Finite Group Databasebeta

← Group #72228126

Character table — Group #72228126

Order 2304.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64
size114461212161616161616161624331212183636484848484848484872441616244848646464646464646496441616244848646464646464646496
order12222243366666642222224666666664366666123366666612366666123366666612
χ11111111111111111111111111111111111111111111111111111111111111111
χ21111111−1+i32−1−i32−1+i32−1+i32−1+i32−1−i32−1−i32−1−i3211111111−1+i32−1−i32−1+i32−1+i32−1+i32−1−i32−1−i32−1−i3211111111−1+i32−1−i32−1+i32−1+i32−1+i32−1−i32−1−i32−1−i3211111111−1+i32−1−i32−1+i32−1+i32−1+i32−1−i32−1−i32−1−i321
χ31111111−1−i32−1+i32−1−i32−1−i32−1−i32−1+i32−1+i32−1+i3211111111−1−i32−1+i32−1−i32−1−i32−1−i32−1+i32−1+i32−1+i3211111111−1−i32−1+i32−1−i32−1−i32−1−i32−1+i32−1+i32−1+i3211111111−1−i32−1+i32−1−i32−1−i32−1−i32−1+i32−1+i32−1+i321
χ411-1-1111111-1-11-1-1-111-1-1111111-1-11-1-1-111-1-1111111-1-11-1-1-111-1-1111111-1-11-1-1-1
χ511-1-1111−1+i32−1−i32−1+i321−i321−i32−1−i321+i321+i32-111-1-1111−1+i32−1−i32−1+i321−i321−i32−1−i321+i321+i32-111-1-1111−1+i32−1−i32−1+i321−i321−i32−1−i321+i321+i32-111-1-1111−1+i32−1−i32−1+i321−i321−i32−1−i321+i321+i32-1
χ611-1-1111−1−i32−1+i32−1−i321+i321+i32−1+i321−i321−i32-111-1-1111−1−i32−1+i32−1−i321+i321+i32−1+i321−i321−i32-111-1-1111−1−i32−1+i32−1−i321+i321+i32−1+i321−i321−i32-111-1-1111−1−i32−1+i32−1−i321+i321+i32−1+i321−i321−i32-1
χ733333-1-100000000-133333-1-100000000-133333-1-100000000-133333-1-100000000-1
χ833-3-33-1-100000000133-3-33-1-100000000133-3-33-1-100000000133-3-33-1-1000000001
χ94-42-200011-11-1-11-104-42-200011-11-1-11-104-42-200011-11-1-11-104-42-200011-11-1-11-10
χ104-42-2000−1+i32−1−i321−i32−1+i321−i321+i32−1−i321+i3204-42-2000−1+i32−1−i321−i32−1+i321−i321+i32−1−i321+i3204-42-2000−1+i32−1−i321−i32−1+i321−i321+i32−1−i321+i3204-42-2000−1+i32−1−i321−i32−1+i321−i321+i32−1−i321+i320
χ114-42-2000−1−i32−1+i321+i32−1−i321+i321−i32−1+i321−i3204-42-2000−1−i32−1+i321+i32−1−i321+i321−i32−1+i321−i3204-42-2000−1−i32−1+i321+i32−1−i321+i321−i32−1+i321−i3204-42-2000−1−i32−1+i321+i32−1−i321+i321−i32−1+i321−i320
χ124-4-2200011-1-11-1-1104-4-2200011-1-11-1-1104-4-2200011-1-11-1-1104-4-2200011-1-11-1-110
χ134-4-22000−1+i32−1−i321−i321−i32−1+i321+i321+i32−1−i3204-4-22000−1+i32−1−i321−i321−i32−1+i321+i321+i32−1−i3204-4-22000−1+i32−1−i321−i321−i32−1+i321+i321+i32−1−i3204-4-22000−1+i32−1−i321−i321−i32−1+i321+i321+i32−1−i320
χ144-4-22000−1−i32−1+i321+i321+i32−1−i321−i321−i32−1+i3204-4-22000−1−i32−1+i321+i321+i32−1−i321−i321−i32−1+i3204-4-22000−1−i32−1+i321+i321+i32−1−i321−i321−i32−1+i3204-4-22000−1−i32−1+i321+i321+i32−1−i321−i321−i32−1+i320
χ156600-22-20000000006600-22-20000000006600-22-20000000006600-22-2000000000
χ166600-2-220000000006600-2-220000000006600-2-220000000006600-2-22000000000
χ1711111111111111111111111111111111−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32
χ181111111−1+i32−1−i32−1+i32−1+i32−1+i32−1−i32−1−i32−1−i3211111111−1+i32−1−i32−1+i32−1+i32−1+i32−1−i32−1−i32−1−i321−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1−i321−1−i32−1−i32−1−i32111−1+i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i321−1+i32111−1+i32−1+i32−1+i32−1−i32
χ191111111−1−i32−1+i32−1−i32−1−i32−1−i32−1+i32−1+i32−1+i3211111111−1−i32−1+i32−1−i32−1−i32−1−i32−1+i32−1+i32−1+i321−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i321−1−i32111−1−i32−1−i32−1−i32−1+i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1+i321−1+i32−1+i32−1+i32111−1−i32
χ2011-1-1111111-1-11-1-1-111-1-1111111-1-11-1-1-1−1+i32−1+i321−i321−i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i321−i321−i32−1+i321−i321−i321−i32−1−i32−1−i321+i321+i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i321+i321+i32−1−i321+i321+i321+i32
χ2111-1-1111−1+i32−1−i32−1+i321−i321−i32−1−i321+i321+i32-111-1-1111−1+i32−1−i32−1+i321−i321−i32−1−i321+i321+i32-1−1+i32−1+i321−i321−i32−1+i32−1+i32−1+i32−1−i321−1−i321+i321+i321-1-11−i32−1−i32−1−i321+i321+i32−1−i32−1−i32−1−i321−1+i321-1-1−1+i321−i321−i321+i32
χ2211-1-1111−1−i32−1+i32−1−i321+i321+i32−1+i321−i321−i32-111-1-1111−1−i32−1+i32−1−i321+i321+i32−1+i321−i321−i32-1−1+i32−1+i321−i321−i32−1+i32−1+i32−1+i321−1−i321-1-1−1−i321+i321+i321−i32−1−i32−1−i321+i321+i32−1−i32−1−i32−1−i32−1+i321−1+i321−i321−i321-1-11+i32
χ2333333-1-100000000-133333-1-100000000-1−3+3i32−3+3i32−3+3i32−3+3i32−3+3i321−i321−i32000000001−i32−3−3i32−3−3i32−3−3i32−3−3i32−3−3i321+i321+i32000000001+i32
χ2433-3-33-1-100000000133-3-33-1-1000000001−3+3i32−3+3i323−3i323−3i32−3+3i321−i321−i3200000000−1+i32−3−3i32−3−3i323+3i323+3i32−3−3i321+i321+i3200000000−1−i32
χ254-42-200011-11-1-11-104-42-200011-11-1-11-10−2+2i32−2i3−1+i31−i3000−1+i32−1+i321−i32−1+i321−i321−i32−1+i321−i320−2−2i32+2i3−1−i31+i3000−1−i32−1−i321+i32−1−i321+i321+i32−1−i321+i320
χ264-42-2000−1+i32−1−i321−i32−1+i321−i321+i32−1−i321+i3204-42-2000−1+i32−1−i321−i32−1+i321−i321+i32−1−i321+i320−2+2i32−2i3−1+i31−i3000−1−i3211+i32−1−i321+i32-11-10−2−2i32+2i3−1−i31+i30001−1+i32-11-11−i32−1+i321−i320
χ274-42-2000−1−i32−1+i321+i32−1−i321+i321−i32−1+i321−i3204-42-2000−1−i32−1+i321+i32−1−i321+i321−i32−1+i321−i320−2+2i32−2i3−1+i31−i30001−1−i32-11-11+i32−1−i321+i320−2−2i32+2i3−1−i31+i3000−1+i3211−i32−1+i321−i32-11-10
χ284-4-2200011-1-11-1-1104-4-2200011-1-11-1-110−2+2i32−2i31−i3−1+i3000−1+i32−1+i321−i321−i32−1+i321−i321−i32−1+i320−2−2i32+2i31+i3−1−i3000−1−i32−1−i321+i321+i32−1−i321+i321+i32−1−i320
χ294-4-22000−1+i32−1−i321−i321−i32−1+i321+i321+i32−1−i3204-4-22000−1+i32−1−i321−i321−i32−1+i321+i321+i32−1−i320−2+2i32−2i31−i3−1+i3000−1−i3211+i321+i32−1−i32-1-110−2−2i32+2i31+i3−1−i30001−1+i32-1-111−i321−i32−1+i320
χ304-4-22000−1−i32−1+i321+i321+i32−1−i321−i321−i32−1+i3204-4-22000−1−i32−1+i321+i321+i32−1−i321−i321−i32−1+i320−2+2i32−2i31−i3−1+i30001−1−i32-1-111+i321+i32−1−i320−2−2i32+2i31+i3−1−i3000−1+i3211−i321−i32−1+i32-1-110
χ316600-22-20000000006600-22-2000000000−3+3i3−3+3i3001−i3−1+i31−i3000000000−3−3i3−3−3i3001+i3−1−i31+i3000000000
χ326600-2-220000000006600-2-22000000000−3+3i3−3+3i3001−i31−i3−1+i3000000000−3−3i3−3−3i3001+i31+i3−1−i3000000000
χ3311111111111111111111111111111111−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32
χ341111111−1+i32−1−i32−1+i32−1+i32−1+i32−1−i32−1−i32−1−i3211111111−1+i32−1−i32−1+i32−1+i32−1+i32−1−i32−1−i32−1−i321−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i321−1+i32111−1+i32−1+i32−1+i32−1−i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1−i321−1−i32−1−i32−1−i32111−1+i32
χ351111111−1−i32−1+i32−1−i32−1−i32−1−i32−1+i32−1+i32−1+i3211111111−1−i32−1+i32−1−i32−1−i32−1−i32−1+i32−1+i32−1+i321−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1+i321−1+i32−1+i32−1+i32111−1−i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i321−1−i32111−1−i32−1−i32−1−i32−1+i32
χ3611-1-1111111-1-11-1-1-111-1-1111111-1-11-1-1-1−1−i32−1−i321+i321+i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i321+i321+i32−1−i321+i321+i321+i32−1+i32−1+i321−i321−i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i321−i321−i32−1+i321−i321−i321−i32
χ3711-1-1111−1+i32−1−i32−1+i321−i321−i32−1−i321+i321+i32-111-1-1111−1+i32−1−i32−1+i321−i321−i32−1−i321+i321+i32-1−1−i32−1−i321+i321+i32−1−i32−1−i32−1−i321−1+i321-1-1−1+i321−i321−i321+i32−1+i32−1+i321−i321−i32−1+i32−1+i32−1+i32−1−i321−1−i321+i321+i321-1-11−i32
χ3811-1-1111−1−i32−1+i32−1−i321+i321+i32−1+i321−i321−i32-111-1-1111−1−i32−1+i32−1−i321+i321+i32−1+i321−i321−i32-1−1−i32−1−i321+i321+i32−1−i32−1−i32−1−i32−1+i321−1+i321−i321−i321-1-11+i32−1+i32−1+i321−i321−i32−1+i32−1+i32−1+i321−1−i321-1-1−1−i321+i321+i321−i32
χ3933333-1-100000000-133333-1-100000000-1−3−3i32−3−3i32−3−3i32−3−3i32−3−3i321+i321+i32000000001+i32−3+3i32−3+3i32−3+3i32−3+3i32−3+3i321−i321−i32000000001−i32
χ4033-3-33-1-100000000133-3-33-1-1000000001−3−3i32−3−3i323+3i323+3i32−3−3i321+i321+i3200000000−1−i32−3+3i32−3+3i323−3i323−3i32−3+3i321−i321−i3200000000−1+i32
χ414-42-200011-11-1-11-104-42-200011-11-1-11-10−2−2i32+2i3−1−i31+i3000−1−i32−1−i321+i32−1−i321+i321+i32−1−i321+i320−2+2i32−2i3−1+i31−i3000−1+i32−1+i321−i32−1+i321−i321−i32−1+i321−i320
χ424-42-2000−1+i32−1−i321−i32−1+i321−i321+i32−1−i321+i3204-42-2000−1+i32−1−i321−i32−1+i321−i321+i32−1−i321+i320−2−2i32+2i3−1−i31+i30001−1+i32-11-11−i32−1+i321−i320−2+2i32−2i3−1+i31−i3000−1−i3211+i32−1−i321+i32-11-10
χ434-42-2000−1−i32−1+i321+i32−1−i321+i321−i32−1+i321−i3204-42-2000−1−i32−1+i321+i32−1−i321+i321−i32−1+i321−i320−2−2i32+2i3−1−i31+i3000−1+i3211−i32−1+i321−i32-11-10−2+2i32−2i3−1+i31−i30001−1−i32-11-11+i32−1−i321+i320
χ444-4-2200011-1-11-1-1104-4-2200011-1-11-1-110−2−2i32+2i31+i3−1−i3000−1−i32−1−i321+i321+i32−1−i321+i321+i32−1−i320−2+2i32−2i31−i3−1+i3000−1+i32−1+i321−i321−i32−1+i321−i321−i32−1+i320
χ454-4-22000−1+i32−1−i321−i321−i32−1+i321+i321+i32−1−i3204-4-22000−1+i32−1−i321−i321−i32−1+i321+i321+i32−1−i320−2−2i32+2i31+i3−1−i30001−1+i32-1-111−i321−i32−1+i320−2+2i32−2i31−i3−1+i3000−1−i3211+i321+i32−1−i32-1-110
χ464-4-22000−1−i32−1+i321+i321+i32−1−i321−i321−i32−1+i3204-4-22000−1−i32−1+i321+i321+i32−1−i321−i321−i32−1+i320−2−2i32+2i31+i3−1−i3000−1+i3211−i321−i32−1+i32-1-110−2+2i32−2i31−i3−1+i30001−1−i32-1-111+i321+i32−1−i320
χ476600-22-20000000006600-22-2000000000−3−3i3−3−3i3001+i3−1−i31+i3000000000−3+3i3−3+3i3001−i3−1+i31−i3000000000
χ486600-2-220000000006600-2-22000000000−3−3i3−3−3i3001+i31+i3−1−i3000000000−3+3i3−3+3i3001−i31−i3−1+i3000000000
χ493333333333333333-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-100000000000000000000000000000000
χ503333333−3+3i32−3−3i32−3+3i32−3+3i32−3+3i32−3−3i32−3−3i32−3−3i323-1-1-1-1-1-1-11−i321+i321−i321−i321−i321+i321+i321+i32-100000000000000000000000000000000
χ513333333−3−3i32−3+3i32−3−3i32−3−3i32−3−3i32−3+3i32−3+3i32−3+3i323-1-1-1-1-1-1-11+i321−i321+i321+i321+i321−i321−i321−i32-100000000000000000000000000000000
χ5233-3-3333333-3-33-3-3-3-1-111-1-1-1-1-1-111-111100000000000000000000000000000000
χ5333-3-3333−3+3i32−3−3i32−3+3i323−3i323−3i32−3−3i323+3i323+3i32-3-1-111-1-1-11−i321+i321−i32−1+i32−1+i321+i32−1−i32−1−i32100000000000000000000000000000000
χ5433-3-3333−3−3i32−3+3i32−3−3i323+3i323+3i32−3+3i323−3i323−3i32-3-1-111-1-1-11+i321−i321+i32−1−i32−1−i321−i32−1+i32−1+i32100000000000000000000000000000000
χ5599999-3-300000000-3-3-3-3-3-31100000000100000000000000000000000000000000
χ5699-9-99-3-3000000003-3-333-31100000000-100000000000000000000000000000000
χ5712-126-600033-33-3-33-30-44-22000-1-11-111-11000000000000000000000000000000000
χ5812-126-6000−3+3i32−3−3i323−3i32−3+3i323−3i323+3i32−3−3i323+3i320-44-220001−i321+i32−1+i321−i32−1+i32−1−i321+i32−1−i32000000000000000000000000000000000
χ5912-126-6000−3−3i32−3+3i323+3i32−3−3i323+3i323−3i32−3+3i323−3i320-44-220001+i321−i32−1−i321+i32−1−i32−1+i321−i32−1+i32000000000000000000000000000000000
χ6012-12-6600033-3-33-3-330-442-2000-1-111-111-1000000000000000000000000000000000
χ6112-12-66000−3+3i32−3−3i323−3i323−3i32−3+3i323+3i323+3i32−3−3i320-442-20001−i321+i32−1+i32−1+i321−i32−1−i32−1−i321+i32000000000000000000000000000000000
χ6212-12-66000−3−3i32−3+3i323+3i323+3i32−3−3i323−3i323−3i32−3+3i320-442-20001+i321−i32−1−i32−1−i321+i32−1+i32−1+i321−i32000000000000000000000000000000000
χ63181800-66-6000000000-6-6002-2200000000000000000000000000000000000000000
χ64181800-6-66000000000-6-60022-200000000000000000000000000000000000000000

Here i is the imaginary unit (i² = −1).