Finite Group Databasebeta

← Group #13181809

Character table — Group #13181809

Order 1728.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72
size144669121218312121818273636544161624243648487241616242436484872144669121218312121818273636544161624243648487241616242436484872
order1332226642662226643336666612333666661226622266426622266466666666126666666612
χ1111111111111111111111111111111111111111111111111111111111111111111111111
χ21111-111-1-11111-111-1-11111-111-1-11111-111-1-11111-111-1-11111-111-1-11111-111-1-11111-111-1-1
χ3111-111-11-1111-111-11-1111-111-11-1111-111-11-1111-111-11-1111-111-11-1111-111-11-1111-111-11-1
χ4111-1-11-1-11111-1-11-1-11111-1-11-1-11111-1-11-1-11111-1-11-1-11111-1-11-1-11111-1-11-1-11111-1-11-1-11
χ522200-200022200-200022200-200022200-200022200-200022200-200022200-200022200-2000
χ641-20200-1041-20200-1041-20200-1041-20200-1041-20200-1041-20200-1041-20200-1041-20200-10
χ741-20-2001041-20-2001041-20-2001041-20-2001041-20-2001041-20-2001041-20-2001041-20-20010
χ84-21200-1004-21200-1004-21200-1004-21200-1004-21200-1004-21200-1004-21200-1004-21200-100
χ94-21-2001004-21-2001004-21-2001004-21-2001004-21-2001004-21-2001004-21-2001004-21-200100
χ10111111111111111111−1+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−i32111111111111111111−1+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
χ111111-111-1-11111-111-1-1−1+i32−1+i32−1+i32−1+i321−i32−1+i32−1+i321−i321−i32−1−i32−1−i32−1−i32−1−i321+i32−1−i32−1−i321+i321+i321111-111-1-11111-111-1-1−1+i32−1+i32−1+i32−1+i321−i32−1+i32−1+i321−i321−i32−1−i32−1−i32−1−i32−1−i321+i32−1−i32−1−i321+i321+i32
χ12111-111-11-1111-111-11-1−1+i32−1+i32−1+i321−i32−1+i32−1+i321−i32−1+i321−i32−1−i32−1−i32−1−i321+i32−1−i32−1−i321+i32−1−i321+i32111-111-11-1111-111-11-1−1+i32−1+i32−1+i321−i32−1+i32−1+i321−i32−1+i321−i32−1−i32−1−i32−1−i321+i32−1−i32−1−i321+i32−1−i321+i32
χ13111-1-11-1-11111-1-11-1-11−1+i32−1+i32−1+i321−i321−i32−1+i321−i321−i32−1+i32−1−i32−1−i32−1−i321+i321+i32−1−i321+i321+i32−1−i32111-1-11-1-11111-1-11-1-11−1+i32−1+i32−1+i321−i321−i32−1+i321−i321−i32−1+i32−1−i32−1−i32−1−i321+i321+i32−1−i321+i321+i32−1−i32
χ1422200-200022200-2000−1+i3−1+i3−1+i3001−i3000−1−i3−1−i3−1−i3001+i300022200-200022200-2000−1+i3−1+i3−1+i3001−i3000−1−i3−1−i3−1−i3001+i3000
χ1541-20200-1041-20200-10−2+2i3−1+i321−i30−1+i3001−i320−2−2i3−1−i321+i30−1−i3001+i32041-20200-1041-20200-10−2+2i3−1+i321−i30−1+i3001−i320−2−2i3−1−i321+i30−1−i3001+i320
χ1641-20-2001041-20-20010−2+2i3−1+i321−i301−i300−1+i320−2−2i3−1−i321+i301+i300−1−i32041-20-2001041-20-20010−2+2i3−1+i321−i301−i300−1+i320−2−2i3−1−i321+i301+i300−1−i320
χ174-21200-1004-21200-100−2+2i31−i3−1+i32−1+i3001−i3200−2−2i31+i3−1−i32−1−i3001+i32004-21200-1004-21200-100−2+2i31−i3−1+i32−1+i3001−i3200−2−2i31+i3−1−i32−1−i3001+i3200
χ184-21-2001004-21-200100−2+2i31−i3−1+i321−i300−1+i3200−2−2i31+i3−1−i321+i300−1−i32004-21-2001004-21-200100−2+2i31−i3−1+i321−i300−1+i3200−2−2i31+i3−1−i321+i300−1−i3200
χ19111111111111111111−1−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+i32111111111111111111−1−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
χ201111-111-1-11111-111-1-1−1−i32−1−i32−1−i32−1−i321+i32−1−i32−1−i321+i321+i32−1+i32−1+i32−1+i32−1+i321−i32−1+i32−1+i321−i321−i321111-111-1-11111-111-1-1−1−i32−1−i32−1−i32−1−i321+i32−1−i32−1−i321+i321+i32−1+i32−1+i32−1+i32−1+i321−i32−1+i32−1+i321−i321−i32
χ21111-111-11-1111-111-11-1−1−i32−1−i32−1−i321+i32−1−i32−1−i321+i32−1−i321+i32−1+i32−1+i32−1+i321−i32−1+i32−1+i321−i32−1+i321−i32111-111-11-1111-111-11-1−1−i32−1−i32−1−i321+i32−1−i32−1−i321+i32−1−i321+i32−1+i32−1+i32−1+i321−i32−1+i32−1+i321−i32−1+i321−i32
χ22111-1-11-1-11111-1-11-1-11−1−i32−1−i32−1−i321+i321+i32−1−i321+i321+i32−1−i32−1+i32−1+i32−1+i321−i321−i32−1+i321−i321−i32−1+i32111-1-11-1-11111-1-11-1-11−1−i32−1−i32−1−i321+i321+i32−1−i321+i321+i32−1−i32−1+i32−1+i32−1+i321−i321−i32−1+i321−i321−i32−1+i32
χ2322200-200022200-2000−1−i3−1−i3−1−i3001+i3000−1+i3−1+i3−1+i3001−i300022200-200022200-2000−1−i3−1−i3−1−i3001+i3000−1+i3−1+i3−1+i3001−i3000
χ2441-20200-1041-20200-10−2−2i3−1−i321+i30−1−i3001+i320−2+2i3−1+i321−i30−1+i3001−i32041-20200-1041-20200-10−2−2i3−1−i321+i30−1−i3001+i320−2+2i3−1+i321−i30−1+i3001−i320
χ2541-20-2001041-20-20010−2−2i3−1−i321+i301+i300−1−i320−2+2i3−1+i321−i301−i300−1+i32041-20-2001041-20-20010−2−2i3−1−i321+i301+i300−1−i320−2+2i3−1+i321−i301−i300−1+i320
χ264-21200-1004-21200-100−2−2i31+i3−1−i32−1−i3001+i3200−2+2i31−i3−1+i32−1+i3001−i32004-21200-1004-21200-100−2−2i31+i3−1−i32−1−i3001+i3200−2+2i31−i3−1+i32−1+i3001−i3200
χ274-21-2001004-21-200100−2−2i31+i3−1−i321+i300−1−i3200−2+2i31−i3−1+i321−i300−1+i32004-21-2001004-21-200100−2−2i31+i3−1−i321+i300−1−i3200−2+2i31−i3−1+i321−i300−1+i3200
χ28333333333-1-1-1-1-1-1-1-1-1000000000000000000333333333-1-1-1-1-1-1-1-1-1000000000000000000
χ293333-333-3-3-1-1-1-11-1-1110000000000000000003333-333-3-3-1-1-1-11-1-111000000000000000000
χ30333-333-33-3-1-1-11-1-11-11000000000000000000333-333-33-3-1-1-11-1-11-11000000000000000000
χ31333-3-33-3-33-1-1-111-111-1000000000000000000333-3-33-3-33-1-1-111-111-1000000000000000000
χ3266600-6000-2-2-200200000000000000000000066600-6000-2-2-2002000000000000000000000
χ33123-60600-30-4-120-20010000000000000000000123-60600-30-4-120-20010000000000000000000
χ34123-60-60030-4-120200-10000000000000000000123-60-60030-4-120200-10000000000000000000
χ3512-63600-300-42-1-20010000000000000000000012-63600-300-42-1-200100000000000000000000
χ3612-63-600300-42-1200-10000000000000000000012-63-600300-42-1200-100000000000000000000
χ37111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ381111-111-1-11111-111-1-11111-111-1-11111-111-1-1-1-1-1-11-1-111-1-1-1-11-1-111-1-1-1-11-1-111-1-1-1-11-1-111
χ39111-111-11-1111-111-11-1111-111-11-1111-111-11-1-1-1-11-1-11-11-1-1-11-1-11-11-1-1-11-1-11-11-1-1-11-1-11-11
χ40111-1-11-1-11111-1-11-1-11111-1-11-1-11111-1-11-1-11-1-1-111-111-1-1-1-111-111-1-1-1-111-111-1-1-1-111-111-1
χ4122200-200022200-200022200-200022200-2000-2-2-2002000-2-2-2002000-2-2-2002000-2-2-2002000
χ4241-20200-1041-20200-1041-20200-1041-20200-10-4-120-20010-4-120-20010-4-120-20010-4-120-20010
χ4341-20-2001041-20-2001041-20-2001041-20-20010-4-120200-10-4-120200-10-4-120200-10-4-120200-10
χ444-21200-1004-21200-1004-21200-1004-21200-100-42-1-200100-42-1-200100-42-1-200100-42-1-200100
χ454-21-2001004-21-2001004-21-2001004-21-200100-42-1200-100-42-1200-100-42-1200-100-42-1200-100
χ46111111111111111111−1+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−i32-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11−i321−i321−i321−i321−i321−i321−i321−i321−i321+i321+i321+i321+i321+i321+i321+i321+i321+i32
χ471111-111-1-11111-111-1-1−1+i32−1+i32−1+i32−1+i321−i32−1+i32−1+i321−i321−i32−1−i32−1−i32−1−i32−1−i321+i32−1−i32−1−i321+i321+i32-1-1-1-11-1-111-1-1-1-11-1-1111−i321−i321−i321−i32−1+i321−i321−i32−1+i32−1+i321+i321+i321+i321+i32−1−i321+i321+i32−1−i32−1−i32
χ48111-111-11-1111-111-11-1−1+i32−1+i32−1+i321−i32−1+i32−1+i321−i32−1+i321−i32−1−i32−1−i32−1−i321+i32−1−i32−1−i321+i32−1−i321+i32-1-1-11-1-11-11-1-1-11-1-11-111−i321−i321−i32−1+i321−i321−i32−1+i321−i32−1+i321+i321+i321+i32−1−i321+i321+i32−1−i321+i32−1−i32
χ49111-1-11-1-11111-1-11-1-11−1+i32−1+i32−1+i321−i321−i32−1+i321−i321−i32−1+i32−1−i32−1−i32−1−i321+i321+i32−1−i321+i321+i32−1−i32-1-1-111-111-1-1-1-111-111-11−i321−i321−i32−1+i32−1+i321−i32−1+i32−1+i321−i321+i321+i321+i32−1−i32−1−i321+i32−1−i32−1−i321+i32
χ5022200-200022200-2000−1+i3−1+i3−1+i3001−i3000−1−i3−1−i3−1−i3001+i3000-2-2-2002000-2-2-20020001−i31−i31−i300−1+i30001+i31+i31+i300−1−i3000
χ5141-20200-1041-20200-10−2+2i3−1+i321−i30−1+i3001−i320−2−2i3−1−i321+i30−1−i3001+i320-4-120-20010-4-120-200102−2i31−i32−1+i301−i300−1+i3202+2i31+i32−1−i301+i300−1−i320
χ5241-20-2001041-20-20010−2+2i3−1+i321−i301−i300−1+i320−2−2i3−1−i321+i301+i300−1−i320-4-120200-10-4-120200-102−2i31−i32−1+i30−1+i3001−i3202+2i31+i32−1−i30−1−i3001+i320
χ534-21200-1004-21200-100−2+2i31−i3−1+i32−1+i3001−i3200−2−2i31+i3−1−i32−1−i3001+i3200-42-1-200100-42-1-2001002−2i3−1+i31−i321−i300−1+i32002+2i3−1−i31+i321+i300−1−i3200
χ544-21-2001004-21-200100−2+2i31−i3−1+i321−i300−1+i3200−2−2i31+i3−1−i321+i300−1−i3200-42-1200-100-42-1200-1002−2i3−1+i31−i32−1+i3001−i32002+2i3−1−i31+i32−1−i3001+i3200
χ55111111111111111111−1−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+i32-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11+i321+i321+i321+i321+i321+i321+i321+i321+i321−i321−i321−i321−i321−i321−i321−i321−i321−i32
χ561111-111-1-11111-111-1-1−1−i32−1−i32−1−i32−1−i321+i32−1−i32−1−i321+i321+i32−1+i32−1+i32−1+i32−1+i321−i32−1+i32−1+i321−i321−i32-1-1-1-11-1-111-1-1-1-11-1-1111+i321+i321+i321+i32−1−i321+i321+i32−1−i32−1−i321−i321−i321−i321−i32−1+i321−i321−i32−1+i32−1+i32
χ57111-111-11-1111-111-11-1−1−i32−1−i32−1−i321+i32−1−i32−1−i321+i32−1−i321+i32−1+i32−1+i32−1+i321−i32−1+i32−1+i321−i32−1+i321−i32-1-1-11-1-11-11-1-1-11-1-11-111+i321+i321+i32−1−i321+i321+i32−1−i321+i32−1−i321−i321−i321−i32−1+i321−i321−i32−1+i321−i32−1+i32
χ58111-1-11-1-11111-1-11-1-11−1−i32−1−i32−1−i321+i321+i32−1−i321+i321+i32−1−i32−1+i32−1+i32−1+i321−i321−i32−1+i321−i321−i32−1+i32-1-1-111-111-1-1-1-111-111-11+i321+i321+i32−1−i32−1−i321+i32−1−i32−1−i321+i321−i321−i321−i32−1+i32−1+i321−i32−1+i32−1+i321−i32
χ5922200-200022200-2000−1−i3−1−i3−1−i3001+i3000−1+i3−1+i3−1+i3001−i3000-2-2-2002000-2-2-20020001+i31+i31+i300−1−i30001−i31−i31−i300−1+i3000
χ6041-20200-1041-20200-10−2−2i3−1−i321+i30−1−i3001+i320−2+2i3−1+i321−i30−1+i3001−i320-4-120-20010-4-120-200102+2i31+i32−1−i301+i300−1−i3202−2i31−i32−1+i301−i300−1+i320
χ6141-20-2001041-20-20010−2−2i3−1−i321+i301+i300−1−i320−2+2i3−1+i321−i301−i300−1+i320-4-120200-10-4-120200-102+2i31+i32−1−i30−1−i3001+i3202−2i31−i32−1+i30−1+i3001−i320
χ624-21200-1004-21200-100−2−2i31+i3−1−i32−1−i3001+i3200−2+2i31−i3−1+i32−1+i3001−i3200-42-1-200100-42-1-2001002+2i3−1−i31+i321+i300−1−i32002−2i3−1+i31−i321−i300−1+i3200
χ634-21-2001004-21-200100−2−2i31+i3−1−i321+i300−1−i3200−2+2i31−i3−1+i321−i300−1+i3200-42-1200-100-42-1200-1002+2i3−1−i31+i32−1−i3001+i32002−2i3−1+i31−i32−1+i3001−i3200
χ64333333333-1-1-1-1-1-1-1-1-1000000000000000000-3-3-3-3-3-3-3-3-3111111111000000000000000000
χ653333-333-3-3-1-1-1-11-1-111000000000000000000-3-3-3-33-3-3331111-111-1-1000000000000000000
χ66333-333-33-3-1-1-11-1-11-11000000000000000000-3-3-33-3-33-33111-111-11-1000000000000000000
χ67333-3-33-3-33-1-1-111-111-1000000000000000000-3-3-333-333-3111-1-11-1-11000000000000000000
χ6866600-6000-2-2-2002000000000000000000000-6-6-600600022200-2000000000000000000000
χ69123-60600-30-4-120-20010000000000000000000-12-360-6003041-20200-10000000000000000000
χ70123-60-60030-4-120200-10000000000000000000-12-360600-3041-20-20010000000000000000000
χ7112-63600-300-42-1-200100000000000000000000-126-3-6003004-21200-100000000000000000000
χ7212-63-600300-42-1200-100000000000000000000-126-3600-3004-21-200100000000000000000000

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