23−ζ13+ζ23ζ13−ζ23−ζ5+ζ7ζ5−ζ7000000
χ302-2-22-1-2002-11133−3−3000-223−3-11−3−33311-1-1−222−2−ζ5+ζ7ζ5−ζ7−ζ13+ζ23ζ13−ζ23ζ13−ζ23−ζ13+ζ23ζ5−ζ7−ζ5+ζ7000000
χ312-2-22-1-2002-111−3−3330002-2−33-11−3−333-1-1112−22−2ζ13−ζ23−ζ13+ζ23ζ5−ζ7−ζ5+ζ7ζ5−ζ7−ζ5+ζ7ζ13−ζ23−ζ13+ζ23000000
χ322-2-22-1-2002-111−3−3330002-2−33-11−3−333-1-111−22−22−ζ13+ζ23ζ13−ζ23−ζ5+ζ7ζ5−ζ7−ζ5+ζ7ζ5−ζ7−ζ13+ζ23ζ13−ζ23000000
χ332-2-22-1-2002-111−3−333000-22−33-1133−3−311-1-12−2−22ζ13−ζ23−ζ13+ζ23ζ5−ζ7−ζ5+ζ7−ζ5+ζ7ζ5−ζ7−ζ13+ζ23ζ13−ζ23000000
χ342-2-22-1-2002-111−3−333000-22−33-1133−3−311-1-1−222−2−ζ13+ζ23ζ13−ζ23−ζ5+ζ7ζ5−ζ7ζ5−ζ7−ζ5+ζ7ζ13−ζ23−ζ13+ζ23000000
χ354444-2-444-4-2-2-2-2-2-2-2-40000222200000000000000000000000000
χ364444-2-4-4-4-4-2-2-2222240000-2-22200000000000000000000000000
χ3744-4-440000-44-40000022−2200000022−2222−220000000000000000000000
χ3844-4-440000-44-400000−2222000000−2222−22220000000000000000000000
χ3944-4-4-200002-2223−2323−23022−22000000−22−226−66−6000000000000000000
χ4044-4-4-200002-2223−2323−230−22220000002−22−2−66−66000000000000000000
χ4144-4-4-200002-22−2323−2323022−22000000−22−22−66−66000000000000000000
χ4244-4-4-200002-22−2323−23230−22220000002−22−26−66−6000000000000000000
χ434-44-4404-40-4-444-4-4400000000000000000000000000000000000
χ444-44-440-440-4-44-444-400000000000000000000000000000000000
χ454-44-4-204-4022-2-222-20000000006−6−66−666−6000000000000000000
χ464-44-4-204-4022-2-222-2000000000−666−66−6−66000000000000000000
χ474-44-4-20-44022-22-2-220000000006−6−666−6−66000000000000000000
χ484-44-4-20-44022-22-2-22000000000−666−6−666−6000000000000000000
χ494-4-444400-44-4-400000000000-4400000000000000000000000000
χ504-4-44-2400-4-2222323−23−2300000−23232-200000000000000000000000000
χ514-4-44-2400-4-222−23−2323230000023−232-200000000000000000000000000

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